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On the Sea Battle Tomorrow That May Not Happen

A Logical and Philosophical Analysis of the Master Argument

by Tomasz Jarmużek (Author)
Monographs 264 Pages
Series: Dia-Logos

Table Of Content

  • Cover
  • Title Page
  • Copyright Page
  • Dedication Page
  • Foreword
  • Contents
  • Part  I Philosophical framework of the topic
  • 1 Introduction
  • 2 Truth and Sentences
  • 2.1 Syntactic approach
  • 2.2 Meanings of expressions
  • 2.2.1 Propositions as meanings of sentences
  • 2.2.2 Pragmatic components of a statement
  • 2.2.3 Sentences that are temporarily determined
  • 2.2.4 Sentences that are temporarily undetermined
  • 2.3 Sentences vs. logical value
  • 2.3.1 Requirements for the concept of truth
  • 2.3.2 Historical background
  • 2.3.3 What owns the truth?
  • 2.3.4 What makes sentences true
  • 2.3.5 The concept of truth employed in the study, concept of false controversy
  • 2.3.6 Presuppositions of sentences
  • 2.3.7 Sentences with modalities and other
  • 2.3.8 Truth, time vs. epistemic concepts
  • 3 Determinism
  • 3.1 The extent of determinism
  • 3.2 Modal components of determinism
  • 3.3 Ontological determinism
  • 3.3.1 Physical determinism
  • 3.3.2 Metaphysical determinism
  • 3.4 The consequences of determinism
  • 3.4.1 Logical determinism
  • 3.4.2 Epistemological determinism
  • 3.4.3 Temporal determinism
  • 3.4.4 Anthropological aspects of determinism
  • 3.5 Determinism vs. the Reasoning of Diodorus Cronus
  • 4 Time
  • 4.1 Cultural time
  • 4.2 Psychological and phenomenological time
  • 4.3 Physical time
  • 4.3.1 From psychological time to physical time
  • 4.3.2 Time in scientific physics
  • 4.3.3 Absolute time
  • 4.3.4 Relative time
  • 4.3.5 Properties of the physical time
  • 4.4 Time measurement, its accuracy and units
  • 4.5 Philosophy of time and its problems
  • 4.5.1 Substantial time vs. attributive time
  • 4.5.2 The direction of an arrow of time
  • 4.5.3 McTaggart’s problematique
  • 4.6 Formal representation of time
  • 4.6.1 Attempts to define moments of time: momentsas points vs. moments without points
  • Part  II The issues
  • 5 The problem
  • 5.1 Aristotle and The Sea Battle Tomorrow
  • 5.1.1 Primary problems concerning modality
  • 5.1.2 Interpretations of De Interpretatione
  • 5.1.3 On Interpretation IX vs. The Reasoning of Diodorus Cronus
  • 5.2 The reasoning of Diodorus Cronus
  • 5.2.1 The definitions of modality vs. Diodorus’ reasoning
  • 5.2.2 Diodorus’ conditional sentences
  • 5.2.3 Conclusions and indications for a reconstruction
  • 5.3 The issue of futura contingentia
  • 5.4 Research problem and the method used
  • 6 Dates, tenses, sentencesvs.time structures
  • 6.1 Dates
  • 6.1.1 Dates and the pseudo-dates
  • 6.1.2 Denotations of the dates
  • 6.2 Grammatical tenses
  • 6.3 Logical values of the sentences within the time structures
  • 7 Logic
  • 7.1 Temporal logics
  • 7.1.1 Temporal interpretation of the positional logic
  • 7.2 Time for the point moments
  • 7.2.1 The similarity of the moments, branches and time
  • 7.3 Axioms of the logical structures of time
  • 7.4 The outline of logics of time R
  • 7.4.1 Grammar
  • 7.4.2 Axioms and rules of deduction
  • 7.4.3 Semantics
  • 7.5 Tense logic
  • Part  III Solutions
  • 8 Reconstructions with operator R
  • 8.1 The Reconstruction of F. S. Michael
  • 8.1.1 Preliminaries
  • 8.1.2 Reasoning
  • 8.1.3 Definitions of modality
  • 8.1.4 Time structure
  • 8.2 Reconstruction of N. Rescher
  • 8.2.1 Preliminaries
  • 8.2.2 Reasoning
  • 8.2.3 Definitions of modality
  • 8.2.4 Time structure
  • 8.3 Calculation of moments
  • 8.3.1 Preliminaries
  • 8.3.2 Reasoning
  • 8.3.3 Definitions of modality
  • 8.3.4 Time structure
  • 9 Other reconstructions
  • 9.1 Reconstruction of A. N. Prior
  • 9.1.1 Preliminaries
  • 9.1.2 Reasoning
  • 9.1.3 Definitions of modality
  • 9.1.4 Time structure
  • 9.2 Reconstruction of P. Øhrstrøm
  • 9.2.1 Preliminaries
  • 9.2.2 Reasoning
  • 9.2.3 Definitions of modality
  • 9.2.4 Time structure
  • Conclusion
  • Summary
  • Bibliography
  • Index

1 Introduction

Imagine the following scene. Here, a man of a reverend appearance, immersed in a philosophical reflection, stands by a picturesque, rocky gulf of ancient Greece. That gulf had already been a theatre of many sea skirmishes in which the Athenians wrestled with their enemies. Its image, therefore, naturally brings up associations with the former battle scenes. This is when Aristotle — who is the reverend man — affected by that scenery and cultivated in contemporary Greece bios theoretikós, asks the famous question: will there be a sea battle tomorrow?

It is quite possible that this scene occurred. What is certain, however — if we resist a philosophical temptation to raise immoderate objections and stick to the common sense plane1 — is that Aristotle actually uttered this famous sentence in such circumstances or he did it elsewhere. All in all, we believe that things of the past belong to a field which may not be affected by anyone or anything. Once shaped, it cannot be altered.

The philosopher’s question did not, however, pertain to the past, but to the future. This question was to illustrate the issue of whether or not the expressions stating something about the future events hold any logical value and thus whether, while making statements about future, we can a priori reasonably believe them being are true or false.

Aristotle was to negatively resolve the problem he faced, opting for the open, underspecified future. He displayed his position in Chapter 9 of On Interpretation, supporting it with the reasoning which then found numerous attempts of interpretation and reconstruction with the use of modern, logical measures. The purpose of this reasoning — as it seems — was to clearly distinguish the field of what used to be from the field of what may or may not happen in the future (further in this book, the argument of On Interpretation shall be often referred to as RA, the abbreviated Reasoning of Aristotle).

Also Diodorus Cronus, a Megarian logician and philosopher, took up this issue in ancient discussions, probably trying to justify a position that the events that are to take place in the future are preordained in a way2. To this ←17 | 18→end, Diodorus made use of a special reasoning (further in the study referred to as RDC, abbreviated Reasoning of Diodorus Cronus)3.

Future4 features — among other things — this difference from the present that, in common experience, it simply does not exist. The more so, there are no events, states of the world, affairs or facts etc.5 that will or may be in the future6. They may indeed — in the best case — only occur.

If however — as Diodorus could have argued — the expressions referring to future events (i.e. events which only will occur!) bear a logical value, the events described by them must be in some way — proportionately to the logical values of the expressions — preordained, even before they occur. Preordained and therefore inevitable and determined.

It would therefore appear that from the objective perspective, the reasoning of Diodorus is in favour of certain concepts of the time and the world that, while ←18 | 19→ensuring a logical value of an expression on the future, lead to a certain version of the fatalism.

Let us briefly look into the issue of expressions. Regardless of whether or not their logical value is preordained before the events described do (or do not) take place, they must contain a time parameter. RDC should therefore take into account both the time of given expression and the section or point in time described thereby. From the linguistic perspective, a reflection on RDC theory must therefore contain certain logic which takes into account the relationship between given language units and the time, more specifically — its appropriate concepts.

On the other hand, in the case of Aristotle’s concept, language and its relationships with the time and the world, expressed in certain explicit and implicit assumptions, are not supposed to determine the logical values of any sentences, but basically leave underspecified at least some of the sentences that describe the future. RA must therefore advocate for a certain asymmetry between the descriptions of the past, present and future world, as they lead to a version of anti-fatalism, hence to a world open to variations of the future events.

In the case of fatalism, the logical values of appropriate language units must of course be based on their relevance against the world described (and in our case, the relevance against the future world). The correctness of expressions gain particular importance as the theory of truth in a classic bivalent approach is also a theory of falsity.

These above preliminary findings show that a study on the concept of Diodorus must give a primary role to the notion of truth and the notion of time.

In this case, however, these notions are involved in various relations. Diodorus tried to show that:

  1. expressions to describe the future are already true or false in the present time, which means that:
  2. the future is closed in a way, determined.

    It seems however that for the expressions about the future to be true:

  3. the future events must be specified, determined.

The third notion that inevitably appears is therefore the notion of determinism. And a contrario, while advocating for logical indeterminacy of statements describing the future, Aristotle was an advocate of open future and thus of the indeterminism of the future.

These very four notions taken together form the overall conceptual framework within which the philosophical discussion between Aristotle and Diodorus is located.

The above diagram does not give precedence to either of the listed concepts. Only the adoption of the relevant theoretical perspective honours some of them, making them more primary. In view of the chosen perspective, the study gives a particular importance to the concept of time characterised in a specific way, probably familiar to the ancients in a way. However in the case of RDC, it must remain in the defined relationship with the other two concepts. Therefore, the first part of the study shall discuss these three basic components and outline them for two reasons:

  1. due to the need to situate the ancient discussion in a broader context which will enable explanation of its role and purpose in a rather complete manner, and outlining a number of additional problems that we encounter when describing the philosophical context;
  2. because of the need to clarify the theoretical assumptions of the study — assumptions without which it would be infeasible to precisely take up the key topic and its further analysis.

When commenting on the individual components, I will try to isolate them as far as possible in order to maintain the general character of the reflection. Of course, this will be neither entirely possible nor desirable. Since the concepts that mark out the framework for the problems of Diodorus reasoning are interconnected, discussing each one separately requires necessarily references to the others. During the analysis and the description of each of them, I will try to determine the expected connection with the subsequent part of the reflection.

1 cf. subsection 1.3.7. Truth and time vs. epistemic concepts.

2 It was argued here that, within his arguments with Aristotle, Diodorus attempted to positively resolve the problem of the sea battle (Prior A. N. [231], s. 138). However, it can be believed that he only meant a temporal characteristics of modal expressions which in ancient times were perceived as leading to a version of determinism. In principle, both subsequent parts of the study are devoted to these problems.

3 The historical, philosophical and logical contexts of this discussion as well as the preserved passages of Aristotle considerations and Diodorus’ reasoning, together with the necessary interpretations shall be exhaustively presented in the next part of the study.

4 When using words: past, present, future, I do not opt for the position of realism in the philosophy of time, corresponding to the so-called A - series ordering according to McTaggart, and thus I decline the position which corresponds to the B -series ordering. I only use these words as natural language constructs by which we globally define what used to be, what is and what will be. The issue of McTaggart’s complex problem and details related to A and B series with reference to the question of Diodorus reasoning shall be further outlined in Chapter 3.

5 For identification of the objective language, I shall use the following expressions: state of affairs event or occurrence (and accordingly, their verb forms: occur and happen). I am going, however, to operate them very neutrally — just like for the words: past, present and future — without opting for any of the ontological schools, but only considering what we are capable of describing using constatives of a natural language. Moreover, I shall discuss this issue in more detail in Chapter 1 where I am going to more evidently advocate for one of the positions.

6 When saying do not exist, I only mean that they do not exist at present. If they did, they would have already taken place by now, and not in the future, should the circumstances allow. This remark is obviously very general and preliminary. Many events — or maybe even all the events, depending on the approach to the structure of the world — are tensely extended. In this very sense, due to the existence in present, they also extend into the future. But before they take place in the future, they may only exist in the present at most, as some stirrings of what is going to occur at a later time.

2 Truth and Sentences

In the present chapter, we shall introduce the issues associated with the language-world reference. Needless to say, the majority of the issues are of a general nature and are the topics of philosophy of language, semiotics and linguistics. However, some appear directly as a result of the considerations relating to the subject of this study, thereby increasing the spectrum of the general concepts. This reason alone is sufficient to justify the fact that many of the concepts will be omitted, some barely mentioned, and certain ones — only indicated. However, the whole chapter constitutes a compact attempt to outline the problematics and the notion of language in terms of the notion of time; it identifies the arising problems, and highlights and presents the assumptions further considered indisputable.

The language we use on a daily basis has many functions. It can be used to express feelings, create new situations, and change others’ attitudes and beliefs. However, carrying out an individual function requires fulfilling a more primary one, commonly referred to as the descriptive–informative function.

Being a part of a human community and benefiting from it requires the participants to be involved in the communication process. This process involves passing information encoded in the language about the broadly defined world. The language is thus a medium enabling communication. Efficient communication depends on various factors. One of them is a matter of understanding a statement or decoding information.

However, communication is not a goal per se. Of particular note is thus — as previously mentioned — the information to be transferred. Statements are particularly valuable when conveying a lot of information on the subject of communication. However, the statements may be carrying little information or even be inconsistent with reality, thus misinforming.

