Evaluating Cartesian Linguistics
From Historical Antecedents to Computational Modeling
Table Of Contents
- About the author
- About the book
- This eBook can be cited
- Table of Contents
- Chapter 1: Introduction
- Chapter 2: Cartesian Linguistics
- 2.1 Species Specificity of Language
- 2.2 Domain Specificity of Language
- 2.3 Language Acquisition
- 2.4 Cartesian Ideas
- 2.4.1 General Introduction
- 2.4.2 Innate Ideas
- 2.5 Poverty of the Stimulus Arguments
- 2.6 Impossibility Arguments
- 2.7 Conclusions
- Chapter 3: The Evolution of Chomskyan Linguistics
- 3.1 Introduction
- 3.2 Linguistic Nativism/Rationalism
- 3.2.1 Situating Chomsky’s Nativism/Rationalism
- 3.2.2 The Problem of Innateness
- 3.3 Innateness and Linguistic Nativism
- 3.4 Chomskyan Linguistics: A Brief History
- 3.4.1 Chomskyan Linguistics as Natural Science
- 3.4.2 The Galilean Style
- 3.4.3 Critique of the Chomskyan Science
- 3.4.4 From Standard Theory to Minimalism
- 3.5 Chomsky’s Arguments for Innateness of Language
- 3.5.1 The Poverty of Stimulus Argument
- 3.5.2 Chomsky’s LAD
- 3.6 Conclusions
- Chapter 4: Language Acquisition
- 4.1 Introduction
- 4.2 Arguments for the Innateness of Language
- 4.3 Empirical Evidence Gathered During Language Acquisition
- 4.3.1 Language Acquisition During Infancy
- 4.3.2 Emerging Language Production in Young Children
- 4.4 Statistical Information: From Sounds to Syntax
- 4.4.1 Sound Patterns and Semantics
- 4.4.2 Statistics and Syntax
- 4.5 The Problem of Negative Evidence
- 4.5.1 The Importance of Negative Evidence for Language Learning
- 4.5.2 Nativism and Negative Evidence
- 4.5.3 Is Negative Evidence Useful for Language Acquisition?
- 4.5.4 Is Negative Evidence Necessary for Language Acquisition?
- 4.6 Conclusions
- Chapter 5: Computational Modeling of Language Acquisition
- 5.1 Introduction
- 5.2 Connectionist Networks
- 5.3 Case Studies
- 5.3.1 Elman’s Early Connectionist Models
- 5.3.2 Relevance of Connectionist Simulations for the Nativist Debate
- 5.3.3 Other computational Models of Language Acquisition
- 22.214.171.124 Models of Speech Segmentation
- 126.96.36.199 Multiple Cue Integration Models
- 188.8.131.52 Modeling of Complex Aspects of Syntax and Semantics
- 5.3.4 Recursion
- 5.4 Conclusions
- Chapter 6: Conclusions
- 6.1 The Cartesian Tradition
- 6.2 Chomskyan Progress
- 6.3 Empiricist Language Acquisition Research
- 6.4 Computational Modeling of Language Acquisition
- 6.5 Model Selection and Limitations of Simulation
Noam Chomsky’s Cartesian Linguistics frames this inquiry into his linguistic work and the resulting debates between rationalists and empiricists. The focus will be on the following key aspects: (i) the historic connection of Cartesian Linguistics to previous linguistic theorizing, (ii) the evolution of Chomsky’s own theorizing, (iii) the empirical work addressing the problem of language acquisition, and (iv) the problem of computational modeling of language learning. Chomsky claims that his view is situated within a rationalist Cartesian tradition and that only rationalists will be able to account fully for all aspects of human language. This work challenges both claims.
There are only remote similarities between Cartesian and Chomskyan commitments. Chomsky holds that (i) language is species-specific, (ii) language is domain-specific, and (iii) language acquisition depends on innate knowledge. Descartes accepted (i), but argued that language is an indicator of domain-general intelligence. Innate resources play a different role for language acquisition for Chomsky and for Descartes.
