A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, (...) Leibniz has been criticized for using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against TVS (...) and show that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal. (shrink)

By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology (...) we adopt. It turns out in particular that a certain natural closure condition imposed on a satisfaction class—namely, closure of truth under sentential proofs—generates a nonconservative extension of a syntactic base theory (Peano arithmetic). (shrink)

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established (...) to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)

Could it be right to convict and punish defendants using only statistical evidence? In this paper, I argue that it is not and explain why it would be wrong. This is difficult to do because there is a powerful argument for thinking that we should convict and punish defendants using statistical evidence. It looks as if the relevant cases are cases of decision under risk and it seems we know what we should do in such cases (i.e., maximize expected value). (...) Given some standard assumptions about the values at stake, the case for convicting and punishing using statistical evidence seems solid. In trying to show where this argument goes wrong, I shall argue (against Lockeans, reliabilists, and others) that beliefs supported only by statistical evidence are epistemically defective and (against Enoch, Fisher, and Spectre) that these epistemic considerations should matter to the law. To solve the puzzle about the role of statistical evidence in the law, we need to revise some commonly held assumptions about epistemic value and defend the relevance of epistemology to this practical question. (shrink)

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, (...) and allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)

In spite of the intuitiveness of epistemic closure, there has been a stubborn stalemate regarding whether it is true, largely because some of the “Moorean” things we seem to know easily seem clearly to entail “heavyweight” philosophical things that we apparently cannot know easily—or perhaps even at all. In this paper, I will show that two widely accepted facts about what we do and don’t know—facts with which any minimally acceptable understanding of knowledge must comport—are jointly inconsistent with the (...) class='Hi'>truth of CLR. The proof works by supposing the truth of “Categorialism,” a thesis about the relation between basic categories and common nouns and predicates, which is itself a heavyweight claim that cannot be easily known to be either true or false. (shrink)

This essay introduces the ‘she said, he said’ paradox for Title IX investigations. ‘She said, he said’ cases are accusations of rape, followed by denials, with no further significant case-specific evidence available to the evaluator. In such cases, usually the accusation is true. Title IX investigations adjudicate sexual misconduct accusations in US educational institutions; I address whether they should be governed by the ‘preponderance of the evidence’ standard of proof or the higher ‘clear and convincing evidence’ standard. -/- Orthodoxy holds (...) that the ‘preponderance’ standard is satisfied if the evidence adduced renders the litigated claim more likely than not. On this view, I argue, ‘she said, he said’ cases satisfy the ‘preponderance’ standard. But this consequence conflicts with plausible liberal and feminist claims. In this essay I contrast the ‘she said, he said’ paradox with legal epistemology’s proof paradox. I explain how both paradoxes arise from the distinction between individualised and non-individualised evidence, and I critically evaluate responses to the ‘she said, he said’ paradox. (shrink)

According to one of Leibniz's theories of contingency a proposition is contingent if and only if it cannot be proved in a finite number of steps. It has been argued that this faces the Problem of Lucky Proof , namely that we could begin by analysing the concept ‘Peter’ by saying that ‘Peter is a denier of Christ and …’, thereby having proved the proposition ‘Peter denies Christ’ in a finite number of steps. It also faces a more general but (...) related problem that we dub the Problem of Guaranteed Proof . We argue that Leibniz has an answer to these problems since for him one has not proved that ‘Peter denies Christ’ unless one has also proved that ‘Peter’ is a consistent concept, an impossible task since it requires the full decomposition of the infinite concept ‘Peter’. We defend this view from objections found in the literature and maintain that for Leibniz all truths about created individual beings are contingent. (shrink)

Despite recent controversies surrounding the principle that knowledge entails truth (KT), this paper aims to prove that the principle is true. It offers a proof of (KT) in the following sense. It advances a deductively valid argument for (KT), whose premises are, by most lights, obviously true. Moreover, each premise is buttressed by at least two supporting arguments. And finally, all premises and supporting arguments can be rationally accepted by people who don’t already accept (KT).