In order to increase the understanding of given statements and to reduce their ambiguity, artificial languages are being created or natural languages clarified. These languages are structured in such a way as to best serve the aim of describing particular objective domain.

Among many classifications dividing statements in particular language, one of the most interesting philosophical (and not just) aspects is the division into true and untrue expressions (false or devoid of logical value).

For the purposes of the study, I would like to determine a few arrangements of the concept of statements, their meanings (content transmitted), logical ←21 | 22→values and finally, I would like to refer these issues to the concept of time. In the subsequent sections of the study, these arrangements shall allow reference to certain issues without their additional clarification.

2.1 Syntactic approach

The deliberations on statement should begin with defining the broad term sometimes used within this chapter. The term in question is declarative statement. By statement, we mean: any graphical sequence of phrases in a particular language, or certain inscription or its phonetic equivalent; compliant with the grammatical structure of given language7.

According to the above definition, the statement does not have to be a sentence in a grammatical sense. However, for quite obvious reasons (that will also be clearly named in this chapter), the statements of interest are either sentences or certain abridgements of sentences, as in some context their utterances fulfil the same informative function as certain sentences. Such statements will be hereafter named declarative statements8. Obviously, by the above definition, statements are related to a particular language used to articulate them, for grammatical and syntactic rules form a language. For example, the following inscriptions:

(1) It is raining.

(2) Haben Sie etwas zu machen?

are statements — respectively — in English and German. As mentioned, sometimes certain phrases not meeting the criteria of syntactic category of a sentence in their informative function are equivalent to other certain statements that belong to the sentence category, namely:

(3) a fifth grade student

in its informative function corresponds to the sentence:

(4) A fifth grade student won mathematics competition.

←22 | 23→if it aims to answer the question:

(5) Who won mathematics competition?

In order to determine this, it is necessary to step outside the purely syntactic aspect9 and consider given phrase in pragmatic aspect. This issue will be discussed later.

From the syntactic point of view, the sentences can be divided into simple, compound sentences and complex sentences. This division is based on the quality and quantity of sentence-forming functors, present in a given sentence.

The definition of the simple sentence or compound sentence can therefore read as follows. By simple sentence, we usually mean such a sentence which comprises exactly one sentence-forming functor; functor of clauses that are not sentences10. On the other hand, a complex sentence is a sentence consisting of at least one sentence-forming functor; clause’s functor.

In the course of further studies on RDC and its logical reconstructions, the subjects of the analysis will be sentential expressions, which, in terms of information, correspond to both simple and complex sentences. Two more following comments shall be added to the issues of syntactic nature.

Firstly, although the term sentence can be used interchangeably with the term sentential expression, only the term sentence will be used in further parts of the study. Such measures are justified by the fact that almost any given sentential expression corresponds to an equivalent informative sentence. The issue of how it can be done will be introduced and discussed in due course. Each use of the term sentence in other meaning, especially broadening its content, will be adequately highlighted.

Secondly, as we focus on the sentential expressions only in their informative function, only constative sentences will be considered. Imperative sentences, ←23 | 24→interrogative sentences and others will be omitted, even though these may also comprise informative components. However, if they contain informative component, we assume that can be expressed in constative sentences.

2.2 Meanings of expressions

Sentential expressions are not only correctly structured sequences of simple phrases. Due to their informative function, many have some — more or less — specified content11. That is because the phrases, that compose these expressions, usually also have specified meanings. Let us see the following sentence:

(6) It is snowing outside.

This sentence analysed as an expression, in the common meaning of its individual simple phrases, transmits the information that it is snowing outside. However, certain sentences seem to be — despite correct structure — meaningless, like the sentence:

(7) The human mind weighs one kilogram, twelve grams.

For in its common meaning the word mind refers to a certain and abstract object, not associated with the concept of weight and unrelated to it, or at most excluding it.

However, the term mind could be considered as having the meaning of the word brain. According to this interpretation, the sentence (7) would convey information that human brain weighs one kilogram, twelve grams. No doubt, this sentence would thus make sense, although, seen as a general sentence — false.

This example shows that the meaningfulness of a sentence depends on the meaning assigned to the individual simple phrases.

2.2.1 Propositions as meanings of sentences

Our reflection on the issue of meaning will start with the reflection of Willard Van Orman Quine who wrote that so-called semantic aspects (not only in linguistic meaning, but also in the logical one) divide into two groups of concepts, leading to certain ambiguity in the use of the word semantics ([233], p. 178). The first use entails issues relating to the concept of the meaning of the phrases and can be an alternative to the term the theory of meaning. I will currently focus on these ←24 | 25→particular issues, while the other use of the term semantics, which meaning is synonymous to theory of reference, will be discussed in the next subsection.

Philosophy and logic is used to discuss the meaning of the simple phrases or corresponding notions. In accordance to the sentences structured from them, propositions correlated to those phrases are mentioned. Therefore, propositions are the combination of meanings or concepts corresponding to simple phrases12. The idea of meaning has been though developed in philosophy in various ways and with diverse consequences for such understood proposition.

The theories of meaning, not from just historical but also substantial point of view, have approached the problem of meaning from various angles. The division based on the problem of existence of meanings and propositions seems to be essential. Most of all, it is associated with the question how the meanings exist, thus what kind of objects they are from ontological point of view? The answers for this question have varied.

On the grounds of psychological approach (also known as associatio- nism), meaning has been comprehended as a certain mental idea associated with a given word. This approach originated mostly from modern British empiricism, following the idea of John Locke [161]. An attempt to reduce the meaning to the specific mental experiences has resulted from nominalistic approach. However, the key issue of associationism is a question if certain phrases correspond to single mental processes (of particular person and in particular moment) or to some types of mental processes, not dependent on a given user of the language. Since mental experiences of various people during communication process vary, meanings, defined as mental experiences, must therefore be subjective and relativised to a certain situation, and any use of the phrase would have been giving it a new meaning. On the other hand, discussion about certain types of mental processes corresponding to a given phrase, results in losing its nominalistic nature. It places though the meaning in a realm dependent on the language users, but not related to any particular person. As psychologism advocated for ←25 | 26→naturalism in explication, it causes an issue, as discussing the types, moves the problem to the field of idealism.

The other approach to the issue of meaning is based on the connotation concept, initiated by John Mill [192]. From its point of view, the meaning of phrases has been looked for from the perspective of physical objects, by means of the concept of connotation, comprehended as a set of monosemous characteristics of objects corresponding to the range of the appellation. The meaning (of general names, but not proper names) has been understood precisely as connotation.

Apart from non-linguistic area, either mental or physical, some concepts also view the meaning as an abstract and ideal object. This approach places the meanings in the similar area as mathematical objects within Platonism in philosophy of mathematics. The contents of the names, or propositions expressed by sentences are to carry the same ontological status as distributive sets, numbers, etc. This approach originated from the philosophy of Plato, modern times and present days, developing in philosophy of Alexius Meinong [187], Edmund Husserl [112], and sensu stricto logically, in writings of Gottlob Frege [76, 77] and Alonzo Church [52].

On the grounds of his phenomenological philosophy, Husserl had developed a concept of intentionality of meaning, that is an act of directing the subject to derogate the meaning of a sign, that is object of meaning. This concept has been studied by Roman Ingarden, who qualified the meanings as certain abstract objects, called intensional objects. However, in Ingarden concept, these objects differ from Husserl’s ideal objects, e.g. by having their own beginning in time, whilst ideal objects are not characterised by any time coordinates. [115].

The greatest impact on the development of logical semantics came from works of Frege. The main ideas of his works Über Sinn und Bedeutung, on the meaning can be presented as follows. Sinn is a sense of an expression, whilst Bedeutung is a referent of an expression, ergo what it refers to. According to Frege, name phrases express their senses which forms a synonym of the term notion, in other words, correspond to certain ideas (Der Begriff ). However, sense does not guarantee existence of the recognised object (therefore the reference of the appellation does not have to exist), but most importantly, it differs from individually associated projections of phrases. On the other hand, proposition in logical meaning (Das Gedanke) is a sense of a declarative phrase, it also differs from associated projections of sentences. All true sentences designate logical values called true, and all false sentences designate logical values called false. Sentences also constitute a certain types of names. Direct speech ←26 | 27→sentences (oratio recta) are appellations of logical values and indirect speech sentences (oratio obliqua), prefixed with e.g. intensional functors13, are the appellations of certain propositions. The following statement illustrates this difference:

(8) John was lying, when he said, he saw Stan.

With a certain understanding of the word lie, it does not matter if the sentence John saw Stan is true. Logical value of dependent clause is thus irrelevant. What is important is that the phrase lie that p means:

i) to say that p,

and

ii) to be sure that the case is not like p claims.

In the above case, dependent clause is not a name for logical value, but for a certain proposition.

Frege’s concept expresses objectivistic approach to proposition, as the meaning expressed by sentence. This approach is constantly present in modern logic and philosophy, in spite of many various nominalistic and subjectivistic alternatives. In my study, while considering examples of various sentences, when it comes to both meaning of simple phrases and propositions, I will be inclined to objectivist approach14.

Obviously, the theory of meaning not only was but has constantly been developed in philosophy, particularly in analytic philosophy. In addition to that mentioned above, many other conceptions of meaning have been proposed, e.g.: as intensional structure (Carnap R. [46].), as use of phrases (Wittgenstein L. [292]), by directives of acceptance of sentences (Ajdukiewicz K. [5]), by knowing verification conditions (Carnap R. [47]). Suffice to say that already in the work The Meaning of Meaning published in 1923, Ogden and Richards [206] offered about sixteen meanings of the word meaning, although some are associated with cultural approach to semiotics.

The problem of the theory of the meaning of linguistic phrases involves not only the question of denotation of a term meaning but also the extent of what can be a meaningful phrase. Individual appellations constitute separate issue — as long as they are not abbreviations of certain descriptions — ←27 | 28→they name specific and unitary objects in the universe of discourse, without conveying any meaning15. This issue is related to a more general problem of proper names, or phrases performing functions of naming or indicating an individual in order to singularise it. Such names may include occasional designations, such as: this, that, these etc. According to certain philosophers, proper names should though preserve the autonomy of assigning objects to conditions e.g. by Tadeusz Czeżowski [54]). Basically, it seems difficult to draw a demarcation line between proper names and other phrases.

Therefore the conclusions from the discussion are neither unambiguous nor generally accepted. One of the reasons for the above is surely the fact that natural language constitutes a complicated and multifaceted formation in constant use. Hence, new linguistic phenomena, resulting from e.g. new ways of use of certain archaic phrases, constantly emerge.

For the purposes of the study, devoted directly to the issue of logical phrases expressing the states of objects, that are to take place in various time intervals or moments, both past and future; the above considerations are fully reasonable. The classical approach to the concept of ontology of truth, which will be discussed in due course, postulates that by having logical value, a statement expresses certain information about specific objective conditions, which are or not, accordingly. Therefore, determining logical value of a statement depends in the first instance on identifying expressed proposition, thus determining the state of the objects according to the statement.

Surely, at the moment I am not going to outline the general theory of meaning16, but simply employ certain existing ideas. Partly historical above considerations enable forming some binding reflections in the subject.

The categories of meaning and proposition can be considered on various grounds, most of all in relation to purely psychological area or to abstract objects domain.

←28 | 29→In the first case, these should be considered as appropriate mental processes present in perceptorium of specific users of particular language hic et nunc, thus essentially as unrepeatable conscious mental acts (Ajdukiewicz K. [5], pp. 109–120) or as types of such processes. Within this approach, meaning and proposition should be considered in a psychological sense.

On the other hand, these ideas can be also seen as not dependent upon individual mental experiences. This approach enables autonomizing the information conveyed within a phrase from individual subjective mental processes. Thus understood meaning of phrases and sentences is logical. The meaning attached to a constative sentence in a language is therefore usually considered in this approach as proposition in logical sense. (Ajdukiewicz K. [2], pp. 148–149).

In my study, I accept the objective view in some generality. For we focus on the sentences expressing information on the world, and these are in essence independent on persons who utter them. From a purely theoretical point of view, the information may not even constitute a content of any particular sentential expression nor many literally different ones.

Propositions are expressed by sentences, or — more generally — by sentential expressions. Therefore, the term sentence will be used not only in a syntactic sense, but in a broader way: sentence will mean a simple or a complex sentence of a language, that, in certain understanding, can be assigned a certain proposition or particular idea relating to the world in the means of reporting17. This definition should reflect the intuitive meaning of broadly accepted fact that constative sentences say something about the world, and it depicts some part of the world.

Therefore, when using the term sentence, I will mean not only a certain syntactic unit of given language, but also a correlated proposition that refers reportedly to some state of the object18.

2.2.2 Pragmatic components of a statement

Identification of propositions from a given sentential expression is rarely simple and direct. It is not only due to the issues with polysemy of individual phrases ←29 | 30→and consequently — sentences but it also involves also the sensitivity of majority of statements to the context of their utterance.

The context of a statement utterance may affect uttered phrases in such a way that literally the same sentences or phrases will induce different propositions19.