Chomsky’s innovative proposals revitalized linguistics during the 1950s, and he has been credited with launching the second cognitive revolution. However, to date, his work has not fulfilled many of the early promises, and recent work has contributed little to a scientific understanding of language acquisition and use. Key concepts like “innateness”, “Universal Grammar”, “I-Language” and “Language Acquisition Device” remain in need of precise definition, the internal coherence of his ontological commitments has been challenged, and the Poverty of the Stimulus Argument does not rule out data-driven domain-general language acquisition. Especially the recent emphasis on a “Galilean Style” of inquiry violates accepted scientific method and, presumably, would have been rejected by Descartes.
Empirical work in developmental psychology has demonstrated that children acquire and practice many language-related cognitive abilities long before they produce their first words. Chomsky’s dictum that language learning is uniform across the species and invariably follows genetically determined stages remains empirically unconfirmed. Computational modeling has accounted for some internal structure of language acquisition mechanisms and simulates the specific ← 11 | 12 → conditions under which children learn language. Contemporary models use samples of child-directed-speech as input and have replicated numerous aspects of human performance.
This work suggests that Chomskyan linguistics is not Cartesian in substance or in spirit. Descartes rejected dogmatism and was wary of those “who take no account of experience and think that truth will spring from their brains like Minerva from the head of Jupiter” (CSM I, p. 21). He engaged constructively with his critics and his science combined empiricist and rationalist elements. Any truly Cartesian Linguistics will revive this part of the Cartesian tradition.
Christina Behme, Dartmouth, Canada, November 10th, 2013 ← 12 | 13 →
Cartesian Linguistics, originally published with the purpose of deepening “our understanding of the nature of language and the mental processes and structures that underlies its use and acquisition” (Chomsky, 1966, p. ix), has generated controversy from the time it was first released in 1966 to its recent 3rd edition in 2009. On the one hand it has been praised exuberantly as “an intellectual tour de force… an unprecedented and – so far – unequalled linguistic-philosophical study of linguistic creativity and the nature of the mind” (McGilvray, 2009, p. 1). On the other hand it has been severely criticized: “Chomsky’s version of the history of linguistics… is fundamentally false from beginning to end – because the scholarship is poor, because the texts have not been read, because the arguments have not been understood…” (Aarsleff, 1971, p. 584). In this book I will evaluate the arguments of both sides.
I will use Cartesian Linguistics as a framework for an inquiry into the linguistic work of Noam Chomsky. Chomsky’s work has been tremendously influential, and a comprehensive evaluation of it would exceed the scope of a single book. I will focus on several key aspects here: (i) the historic connection of Cartesian Linguistics to previous linguistic theorizing, (ii) the development of Chomsky’s own theorizing, (iii) the empirical work addressing the problem of language acquisition, and (iv) the problem of computational modeling of language learning. Each of these themes will be dealt with in one chapter.
Broadly speaking, there are two philosophical positions regarding language acquisition. Either all our linguistic knowledge comes directly (perception) or indirectly (inference, induction) from sense experience (empiricism), or at least some of our linguistic knowledge is innate rationalism). Similarly, in psychology, empiricism (sometimes called the ‘blank slate’ or tabula rasa view) holds that virtually everything is learned through interaction with the environment, and nativism is the view that certain skills or abilities are hard wired into the brain at birth. Currently no one holds either the pure empiricist or pure rationalist view, and I will introduce more nuanced positions as I discuss proponents of either tradition.
Chomsky has defended throughout his career a rationalist/nativist view of language acquisition and language use. He has claimed that this view can be traced ← 13 | 14 → back to important linguistic, philosophical, and scientific precursors. According to Chomsky these have been largely neglected:
Modern linguistics, however, has self-consciously dissociated itself from traditional linguistic theory and has attempted to construct a theory of language in an entirely new and independent way. The contributions to linguistic theory of an earlier European tradition have in general been of little interest to professional linguists, who have occupied themselves with quite different topics within an intellectual framework that is not receptive to the problems that gave rise to earlier linguistic study or the insights that it achieved; and these contributions are by now largely unknown or regarded with unconcealed contempt. (Chomsky, 1966, p. 1)
These remarks were written in 1966 but are repeated, without comment, in 2002 and 2009. I will show that while they may have had some justification in the 1960s, they are not applicable to contemporary linguistics. When dealing with the historic antecedents I will focus on two distinct but closely interrelated aspects. First, I give a brief account of Chomsky’s original proposals as expressed in the 1966 edition of Cartesian Linguistics. Second, I show how the term ‘Cartesian Linguistics’ has been used by Chomsky and some of his close followers over the last five decades to argue for the superiority of their linguistic theorizing.