In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated (...) for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)', by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. Main tools used in proofs are Zermelo-Fraenkel (ZF) set theory and classical logic. (shrink)

The suggestion of something akin to a ‘relativist solution to the Mind-Body problem’ has recently been held by some scientists and philosophers; either explicitly (Galadí, 2023; Lahav & Neemeh, 2022; Ludwig, 2015) or in more implicit terms (Solms, 2018; Velmans, 2002, 2008). In this paper I provide an argument in favor of a relativist approach to the Mind-Body problem, more specifically, an argument for ‘1st/3rd person relativism’, the claim that ‘The truth value of some sentences or propositions is relative (...) to 1st and 3rd person perspectives’. The argument for 1st/3rd person relativism is close to a forma proof. It is shown that, just by assuming the 1st/3rd person distinction itself and using first order logic and set theory, ‘1st/3rd person relativism’ follows as a theorem. Some consequences of ‘1st/3rd person relativism’ to the Mind-Body Problem are evaluated. It is shown that ‘1st/3rd person relativism’ predicts the existence of an (apparent) Explanatory Gap; explains why the Explanatory Gap is just apparent (and the origins of such illusion); dissolves the Hard-Problem; provides a possible solution the problem of Mental Causation; explains why Mental Causation looks like a problem in the first place and accurately predicts the actual empirically found correlation and covariation between conscious experiences and brain states. This explanatory power of ‘1st/3rd person relativism’ is particularly impressive since it was not designed as a possible solution to the Mind-Body problem in the first place. (shrink)

In his "Ontological proof", Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is (...) positive. Given axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false. (shrink)

As the 19th century drew to a close, logicians formalized an ideal notion of proof. They were driven by nothing other than an abiding interest in truth, and their proofs were as ethereal as the mind of God. Yet within decades these mathematical abstractions were realized by the hand of man, in the digital stored-program computer. How it came to be recognized that proofs and programs are the same thing is a story that spans a century, a (...) chase with as many twists and turns as a thriller. At the end of the story is a new principle for designing programming languages that will guide computers into the 21st century. -/- For my money, Gentzen’s natural deduction and Church’s lambda calculus are on a par with Einstein’s relativity and Dirac’s quantum physics for elegance and insight. And the maths are a lot simpler. I want to show you the essence of these ideas. I’ll need a few symbols, but not too many, and I’ll explain as I go along. -/- To simplify, I’ll present the story as we understand it now, with some asides to fill in the history. First, I’ll introduce Gentzen’s natural deduction, a formalism for proofs. Next, I’ll introduce Church’s lambda calculus, a formalism for programs. Then I’ll explain why proofs and programs are really the same thing, and how simplifying a proof corresponds to executing a program. Finally, I’ll conclude with a look at how these principles are being applied to design a new generation of programming languages, particularly mobile code for the Internet. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...) logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A (...) syntactic characterization of these logics is left for further work. In this paper, based on our previous work on a functionally complete extension of Belnap’s logic, we present a sound and complete tableau calculus for these logics. It crucially exploits the Cartesian nature of the four values, which is reflected in the fact that each proof consists of two tableaux. The bi-facial notion of truth of Z&S is thus augmented with a bi-facial notion of proof. We also provide translations between the logics for semi-classical negation and classical logic and show that an argument is valid in a logic for semi-classical negation just in case its translation is valid in classical logic. (shrink)

In order to make sense of Scotus’s claim that rationality is perfected only by the will, a Scotistic doctrine of truth is developed in a speculative way. It is claimed that synthetic a priori truths are truths of the will, which are existential truths. This insight holds profound theological implications and is used on the one hand to criticize Kant's conception of existence, and on the other hand, to offer another explanation of the sense according to which the existence (...) of things is grasped. (shrink)

How is the burden of proof to be distributed among individuals who are involved in resolving a particular issue? Under what conditions should the burden of proof be distributed unevenly? We distinguish attitudinal from dialectical burdens and argue that these questions should be answered differently, depending on which is in play. One has an attitudinal burden with respect to some proposition when one is required to possess sufficient evidence for it. One has a dialectical burden with respect to some proposition (...) when one is required to provide supporting arguments for it as part of a deliberative process. We show that the attitudinal burden with respect to certain propositions is unevenly distributed in some deliberative contexts, but in all of these contexts, establishing the degree of support for the proposition is merely a means to some other deliberative end, such as action guidance, or persuasion. By contrast, uneven distributions of the dialectical burden regularly further the aims of deliberation, even in contexts where the quest for truth is the sole deliberative aim, rather than merely a means to some different deliberative end. We argue that our distinction between these two burdens resolves puzzles about unevenness that have been raised in the literature. (shrink)

In this paper we give some formal examples of ideas developed by Penco in two papers on the tension inside Frege's notion of sense (see Penco 2003). The paper attempts to compose the tension between semantic and cognitive aspects of sense, through the idea of sense as proof or procedure – not as an alternative to the idea of sense as truth condition, but as complementary to it (as it happens sometimes in the old tradition of procedural semantics).