This subject is being developed nowadays as part of logical pragmatism. Published in 1938, work of Charles Morris Foundations of the theory of signs [196] has had a significant influence on the formation of this discipline. In his study, Morris divided semiotic research into three subdisciplines: syntactics, semantics and pragmatics. Pragmatics was to analyse relations between language and its users (phrases, marks, statements, etc). In the objective field of pragmatics, among others, the following issues are discussed: casualness phenomenon, sentential attitudes, presuppositions, conversational implicature and speech act (Tokarz M. [282], p. 108).

In pragmatic research, sentence as certain abstract grammatical unit is distinguished from its utterance by particular person in certain time and circumstances. For in terms of meaning, the meanings of sentences in a natural language depend on a context. Thus, meanings conveyed through them do not have to be a function of meaning of simple phrases. Only knowing a context allows to identify proposition expressed and to establish their logical value. Let us consider the following statement:

(9) He is lying to you.

Sentence (9) does not express any proposition unambiguously. For it is not clear who stands for the personal pronouns used in the sentence (9). Therefore their referents are unknown. Finally, the time of the lie is also unknown. ←30 | 31→Whether it is a current period of time (at this moment? this year?), past tense, future, or some continuity (e.g. lying for a month?). Without the context of (9), it is not possible to answer any of the above questions, nor identify the proposition expressed in the statement. (9) seen as abstract does not express any proposition; therefore, it cannot be neither true nor false.

To each such sentential expression can be attached a list of questions aiming to supply so much missing information to determine the proposition expressed. There is no way to create a general list of questions allowing to determine the contexts of all the statements. However, creating a complete list of relevant questions for each particular sentential expression could be possible. Establishing the context provides information required to form the sentence equivalent to the sentential expression, that is not a sentence. For example, for the expression:

(10) Fire!

information needed could come from the following list of questions: What is on fire?, Where the fire takes place?, When the fire takes place? Knowing the answers to these questions allows us to formulate an equivalent informative sentence:

(11) (Object x) (in place y) is on fire (in time of z).

by inserting phrases corresponding to the transmitted information in brackets20. By supplying missing information, a statement is being created; it is not sensitive to the aspects of statement context which have been expressed explicitly. For example, we could get a sentence:

(12) Private office of the Prime Minister in Warsaw is on fire on 20 May 2010.

The context should of course provide information on the meaning of to lie or fire, if the phrases do not convey a clear meaning. If so, to the above list there should be also added a question: What does ‘lying’ mean? or ‘fire’. This problem applies particularly to the indistinct terms and ultimately a good criterion to decide if a given object qualifies to a given meaning. However, I shall not focus on this problem, assuming that if any declarative statement expresses a proposition, thus shows reporting attitude towards certain state of affairs, then the criteria to establish the statement’s logical value can be explicated by operationalising it in a certain way.

←31 | 32→To sum up, knowledge of the context provides information that enables determination of the proposition expressed in a given statement. The proposition can be then expressed with a statement insensitive to a context. Logical value of the statement determines the knowledge of the world.

This study will be based on the viewpoint that propositions should meet at least the first of two following conditions described by Gottlob Frege. Frege postulated that proposition should have permanent objective reference ([77], p. 52). An issue of objective perspective of the language is currently omitted. Let us look at this postulate from a linguistic perspective. The same grammatically understood sentence may be used in different meanings or contexts, expressing different propositions. For example, in the expression:

(13) Stan is a frog.

we can say that certain animal called Stan is a specimen of frogs, or teasingly and a bit poetically state that Stan (a specimen of homo sapiens) is a good breaststroke swimmer.

Therefore, in the above examples, this sentence is the same from grammatical point of view, but differs from the expressed content’s, thus propositional, point of view. This is effective in different objective respect, as in each case the sentence is about completely different objects and characteristics.

In everyday practice, the majority of statements are of the same nature as the above examples. Therefore, while analysing statement pragmatic components, complementing a given statement with necessary information should be considered.

Within logical pragmatism, one of the most important studies is Indexical expressions by Yehoshua Bar-Hillel [21], where the subject of logical pragmatism has been situated within natural language as an investigation of relations between linguistic phrases and their specific use in determined contexts. Further studies on the structural point of view of the context can be found in the works of Richard Montague: Pragmatics [193], Pragmatics and intensional logics [194] and in the article of Dana Scott Advice on modal logic [257] (this approach will be discussed in due course). These issues have been discussed also by David Kaplan in On the logic of demonstratives [130] and by Max J. Cresswell in Logics and Languages [50].

Moreover, Scott and Montague in their works proved a redundancy of logical propositions in an interpretation of colloquial sentences — sentences do not express propositions, but their specific utterances. In opposition to this opinion and pro necessity to include propositions in his work Pragmatics argued Robert Stalnaker [263]. The development of modern pragmatics issues and research ←32 | 33→on the context have substantially benefited from works of Saul Kripke [138, 139, 140], on relational semantics of possible worlds, used to clarify the definition of context and interpretation of intensional phrases21.

The problem of context is directly connected with the second condition laid down by Frege, that is that the logical value of logical proposition should remain fixed22 ([77], p. 52). For in various contexts, the same proposition could carry seemingly different logical value. For example, sentence:

(14) I am in Toruń.

seems to change the logical value depending on the context of its utterance. For in different contexts, it expresses different propositions. According to Frege’s idea, logical value of propositions does not change under any circumastances. Therefore, occasional and all other expressions of which the list of missing information is not completed, will express different propositions, depending on their parametrisation. According to Frege’s beliefs, if those propositions differ in logical value, then they are not identical, but carry different information on characterised domain.

Note that the principle established above is only an implication. It means that it is possible that a certain statement in different circumstances carries the same logical value, while expressing completely different proposition. Instead of sentence (14), sentence ‘I am here’ could be investigated, as it is true in every context, but almost every time, after parametrisation, it expresses different proposition. In the study, we shall accept a possibility that the same proposition carries a different logical value in different time contexts. The acceptance of such possibility shall be reasoned in due course.

Obviously, the problem of identifying the expressed proposition is purely pragmatic, not theoretical. I assume that in many cases, it is possible ←33 | 34→to translate phrases, dependent semantically upon the context, into sentences independent of it, or aka eternal sentences. In the works related to pragmatics, on occasional phrases, there is some criticism towards belief that for each expression dependent on the context there is an eternal sentence, equivalent in meaning; considering casual phrases as natural elements of colloquial language (cf. Bar-Hillel Y. [21], Levinson S. [158]). However, I will not try to draw a demarcation line between occasional phrases that can be replaced by certain eternal sentences, and ones that cannot. Certainly, for many statements of constative character, after parametrisation, there can be given sentences expressing, in particular context, the same information as the statement. Moreover, this is the reason why these statements are called sentential expressions.

Let us get back to the issue of context formally developed by Dana Scott. In the above-mentioned article Advice on modal logic, the author has provided a definition of the context of uttering given sentence. The definition gives guidelines on factors affecting the information carried in the statement. According to Scott, the index, or formal representation of the context, is a certain coordinate n as follows:

pict

where w means possible world, t moment of time, trio x,y,z Cartesian coordinates of a position in space, a a person forming a statement. Free space in coordinate n is for other important parameters of a given context.

As can be seen, in this definition, time is one of the parameters. In eternal sentences, the value of this parameter is usually given in the sentence and does not need to be considered to clarify when given state of affairs occurred. See examples below:

(15) On the 15th of July 1410 Polish and Lithuanian forces won the Battle of Grunwald.

(16) It is raining in Toruń.

The first example expresses proposition independent of time of the statement, in terms of content of communication (obviously not necessarily in terms of its logical value). The second example is dependent on time when (16) is uttered. Uttered on 13th of October 2002 means that on 13th of October 2002 it is raining in Toruń. More generally, at any time uttered t, means that at the time t it is raining in Toruń.

In studying the reasoning of Diodorus, both types of statements will be useful. Therefore, corresponding categories used in subsequent analyses shall be defined.

←34 | 35→

2.2.3 Sentences that are temporarily determined

While considering various phrases in terms of syntactics and semantics, we have formulated a definition of a sentence, based on idea of proposition. We have also indicated various pragmatic circumstances related to assigning propositions to certain phrases. However, I have assumed that in many cases, those circumstances may be taken into account in a suitable sentence independent of context, expressing the same proposition as the statement dependent on the context. We are mostly interested in the aspect of time expressed in a sentence; therefore, this type of sentences we would like to name as sentences determined in time.

As sentences determined in time, we will mean simply sentences expressing any state of affairs at determined in them time23. A set of such sentences will be assigned a symbol STD24.

2.2.4 Sentences that are temporarily undetermined

Another type of sentences represent such statements as (16). Parametrizing them gives us sentences determined in time. For further purposes of the study, we shall need a category of a sentence parametrised by all the aspects except time. Completing such sentence with a missing value of a time parameter gives us a sentence of STD.

Procedurally, specifying the value of time parameter should be considered as assigning a variable, ranging over set of certain time objects of given value25.

Sentences of above-mentioned type will be called sentences undetermined in time, their set marked with symbol STU26.

←35 | 36→Two more remarks are worth making. Firstly, sentences belonging under STU do not express propositions, as they do not have permanent objective reference. Therefore, they are neither true nor false27. Secondly, given any s1 STU and adding two different time variables t1t2, we receive two different sentences determined in time s1,t1s1,t2 that express different propositions and may carry different logical values. Given any s1 STU and adding any value of a time parameter, we receive such s1 that s1′∈ STD and of course it expresses some proposition. Therefore, adding a value of time parameter can be seen as complementing sentences undetermined in time with time aspect of the context.

Assume that both defined sets are nonempty. Moreover, they sum up to a set marked as S that henceforth will be called simply a set of sentences. Its elements split in a disjoint and independent way into sentences determined in time and sentences undetermined in time.

2.3 Sentences vs. logical value

Insofar discussed the concept of meaning as a content expressed by particular sentence, or in general terms statement, is rather of pragmatic-linguistic nature. However, according to above-mentioned Quine’s remark, semantics in a narrow sense, can be seen as denotational theory.

Accordingly, in logic there is a different concept of meaning than expressed by particular utterance of content or proposition. In terms of logic, meaning represents a logical value of given sentence, which it carries in its model. This concept derives from ideas of Gottlob Frege28.

However, not interpreted sentences are not able to carry logical value. For they are not associated with any propositions and do not say anything about any subject. Although, they can carry different logical values under different interpretations. This problem is evident in the analysis of constructed language, such as a language of First Order Logic (hereinafter: FOL). Let us consider the following phrase FOL

(17) xp(x,y)

←36 | 37→If the formula (17) is interpreted in reference to a natural domain, and predicate p is attributed a relation of ‘smaller than’ <, then its logical value will depend solely on a denotation of free variable y. For denotation function assigning y number 0, formula (17) will be false because natural number smaller than 0 does not occur. On the other hand, for any denotation function that to y attributes natural number other than 0, the formula (17) will be true. However, if (17) is referred to the domain of real numbers in relation of ‘smaller than’, then for any denotation function, this formula will be true.

Also in natural language, the same phrases can — as mentioned above — carry various informative content. The following sentence:

(18) The sun is sitting on the sofa.

depending on the interpretation can be senseless or senseful: false or true. All depends on the proposition associated with a given sentence. Obviously, interpreting phrases from natural language is not as precise as interpreting formulas in a constructed language. However, when the proposition expressed in a given sentence is known, we can try to establish its logical value.

2.3.1 Requirements for the concept of truth

Stating that certain statements are true or false, we usually operate some concept of truth. This issue becomes more important when we notice that we will be working on sentences expressing propositions on the states of affairs that take place in various times, particularly in future. Therefore, we need to specify few matters of logical value that will allow analysis of various sentences without any restrictions imposed on the value of time parameter.

The remarks of Bertrand Russell [250], about the concept of truth, additionally amended, should prove useful. First of all, the concept of truth must be also the concept of false. In addition, it should specify the carrier of truth (and false), and the reason why the carriers of truth are true (or false).

2.3.2 Historical background

The issue of the concept of truth should be considered from the perspective close to historical one29, in an attempt to indicate the constituents of the concept ←37 | 38→of truth that seem key for the study, and clarify the close proximity where the outline of concept of truth in demand is located.

The term truth, in different stylistics is often being used in different language contexts. Suffice to say that Polish or English speakers speak30 frequently about true opinions, true things (e.g. real, true picture), true convictions, true beliefs etc. However, sometimes they also speak about true propositions or true sentences. The aim then is the propositional understanding of truth carriers (Woleński J. [295], p. 172). This very technical sense of the word true, in reference to propositional objects constitutes the matter of philosophical analysis within discussion on the concepts of truth.

Basically, the established concepts of truth can be exhaustively divided into epistemic and non-epistemic (Künne W. [142], p. 145). The epistemic concepts lead the question of truth of sentences to rely on the cognising subject and conditions in which it can state if the sentence is true. On the other hand, the non-epistemic concepts are based on a belief that logical value does not depend on the cognising subjects, but entirely on the objective perspective, that is a necessary and sufficient condition for adequate sentence to carry a logical value. Based on the non-epistemic concepts, the knowledge of the subject about the logical value of a given sentence is irrelevant. For presumably, there are many sentences of never known logical value. For example, the sentence:

(19) Napoleon Bonaparte one minute before his death had an odd number of hair on his head.