Chomsky (1966) claims that some of the allegedly neglected insights have been those of René Descartes. I will give a detailed account of the role ‘innate ideas’ and ‘poverty of the stimulus’ arguments (both prominent elements in support of contemporary nativist/rationalist positions) played in Descartes’ writings. It will become evident that insofar as Descartes concerned himself specifically with linguistic theory, his insights are equally compatible with the theories of contemporary nativists and empiricists. Furthermore, a close reading of Descartes’ own work makes it dubious that Chomsky’s work can be traced back to a coherent rationalist tradition of which Descartes was one important founder.
My discussion of Descartes’ writings focuses on issues that are specifically important to Chomsky’s linguistic theories. Chomsky holds that Descartes’ commitment to innate ideas foreshadows his own postulation of an innate domain specific language acquisition device (LAD). Focusing on three fundamental claims of Chomsky that (i) language is species specific, (ii) language is domain-specific, and (iii) language depends on innate knowledge, I will provide textual evidence supporting the conclusion that, while Descartes believed that language is species specific, he was committed neither to the view that language is domain specific nor to the view that language acquisition depends on innate knowledge in a sense that is compatible with Chomsky’s use of these terms. Further, I will show that ← 14 | 15 → Chomsky misunderstands important arguments for Descartes’ belief that animals could not acquire language.
Descartes’ writings demonstrate that he believed that language is species specific. Virtually all humans acquire language and use it regardless of a wide range of differences in their age, health, and intelligence. On the other hand, no animal has cognitive abilities that would allow the use of language. The fact that language is species specific could be explained in two different ways. The first scenario is that only humans have a domain specific language faculty. In this case it would be possible that an animal that had implanted an artificial language faculty would behave in ways that are indistinguishable from a human being. In the second scenario language is an indicator of general intelligence (thought and reason in Descartes’ terminology). In this case it would not be possible to ‘construct’ an artificial language faculty that is independent of ‘general intelligence’. I will provide evidence for my claim that Descartes was committed to the second scenario.
When Descartes discusses the differences between animals and humans he stresses repeatedly that very little reason is needed to use language. This could indicate he believed, like Chomsky, that humans have a domain specific language faculty that is independent of ‘general intelligence’. I will show that the purpose of Descartes’ comparative examples is to show that the most fundamental difference between humans and animals is that only humans have a mind. Language requires a rational mind, and, according to Descartes, animals lack such a mind (Gunderson, 1964; Miel, 1969). Having a rational mind does not entail having domain-specific mental faculties. In fact it is well established that for Descartes minds are indivisible: “we cannot understand a mind except as being indivisible… we cannot conceive of half a mind” (CSM II, p. 9) and that the essence of mind is thought. I will show that these strong commitments prevent Descartes from holding that language is domain-specific. Seemingly, Chomsky does not understand this commitment of Descartes (e.g., Chomsky, 1975b, 2010b). For Chomsky, animals have some form of ‘general intelligence’. But they do not acquire language because they lack a domain-specific language faculty. This is an inportant difference in the views of Descartes and Chomsky.
Next, I discuss textual evidence supporting a possibly surprising view about Descartes’ commitments regarding language acquisition. He states that language “can be acquired without any process of reasoning… [based] on experience alone” (CSM, II, p. 403), that we learn language by connecting words with their meanings and remembering later upon encountering words which things they signify and vice versa (CSMK, III, p. 307) at a time when our thoughts are ‘confused’ and based of ‘misconceptions’. Of course, the language we acquire under such ← 15 | 16 → circumstances is not a perfect tool for the correct expression of our thoughts. But while engagement with philosophical or scientific work requires that we employ new ways of thinking, Descartes does not suggest that our language needs to be changed. Descartes also does not hold that language acquisition is a mechanical process of brain maturation in accordance with ‘deterministic physical principles’, as Chomsky (2010b) incorrectly suggests.