This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not (...) want to equate falsity with the non-existence of a proof since this would render a statement such as “pi is transcendental” false prior to 1882. In addition, the intuitionist account of negation as shorthand for the derivation of absurdity is inadequate, particularly outside of purely mathematical contexts. To deal with these issues, I investigate the dual of intuitionistic logic, co-intuitionistic logic, as a logic of refutation, alongside intuitionistic logic of proofs. Direct proof and refutation are dual to each other, and are constructive, whilst there also exist syntactic, weak, negations within both logics. In this respect, the logic of refutation is weakly paraconsistent in the sense that it allows for statements for which, neither they, nor their negation, are refuted. I provide a proof theory for the co-constructive logic, a formal dualizing map between the logics, and a Kripke-style semantics. This is given an intuitive philosophical rendering in a re-interpretation of Kolmogorov’s logic of problems. (shrink)

Faith is the highest truth that ensures the happiness and salvation of man in the world and in the Hereafter. But the essence of superstitious is invalid and wrong. The realization of this happiness and salvation is possible by having a true faith. Another consequence of the true faith is the ability to recognize that this belief is right. Believing in true faith, ensures rightness and makes possible to prove and disclose this truth. It is important to have (...) true faith and accurate affirmation. This certainty requires certain criteria for accuracy and precision. In addition, this situation involves advocating the faith and delivering it to other people. This is closely related to the recognition and proof of these truths. It also makes it necessary to explore the distinction between presumption and believing as well as knowledge and ignorance. It requires examination of the concepts of certainty, doubt, evidence, persuasion and proof and what they have implied in terms of faith. The examination of the proofs of faith in terms of persuasion and proof also increases the understanding of the certainty of a belief. (shrink)

The paper proposes two logical analyses of (the norms of) justification. In a first, realist-minded case, truth is logically independent from justification and leads to a pragmatic logic LP including two epistemic and pragmatic operators, namely, assertion and hypothesis. In a second, antirealist-minded case, truth is not logically independent from justification and results in two logical systems of information and justification: AR4 and AR4¢, respectively, provided with a question-answer semantics. The latter proposes many more epistemic agents, each corresponding (...) to a wide variety of epistemic norms. After comparing the different norms of justification involved in these logical systems, two hexagons expressing Aristotelian relations of opposition will be gathered in order to clarify how (a fragment of) pragmatic formulas can be interpreted in a fuzzy-based question-answer semantics. (shrink)

Spinoza distinguishes between causation that is external, as in A causing B where A is external to B, and causation that is internal, where C causes itself (causa sui), without any involvement of anything external to C. External causation is easy to understand, but self causation is not. This note explores an approach to self-causation based upon Gödelian undecidability and draws upon ideas from an earlier study of Gödel’s proof and the quantum measurement problem (Zwick, 1978).

Mistakes can be made in both personal and official accounts of past events: lies can be told. Stories about the past have many functions besides truth-telling: but we still care deeply that our sense of what happened should be accurate. The possibility of error in memory and in history implies a commonsense realism about the past. Truth in memory is a problem because, coupled with our desires to find out what really happened, we recognize that our individual and (...) collective access to past events may be indirect. This chapter sketches some approaches, from across the disciplines, to such problems about authority over the past. I open up recent lines of research on autobiographical memory which should be more accessible in the humanities and social sciences. Psychological work on constructive remembering should not be seen as sceptically challenging the very possibility of everyday authority over our own past, but as identifying specific forms of fallibility. I argue that the study of historical and social processes is an integral part of the cognitive sciences of memory, not a humanistic curiosity. (shrink)

The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...) of derivations are collections of derivations in the associated “dedicated” natural-deduction proof-system, and functions therein (with no appeal to models, truth-values and elements of a domain). The compositionality of the semantics is analyzed. (shrink)

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.

Proofs of God in Early Modern Europe offers a fascinating window into early modern efforts to prove God’s existence. Assembled here are twenty-two key texts, many translated into English for the first time, which illustrate the variety of arguments that philosophers of the seventeenth and eighteenth centuries offered for God. These selections feature traditional proofs—such as various ontological, cosmological, and design arguments—but also introduce more exotic proofs, such as the argument from eternal truths, the argument from universal (...) aseity, and the argument ex consensu gentium. Drawn from the work of eighteen philosophers, this book includes both canonical figures (such as Descartes, Spinoza, Newton, Leibniz, Locke, and Berkeley) and noncanonical thinkers (such as Norris, Fontenelle, Voltaire, Wolff, Du Châtelet, and Maupertuis). -/- Lloyd Strickland provides fresh translations of all selections not originally written in English and updates the spelling and grammar of those that were. Each selection is prefaced by a lengthy headnote, giving a biographical account of its author, an analysis of the main argument(s), and important details about the historical context. Strickland’s introductory essay provides further context, focusing on the various reasons that led so many thinkers of early modernity to develop proofs of God’s existence. -/- Proofs of God is perfect for both students and scholars of early modern philosophy and philosophy of religion. (shrink)