Intuition and historical knowledge suggests that this sentence has a logical value: it is true or false. However, it is not possible to clearly identify its logical value, as we do not have in our command appropriate cognitive qualities and probably we never will. Perhaps the reason for this is also indistinctness of terms used in the sentence (19).

In the book, we will rather focus on the non-epistemic concept of truth. The epistemic concepts will be mentioned in due course as they often provide grounds for discussion on the concept of logical value of sentences about the past as well as the future.

The non-epistemic concepts of truth can be divided into relational and non-relational ones (Künne W. [142], p. 145). The essence of this division is based on the issue of explication of the idea of truth. The relational concepts, in definiens express belief that truth is to be a bi-argumental relation between ←38 | 39→the linguistic and objective perspectives, indicating a certain applicability, adequacy or consistency. On the other hand, the non-relational concepts do not use the term of bi-argumental relation truth or false in relation to the logical value carriers.

Among supporters and also precursors of the relational approach to the question of truth, first of all we should mention Saint Thomas Aquinas. This philosopher wrote that () For, since the truth of the intellect is ‘the adequation of intellect and thing,’ inasmuch as the intellect says that what is is and what is not is not ([278], I vol. ch. 59, pp. 127–128). The above-mentioned equation is usually described by formulary adaequatio intellectus et rei. Another work of Saint Thomas states: () For this reason truth is defined by the conformity of intellect and thing; and hence to know this conformity is to know truth ([279], quest. 16, art. 2, p. 249). The issue of agreement has been discussed also by Kant who claimed that the truth is the agreement of cognition and its subject, using the term cognition in a meaning of proposition ([126], s. 102).

On the other hand, philosophers formed also non-epistemic and non-relational concepts of truth31 who without trying to define the truth based on the idea of relations between its carrier and objective perspective. One of the initial outlines of such a concept can be found in Plato’s Sophist, where the Athenian philosopher states that a true sentence32 states something is, as is, on the other hand, false one states things that are other than the facts() In other words, it speaks of things that are not as if they were ([222], 263B, p. 93)33. Interestingly, the Ancients are ascribed the use of such grammatical constructions that require some supplementation, or — as named in this case — parameterisation, to express proposition unambiguously. In particular, such sentences, according to given definition, can be elements of a set of sentences undetermined in time STU (cf. K¨unne W. [142], pp. 146–155), e.g.:

(20) Socrates leads a discussion.

←39 | 40→In any case, this issue shall be characterised closer, while describing semiotic beliefs of Diodorus Cronus, as it will be of importance.

Plato’s concept has been then developed by Stagyrite, giving a full weight and clearer conceptualisation to the classical definition of truth. The famous passus 1011b of Metaphysics reads as follows:

The above passage can be understood i.a. as follows: statement that it is not as it is, or that it is as it is not, is false. On the other hand, a statement that it is as it is, or it is not as it is not, is true.

The Aristotle concept permanently joined European scientific thought, forming basis for further deliberations on the problem of truth. In the past century, Alfred Tarski essayed to polish it, consciously adverting to the idea of Aristotle34. In his works, he separated objective language from metalanguage, thereby indicating how to avoid semantic antinomies35.

Alfred Tarski described a measure to define the predicate true. Because in his conception, the carriers of truth are to be constatives (not propositions), therefore truthness needs to be in reference to the language L. The definition of truth for language L should meet the general principle called T-convention, of the following form:

(T) Sentence x is true in language L if and only if p,

where x stands for metalanguage appellation of the sentence of objective language, and p is its translation into the metalanguage.

According to Tarski, T-convention is not in fact the definition of truth, but a methodological principle regulating the construction of the definition of truth in the language:

←40 | 41→However, the method of constructing the definition of truth given by Tarski, is not appropriate for a colloquial language, as there are many levels of language, often undifferentiated (as colloquial language is a so-called language semantically universal), and its structure is not clearly defined, what can easily lead to semantic antinomies ([271], p. 14). According to Tarski, the meaning of the problem [i.e. defining truth for natural language] is more or less vague, and its solution can have only an approximate character ([272], p. 370). Tarski’s concept of truth can be primarily used with constructed languages, as a theory of the conditions of correctness of expressions in a given language. The key quality of the discussed concept of truth is that it does not provide a criterion to determine if given sentence is true or not ([273], p. 317). It only provides methods to construct definition of truth for a given formalised language36

While outlining the concept of truth for the types of sentences we will be working on, we will consider guidance on levels of language, however, bearing in mind that we are primarily interested in sentences in colloquial language.

Addressing this issue, we will point to another problem. It arises from relativisation of the idea of truth to a given language and is related to the question on the carrier of logical value.

2.3.3 What owns the truth?

Amongst the possible candidates to the carriers of the truth or false — sentences understood obviously as constative sentences and expressing certain idea, content) and propositions, which are what the constative sentences express — were mentioned most frequently.

Following the famous argument of Alonzo Church [52] (cf. Grayling A. C. [86], pp. 20–21), we will lean towards the view that the carriers of logical value are propositions. Church argued that different sentences (e.g. from different languages) carry exactly the same logical values despite completely different forms of writing. What gives them identical logical value is the fact that they express the same proposition37. The logical value is determined by the ←41 | 42→expressed propositions38. However, it does not mean that it is not possible to mark sentences e.g. true. Some of modern authors write that truth is implicitly and imitatively also a property of sentences (cf. Barwise J., Etchemendy J. [24], p. 26), and the same can be probably said about false.

In the study, I will not be writing about propositions, but truthness or falseness will rather mark sentences, provided that according to the above-mentioned definitions, the sentences are expressing certain propositions and they co-determine logical value of the sentences.

They co-determine since the problem of logical value of sentences, according to one of the presented postulates on the theory of truth, can be considered from a non-linguistic point of view. For within non-epistemic concepts of truth, truthness or falseness of the sentences is mostly a consequence of objective aspect of discourse.

2.3.4 What makes sentences true

That certain sentences are true or not is decided by certain objects: It raises a question: what types of objects are they?

This reference to a given objective domain is the reason for proposed answers to the above questions to be included in so-called ontology of truth (Mulligan K., Simons P., Smith B. [199], p. 287).

Regardless of whether in given concept in explication of the word true or its different stylistic forms, requires a binary relation (between the logical value carriers and something that belongs to the objective aspect), or not39, true sentences must state something, or mean something (e.g. indicate a state of affairs, cf. Tarski A. [272], p. 223).

In order to determine these objects, philosophers introduced different theoretical terms, usually referring to well-developed concepts describing — in the words of Russell — the kind of thing that makes a proposition true or false ([249], p. 185). Following Peter Simons when writing that: classical theory of truth requires certain essence for simple statements about the world, he adds: well known under various names, such as ‘status’, ‘condition’, ‘process’ and ‘occurrence’ (), the majority of them are the truthmakers ([258], p. 159).

←42 | 43→Amongst many proposals for the so-called truth-makers, or verifiers; further I shall use verifiers), there are i.a. facts.

The concepts of the facts have been presented in various ways by: George Edward Moore [195] — as simple theory of facts and Bertrand Russell [249], who has developed the concept of truth-makers so it could correspond to different levels of sentential complexity, singularising unitary objects, different levels relations and the facts that are to correspond to complete sentences. Not without an impact on Russell’s theoretical ideas wasThe Tractatus Logico-Philosophicus of Ludwig Wittgenstein, where the author introduced his so-called picture theory of language. Let us analyse the following theses from The Tractatus:

1 The world is all that is the case.
1.1 The world is the totality of facts, not of things.
2 What is the case — a fact — is the existence of states of affairs.
3 A logical picture of facts is a thought.
3.01 The totality of true thoughts is a picture of the world.
4.024 To understand a proposition means to know what is the case if it is true. (One can understand it, therefore, without knowing whether it is true.) (Wittgenstein L. [291]).

The concepts of truth-makers are therefore clearly metaphysical40. For discussing the description of the world from linguistic point of view, they introduce certain objects constituting the structure of the world.

Wittgenstein’s beliefs have had a major impact on Russell’s considerations, especially from the days of The Philosophy of Logical Atomism. However, in the later period — as verifiers verifier — instead of the facts Russell introduced other elements of the structure of the world, called occurences ([248], pp. 284–288).

Apart from the above-mentioned candidates for the truth-makers (verifiers), many other objects with their appropriate concepts have been proposed. Also as verifiers situations were proposed, the idea introduced by Roman Suszko41 and developed by Bogusław Wolniewicz [296]. The situation was here understood as each fragment of reality, verifying a sentence (p. 14). The theory of situation has been also developed by Jon Barwise and John Perry [25].

As for newer proposals, we should mention so-called moments of which concept has been formulated by already-mentioned Mulligan, Simons and ←43 | 44→Smith[199]. Obviously, the word moment has been understood by them in a completely different way than it will be in further parts of the book. By moments, they meant objects existentially independent but requiring existence of other objects. The above-mentioned authors give the following examples of moments: smiling lips or a slip of a man as examples of truth-makers for following sentences consecutively: ‘A face smiles.’, ‘A man slips.’ (p. 290). The concept of moments developed from works of Husserl (in any case, the term moment, as the authors admit, has been taken from Husserl) about the terms of ontological dependence and independence, and associated with them problem of wholeness and partiality (p. 294).

Apart from the signalised above proposals, there is one more concept that sparks philosophers’ attention. By this, I mean the concept of state of affairs. On the basis of this concept, Ludwik Borkowski formulated the definition of truth as follows:

The sentence is true if and only if it describes a certain state of affairs (claims existence of a certain state of affairs) and this state of affairs exists (happens) ([36], p. 119).

This definition imposes the two following conditions on the accuracy of given sentence: Firstly, the sentence must state something. It has to be a state of affairs. Secondly, the described state of affairs must exist. These guidelines, as will be seen further, will prove to be extremely valuable while we start to analyse sentences describing future or past states of affairs, i.e. the states of affairs that surely do not exist currently.

In the concept of truth, outlined below, for truth-makers the term state of affairs will be used. Although the term will not be here closely defined — as it would require broader discussion much beyond the subject of this book — however, it shall become clearer during case study. It can be assumed a primitive notion.

Finally, we will enunciate one more important remark. The verifiers, no matter how understood, do not make all the types of true sentences true. For there are such sentences of which the logical values seem independent of any objective conditions. Such sentences are usually called analytical (respectively true or false). Although there are many definitions of analytical sentence, quite often of different ranges (one of the most comprehensive lists of various approaches can be found in the work of B. Mates [177]), however, the cofeature of such sentences is that their logical value is based on two matters: structure and meaning of phrases present in it. Probably the most popular example of a sentence analytically true in English is as follows:

(21) Every bachelor is an unmarried man.

←44 | 45→If we tried to parametrise such sentence, stating e.g. that:

(22) In place x, in time t each bachelor is an unmarried man.

then, irrespective of the values of x and t, the sentence would still be true (although of course expressing different proposition, less general). For sentence (21) states that any bachelor is a man without a wife and, according to classical42 approach to analytical sentences, its logical value does not depend on any objective conditions. Therefore, introducing additional restrictions cannot have any influence on its logical value. That truthness (or respectively, falseness) of analytical sentences does not depend on any state of affairs, is the reason why they will not be interesting, thus not taken into account.

However, for the issues discussed in this book, the sentences of logical value dependent on the objective perspective are important. Therefore, we will be interested in sentences usually called synthetic, or those that doubtlessly increase our knowledge on the empirical world, stating that things in the world are so in some time. These are e.g. sentences as follows:

(23) Last Friday Mars extra-close opposition took place.

(24) On 12th of December 2007 Jan Kowalski won 2 million zloty in Lotto.

(25) Today I am totally overfed, after having two plates of zur kujawski prepared by my mum.

2.3.5 The concept of truth employed in the study, concept of false controversy

We have established that propositions will be the carriers of logical value, and the states of affairs will be truth-makers of propositions and sentences expressing them. We will now proceed to attempting to create a certain outline of the definition of truth and to indicating the issues associated with the corresponding definition of false.

A substantiation for the use of truth-makers in the proposed definition of truth is the following attempt to apply to discussed question T-convention, as follows:

Obviously, in this case, we are not interested in the relativisation of sentences with STD to a language, in which the sentences have meaning — for I have assumed that to STD sentences expressing proposition are assigned. Let us substitute z with the following questions:

(27) Jan is going to school in moment t.

(28) Jan went to school in moment t.

Let us assume that (27) is uttered in moment t, and (28) in any other later moment44. Then with the use of (26) we get:

(29) ‘Jan is going to school in moment t.’ is true if and only if Jan is going to school in moment t.

and

(30) ‘Jan went to school in moment t.’ is true if and only if Jan went to school in moment t.