After establishing these points about language acquisition I will show that my reading of Descartes is compatible with his theory of innate ideas. Discussing the frequently cited passages in Comments on a Certain Broadsheet (CSM I, p. 304), where Descartes asserts that all ideas are innate, I show that a careful reading of the context reveals that Descartes’ main goal here was to refute the scholastic account of sense perception. On this interpretation what is innate is not the content of sensory ideas but the faculty of sense perception. This interpretation allows for a coherent Cartesian account of language acquisition, and suggests that the role that Cartesian innate ideas play for language acquisition is very different from the role innate knowledge plays for Chomskyan accounts. For these reasons I suggest that, from a perspective of ‘the history of ideas’, it is quite misleading to call Chomsky’s approach to linguistics Cartesian. I discuss some of the reasons Chomsky provides for interpreting Descartes in a very unconventional “hybrid” way and suggest that this does not reflect any genuine Cartesian commitments.
In the next chapters I connect the historic antecedents of Cartesian Linguistics to contemporary debates in linguistics, philosophy of language, and developmental psychology. Today virtually all researchers agree that extreme rationalism/nativism (all knowledge is innate) is as implausible as extreme empiricism (nothing is innate). Thus, recently the debate concerns mainly how much of our knowledge extends beyond our sense experience. Empiricist and rationalist researchers inquire about the character of the interaction with our linguistic environment, and the nature of the mechanisms that allow us to acquire linguistic knowledge. As we learn more about the structure of the human brain and the learning mechanisms available to children, we can develop more tools to (i) clarify boundaries between innate and acquired linguistic knowledge, and (ii) evaluate how pre-linguistic infants can extract information from their environment. Furthermore, research in linguistics has provided new insights regarding the status of core issues such as types of grammars, recursion, and the role of linguistic intuitions and empirical testing. Recently, computational models of language acquisition have provided additional means for testing different hypotheses. The information gained from these different sources has important implications for subsequent philosophical theorizing. ← 16 | 17 →
In chapter 3 I provide an overview of the evolution of Chomsky’s theorizing during the past six decades. My inquiry focuses on the work of Chomsky and his closest followers and I will use the term ‘Chomskyan’ only to refer to this restricted group, not to the much larger community of linguists that have been influenced by Chomsky in some way but departed in important points from the views he defends. I chose this focus because Chomsky has been such an influential figure, and is widely considered as instrumental to the cognitive revolution of the 1950s even by those who disagree with his views (e.g., Sampson, 1980; Katz, 1981, 1996; Seuren, 1998; Boden 2006). Linguists, cognitive scientists, and philosophers continue to look to him for inspiration. I provide comprehensive evidence for my conclusion that this trust in Chomsky’s intellectual leadership is no longer justified.
My main focus is on the claim that Chomsky’s work has situated linguistics firmly within the natural sciences and provided a better understanding of language acquisition and language use (McGilvray, 2009, 2012). I discuss how the core claims of Chomskyan theorizing have changed over time, and show how this affected his attitude towards ‘traditional scientific practice’. I introduce several criticisms of Chomsky’s work, concerning methodological and conceptual issues, and show that Chomsky has failed to address them satisfactorily. Further, I evaluate the contributions that Chomsky’s work made to our understanding of how children learn language. Chomsky’s definition of what language is, and thus what children acquire when they learn language, has changed considerably. I argue that these changes have not led to a better understanding of language acquisition.
I give a detailed account of the evolution of Chomsky’s linguistic theories. Early in his linguistic career Chomsky focused on syntax and grammar (e.g., Chomsky 1951, 1956, 1957, 1959, 1965a,b, 1966, 1968). Some important contributions of Chomsky’s early work were the proposals that (i) human languages have syntactic universals, (ii) a grammar defines the class of grammatical sentences, and (iii) the universals define a range of possible grammars (and by implication rule out any logically-possible grammar not contained within that range). Chomsky claimed that human languages cannot be generated by simple constituency grammars alone, and proposed that an additional series of transformational rules is needed to generate all grammatical sentences of human languages. This early work contributed to clarifying important conceptual issues, provided a scientific framework for linguistics, and had an impact that reached far beyond linguistics. I discuss some of these early contributions and show how they were relevant to Chomsky’s theories of language acquisition.
