Theodicy - From a Logical Point of View

by Paul Weingartner (Author)
©2021 Monographs 168 Pages
Series: Wissenschaft und Religion, Volume 30


The aim of the book is to refute the claim that God’s omniscience, omnipotence and benevolence on the one hand and the existence of evil on the other are together inconsistent. This is shown first by unmasking many types of such claims as either logical fallacies or as presupposing false assumptions. Secondly the author formulates God’s attributes of omniscience, omnipotence and benevolence and the existence of 10 types of evil in an axiomatic system. This contains the theorems about God’s knowledge, will, causation and benevolence without leading to any inconsistency. It proves the compatibility between God’s attributes of omniscience, omnipotence and benevolence with the fact of existence of evil. The author offers a consistency proof for the whole axiomatic system with the help of a model in which all axioms and theorems are satisfied.

Table Of Contents

  • Cover
  • Title
  • Copyright
  • About the author
  • About the book
  • This eBook can be cited
  • Preface
  • Contents
  • 0. Introduction
  • 0.1. Underlying Logic and Terminology
  • 0.2. Definitions
  • 0.3. Principles of Deduction
  • 0.4. Interpretation
  • 1. The Task of Theodicy
  • 1.1. God Is Omnipotent and All-Good
  • 1.2. There Is Evil
  • 1.3. Possible Conflict
  • 1.4. The Question of Leibniz
  • 2. Logical Fallacies
  • 2.1. God’s Will Is Always Fulfilled
  • 2.1.1. Does God Will that Evil Occurs?
  • 2.1.2. Confusion Concerning Negation
  • 2.1.3. Wrong Application of Modus Tollens
  • 2.1.4. Wrong Neglect of Should
  • 2.2. Tertium Non Datur
  • 2.2.1. Argument with Ambiguity
  • 2.2.2. Confusion Concerning Tertium Non Datur
  • 2.2.3. Ambiguity of Contradiction
  • 2.2.4. The Thesis of the All-Willing God
  • 2.2.5. AWG Does not Follow from Omnipotence
  • 2.3. No Limits for an Omnipotent Being?
  • 2.3.1. Contradictory Definition
  • 2.3.2. Translation into Propositional Logic
  • 2.3.3. Analogous Result
  • 2.3.4. Contradictory Definiens of Omnipotence
  • 2.4. Evil as Lack or Privation Is Unreal
  • 2.4.1. Is Evil Unreal?
  • 2.4.2. Evil Is Real
  • 2.4.3. Ambiguous usage of Privation
  • 2.5. Hume’s Argument from Evil
  • 2.5.1. Fallacy and False Premise
  • 2.5.2. The Invalidity of Hume’s Argument
  • 2.5.3. The Falsity of Hume’s Second Premise
  • 3. False Assumptions
  • 3.1. Wrong Definitions of First Cause and First Being
  • 3.1.1. Wrong Definition of God
  • 3.2. All-Causing God?
  • 3.2.1. Two Theses of an All-Causing God
  • 3.2.2. ACG Does not Follow from AWG
  • 3.3. Religious Fatalism
  • 3.3.1. The Thesis RFT
  • 3.3.2. The Alleged Support of RFT
  • 3.4. Does God Possibly Will Evil?
  • 3.4.1. Dilemma
  • 3.4.2. Solution to the Dilemma
  • 3.5. Epicur’s Argument
  • 3.6. Does God Eliminate Every Evil?
  • 3.6.1. Interpretation (a)
  • 3.6.2. Interpretation (b)
  • 4. Axiomatic System of Theodicy: Omniscience, Omnipotence, Benevolence
  • 4.1. The First Three Axioms of the System
  • 4.2. Conflict
  • 4.3. Omniscience
  • 4.3.1. Logically Omniscient and Logically Infallible
  • 4.3.2. Knowledge of the Universe
  • 4.3.3. Omniscience and Evil
  • 4.3.4. Biblical and Church Documents Concerning Omniscience
  • 4.4. Omnipotence
  • 4.4.1. God’s Causation
  • 4.4.2. The Power of God
  • 4.4.3. God as a Sufficient and Necessary Cause
  • 4.4.4. Omnipotence and Evil
  • 4.4.5. Biblical and Church Documents Concerning Omnipotence
  • 4.5. Benevolence. God Is All-Good
  • 4.5.1. Axiom of Benevolence
  • 4.5.2. God’s Benevolence and Will
  • 4.5.3. God’s Benevolence and Love
  • 4.5.4. God Is Just and Merciful and Full of Love to Humans
  • 4.5.5. Benevolence and Evil
  • 4.5.6. Biblical and Church Documents Concerning Benevolence
  • 4.5.7. Biblical and Church Documents Concerning Justice, Mercy and Love
  • 5. An Axiomatic System of Theodicy: Evil
  • 5.1. Different Kinds of Evil
  • 5.1.1. Definition of Metaphysical Evil
  • 5.1.2. Conditional Will
  • 5.1.3. Definition of Natural Evil
  • 5.1.4. Definition of Necessary Evil
  • 5.1.5. Definition of Legitimate Evil
  • 5.1.6. Definition of Moral Evil
  • 5.1.7. Definition of Soul-Making Evil
  • 5.1.8. Definition of God’s Punishment
  • 5.1.9. Definition of Undeserved Evil
  • 5.1.10. The Different Types of Evils Are Real Facts
  • 5.2. Evil Is Accompanied by Good
  • 5.2.1. No Evil Without some Good
  • 5.2.2. Every Evil Is Accompanied by some Good
  • 5.3. God’s Will and Moral Evil
  • 6. Consistency Proof
  • 6.1. The Model OBE
  • 6.2. The Consistency of the Axioms
  • 6.2.1. Axioms A1–A6
  • 6.2.2. Definitions D9–D11
  • 6.2.3. Axioms A7–A15
  • 6.2.4. Axioms 16–18
  • 6.2.5. Consistency of the Axiomatic System
  • 6.3. The Consistency of Important Theorems
  • Index
  • Index of Names
  • Bibliography
  • Series Index