Mümkün varlıkları aracı kılmadan Vâcibü’l-Vücûd’un varlığını ispatlama çabalarının bir sonucu olan sıddıkîn burhanı ilk defa Müslüman filozoflar tarafından dillendirildi. İbn Sînâ (ö. 428/1037) da Fârâbî’nin etkisiyle yeni bir burhan açıkladı ve buna sıddıkîn adını verdi. Molla Sadrâ (ö. 1050/1641) varlığın asaleti ilkesini mutasavvıflardan, teşkîk ilkesini de Sühreverdî’den iktibas ederek yeni bir sıddıkîn burhanı dillendirdi. Bu burhanın, varlığın asaleti, basîtliği/yalınlığı, teşkîkî ve ma’lûlün illete ihtiyacı olmak üzere bazı öncülleri vardır. O, bu öncülleri açıkladıktan sonra teselsüle ihtiyaç duymadan Vâcibü’l-Vücûd’un varlığını ispatlar. Onun (...) burhanı diğer sıddıkîn burhanlarına nispetle bazı üstün özelliklere sahiptir. Öncelikle bu burhan varlığın asaleti ilkesi üzerine bina edildiğinden dayanağı varlık kavramı değil, varlığın nesnel hakikatidir. İkincisi bu burhan Vâcibü’l-Vücûd’un zâtını ispatlamakla birlikte Vâcibü’l-Vücûd’un birliğini ve kemâlî sıfatlarını ispatlar. Üçüncüsü bu burhana göre mümkün varlıklar hiçbir aracı olmadan Vâcibü’l-Vücûd’a bağımlı olduklarından burhanın açıklanmasında teselsül ve kısır döngüden yararlanma ihtiyacı yoktur. Molla Sadrâ’nın teselsül ve kısır döngüden de yararlanarak Vâcibü’l-Vücûd’un varlığını ispatladığı burhanlar da vardır. Molla Sadrâ bu burhanıyla hem Vâcibü’l-Vücûd’un varlığını ve hem de onun kemâlî sıfatlarını ispatladığını iddia eder. Bu çalışmada bu iddia incelecek ve ispat-ı vacip meselesinde Molla Sadrâ’nın ne gibi yenilikler getirdiği ele alınacaktır. ABSTRACT A result of the attempts to prove the existence of The Necessary Existence without the mediation of possible beings, proof of the truthful was first expressed by Muslim philosophers called it sıddıkin. Mullā Ṣadrā’s “proof” that he explains has certain premises such as the fundamental of existence, indivisibility of the existence, existential gradation, effect’s need for cause. After explanining these premises, Mullā Ṣadrā then proves the Necessary Existence without needing succession. Mullā Ṣadrā’s proof of the truthful has certain superior features tan the proofs of truthful expressed before him. First of all, as this proof is built upon the principle of the fundamental of existence, its foundation is the external truth of existence, not the concept of existence itself. Secondly, this proof proves the unity and perfection attributes of The Necessary Existence as well as proving the existence of the Necessary Existence. Thirdly, according to this proof, as all possible existences are dependent on The Necessary Existence without any mediation, there is no need to benefit from succession and vicious circle in explaining the proof. However, Mullā Ṣadrā proves the Necessary Existence by benefitting from succession and vicious circle in other proofs. Mullā Ṣadrā asserts that this proof demonstrates the presence of The Necessary Existence and its perfection attributions. This study examines this assertion and addresses what kind of innovations was brought by Mullā Ṣadrā in terms of proving The Necessary Existence. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for (...) groups of formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

For any natural (human) or formal (mathematical) language L we know that an expression X of language L is true if and only if there are expressions Γ of language L that connect X to known facts. -/- By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to neither True nor False.