This is a strange consequence, as one would like to acknowledge that the sentence (28) in some sense results from sentence (27), therefore the reason why the sentence (27) is true, makes also the sentence (28) true. Sentence (27) is true, when Jan goes to school in moment t, but what if in next moment, say t, Jan has already arrived at school. For we will not decide that the sentence ceased to be true. Its trueness is based on the fact that in moment t the state of affairs is that Jan is going to school; in t the state of affairs may be different, but this is not important any more. Now it is clear why the sentence (28) results from (27). For they relate to the same state of affairs, if one is true, the other is true too, but in different time45.

←46 | 47→Why then both sentences differ from grammatical point of view? The difference is of course in the grammatical tense forms. One is expressed in present tense, the other one in past tense. It arises from the position in time of the person uttering (27) and (28) in relation to the state of affairs expressed in the sentences. In the first example, the sentence is formulated in time t approximately equal to t, and in the second example, in time t′′ later than t. This observation gives some insight into the nature of tenses and functions they fulfil. This problem will be analysed in more detail in due course.

Apparently the definition of truth should not prefer any position in time. It means that a true sentence (if true) is simply true regardless of whether it states about the past, present or future states of affairs.

Let us look into the issue again, from the objective perspective. The states of affairs are organised in time. For example now, when I write these words using a computer, it is 20 : 45 Central European Summer Time, but just five minutes ago, when I ate delicious apple pie, called staropolski jabłecznik, it was 20 : 40 Central European Summer Time. The individual states of affairs I have encountered can be organised by the direction of time flow. The same applies to the future states of affairs I will be participating in. They can also be seen as organised in time considering binary relation ofbeing earlier or its converse being later46.

The sentences belonging under STD express occurrence of certain state of affairs in time defined in them. Such understanding of sentences enables forming the following definition of truth, that seems not to be sensitive to time of utterance of the sentences:

(31) For any simple sentence z STD:F(z) is true if and only if the state of affairs marked by sentence z happens.

Taking the sentence (27) in its different (in terms of grammatical tense) variant forms, we find that it is true if and only if in t the state of affairs is so Jan ←47 | 48→goes to school. The word goes means here present tense in relation to described state of affairs, not to the time of utterance of any sentence.

However, the question arises about the issue of phrase takes place — how it should be interpreted? For the states of affairs can also be qualified as past, present and future, even from our position in time. Therefore, it would be about the place in a certain time order, set by consecutive values of a time parameter. The world can be perceived as a history of consecutive states of affairs47. Given state of affairs is taking place if situated somewhere in the history of the world. The whole history of the world can be divided into certain sections, called temporal parts of the world, or the states of the world (in short Si, where i I, or to the adequately adjusted to the cardinality of a set of such sections of a set of numbers). Of course the states of the world are also organised in time. The individual states of affairs can be considered as elements of given states of the world, that are certain total states of affairs in a given time.

In the light said above, the history of the world H can be described as a set of e.g. forms {S0,S1,,Sn}48. In turn, stating that given state of affairs — e.g. s2belongs to H, may mean that there is such S2 that S2 H and s2 belong to S2. Therefore the state of affairs s2 in some sense is a part of the temporal parts of the world S2.

The history of the world can be presented graphically by means of an axis, where the value of the time parameter increases from left to right, and individual states of affairs are located in the corresponding time values. Following this line of thought, I will reformulate (31) as follows:

Obviously, by the history of the world, we do not mean only what was, but also what will be, what is etc. Therefore, we look at the history from somewhat timeless perspective. This approach is purely theoretical and does not yet settle the way ←48 | 49→of judging such sentences, which state about future, although e.g. future does not exist or is not preordained. This problem will be tackled in due course. See the following figure presenting the history of some (lets take a chance that our) world, seen from atemporal perspective. Although the figure settles the existence of both a part of past and a part of future from present perspective. However, it should be considered also a visual aid only.

PIC

The above figure presents a part of history in the past, a fragment of present and a fragment of future. The concept of truth, discussed above, does not give precedence to any of these fragments. It does not state if the sentences about future carry own logical value in present or not. It only says that a sentence is true if and only if in time defined in the sentence described state of affairs takes place. Obviously, if there are no fragments of future (i.e. if the history of the world finishes in present, e.g. because it is not preordained how it will develop), then the sentences about future cannot be true.

According to definition 2.3.1, we can create a definition of false, by contradiction. Of course it requires the adoption of semantic law of excluded middle (or bivalence) which states that:

(32) For any z STD:z it is true or z false.

what through classical logic gives:

(33) For any z STD:z is not true if and only if z is false.

and through 2.3.1, the following fact:

Actually, this fact can be considered a definition of false. Fact 2.3.2 formed only by implementing (32). However, the use of semantic law of excluded middle encounters at least three objections. The first one is associated with determinist ←49 | 50→consequences, second, with existence of sentences that due to their objectlessness does not seem false nor true, and finally, third one resulting in general from questioning of this law, put forward on the basis of so-called semantic anti-realism.

The first objection shall be mentioned and elucidated now, while the other two will be the matter under discussion in further subchapters.

According to some philosophers, one of the sources of deterministic consequences RDC is the use of (32). On the one hand, it is said that we do not assume that sentences about future carry any specific logical value, but on the other hand, we claim that they are true or false49 in any given time. But then any sentence z STD must be true or false, and none carries any other intermediate value (e.g. the sentences about future could carry propounded by Jan Łukasiewicz value 12 [168])50.

Assume that we agree to the bivalence principle for sentences about future (at the moment, the case of past is not being considered)51.

(34) For any z STD, such that ‘z’ describes the present state of affairs: z is true or z is false.

According to our previous considerations (31) a sentence stating something about the present state of affairs is false if in present the described state of affairs does not occur. The sentences stating about future time can certainly be characterised as a special case of sentences about present time, in a moment they state about.

However, the problem arises when we want to use the definition of false (fact 2.3.2.) for any earlier moments. What does it actually mean that history of the world does not contain the state of affairs marked with z (where z is such a sentence about future that says something about certain state of affairs s in moment t2)? Does it mean that:

i) in moment t2, s does not belong to the history of the world,

←50 | 51→or does it mean that:

ii) in moment t1 (such as t1 is anterior to t2), s does not belong to the history of the world?

The above distinction is crucial for propounding the third logical value. In fact, it comes down to understanding the meaning of the history of the world and its appropriate status, however, it affects the strategy of ascribing logical values to sentences. Let us try to face those questions sequentially, referring to both cases. Starting from the first one, as it is less general.

In moment t2, the appropriate temporal part containing all state of affairs belongs to the history of the world. If state s is missing, the sentence z is false. The sentence is false also if H it breaks in one moment and there is no appropriate temporal part (marked with index 2)52. It seems quite clear. However, the anterior falseness, in moment t1 proves problematic. Thereby we proceed to the second case.

Various strategies are available, and they can be focused around three main conceptual oppositions. First one: determinism and indeterminism. It can be acknowledged that the history of the world is complete in any moment of time, i.e. proper s-es belonging to proper S-es is preordained, therefore, the world is somehow ready both in the past and in future (e.g. the future states of affairs are unambiguously designated by present ones, just as present states by past ones). As a consequence, each sentence has a single constant logical value in each temporal part of the world. On the other hand, there is an opposite indeterministic standpoint. It would mean that not every sentence has a single constant logical value in each temporal part of the world.

The opposition to logical value issues is useful in describing the indeterministic standpoint. For logical value can be approached in classical way, with two logical values, or in non-classical way, allowing more than two of them. In the latter case, at least some questions about the future would adopt an ←51 | 52→intermediate logical value: would be neither true nor false. On the other hand, the two classic logical values could be used, while rejecting an assumption that there is only one history of the world. Allowing different alternative solutions, the sentence would carry a classic logical value, but depending on the scenario within which it would be considered.

The above approaches can be supplemented with another opposition. The opposition between the static and dynamic attitude towards logical values. Within static attitude towards a logical value, sentences carry constant logical value in every considered scenario. Particularly, when dealing with determinism, there is only one scenario of the future history of the world. The dynamics in valuating the sentences involves the ability of sentences to change logical values depending on perspectives in time. For example, sentences about certain future states of affairs are false until the state of affairs they describe occurs in the history of the world. However, if in the defined temporal part such a state of affairs does not exist, the sentence becomes false in a static sense. On the other hand, the sentences could be considered true, if there is every indication that what they state will happen, and their logical value becomes static only in the temporal part they state about (becoming e.g. forever false).

The dynamics of logical values could also be of the following nature. Sentence z is false in t1 if in t2 indicated a state of affairs does not occur, i.e. it does not exist in the history of the world, that is even earlier it had not occurred, sentence in t1 therefore in a way inherits the falseness from the future and then it is always false53.

In the case of indeterminism, regardless of the strategy, the history of the world would have been of dynamic nature. While the case of determinism is fully static in valuating. In fact, determinism deserves to be considered fully ontologically ←52 | 53→deterministic — for it creates the strongest and indisputable foundations for unlimited bivalence principle.

The approach integrating the above opposition provides an opportunity to consider the competitive versions of the history, which emerge from the same past. Its advantage is that it also allows the application of the law of the excluded middle. When there is only one version of the history, it is determinism. The opposite situation represents indeterminism.

In the following chapter, we shall examine the possible ways of implementation of the conditions in question for the determinist case. Therefore, this chapter is devoted to the wide discussion on the question of determinism. The logical value of the sentences about the future requires though for the future to be in a way objectively established in present (cf. Łukasiewicz J. [167], p. 122). I may mean that such things as the full causes of all future events are present in already shaped history. Without them, there is no guarantee of the nature of future states of affairs, therethrough future history of the world may allow different alternative expansions. The line representing the future and present would then break in each now, further creating only numerous possibilities of which only certain ones will be updating along the passage of time.

Apparently, without additional assumptions, we are not able to give a full general concept of truthness or falseness of sentences. It does not mean that we will give up deliberations on the law of the excluded middle. Some arguments in favour of use of the law of the excluded middle in researches on RDC and against it shall be considered in the second part, in the subchapter on sentences about future, where we will present also the strategy of further works, accentuating the modelling of branches of history.

To sum up, the definition of false can be created in more natural way without adopting the principle of bivalence, simply adding it to our deliberations. However, if we allow the alternative histories, true or false of the sentence about future shall be viewed in relation to a given alternative future history of the world.

2.3.6 Presuppositions of sentences

The second objection regarding the bivalence principle stays close to the problems considered by Bertrand Russell within the theory of descriptions and arising from it an issue of presupposition [245, 246]. In his famous example, Russell examined the following sentence:

(35) The present king of France is bald.

←53 | 54→This sentence, due to lack of such object as a present king of France, causes many problems when interpreted. One is that however valued true or false, it seems to state an existence of an object described in it by present king of France. Of course, Russell decided that sentence (35) could be rephrased as a conjunction of the following three sentences:

(36) There is at least one such object as the present king of France.

(37) there is at most one such object,

(38) such object is bald.

The above paraphrase created an opportunity to express sentence (35) in language FOL as follows:

where — from the logical point of view — arises the formula:

(40) x[PKF(x) ∧∀y(PKF(y) y = x) B(x)].

In sentence (40) (besides other conditions), certain presupposition of sentence (35) is explicated; it states that in the universe of reflections in general exists such object as the present king of France.

Similar problems, as in the sentence considered by Russell, may of course appear if sentences express propositions stating about other fragments of time, not only present. Some sentences may though not only assign certain characteristics to not existing objects, but even state that these objects possess certain characteristics in future (or even past!) time t, that will never exist in the history of the world. See the following example:

(41) In 2045 Toruń will host Winter Olympics.

It states that in year 2045 in the castle-town where Nicolaus Copernicus was born, sporting event called Winter Olympics will take place. In which case would we decide this sentence to be false? Is it only if in Toruń in year 2045 the Olympics will not take place? What if for any reason the idea of the Winter Olympics ceases to exist, or, worse still, the history of our world finishes before the year 2045? In such case, this sentence will prove objectless, and it would seem that also devoid of any logical value. For neither what it states happen nor its negation.

This problem may relate to sentences about different parts of the history of the world, in which the claimed states of affairs are supposed to happen. It needs ←54 | 55→to be tackled in order to remain on the grounds of bivalent logic55. In order to eliminate this problem, we shall propose a certain general principle of understanding such statements, close to discussed considerations of Bertrand Russell.

Let us consider some examples of questions of obvious objectlessness. They relate consecutively to the past and the future:

(42) Socrates in V BC watched television.

(43) Socrates will lead a discussion in 2050.

Both sentences are determined in time — localise certain state of affairs in defined time frame. With the proper understanding of the individual phrases forming them, they also express certain propositions. In the standard meaning of appellation ‘Socrates’, it refers to a certain historical figure, important for the history of European philosophy and culture. The propositions expressed by (42), (43) state consecutively that Socrates watched television in V century before the Common Era, although the television is an invention of the end of previous millennium, and that Socrates, a historical figure, will lead a discussion in the middle of our century. Both propositions are therefore characterised by the states of affairs that had not or will not happen.

Thus it appears that these sentences cannot be neither true nor false, but rather deprived of logical value. Unless — following the Russell’s example — we decide that the sentences carry proper presuppositions.