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This book is concerned with the problem of theodicy. It can be put into the question: Why is there evil if God is omnipotent and all-good? Or: Why is there evil if God is omniscient, omnipotent and all-good? The meaning of the word “theodicy” (from Greek) contains a task: it is the task to defend the compatibility of God’s attributes—especially those of omnipotence and benevolence—with the fact of occurring evil in the world. This book is an attempt to fulfill this task.

After a short discussion of the task of theodicy (ch.1), this task will be carried out in six chapters as follows:

Chapters 2 and 3 discuss arguments against the compatibility between God’s attributes and the existence of evil. Chapters 4 and 5 offer an axiomatic system of theodicy. Chapter 6 shows that this axiomatic system is consistent. More accurately, chapter 2 shows that many arguments against the compatibility of God’s attributes with the existence of evil are logical fallacies. Chapter 3 shows that many arguments against this compatibility rest on false assumptions concerning definitions of God, of First Cause, of First Being, concerning an All-Willing or All-Causing God or concerning the elimination of all evil. Chapter 4 offers an axiomatic system with the axioms that God is omniscient, omnipotent, and all-good. The respective axioms contain necessary conditions for these attributes. Further axioms deal with God’s will, God’s causation, God’s power, and God’s love. Chapter 5 continues the axiomatic system with respect to different types of evil. After ten different types of evil are defined, theorems about the relations of God’s attributes to the properties of these evils are proved. The topics of chs. 4 and 5 are treated in a more general context and with much greater detail in Weingartner (2021). Chapter 6 provides a consistency proof for the axiomatic systems. This is done by constructing a model OBE which is an extension of classical 2-valued Propositional Calculus (CPC). It is a 10-valued decidable logic (5 values for true, 5 values for false) with the classical operations ¬, ←13 | 14→→, ∨, ∧, ↔ such that all theorems of CPC hold. In addition 18 operations are defined by matrices (truth-tables) for the concepts used in the axiomatic system. The consistency proof consists in showing that all axioms and theorems are satisfied in the model OBE.