Techne and Truth. The problem of techne in the dispute between Gorgias and Plato -/- The source of the problem matter of the book is the Plato’s dialogue „Gorgias”. One of the main subjects of the discussion carried out in this multi-aspect work is the issue of the art of rhetoric. In the dialogue the contemporary form of the art of rhetoric, represented by Gorgias, Polos and Callicles, is confronted with Plato’s proposal of rhetoric and concept of art (techne). (...) The ingenuous and dramatic structure of the dialogue composed of three acts, in each of which Socrates’ consecutive interlocutors emerge, is difficult to interpret. It seems, however, that even though the first conversation between Socrates and Gorgias constitutes a small part of the dialogue, it forms the foundations for the discussion. This part, dealing with such important issues as the subject of art, knowledge, power and relation between art and good, is the starting point for the conversations which follow. What do the differences between the Gorgias’ and Plato’s concepts of art consist in? Any attempt to answer the question requires presentation of the background for the discussion taking place in Plato’s work as well as the reconstruction of Gorgias’ vision of the art of rhetoric and art in general, defining the relation between art and knowledge. The latter may be undertaken on the basis of two paraphrases of the treatise “On Non-existence”, two epideictic speeches entitled “Helen” and “Palamedes” and some smaller fragments which have been preserved from Gorgias’ creative output. The treatise “On Non–existence”, very paradoxical in its philosophical meaning, testifies to new, sophistic thinking represented by Gorgias of Leontinoi. The treatise is the polemic and attack on Eleatism based on certain principles and methods elaborated by the Eleatics themselves. It also shows that Gorgias – using traditional Eleatic schemes – is opposed to this tradition. Even though the treatise does not discuss the problem of art directly, it anticipates the considerations from epideictic speeches. “Helen” and “Palamedes” constitute further stages in the development of Gorgias’ thought and concept of art combining typically epideictic elements with some philosophical convictions. Gorgias refers to the Eleatic theme considering the issues of truth, knowledge and belief, yet defining them in the empirical spirit. Solutions in the cognitive sphere determine the horizon of Gorgias’ rhetoric. The word is separated from the existence. Human cognition is limited and therefore the word and visual images affect the belief. This promotes the great importance of rhetoric, painting and sculpture, i.e. the areas which influence in a specific way – creating the “delusion” (ἀπάτη). Through idealization art provides pleasure, which is its objective. Therefore the task of art is to create delusion. The rhetor of Leontinoi discusses the issue of “how?” to use the word ‘rhetoric’. Gorgias is aware that rhetoric may be used to talk about what is unknown and that technical correctness of a rhetoric statement is not identical with the truthfulness of the proclaimed message. Mentioning it, Gorgias shows his respect to the truth as a value which should be respected in speech on the one hand, and on the other emphasizes that the truth in itself has no persuasive power. For this reason it is not enough to proclaim the truth, but, to convince the listeners, the orator should possess the skill of speaking. What is then the relation between truth and art emerging from epideictic speeches? Gorgias undoubtedly emphasizes the formal aspect of speech, as rhetoric is art, thus an ability based on certain principles. According to Gorgias, the truth is the value which should be respected in speeches. Rhetoric is able to create a fictive world, as a great range of reality remains outside direct human experience. Rhetoric does not oppose the truth but discussing not only what is directly given concerns the area outside the sphere of direct experience. This concept of rhetoric is the basis of the discussion about art carried out in the dialogue “Gorgias”. Even though the first of the discussions in the dialogue – the conversation between Socrates and Gorgias – is directly concerned with rhetoric itself, numerous remarks testify to its much wider character. This is best exemplified by the way of carrying out the conversation by Socrates, who, asking questions about rhetoric practised by Gorgias, throughout the whole conversation compares it with other skills. Additionally, the manner and the structure of the conversation prove that Plato considers the issue of rhetoric from a wider perspective determined by the issue of art. The specific feature of the conversation is ordering it around main issues – such notions as πρᾶγμα, ἐπιστήμη, δύναμις, each of which has its own meaning in Plato. In the first part of Gorgias Plato presents the principles previously occurring in other dialogues in a certain order, thus constructing the structure of the conversation with Gorgias. The notions are not novum in Plato but the fact that he clearly wants to systematise them and present a certain concept of art is a new and significant aspect. This tendency is of paramount importance for the discussion because Gorgias’ answers are evaluated by Plato from the perspective of this clearly set concept