The accentuation of a preposition requires further insight into their logical structures. The following remarks of Frege from Über Sinn und Bedeutung shall prove helpful:

In line with them, places, dates and time frames can be seen as objects, and their linguistic marks as appellations, e.g. individual or general names, and the latter as predicates. In relevant sentinental functions, they form true phrases ←55 | 56→for certain objects, and for others false (e.g. ‘television — ‘(x)-that is a television’ etc.). In order to make a point, the existence of presupposition in such sentences can be acknowledged even for individual appellations; that it is such element of domain which is identical to the denotation of an appellation (e.g. ‘Socrates’ — ‘x = Socrates’)56.

This approach enables translation of analysed sentences into language FOL. Then, the used examples of sentences shall adopt the following (and in this case similar) logical form.

If the sentences like (42), (43) will be understood in such way, then of course for any interpretation (where an interpretation means a model as in the model theory for FOL) they will carry logical values. They will be true, if: i) appropriate objects will belong to the domain, ii) those objects will be in indicated relations between them. However, if at least one of these conditions is not met, such sentences will be false

As a result, state of affairs should be considered under set theory. This issue shall not be elaborated. However, the evidence shows that when discussing states of affairs we mean objects in defined relations, in a certain time. The set theory ←56 | 57→approach to the empirical world is not an isolated one, for it is acknowledged in the literature58. The question of how far the ideas of the set theory can be applied to the empirical world that is variable and highly dynamic, we shall leave open59. We assume that it is a valid instrument leastways to demonstrate the existential presuppositions behind the analysed statements. The question of the general structure of reality the statements refer to is however another issue and strictly metaphysical problem. This issue shall not be discussed in this study60.

Let us return to the question of presupposition. We have tried to indicate that presented sentences can be considered as assuming an existence (in fact belonging to described domain) of certain objects. However, not all the sentences in natural language can be transformed into so-called existential sentences. Many of them are of completely different structure. Let us see e.g. the following sentence:

In accordance with the previously discussed method, the logical form of (45) could be presented in the following manner:

However, the evidence shows that the above sentence is true even if there are no Martians, as the above implication is then emptily satisfied. On the other hand, negation (45) is true when it is logically equivalent to the sentence:

(47) x[M(x) ∧∀y(¬t(y) ∨¬MS(x,y))].

It is equally disturbing consequence as the previous one. Sentence (47) is therefore true if there are any Martians in the domain, but there is not at all any moment in time, or in a given moment they are not chess masters. Nevertheless, we would like to determine that sentence (45) is also false if there are no Martians. There is a simple way to achieve it. It must be assumed that the general expressions also assume belongingness to the domain of the discussed objects. It should be determined that sentence (45) expresses information presented e.g. as follows:

(48) xM(x) ∧∀x[M(x) →∃y(t(y) MS(x,y))].

In such understanding, (45) could not be true if Martians do not belong to the domain of discussion, and its falseness would be based i.e. on the very fact that they do not belong to the domain.

It is worth to mention that the definitions of truthness and falseness of the sentences in their presented interpretation based on a fragment of theory of descriptions and translation into formula FOL, do not pose a problem in relation to the so-called existential sentences containing a verb to exist62. Given that this verb should not be understood as belonging under the domain, but as belonging under the domain of existing objects (similarly, as we would understand swimming as belonging under domain of objects that swim). Therefore, it should ←58 | 59→not be considered as existential quantifier, at least not in relation to the synthetic sentences63. Let us consider e.g. the following sentence:

(49) A philosopher exists.

According to the proposed parametrising measure, the question should arise: when does a philosopher exist? For existence, just like every state of affairs, relates to a time localisation (and, as some may reasonably add, also a spatial one; we are, however, for obvious reasons interested essentially in the aspect of time. There were periods in history when philosophers did not exist. Let the sentence refer to 24th of July, 2003. Then statement (49) is equivalent, according to the expressed proposition, to the following sentence determined in time:

(50) A philosopher exists on 24th of July 2003.

can be rephrased in the above-proposed vein as follows:

Obviously, the negation of sentence (50) would adopt the following logical form:

Let us sum up the above observations. In order to examine the sentences stating about states of affairs within bivalent logic, we need to assume at least that they presuppose certain issues of existential nature (in the meaning of belonging of the objects to given and considered domain)66. Often, these assumptions can be emphasised by analysing their structure from the viewpoint of FOL.

←59 | 60→On the other hand though, we do not claim that all the sentences of the type of our present interest can be well analysed in terms of their logical form within FOL. Moreover, we do not offer a formula for proper translation of any sentence. We postulate though that the assumption that expressions presuppose their own objective reference is a natural assumption and a forms proper, i.e. close to our linguistic practice, way to avoid expressions making statements about certain states of affairs in an objectless manner, and therefore surely not carrying either of the two logical values. I suggest lending the substance to the proximity of this approach to a regular linguistic practice with a means of an experiment involving reading following fragment and choosing one of the answers.

Two neighbours are talking. One says: ‘Mrs Kowalska, you should go to Szewska Street, because in the newly opened Social Insurance Institution they give extra money to people with the lowest pension’. Mrs Kowalska thanks and then goes to Szewska Street. To her surprise and disappointment, she learns that despite the enormous expansion and profligacy the institution raises its more and more modern buildings, there has not been one on Szewska Street built yet. Therefore, frustrated she heads back home. When she meets the neighbour, she says with a just reproach: (?)

Well, what does Mrs Kowalska say?

(a) Your statement has not been neither true nor false.

(b) Your statement misled me. You have given me false information!

I believe that Mrs Kowalska (if she is still on speaking terms with her neighbour) rather says something that expresses a meaning similar to (b). After all, she believes that the statement, that the said branch of the institution exists in reality, belongs to the content of information she received from her neighbour. For this is a regular presupposition in natural language, that while ascribing certain qualities to certain objects, we believe them to belong to certain domain. Stating in particular about objects from physical world, we assume their participation in the physical world, or existence.

In conclusion, we will add that the accepted here perspective of considering sentences is independent of FOL, what entails the following fact. In further analysis, we will be using propositional logic with suitable modal operators. These sentences shall be represented by means of sentential variables, without going into their internal structures. Therefore there is no practical requirement of translating any sentences into language FOL. However, as we can see, the question of interference between the objectless statements and the principle of bivalence can be solved by the requirement of adding to the statements the conditions of their objectiveness.

←60 | 61→

2.3.7 Sentences with modalities and other

Further comments will begin with an interesting fragment of the work of Marek Tokarz:

() the most important laws of nature, always being idealisations, would become meaningless. As an example, let us consider one of Newton’s laws, intentionally in quite archaic stylisation:

If a material object is not under the influence of nay force, the object moves with constant velocity in a straight line.

It has not been possible to find on the Earth nor in space such material object that is not under influence of any force. Nevertheless, Newton’s law has a certain content and it is a weighty one. It does not state about our random part of the Space, but about all spaces possible to be thought about, even about those where certain objects are not under influence of any force ([282], p. 111, author’s translation).

This passage expresses very important information about certain class of sentences, the so-called laws of science. These sentences do not state anything about any particular states of affairs nor about their occurrence in any time. They are invariant against time and space (cf. Such J. [265], p. 519). Among other things, it means that their logical value is insensitive to the time parameter, even though they undoubtedly belong to the set of constative sentences. Therefore, there are some reasons to, after the subtracting analytic sentences from set Z, exclude other types of sentences. These are such sentences which do not state any real states of affairs.

Tokarz indicated certain modal component of Newton’s law. Obviously, there are plenty of statements that are explicitly modal. Let us discuss another four sentences:

(53) It is allowed for a man to ride a horse.

(54) It is necessary, that Supremely Perfect Being exists.

(55) It is possible that hokey players took testosterone.

(56) Jan knows that Warsaw is the capital of Poland.

These sentences from syntactic point of view should be considered as comprised of simple sentence and congruent sentence-forming functor of sentential argument. This functor is a certain modality (or a method: modus) operating on simple sentence. In the presented sentences, in their proper sense, the matter involves modalities, respectively: deontic, alethic, epistemic. There appears a problematic question if the sentences state about some states of affairs, stating their occurrence (or not) in our real world, or only state that e.g. certain states ←61 | 62→of affairs either occur in a possible world or occur in all possible worlds in respect to the initial world, as such modalities used to be interpreted within semantics of possible worlds.67

We are however interested in sentences of factual nature, i.e. stating something about occurrence of the states of affairs in a given time and in the considered world, not in various other possible worlds.

Some of the above sentences though do not need to have modal qualification characterised by the idea of possible worlds. Of course, it depends on proposition they express. For example, sentence (53) may simply state that in a given time and country if someone is riding a horse does not break the law. Similarly sentence (55) is allowed to be understood as carrying information that certain hokey players in some time have testosterone (hence they can use it, having it somehow at hand). The presented understanding of (53) and (55) is of course only one of many and claiming that each modal sentence can be remodelled into modeless ones without loss of sense, is undoubtedly false.

In further, formal reconstructions of RDC, the sentential letters will be ranging over primarily factual and simple sentences. The complex sentences will be constructed with the use of the classic logical functors (conjunctions , negations ¬ and others, defined by the former ones (, , , etc.)). These functors are of course extensional (as opposed to modally understood functors from sentences (53)–(56)) which means that the logical value of the sentences featuring them is a function of logical value of simple sentences (while in modal sentences the matter involves intensional functors which use results in logical value of complex sentence not exclusively dependent on logical value of simple sentences. However, while analysing various sentences of the colloquial language, it has to be noted that it is easy to make a mistake in valuating a functor. See one of the most illustrative examples:

(57) On 12th of September 1683 the king of Poland, Jan III Sobieski had arrived near Vienna and his army broke the siege.

Sentence (57) is an example of sentences determined in time. Undoubtedly, from syntactic point of view, it consists of two simple phrases that with a certain (intended) meaning can be presented as follows:

The main functor joining these sentences is ‘and’. By inattention, we could therefore believe that (57) is a conjunction of two atomic sentences (58), (59) from the set STD, where the time parameter is adequately generalised into both sentences. It is true that it is a conjunction, but not classical, extensional. For in its intended meaning, this sentence is not de facto logically equivalent to sentence:

(60) On 12th of September 1683 the army of the king of Poland, Jan III Sobieski had broken the siege and the king arrived near Vienna

even though the regular conjunction is a symmetric operation:

(61) A B B A.

It is not equivalent because sentence (57) states that this state of affairs that the king Jan III Sobieski had arrived near Vienna has been in some sense (e.g. causal) the reason that the army of the king Jan III Sobieski broke the siege. Moreover, between both states of affairs, although it takes place on 12th of September 1683, there is a certain sequence of tenses. First king Jan III Sobieski had arrived near Vienna, and then his army broke the siege.

This example shows that sentence (57) within our theory cannot be considered as a complex sentence. For it does not include a classical functor in its structure. The modal component is included in its intentionality of meaning; as a result, this sentence does not simply indicate some state of affairs but also qualifies certain measure in which the states of affairs affect one another. Obviously, we could establish a form of the sentence that would be less modal e.g.

(62) On 12th of September 1683, the fact that the king of Poland, Jan III Sobieski had arrived near Vienna, had been the reason (one of reasons) that his army broke the siege.

But in fact not only states of affairs are being indicated but also their modal qualifications.

In the analysis of RDC, we will employ only sentences that — according to heuristically introduced sense of this conceptualisation — indicate or not the occurrence of some state of affairs. We assume that such sentences belong to a set of considered sentences S. For obvious reasons, we are not able to provide precise criterion of division of sentences of natural language into modal and ←63 | 64→non-modal (only modally qualifying state of affairs or indicating state of affairs), but only to signalise this problem68.

In discussed further reconstructions, the complex sentences will be created with the use of extensional functors, but not only. For RDC in its essence is a stricte modal argument. For the thing is that it centres around certain temporal modalities. Such are i.a.: tensal functors (FIt will be the case that, PIt was the case that), or modalities occurrence in given timeR, which we will use to build also complex sentences.

It needs to be stressed that the reasoning of Diodorus — discussed in due course — aims i.e. to define the modal functors It is necessary to oraz It is possible to in the very temporal terms, therefore characterises them in their temporal aspect. Therefore, these modalities, along with the above-mentioned ones, will be the only types of modalities we shall use. Other functors will only have extensional character. All of them will be thoroughly described in the second part of the book.

2.3.8 Truth, time vs. epistemic concepts

At the beginning of this section, discussing bivalence principle in relation to the statements about the future and past, we have highlighted objections from so-called epistemic concepts of truth. Now we will briefly discuss them, considering the trend associated with the so-called semantic anti-realism of Michael Dummett69. Within the semantic anti-realism, the unlimited use of the law of excluded middle (or bivalence principle) and the use of idea of truth with no regard to the cognitive access to the domain stated by qualified sentences as true (or false), are being questioned.

The epistemic concepts of truth emerge from the tradition of pragmatic and Kantian philosophies. Of course within the pragmatism, quite large theoretical differentiation dominated. In terms of the concept of truth, the creators of the pragmatism fluctuated between the idea of usefulness, as constitutive ←64 | 65→for the truth, and the idea of consensus and approaching during the process of knowledge development, called ideal truth (James W. [117], Dewey J. [58], Peirce Ch. S. [212]).