During the following decades Chomsky “has overturned and replaced his own established systems with startling frequency” (Smith, 1999, p. 1). I discuss some of ← 17 | 18 → the milestones of these conceptual changes. In the 1960s Chomsky proposed that the true subject of linguistic inquiry should be the “deep structure” of language. He suggested that this deep structure is the same for all human languages and only indirectly reflected in the ‘surface structures’ of languages such as English. Chomsky suggested that a set of transformational rules converts deep structures to surface structures. Over the next two decades the complexity of the proposed rules increased continually. An important conceptual “innovation” of the 1980s was the introduction of the competence and performance distinction and the E- and I-language distinction. Chomsky insisted that the object of linguistic study should be the physical parts of biological brains that constitute language (I-language), and he suggested that the focus of non-Chomskyan linguists on E-language is misguided. He held now that E-language is an arbitrary, artificial construct “that is understood independently of the properties of the mind/brain” (Chomsky, 1986a, p. 29), and the study of E-language will not reveal anything interesting about the nature of language.
In the 1990s a sweeping reconceptualization greatly reduced the complexity of Chomskyan system and eliminated deep structure. The resulting Minimalist Program is based on the assumption that syntax is a computational system that provides the optimal solution to the problem of relating sound and meaning. This proposal has been severely criticized, even by theorists closely associated with Chomsky’s earlier work (e.g., Culicover, 1999; Jackendoff, 2011; Jackendoff & Culicover, 2005; Newmeyer, 2008). I show that these critics are justified.
If we conceive of language as well-defined part of the physical brain, then the brain should be the main object of linguistic study. However, Chomsky’s own research has not contributed directly to locating language in the human brain. Further, because Chomsky continues to perceive of empiricist linguistics as behaviourist dogmatism he essentially ignores the results of these researchers. Critics have suggested that this attitude leads to a “time wasting rediscovery of facts or principles that had long been common knowledge outside the Chomskyan camp” (Sampson, 1980, p. 160).
Further, the conceptual move from ‘language’ defined as set of sentences or expressions to ‘language’ as part of human brains is problematic. Essentially, this move has never been fully completed, and Chomsky continues to treat language as both: as sets of sentences and as biological object (e.g., Chomsky 1986a, 1995, 2000a,b, 2007b, 2012). This inconsistent treatment blurs the distinction between the object of linguistic study (sentences of a language and their logical relations), and the object of physiological/neurological study (brain structures involved in generating the sentences linguists can ← 18 | 19 → analyze). Chomsky’s conflation of the physical tokens of sentences with the non-physical types of sentences results in the untenable view that languages are both finite (as parts of human brains) and infinite (as grammatical strings of words). It may seem that on a charitable interpretation this dilemma dissolves, if we consider the language faculty as a biological part of the brain that produces a (potentially infinite) set of linguistic expressions. I show that this interpretation raises different problems for Chomsky’s account, and suggest that his view rests on a metaphysically incoherent foundation.
While some important details of Chomsky’s theories have changed over the years, he has remained consistent in his core assumptions about language acquisition. He continues to use Poverty of the Stimulus Arguments as a crucial component of support for his postulation of an innate domain specific language acquisition device (LAD). This LAD supposedly is a largely genetically determined part of our biological endowment. I provide a detailed account of Chomsky’s definitions of the language faculty and show that Chomsky still needs to provide a coherent hypothesis that could be experimentally confirmed or falsified.
My literature review reveals that the nature of the LAD is still shrouded in mystery. This may seem surprising because for Chomskyans the LAD can “provide an implicit definition of the notion ‘human language’” (Allen & van Buren, 1971, p. 14), and a lot of conceptual work has gone into explaining and re-explaining it. According to Chomsky his ideas regarding the study of the LAD “crystallized into a distinctive approach to the topic by 1980. In the years since many specific variants have been developed and explored” (Chomsky, 1995, p. 13). However, the frequent re-evaluations of earlier variants and wholesale reconceptualizations of previous theories have resulted so frequently in “substantially different conceptions of the mechanisms of language” (Ibid., p. 219), that it has become increasingly difficult to evaluate Chomsky’s theoretical commitments at a given point in time. To date Chomsky’s work has not provided an unambiguous hypothesis that can be empirically tested.