consisting of not only established notions but also certain principles. The discussion between Socrates and Gorgias introduces a theme which is crucial for the dialogue: the relation between art and good, i.e. the technical and ethical spheres. The issue is introduced by Gorgias, who mentions that rhetoric may be used for evil purposes. On this basis Socrates proves that if rhetoricians can use rhetoric for evil purposes, they have no knowledge concerning the subject of their art – justice, because one who knows what is just, always acts justly. Thus the relation between the technical and ethical spheres transpires to be the main point of contention. The question is whether a technician following the principles of the art he practices may act against good. This paradoxical statement based on the well-known Socrates’ principle "nemo sua sponte peccat" acquires philosophical foundations in the dialogue. In its remaining two parts Plato presents a justification, placing the principle within the framework of a certain concept of art, as a result of which not only rhetoric but also many other skills are criticised. The notions on which the conversation with Gorgias focuses are more precisely defined in the subsequent parts of the dialogue. Additionally, Plato presents twice the conditions which art should fulfill. They oblige the “technicians” to know the nature and purpose of the art and to know the causes of undertaken activities and to be able to justify them. These conditions determine the relation between the two spheres – technical and ethical. According to Plato, art may not act against good because it should be the objective of its activities. Certain concepts of good and knowledge outlined in the dialogue are the guarantees of “technicality”. Good, which should be respected by every art, is understood objectively and is contrasted with subjective pleasure. Knowledge, which should be the basis of art, opposes experience, which uses observation and recollection. Additionally, the definition of knowledge, significance of order in the world assuming the form of “geometrical equality”, significance of mathematics becoming the ideal of exactness indicate that Plato’s concept of knowledge is formed in Gorgias. These conclusions render it impossible that the results of any activity deserving the name of art should oppose good. And this is Plato’s main reproach of Gorgias’ concept, who wrote about false speeches possessing the power of conviction because they were written according to the principles proof of art or who defined tragedy as “a deceit, where he who cheats is more just than he who does not and the cheated is wiser than he who was not cheated”. Such determination of the relation between the technical and ethical sphere resulted from Gorgias’ concept of the world and fundamental philosophical principles. The whole concept of art described by Plato in the dialogue opposes the view presented by Gorgias. According to Plato, every technical activity has a defined object (ἔργον), is based on knowledge (ἐπιστήμη) and is always aimed at the good of human soul or body. The danger revealed and presented in the dialogue by Plato exists in the very concept of art presented by Gorgias, i.e. in its empirical foundations and the resulting understanding of the relation between art and good. Gorgias’ concept of art based on empirical cognition, which concerns the world of phenomena and rejects the possibility of perfect knowledge, leads, according to Plato, to a dangerous falsification of the relation between art and good. Plato proves that this weakness of Gorgias’ concept is revealed when confronted with these representatives of “the magnificent art” who are not protected against radicalism by the adherence to the moral tradition. The comparison of two, completely contrasting concepts of art based on different philosophical understanding of knowledge and good is decisive for the criticism of rhetoric in Gorgias. The concept presented by Plato criticises contemporary rhetoric and sophistry but determines the direction of research of the real art of rhetoric. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? It turns out that, in a wide range of cases, we can get some nice answers to this question, but only if we work in a framework that is somewhat different from those usually employed in (...) discussions of axiomatic theories of truth. These results are then used to address a range of philosophical questions connected with truth, such as what Tarski meant by "essential richness" and the so-called conservativeness argument against deflationism. -/- This draft dates from about 2009, with some significant updates having been made around 2011. Around then, however, I decided that the paper was becoming unmanageable and that I was trying to do too many things in it. I have therefore exploded the paper into several pieces, which will be published separately. These include "Disquotationalism and the Compositional Principles", "The Logical Strength of Compositional Principles", "Consistency and the Theory of Truth", and "What Is Essential Richness?" You should probably read those instead, since this draft remains a bit of a mess. Terminology and notation are inconsistent, and some of the proofs aren't quite right. So, caveat lector. I make it public only because it has been cited in a few places now. (shrink)