The inspiration of different trends of pragmatism have led to arising criticism of non-epistemic concepts of truth, and also to formulating the epistemic concepts. This criticism can be found in various works referring to extremely different trends in philosophy: from postmodern philosophy to philosophy cultivated within analytic tradition70.

Within the criticism of the non-epistemic concepts of truth, one trend can be distinguished, and it is called anti-realism. On its basis, some thinkers consider traditional dispute about cognition and object of cognition on linguistic, semantic grounds. Then the anti-realism takes form of semantic anti-realism. This attitude is understandable in the opposition to semantic realism, stating that:

Thus the semantic realism stance accepts the thesis that many sentences of the language carry a certain logical value, despite the fact that nobody will ever be in such epistemic position to be able to establish this value. In the semantic realism, the key roles play two issues. Firstly, that the domain about which given sentence states, is (was or will be in given moment) independent of cognition. Secondly, that between a sentence (proposition) and what it refers to, there is a relation of such nature that the sentence is true (or false) regardless of whether any object performs an adequate act of cognition. These two characteristics cause the stance to be the realism, and to be semantic realism.

Questioning the two above postulates, anti-realism thus rests upon:

() In essence this kind of anti-realism consists in the rejection of theories of linguistic meaning which identify semantic comprehension with understanding of the truth-conditions of statements where these conditions may transcend the recognitional capacities of speakers of the language. () there is general agreement among the authors mentioned that what is problematic about realist accounts of meaning is their common attachment to a notion of truth as objective conformity between, on the ←65 | 66→one hand, statements (and unuttered thoughts) and, on the other, objects and features in an independent, pre-structured world (Haldane J. [95], p. 17).

So anti-realists question the validity of considering sentenced as true or false without regard to the possibility of verifying them. In particular, this concerns the sentences stating about past states of affairs (not to mention the sentences about the future!) about which we can formulate plenty of statements, but very few can be analysed in any way in the context of their objective reference. One of the most famous anti-realists is Michael Dummett. He claims that, in the absence of appropriate evidence or traces from the past, we are not able to determine the logical value of many sentences within this class. Dummett suggests a criterion used in intuitionistic logic, where the recognition of a sentence entails indicating its effective proof. As long as the sentence is not proved it is not true nor false. Dummett’s stance leads to the rejection of the principle of bivalence that states that each sentence carries one of these two values. This consequence, transposed into the domain of the synthetic, empiric sentences, results also in rejecting the unlimited use of the law of the excluded middle. The idea of truth is though replaced by Dummett by an idea of the effective decidability (cf. Dummett M. [66], McDowell J. [182]).

The previously discussed definition of truth has been however conceived as a non-epistemic definition. For we are interested in various sentences along with their logical values regardless of the cognitive access to any fragments of the history of the world. Such interpreted idea of truth is certainly not consistent with the anti-realistic approach. The following remarks are not so much to defend the outlined approach, and the more to account for a polemic with the anti-realism, but to explain some of its details. This summary provides a better opportunity for it.

The starting point for further discussions may be the observation that the proposed definition of truth does not constitute a criterion of truth. These questions are often distinguished in literature (Woleński J. [295], p. 175). This concept does not state the conditions required to be met for the sentence to be true, but what it means that given sentence is true. This point of view is practically consistent with one of the remarks of Alfred Tarski, expressing a cofeature of many non-epistemic concepts of truth:

Anything can be achieved by means of substantially accurate for language learning definition of truth, one thing is unquestionable: this definition does not provide any criterion in each particular case useful for determining if in a given language a sentence is, or is not, true: moreover, ←66 | 67→this definition has not been intended to provide such criterion (Tarski A. [274], pp. 21–22, author’s translation).

Since the concept of truth is not a criterion for truthness nor for falseness of sentences, in fact it can be discussed even if there were no true nor false sentences. What makes given sentences true or false is not only the presence or absence of the states of affairs indicated by these sentences. The fact that the sentence related to certain state of affairs is therefore related to the proposition it expresses, thus to the information transmitted. In order to emphasize this point, let us quote once more Wittgenstein.

4.024 To understand a sentence means to know what is the case if it is true (One can understand it, therefore, without knowing whether it is true.) (Wittgenstein L. [291]).

In this book, we are convinced that the sentences may be true or false regardless of the possibility to determine their logical values. The understanding of the proposition expressed by given sentence is, therefore, equivalent to the knowledge of the objective conditions under which it is true and — by negation — conditions under which it is false. Tadeusz Szubka calls such an approach truth-conditional theory of meaning and opposes it to the verificational theory of meaning, corresponding to the Dummett’s ideas, where the understanding of the meaning of a sentence reduces to the knowledge of the conditions under which its adoption or rejection is justified ([267], p. 77 and others), not recognising its logical value.

According to the first approach, knowing a proposition expressed by following sentence:

(63) On 20th of July 2003 it was snowing in Toruń.

we do not know which circumstances should take place for the sentence to be true. However, because in Toruń, according to the calendar, on 20th of July 2003 it was not snowing, it is false71.

But what if we consider a sentence from further past (e.g. from the time when there were no qualified dentists and part of their duties have been fulfilled by blacksmiths):

(64) On 15th of January 1410 a tooth of Ziemowit from Pyrzyce is suffering from tooth decay.

←67 | 68→Even though from the anti-realistic point of view, this sentence is out of reach of the effective decidability and it cannot be assigned any of two logical values (not even decided to be true or false), within the classical approach72 it meets the requirements of bivalence principle (even if it is seemingly objectless — considering previous propositions concerning presuppositions). Of course, its logical value is not known and it probably never will due to the absence of adequate cognitive access. Sentence (64) may however express a proposition very similar to the one expressed by the sentence stating about a suffering from tooth decay a tooth of a latter-day person, which we can verify/classify. The conditions imposed on its truthness in the past will in fact be not very different, except for the fact that we cannot refer to any direct medical opinion stating that Ziemowit’s tooth is suffering from tooth decay — but it is not a condition for the proposition, therefore it does not result in sentence (64) not carrying logical value.

The problem whether the conditions imposed on the truthness of such sentences are (or will be) met, in fact more often than not surpass our cognitive possibilities. It would mean that there is simply a lot of truths that exceed our cognition73, even if those truths are relativised to our method of verification of given statements and conditions currently imposed on them.

While applying such not limited by time idea of truth, problems related to reference of individual names such as ‘Ziemowit from Pyrzyce’ may arise. For in 1410 in Pyrzyce, there may have lived many Ziemowits. A proposition expressed in sentence (64) may state that Ziemowit in case is the one e.g. known from some given historical context. Then appellation ‘Ziemowit from Pyrzyce’ is an individual name. Sentence (64) may however express proposition stating about any person in the defined time bearing this name. Then the appellation ‘Ziemowit from Pyrzyce’ should be considered a general name of content someone who bears a name Ziemowit from Pyrzyce and believe that the sentence expresses existential proposition, that on 15th of January 1410 there is at least one such person called Ziemowit from Pyrzyce whose tooth suffers from tooth decay. ←68 | 69→Similar measures can be undertaken in solving problems arising in the analysis of sentences about future states of affairs74.

Obviously, there are many objects for which we cannot provide such individualising specification. We are also not able to provide it for many phenomena or states of affairs. For plenty of them irrecoverably escaped into the abyss of history, others will only make an appearance in future. However, it means only that from our position in time we are not able to express any propositions about them. But if possible in any circumstances, these propositions carry (at least in relation to past) one of two logical values.

This situation seems unsatisfactory. Travesting Wittgenstein one can say that the borders of our language are the borders of our description (true or false) of the world. It does not mean however, that from our position in time, future and past world can be fully described.

In the next chapter, we will focus on describing the objective conditions necessary to be met so even the propositions stating about future states of affairs could carry at least one of the two logical values.←69 | 70→

7 Thereby, we exclude those elements of communication that do not comply with the grammatical rules. I assume, however, that if these carry any meaning, it can be articulated with the use of some statement. Obviously, this means that if something cannot be articulated with the use of some statement, it does not carry any meaning.

8 As you can see, presented approach is not purely syntactic. For syntactic approach considers sentences (and other expressions) of particular language as finite sequences of simple phrases (cf. e.g. Tokarz M. [281], pp. 11–13), without referring to their informative function, therefore also to their content.

9 Actually, the same applies to other types of statements. For example, rhetorical questions are used in common language in order to express beliefs, rather than ask a question. Sometimes even individual words, such as fire, uttered in right context, can be equivalent to other statements; in this case to: There’s a fire! This example comes from Ajdukiewicz K. ([7], p. 27).

10 This definition is explicitly based on the concept of categorial analysis of Kazimierz Ajdukiewicz. It will though not be reminded, as it constitutes permanent and active elements of philosophical and logical culture. Therefore, I will not be introducing the definitions of functors — either functor-forming, name-forming or sentence-forming, as these terms can be found in the works of Ajdukiewicz ([3, 4, 8]).

11 Or meaning, or sense.

12 Hereinafter, we will see that propositions expressed by sentences are not always functions of the meaning of the simple phrases used to structure the sentence. This issue has been emphasised by Frege in words: never to ask for the meaning of a word in isolation, but only in the context of a proposition ([75], p. 10). When it comes to relation between proposition and ideas, there has been a dispute resulting in isolating two viewpoints on the subject: ideas priority (known as allogenic theory) and antithetic, stating that propositions are objects sui generis (known as idiogenic theory) (cf. Woleński [295], pp. 33–34). However, we are more interested in determinations not related to the origin of propositions, but their function in transmitting information.

13 Intensional functors create complex sentences, so their logical value is not unequivocally determined by logical value of simple sentences.

14 Naturally, it does not mean that I believe that objective sense of a sentence is and must be always directly grasped.

15 However, some philosophers believed that individual names had meanings. For example, Duns Scotus used a term haecceitas as a certain elementary essence characterising individuals. Others, in turn, claimed they had no meanings (Mill J. S. [192], Russell B. [247], Dąmbska I. [56]).

16 It would be difficult, especially on the grounds of modern discussion, where in the context of, amongst others, Quine’s criticism of meaning and his concept of indeterminacy of translation, the attempt to define meanings of sentences as propositions; or propositions as meanings of sentences, may be classified as a vicious circle, and surely is not satisfying (Grayling A. C. [86], pp. 27–28). Current state of our presentation allows to clarify general concepts, so to be able to use them without unnecessary confusion in solving other problems.

17 This definition has been formed based on the definition of constative sentence by Ajdukiewicz K. ([7], p. 28).

18 I do not call this kind of proposition a logical proposition. For it does not have to be either true or false, and these terms usually are reserved for propositions carrying logical value. Many sentences about future, discussed below, doubtlessly express specified propositions, but — considering Aristotle’s concerns presented in the second part of the book — do not have to carry any logical value.

19 This is also — in a diachronic aspect — due to a linguistic practice and its historical and social conditioning, that change the meaning of the phrases and introducing new meanings. In a classic approach, propositions are designed as eternal objects insensitive to changes: they do not come into being nor disappear. (cf. Lycan W. G. [164], pp. 76–87). Disappear or come into being can at most languages or phrases used to express the propositions. For this study, it is not necessary to opt that far in the characteristic of propositions. Claiming that they differ from sentences and sentential expressions would suffice. The fact that the latter change their meanings due to conditions suggests a conclusion that they express different propositions at that moment (if still carry any sense at all). In this case, when analysing the sentence, it is handy to assign them appropriate indexes, which correspond to different propositions expressed. The above-mentioned approach to propositions is therefore instrumental. The classic approach will be further narrowed in the last section of this chapter, where we will discuss the epistemic concepts of truth.

20 Such information can be called values of parameters, and an action of supplying parameterisation.

21 Transformation procedures from certain statement to its logical value, through context, proposition and possible world shall not be described within this study. It can be found e.g. in work of Jacek Malinowski The Pragmatic interpretation of utterances [175]. In this article, the author considers the problem of arranging, under logical pragmatism, two definitions of meaning: as proposition expressed in a statement or as logical value denoted by a statement.

22 As it clearly arises, other important issue on logical value is a question about what carries logical value — statements or propositions. Obviously, Frege opted for propositions. Nowadays, many philosophers believe otherwise. I will address this issue and take a position on it in one of the next subchapters, meanwhile tentatively using terms logical value, true, false, either relating to sentences expressing propositions, or to propositions itself.

23 Determining time may be of various accurateness, e.g. sentence ‘Tomorrow Jan will go to work.’ does not specify when a given state of affairs will take place; but the sentence ‘Jan will go to work after 20th of April 2003.’ is under my definition of a sentence determined in time. Detailed consideration on different types of sentences and their reference to time will be provided in the further part of the book.

24 The concept of such sentences is similar to Quine’s concept of eternal sentences, that is sentences which logical value is constant through contexts ([235], pp. 221–222).

25 Formal conceptual apparatus to represent the defined sentences and time shall be presented in further parts of the book, featuring a formal analysis of ancient reasoning. We will also reflect there on the domain for time variable. For it requires — as you can see — certain form of dating.

