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Switch to: References
Citations of:
Logic, Semantics, Metamathematics: Papers from 1923 to 1938
Alfred Tarski & J. H. Woodger (eds.)
New York, NY, USA: Hackett Publishing Company (1983)
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A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science. |
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The aim of this paper is to show that the account of objective truth taken for granted by logicians at least since the publication in 1933 of Tarski’s “The Concept of Truth in Formalized Languages” arose out of a tradition of philosophical thinking initiated by Bolzano and Brentano. The paper shows more specifically that certain investigations of states of affairs and other objectual correlates of judging acts, investigations carried out by Austrian and Polish philosophers around the turn of the century, (...) |
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In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...) |
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The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of variables, one obtains, (...) |
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In this paper I will address the question of rationalizing mental causation which is involved in the processes of epistemic justification. The main problem concerning mental causation consists in the apparent incompatibility of the three following claims: (i) the subject's mental states (in particular his belief states) are realized by neural states of the subject's brain; (ii) the justifying character of belief transition consists in the fact that there are certain broadly logical relations between the contents of the relevant beliefs; (...) |
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Justification of theorems plays a vital role in any rational human activity. It is indispensable in science. The deductive method of justifying theorems is used in all sciences and it is the only method of justifying theorems in deductive disciplines. It is based on the notion of proof, thus it is a method of proving theorems. In the Warsaw School of Logic (WSL) – the famous branch of the Lvov-Warsaw School (LWS) – two types of the method: axiomatic deduction method (...) |
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According to the interpretational theory of logical validity (IR), logical validity is preservation of truth in all interpretations compatible with the intended meaning of logical expressions. IR suffers from a seemingly defeating objection, the so-called cardinality problem: any instance of the statement ‘There are n things’ is true under all interpretations, since it can be written down using only logical expressions that are not to be reinterpreted; yet ‘There are n things’ is not logically true. I argue that the cardinality (...) |
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The main research goal of the work is to study the notion of co-topos, its correctness, properties and relations with toposes. In particular, the dualization process proposed by proponents of co-toposes has been analyzed, which transforms certain Heyting algebras of toposes into co-Heyting ones, by which a kind of paraconsistent logic may appear in place of intuitionistic logic. It has been shown that if certain two definitions of topos are to be equivalent, then in one of them, in the context (...) |
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Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I (...) |
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Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland :355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence relations in Gentzen systems generates a form (...) |
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Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) |
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Corcoran, J. 2007. Syntactics, American Philosophy: an Encyclopedia. 2007. Eds. John Lachs and Robert Talisse. New York: Routledge. pp.745-6. -/- Syntactics, semantics, and pragmatics are the three levels of investigation into semiotics, or the comprehensive study of systems of communication, as described in 1938 by the American philosopher Charles Morris (1903-1979). Syntactics studies signs themselves and their interrelations in abstraction from their meanings and from their uses and users. Semantics studies signs in relation to their meanings, but still in abstraction (...) |
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I discuss some questions of quantum physics, for instance the validity and limitations of the basic language of set theory to deal with problems related to elementary particles. I also present a sketch of a formalization of a “metaphysics of structures”, which might be useful for a kind of “ontic structural realism”, and briefly review the concept of quasi-truth, which underlies my way of understanding scientific theories and the scientific activity. |
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This paper argues that there are three reasons why we should regard Wittgenstein's Tractatus as a forerunner of formal semantics: Wittgenstein is convinced that we can apply formal notions to natur... |
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Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) |
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I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism. |
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Paul Horwich is aware of the fact that his theory as stated in his works is directly applicable only to a language in which a word, understood as a syntactic type, is connected with exactly one literal meaning. Yet he claims that the theory is expandable to include homonymy and indexicality and thus may be considered as applicable to natural language. My concern in this paper is with yet another kind of ambiguity—systematic polysemy—that assigns multiple meanings to one linguistic type. (...) |
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We extend the Embracing Revenge account of the semantic paradoxes by constructing two distinct consequence relations that reflect, in different ways, the transfinitely-many-valued semantics developed in earlier work. In particular, we adapt the underlying ideas of “gappy” approaches based on K3, and “glutty” approaches based on LP, to the Embracing Revenge framework, by treating the infinitely many non-classical truth values as infinitely many ways that a sentence might fail to receive a classical truth value in the former case, and as (...) |
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Logical nihilism is the view that the relation of logical consequence is empty: there are counterexamples to any putative logical law. In this paper, I argue that the nihilist threat is illusory. The nihilistic arguments do not work. Moreover, the entire project is based on a misguided interpretation of the generality of logic. |
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Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) |
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On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succedent. This interpretation goes against its own ecumenical ambitions, endowing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert. |
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This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence. |
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A relativized version of Tarski's T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain's card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in (...) |
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Symbolic logic is sited at intersection of philosophy, mathematics, linguistics and computer science. It deals with the structure of reasoning, and the formal features of information. Work in symbolic logic has almost exclusively treated the deductive validity of arguments: those arguments for which it is impossible for the premises to be true and the conclusion false. However, techniques from twentieth-century logic have found a place in the study of inductive or probabilistic reasoning, in which premises need not render their conclusions (...) |
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Though it''s difficult to agree on the exact date of their union, logic and artificial intelligence (AI) were married by the late 1950s, and, at least during their honeymoon, were happily united. What connubial permutation do logic and AI find themselves in now? Are they still (happily) married? Are they divorced? Or are they only separated, both still keeping alive the promise of a future in which the old magic is rekindled? This paper is an attempt to answer these questions (...) |
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In the original publication of the article, in Definition 4, the sixth line which reads as. |
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Tarski's theory of truth brings out the question of whether he intended his theory to be a correspondence theory of truth and whether, whatever his intentions, his theory is in fact a correspondence theory. The aim of this paper is to answer both questions. The answer to the first question depends on Tarski's relevant assertions on semantics and his conception of truth. In order to answer the second question Popper's and Davidson's interpretations of Tarski's truth theory are examined; to this (...) |
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I shall elaborate more on the idea of anti-irrationalism proposed by the Polish analytic philosopher Kazimierz Ajdukiewicz, a prominent member of the Lvov-Warsaw School of philosophy and logic. In my reading, anti-irrationalism stands in opposition not only to overt irrationalism, which is made clear by the term itself, but also to all forms of rationalism that tip toward something like worship of reason. Having characterized anti-irrationalism as it originally appeared in Ajdukiewicz’s works, I shall propose a certain reformulation of it, (...) |
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