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our (...) theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to. (shrink)

A new proof style adequate for modal logics is defined from the polynomial ring calculus. The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra???Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S 5, and can be easily extended to other (...) modal logics. (shrink)

Proof by refutation of a geometry theorem that is not universally true produces a Gröbner basis whose elements, called side polynomials, may be used to give inequations that can be added to the hypotheses to give a valid theorem. We show that (in a certain sense) all possible subsidiary conditions are implied by those obtained from the basis; that what we call the kind of truth of the theorem may be derived from the basis; and that the side polynomials (...) may be classified in a useful way. We analyse the relationship between side polynomials and kinds of truth, and we give a unified algorithmic treatment of side polynomials, with examples generated by an implementation. (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, (...) but the other does not.). (shrink)

The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable proof-theoretic properties. We start by showing that, due to a strong form of invertibility of the truth rules, cut is eliminable in the systems via a standard strategy supplemented by a suitable measure of the number of applications of truth rules to formulas in (...) derivations. Next, we notice that cut remains eliminable when suitable arithmetical axioms are added to the system. Finally, we establish a direct link between cut-free derivability in infinitary formulations of the systems considered and fixed-point semantics. Noticeably, unlike what happens with other background logics, such links are established without imposing any restriction to the premisses of the truth rules. (shrink)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral proof rules has (...) a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

Thought is the primary realm in which truth and falsity may occur and speech the secondary realm of this occurrence while the realm of external being has no truth and falsity in itself. The first and last points are directly asserted by Aristotle in one text: ‘Falsity and truth are not in things-it is not as if the good were true, and the bad were in itself false- but in thought.’ (Met., E, 1027b25-27; cf. Met., K, 1065a22-23) (...) The second point is also somehow implied: ‘As there are in the mind thoughts which do not involve truth and falsity, and those which must be either true or false, so it is in speech.’ (OI, I, 1, 16a9-11) 1) Truth and falsity belong only to co-positings and positing aways and not to incomposites Truth and falsity do not belong to the realm of external being but only to the realms of thought and language. However, they do not belong to all the elements in these realms. Neither do they belong to incomposite elements in thought (‘With regard to simple things and essences, falsity and truth do not exist even in thought.’ (Met., E, 1027b26-28; So., Γ, 6, 430a26-b4)), nor to such elements in language. Consequently, all incomposites are incapable of being true or false. (cf. Met., Θ, 1051b17-22 and b26-27) Where we have no co-positing or positing away, of the kind made by copula or verb, we cannot have truth and falsity though we can have significance: ‘“Man” and “white”, as isolated terms, are not yet either true or false. In proof of this, consider the word “good-stag.” It has significance, but there is no truth or falsity about it, unless “is” or “is not” is added, either in present or in some other tense.’ (OI., I, 1, 16a14-18) Therefore, any other kind of co-positing cannot be the subject of truth and falsity. One good example of co-positings not made by copula or verbs are simple negations: ‘He that uses the expression ‘not-man,’ if nothing more be added, is not nearer but farther from making a true or a false statement than he who uses the expression “man.”’ (OI., I, 10, 20a34-36) It is indeed a co-positing or a positing away that is the subject of truth and falsity: ‘For it is co-positing (σύνθεσιν) and positing away (διαίρεσιν) that truth and falsity is about.’ (OI., I, 1, 16a12-13) Co-positing is so vital for truth-falsity that ‘of the things that are never said based on co-positing, nothing is true or false.’ (Cat., 10, 13b9-11) This co-positing can be both in thought (‘where the alternative of true or false applies, there we always find a sort of combining of objects of thought in a quasi-unity … For falsehood always involves a combining’ (So., Γ, 6, 430a26-b2) and ‘truth or false is a co-positing of concepts of thought’ (So., Γ, 6, 430a11-12) and in language because they are produced in thought: ‘There is not only the true or false assertion that Cleon is white but also the true or false assertion that he was or will be white. In each and every case that which unifies is thought.’ (So., Γ, 6, 430b4-6) 2) Correspondence to external world Although truth and falsity belong to thought and language and not to external world, their basis is in the external world. It is, in fact, the correspondence of thought and language to external world that makes what is true, true and what is false, false: ‘To say of what is that it is, or of what is not that it is not, is false, while to say of what is that it is, and of what is not that is not, is true.’ (Met., Γ, 1011b26-27; cf. Met., Θ, 1051b2-5) When the two realms are correspondent, we can transfer from one to the other: ‘If it is true to say that a thing is white, it must necessarily be white; if the reverse proposition be true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement, it follows that it is not white.’ (OI., I, 9, 18a39-b3) This possible mutual transformation does not, however, imply that each realm is the basis of the other. In fact, it is only the external world that is the basis of truth and falsity in thought or language and not vice versa: ‘it is not because we think that you are white, that you are white, but because you are white we who say this have the truth.’ (Met., Θ, 1051b6-9; Cat., 5, 4b8-10) Aristotle even calls the external world the ‘cause’ of truth in the realm of language while the converse causation is not approved: ‘Whereas the true statement is in no way the cause of the actual thing’s existence, the actual thing does seem in some way the cause of the statement’s being true: it is because the actual thing exists or does not that the statement is called true or false.’ (Cat., 12, 14b18-22) This one-sided relation Aristotle calls ‘reciprocation as to implication of existence’: ‘For there being a man reciprocates as to implication of existence with the true statement about it: if there is a man, the statement whereby we say that there is a man is true, and reciprocally- since if the statement whereby we say that there is a man is true, there is a man. And whereas the true statement is in no way the cause of the actual thing’s existence, the actual thing does seem in some way the cause of the statement’s being true: it is because the actual thing exists or does not that the statement is called true or false,’ (Cat., 12, 14b14-22) Aristotle attaches falsity to not-being: ‘We cal things false in this way, then, either because they themselves do not exist, or because the appearance which results from them is that of something that does not exist.’ (Met., Δ, 1024b24-26) Or: ‘A false formula is the formula of non-existent objects, in so far as it is false.’ (Met., Δ, 1024b26-27) This correspondence to ‘non-being’ is, however, more a miscorrespondence: ‘Hence every formula is false when applied to something other than that of which it is true, e.g. the formula of a circle is false when applied to a triangle.’ (Met., Δ, 1024b27-28) . (shrink)