26 The concept of these sentences corresponds to the sentences analysed in the Ancient times and in the Middle Ages. These sentences can change their logical values in relation to different time frames. This particular concept of sentences has been used in creating logic of time by Arthur North Prior ([230], p. 8).

27 For they are of similar nature as open formulas in classical logic of quantifiers, i.e. a logical value depends on the interpretation of free variables.

28 Frege distinguishes between the above-mentioned Sinn and Bedeutung, or sense from denotation. True sentences indicate logical value of truth, and false sentences — of false [76].

29 This discussion does not aspire to be called comprehensive. According to the experts on the subject, the full outline of the issue of truth has not yet been studied (Woleński J. [295], p. 175).

30 Obviously, much like other languages users.

31 Detailed in this study concepts of Plato and Aristotle have been considered non-relational by e.g. the above-mentioned Künne W. [142], pp. 146–155.

32 Plato sees sentence as logical value carrier, mentioning relationship between noun and verb. However, the type of those sentences is not specified([222], 261C–262E, pp. 89–92). Similar understanding had Aristotle (Reale G. [236], pp. 533–536); however, only in his writings, more precise considerations on the types of sentences that can be true or false, can be found ([11], 17a, p. 71).

33 Translated literally from Greek it means: states nothing as being (translator note, p. 93).

34 Tarski adverted to i.a. previously cited passage from Metaphysics, writing that none of heretofore given conceptualisations is sufficiently precise and clear ([272], p. 233).

35 In particular with regard to the so-called liar paradox ascribable to Eubulides of Miletus (cf. Tarski A. [271], §1, [272], §7, §8), that seems to strike especially, according to the above-introduced classification, classical version of the concept of truth.

36 Or for the language meeting various formal conditions, such as: a full dictionary of expressions, strict syntactic rules relating to the structure of the sensible phrases in the language, unambiguity of functions performed by given language units, constant logical value for similar phrases independent of a context, or lack of casual phrases etc.([273], pp. 313–314.).

37 This argument is quite convincing, even for authors declaring reluctance to accepting the existence of such objects as propositions (cf. Woleński J. [295], p. 173).

38 Therefore, propositions have been assigned two out of three traditionally assigned to them roles: meaning of sentence and carrier of logical value. Third one is the subject of propositional attitude (see Hart W. D., McGinn C. [98], p. 299).

39 What — as mentioned above — is to be a criterion of a division into relational and non-relational concepts.

40 On a side note, by metaphysics I mean the ontology of what exists, or real world. On the other hand, the ontology is a wider discipline, which domain is a set of possible objects, not only existing ones.

41 Drawing inspiration from Wittgenstein’s Tractatus (cf. Omyła M. [208]).

42 I use term classical, since it is known that nowadays some authors object to the division of sentences into analytical and non-analytical, as indistinct; and to the analyticalness of analytical sentences as based on non-analytical source in the shape of determining process, stabilising the semantic convention for synonymous phrases. I mean here particularly the criticism of Quine [234]. In my study though, I favour the approach I have described as classical, at least in the operational extend.

43 Where f(z) = ‘z’, i.e. f is a function assigning to z STD its any metalanguage appellation ‘z’. This procedure is applied to prevent objections of some authors to quantifying over objects of type x, where x is not a non-dependent phrase, but only a graphic component of the phrase of type ‘x’ cf. Woleński J. [295], p. 217, Black M. [33], p. 326). However, in contexts other than definitions of truth or false, even predicating a quantification, for simplification, I will use just ‘x’.

44 For the purposes of the presentation of the question of truth and false, I use quite intuitive term moment. In the chapter on the issues related to time and in the further chapters, I shall try to clarify them.

45 In the discussed concept, in the first place, the propositions are true, and imitatively, the sentences. Meanwhile, within semantic definition of Tarski, the types of inscriptions of given language are considered, or meaningful sentences, not their meanings (or in our terminology propositions) (cf. Woleński J. [295], p. 228). The above problems result also from uncritical use of T-convention, without paying attention to the types of the logical value carriers and — as will be shown below — the ratio of time of statement to the transmitted content.

46 Note that this relation depends on the reference system of measurement. For as known, within modern physical time science, the time is not absolute. This issue will be discussed further, in the section devoted to time. However, for the purposes of the current deliberations, the time shall be considered as absolute — from certain reference system.

47 Developing natural intuitions related to the ordinal character of time in relation to events, present both in colloquial and philosophical thinking about time. For example, Broad wrote that all events in the world history take their places in singular chain of moments (Broad C. D. [39], p. 334).

48 This is only an example. I do not presume anything about setwise structure of time, nor about cardinality of a set of values for the time parameter, apart from its certain direction. It is possible to — and in fact I will — consider branching time (and its other possible variants); however, the individual states of affairs will be still situated in the parts of the history of the world, defined by the value of time, or its branches.

49 However, from the historical point of view, the use of this law to analyse RDC — shown in due course — seems desirable. Therefore I will try to champion it.

50 For as it has been accepted, logical values of true and false are usually represented respectively by1 and 0.

51 Which constitutes a harmless assumption, although as I will explain in due course, not widely accepted — especially on the grounds of some so-called epistemic concepts of truth.

52 Depending on preferences, it can be said about lack of further temporal parts — it would mean absolute end of H and a flow of time; or it can be assumed that all later temporal parts are empty, meaning that time flows emptily. The temporal parts are though to correspond to the subsequent time points. For the semantic purposes, it seems that it would be better to adopt empty temporal parts. Then we know where the sentence is false. For in the absence of temporal part, the problem of Plato’s beard occurs, as it is not known what the sentence relates to. In order to avoid this problem, we will offer a certain method of rephrasing sentences, so the condition of existence of an appropriate moment in time belongs to the content of the proposition.

53 Different interpretations e.g. RDC indicate such approach as correct in an attempt to recreate a deterministic livery of argument of Diodorus. In practice, while reconstructing formal aspect of the theory, one should adopt a formula stating that if a sentence p is true now, it had been that p would be true. This line of thought is also present in the deliberations far from the currently tackled issues. For example, Lemmon, while considering the problem of truthness of statements (in cited work he specified propositions, sentences and statements, appropriately conceptually differentiating them) he wrote that a statement expressed in a sentence ‘Brutus killed Caesar.’ was true in any time, adding: it was assumingly true even before 44 BC, when it could had been expressed by the sentence ‘Brutus will kill Caesar.’; in further part continuing: we are coming close to the problem of sentences about future. All I can say is that ‘Chè sera sera’ is a logical truth, not a version of determinism () (cf. [153], pp. 97–98).

54 Where respectively PKF() — to be present king of France a B() — to be bald.

55 And not on the ground of multivalent logic, or logic with so-called gaps. The reason for constructing such logics is — among others — not only indicated problem of sentences about future, but also the lack of denotations for certain phrases used in sentences (cf. Priest G. [227], pp. 128–131).

56 Admittedly, individual constant itself (e.g. s) should ensure belonging of given object under a domain in given interpretation. However, it may turn out that in time stated in the sentence, there is no domain that denotation s belongs under. (For we do not select a formula to represent given domain, but rather the domain in certain temporal part turns out to be as it is.) Then neither a sentence in a form ‘A(s)’ (where A is a metavariable for any sentence where s occurs in), nor a sentence in a form ‘¬A(s)’ would be true. Another issue is of course defining constant s so each variable occurring in identity predicate with s denotes exactly one singularised object. The phrase ‘x = s’ can be considered as definitionally equivalent to the phrase s(x) ∧∀y,z(s(y) s(z) y = z)’, where the object denoted by variable x is said to have certain characteristic defining the object described in sentence s. This procedure guarantees singularity of possible object x, such that x = s. The issue of such object belonging to the domain becomes one of truth conditions imposed on the sentence. Of course a similar measure should be undertaken for all individual constants, leastways for those not determined as having denotations in a given domain. Intention to introduce an identity predicate shall become clear in the below examples.

57 Where individual extralogical symbols indicate respectively: t - individual constant denoting specific interval or point in time, s - person of Socrates, P - unary relation being a television or being a discussion, and R means ternary relation, depending on interpretation: watching (by someone, something, sometime) or leading/doing (by someone, something, sometime).

58 For example, Andrzej Grzegorczyk writes: Reality is: objects (things) of different qualities, connected by relations, forming various sets ([92], p. 22).

59 There is also some criticism on this matter. For example, Adam Grobler expresses the following opinion, of which the second part relates directly to the discussed issue: The very concept of ‘correct type of a model’ assumes that although the world’s structure may not correspond to, commonly called, ‘ontological commitments’ of language, it does have a structure (accurately) describable in terms of individuals, functions and relations. Meanwhile, it cannot be excluded that the world, as it is, is a formless ‘thing in itself’, and if not formless, then made of something not resembling our individuals, functions and relations ([88], p. 31, author’s translation).

60 In the part on idea of time I will slightly focus on the issue of time ontology. It may shed some light on the issue of relations between states of affairs as static formations and time intervals in which they take place. It is worth to add that on the basis of specified answers to some outlined earlier uncertainties about the definition of truth and false and concept of the history of the world, in that sense of understanding of the sentences about future (and in general, analysed sentences) as presented in this chapter, interesting ontology based on the set theory can be developed. The temporal parts or states of the world can be seen as structures; states of affairs as their substructures. Then the history of the world would be a set of structures, and the time parameter would determine the structure in which given sentence would have been effective. Two basic problems to be solved are: in the first instance, the order within structures (depending on the adopted formal nature of time and in such general way not to settle the issue, and also the relation of time and states of affairs which shall be discussed in due course), and also an issue of sentences stating not about punctual states of affairs (discussed further), but aboutongoing states of affairs and their variations. Such ontology shall not be presented herein. This idea, however it seems to be inspiring, is only indirectly related to the subject of this study.

61 Where respectively M() - be a Martian, MC(,) - be a chess master in some time, and t() - be a time frame.

62 For example the quoted definition of Aristotle from 1011b seems to apply only to existential sentences (cf. Woleński J. [294], p. 44).

63 This function is sometimes fulfilled by a verb to be. It is though only one of its many functions (cf. Khan Ch. [132]). The relevance of this distinction can be observed in an imaginary example of entailment of sentence ‘A man 100 meters tall exists.’ from the additional premiss and one of the principles of FOL, in the form of ‘A(a) →∃xA(x)’ that is made in (Woleński, J. [295], p. 144).

64 Where respectively: P() is a predicate of being a philosopher, t is a constant denoting a date of 24th of July 2003, E(,) is a predicate of existing in a certain time.

65 Not: x,y(P(y) y = t ∧¬E(x,y)), for the sentence would have been stating that in the domain, in an adequate time, there is an object of the quality of being a philosopher, but there is not. Personally I cannot see here any contradiction. As the philosopher could have been only an intended object, e.g. of purely literary fiction.

66 In any case it not being the only approach to the question of presupposition, although herein sufficient. The overview of modern approaches to the question of presupposition can be found in the work of Beaver D. [28].

67 For example, within the apparatus of modal logic, it is allowed to interpret A usually as there is a world W, available from W, that A in W is true, but knows that A is interpreted as for each W available from W, A is in W true.

68 For there is multum modalities. When asked: what can be modal, the author of book Modality in Logic and Philosophy answers, providing as many as eleven categories of different types objects, of which one, very extensive corresponds to sentences or propositions (Żegleń U. [306], p. 27). In turn, a comprehensive classification of modality concerning the sentential arguments and its explanation can be found in the work of Jerzy Perzanowski [214].

69 Omitting other epistemic concepts of truth e.g. concept of obviousness conceived by Descartes [57], and developed by Francis Brentano [38], or concept of cohorency (Neurath O. [201]).

70 In order to indicate the extent of the criticism, a list of the following works should suffice: Sellars W. [255], Putnam H. [232], Rorty R. [244].

71 Obviously, the sentence could be understood in many ways, e.g. by checking in different calendar, according to which July is one of the winter months. In that situation, though, it would express different proposition than in the given meaning.

72 This approach refers not only to so-called the first Wittengstein but also to Frege, and nowadays developed by Davidson (Szubka T. [267], p. 137) and Polish school of logic and philosophy.

73 An interesting argument — known as The Knowability Paradox — in favour of the existence of such truths going beyond their cognitive possibility, developed by Fitch F. B. ([73], pp. 138–139). It is being perceived as an argument directed against the semantic anti-realism among others by Wiliamson T. ([290], s. 270–301). An outline of newer argument — according to its author based on Fitch’s argument — is given by Künne W. ([143], pp. 167–169).

74 The authors have adopted here various strategies in a situation called by Smart naming future, and in particular individuals, so as to be able to utter sentences about detailed states of affairs. One of them is presented by Smart, following Quine who proposes to dispose of individual names in favour of proper predicates and quantifiers assuring onlyness of such objects ([260]), pp. 93–94). This is an identical strategy as the one I have described in the subchapter on presuppositions.

←70 | 71→

Biographical notes

Tomasz Jarmużek (Author)

Tomasz Jarmużek is Professor of Logic at the Nicolaus Copernicus University in Toruń (Poland). His research focuses on philosophical logic and its applications in philosophical problems. He is also interested in the proof theory with a special emphasis on the tableau methods.

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