Other main concepts of Chomsky’s work remain ill defined. I discuss the example of ‘innateness’ and show that (i) Chomsky’s own work has not contributed to clarifying this important concept, and (ii) his use of the term ‘innate’ is inconsistent and has frequently misled his followers and his critics alike. Specifically Chomsky’s repeated claims that he has never defended an innateness hypothesis are misleading and should be replaced by clear statements of the current hypothesis. This would allow to evaluate whether or not this hypothesis is viable. ← 19 | 20 →
Chomsky’s commitment to accounting for empirical data has seemingly waned. More precisely, he and some of his followers have become more selective regarding the subset of empirical data they consider to be acceptable for linguistic theorizing. His wholesale dismissal of data gathered by researchers outside his own school is never explained based on studies that have exhibited problematic methods or produced unrepeatable results. In this context I discuss a particularly troublesome aspect of Chomskyan science: the many imprecise formulations and contradictory statements that have allowed him to escape criticism. I suggest that Chomsky needs to provide a clear account of his position and of his contributions to linguistics. Until such an account is provided, it is not possible to evaluate whether his contributions have been substantial.
In chapters 4 and 5 I discuss work of experimental and computational language acquisition researchers and show that they are paying close attention to the conditions under which children acquire language. Specific aspects of language acquisition (e.g., word segmentation, acquisition of grammatical categories, past-tense formation, auxiliary fronting in question formation, etc.) are under intense empirical investigation. Researchers work with young children and attempt to develop computational models that simulate the performance of children. This ‘empiricist work’ is the focus of the second part of this book. Chapter 4 introduces the results of some of the work that has been completed by developmental psychologists, and chapter 5 focuses on computational models of language acquisition that are informed by results obtained from the work with children.
Chapter 4 focusses mainly on the first steps of language acquisition that have been largely neglected by Chomsky’s research. Children need to master many cognitive skills in order to acquire and use language. Several of these skills need to be in place long before children begin producing the grammatically complex utterances that are often the focus of Chomsky’s work. One of these skills is the ability to produce the sounds of their native language and to combine them into words and eventually into grammatically correct sentences. It takes a considerable amount of learning before children can reliably produce recognizable words. These learning processes occur over several months and set the stage for later learning. Yet, they are virtually neglected in the Chomskyan approach.
Further, I highlight some of the abilities that the young language learner has to acquire before she can produce her first meaningful sentences. I discuss in some detail the stages that precede the production of single and multi-word utterances. In the first months of life the infant goes through a phase of vocalization during which she identifies, acquires, and practices the sounds that are common in her language. This babbling stage lasts several months. Around the first birthday, ← 20 | 21 → most infants speak their first meaningful words, and they gradually expand their productive vocabulary. Empirical research has shown that the initial pace of vocabulary learning (from birth to 18 months) is very modest. It has been suggested that during this time children acquire and practice many cognitive abilities. An infant needs to be able to see object boundaries before she can form the hypothesis that ostensive definitions apply to whole objects. She needs to be able to perceive similarities and differences between objects before she can categorize them. Further, she needs to be able to resolve the conflict between the mutual exclusivity assumption (one name for one object, e.g. ‘dog’ for the family pet) and the need for taxonomic categorization (e.g. ‘dog’ for any dog-like object). Children acquire and practice these abilities over an extended time period. Gradually they learn to categorize the world and to understand how words refer to objects, actions, and properties. One hypothesis suggests that once the child has acquired this knowledge, she can slot with ease new words into existing categories (Deacon, 1997). According to this view, general learning mechanisms could account for language acquisition, and an LAD would not be needed.
The fast acquisition of vocabulary and syntax after the second birthday (vocabulary spurt) is frequently used as supporting evidence for the existence of language-specific learning mechanisms that mature at genetically predetermined times (e.g., Chomsky, 1975a, 1985; Lightfoot, 1989; Pinker, 1994; Smith, 1999). I discuss recent work that offers an alternative account for the vocabulary spurt. On this view the vocabulary spurt is an inevitable result of the infant’s immersion in words of varying difficulty, not evidence for the existence of an innate language faculty that is shared by all members of the human species. Further, empirical work has shown that not all children go through a well-defined vocabulary spurt. And in cases where a vocabulary spurt occurs its timing varies widely between individual children. These findings suggest that the vocabulary spurt should not be considered as evidence for genetically predetermined stages of language acquisition.
- ISBN (PDF)
- ISBN (ePUB)
- ISBN (MOBI)
- ISBN (Hardcover)
- Publication date
- 2014 (June)
- Noam Chomsky Rene Descartes Rationalismus Spracherwerb Empirismus
- Frankfurt am Main, Berlin, Bern, Bruxelles, New York, Oxford, Wien, 2014. 267 pp.