Remark concerning chapters 4,5 and 6: In this book (abbreviated as THEO) some parts of my book: An Axiomatic Study of God (abbreviated as ASG, published by De Gruyter, Berlin 2021) have been taken over for chapters 4, 5 and 6 (chapters 1–3 are untouched). The topics of these parts concerning chs. 4 and 5 are treated in ASG in a much wider and more general context. The parts taken over concern the axioms, theorems and several of the definitions of THEO. The reason is the following: The present Theodicy aims at showing by rigorous proof that God’s omniscience, omnipotence, benevolence and the existence of evil are together consistent. This can be done only with a precise method of proof which is available in an axiomatic system. Such an axiomatic system has been developed in my book ASG which is an axiomatization of a central part of Natural Theology. Axioms and theorems describing God’s omniscience, omnipotence and benevolence cannot be different in the two books, otherwise the books would be inconsistent and at least one group of axioms and theorems would be false. This also holds for the justification of the different parts of the axioms in general and for the indirect proofs. Similarly the definitions of the different kinds of evil and of attributes of God cannot be different in both books for the same reason. This also holds for the respective justification and explanation of the definitions. Axioms, theorems and definitions which are taken from ASG are marked with ASG and number. Indirect proofs, justifications and explanations are referred to ASG with footnotes. One could just take over the axioms, theorems and definitions but make references to ASG for justification and explanation. This, however, would make the book THEO hardly readable and not self-contained. Finally the mathematical matrices for ←14 | 15→the ten-valued logic serving as a model (OBE) for the consistency proof of the axioms and theorems cannot be different in the two books either. They prove the consistency of the whole axiomatic part of THEO and of a part of the much larger axiomatic system ASG. The author wants to thank the De Gruyter Publishing Company and the editors of Philosophical Analysis for the kind permission.

0.1Underlying Logic and Terminology

The underlying logic of the axiomatic system of chs. 4 and 5 and of the arguments in chs. 2 and 3 is 2-valued Classical Propositional Calculus (CPC) extended by epistemic and deontic operations and propositional quantifiers and restricted by intuitionistic and relevant inference (cf. 0.3).

(1)We use the following types of variables: propositional variables p, q, r; individual variables x, y, z for creatures (cr) for living systems (ls) and for human beings (H); individual variable b for divine being (used only in axiom A1); individual constant g for God. Individual variables x, y, z on the one hand and variable b on the other refer to different universes of discourse. In this sense the axiomatic system is two-sorted. Whereas the universe of discourse for the variables referring to creatures is non-empty the other universe of discourse is allowed to be empty. The reason for this is as follows: Since we know that humans, living things and other things of our universe exist (in space and time) the universe of discourse for the variables x, y, z referring to creatures cannot be empty. On the other hand if the universe of discourse of the variable b would be non-empty the existence of God, ∃b(b = g), would be provable by the usual logic of identity. This would be completely unacceptable. Therefore such existence postulates have to be explicitly made by special axioms as it is done by axiom A1 (ch.4). When ←15 | 16→using more than one variable of the same type we assume referential difference, but we drop the additional remark: x ≠ y, p ≠ q for reasons of simplicity.

(2)The copula ‘is’ is expressed by two primitives ∈ and e where ∈ is used for individual variables or constants (representing individuals) and e for propositional variables representing states of affairs. For example: ‘gOS’ for ‘g is omniscient’ or ‘xH’ for ‘x is human’; ‘peME’ for ‘the state of affairs p is a moral evil’.

(3)Concerning states of affairs also the set-theoretical elementhood relation ε is used as for example: ‘p ε T (LM)’, ‘p ε T (CR)’, ‘p ε T (g-Essence)’, ‘Op ε T (g-Commands)’ standing respectively for ‘the state of affairs p is an element of the theorems of Logics and Mathematics’, ‘p is an element of the theorems of creation’, ‘p is an element of the theorems of God’s Essence’, ‘Op is an element of the theorems of God’s Commands’.

Norms—written as Op, Oq, Or… —are understood as being translated into that-clauses such that they can be true or false. Thus “it is forbidden to lie” or “lying is forbidden” or “that lying is forbidden is true” are theorems of God’s Commands and therefore theorems.


ISBN (Hardcover)
Publication date
2021 (June)
Theodicy Evil Omnipotence Benevolence Omniscience Consistency Logical Fallacies False Assumptions
Berlin, Bern, Bruxelles, New York, Oxford, Warszawa, Wien, 2021. 168 pp.

Biographical notes

Paul Weingartner (Author)

Paul Weingartner holds a PhD in philosophy and physics. He was a Research Fellow at the University of London and at the University of Munich. He was Professor of Philosophy at the University of Salzburg from 1971-99 and Chairman of the Institut für Wissenschaftstheorie from 1972-2008. He received an honorary doctorate from the University of Maria Curie Skłodowska, Poland, in 1995 and is a member of the New York Academy of Science. He is author of several books and research articles.


Title: Theodicy - From a Logical Point of View