Pragmatists are usually very antagonistic toward the correspondence theory of truth. They contend that the evidence-transcendent standard entailed by the theory is antithetical to the pragmatist methodology of elucidating concepts by exposing their practical bearings. What use could truth be to us if it offers a target we cannot even see? After judging the correspondence theory to be in violation of the Pragmatic Maxim, the pragmatist is prone to banishing it to the wastelands of empty metaphysics, where nothing (...) of practical importance could ever grow. This article makes the case that this unjust condemnation must be appealed and overturned. The ground for my case is an argument to the effect that the correspondence conception of truth can be practically advantageous, which provides proof of the fact that, contrary to popular pragmatist belief, the correspondence theory does comply with the Pragmatic Maxim. (shrink)

Interesting as they are by themselves in philosophy and mathematics, paradoxes can be made even more fascinating when turned into proofs and theorems. For example, Russell’s paradox, which overthrew Frege’s logical edifice, is now a classical theorem in set theory, to the effect that no set contains all sets. Paradoxes can be used in proofs of some other theorems—thus Liar’s paradox has been used in the classical proof of Tarski’s theorem on the undefinability of truth in sufficiently (...) rich languages. This paradox (as well as Richard’s paradox) appears implicitly in Gödel’s proof of his celebrated first incompleteness theorem. In this paper, we study Yablo’s paradox from the viewpoint of first- and second-order logics. We prove that a formalization of Yablo’s paradox (which is second order in nature) is non-first-orderizable in the sense of George Boolos (1984). (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology (...) suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to deductive conclusions without any need for other representations.

An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines (...) a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.1. (shrink)

Eristic has been studied more and more intensively in recent years in philosophy, law, communication theory, logic, proof theory, and A.I. Nevertheless, the modern origins of eristic, which almost all current researchers see in the philosopher Arthur Schopenhauer, are considered to be a theory of the illegitimate use of logical and rhetorical devices. Thus, eristic seems to violate the norms of discourse ethics. In this paper, I argue that this interpretation of eristic is based on prejudices that contradict the original (...) intention of modern eristic. Eristic is not an art of being right or winning an argument, but an art of protecting oneself from the one who deliberately violates norms of discourse ethics to gain argumentative acceptance. For this reason, eristic must be seen as a discipline of Enlightenment philosophy and a correlate of discourse ethics. Especially in the age of alternative facts and post-factual politics, this makes eristic a valuable discipline. (shrink)

The concept of truth and competing philosophical theories on what truth amounts to have an important place in contemporary philosophy. The aim of this chapter is to give a synopsis of different theories of truth and the particular philosophical issues related to the concept of truth. The literature on this topic is vast, and we must necessarily be rather selective and very brief about complex questions of interpretation of various philosophers. The focus of the chapter is (...) mainly on selected systematic issues and the most influential and well-established philosophical theories and key concepts. (shrink)

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...) problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. (shrink)

Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are (...) elaborated, and examples of cyclic and convergent causation are given. Soundness and completeness proofs are sketched. (shrink)

Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, strong modal (...) force, generality, topic neutrality, basicness, and (quasi-)apriority, (v) the veridicality of logic and its applicability to science, (v) the normativity of logic, (vi) error, revision, and expansion in/of logic, and (vii) the relation between logic and mathematics. The high explanatory power of the truth-theoretic approach does not rule out an equal or even higher explanatory power of the proof-theoretic approach. But to the extent that the truth-theoretic approach is shown to be highly explanatory, it sets a standard for other approaches to logic, including the proof-theoretic approach. (shrink)