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TheTractatusfirst appeared in 1921, the same year that Post's “Introduction to a General Theory of Elementary Propositions” appeared in theAmerican Journal of Mathematics. As the latter is the first piece clearly to present and exploit the distinction between a deductive system and a truth-functional interpretation of such a system, we may conclude that Wittgenstein's views had been arrived at somewhat before a variety of logical concepts had received the clarification and refinement incipient on the now taken-for-granted distinction between proof and (...) |
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Responding to the paradox of inference and the related problems in philosophy of logic, this paper argues for the necessity of distinguishing between two different objects of justification: logica utens and logica docens. Then, equipped with Peirce’s critical common-sensist conception of logica utens and his classification of sciences, I propose a diagnosis of and a solution to the problem of justification of logic. I argue that this alternative approach successfully avoids circularity in which most attempts in philosophy of logic have (...) |
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This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...) |
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Thought: A Journal of Philosophy, EarlyView. No categories |
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There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...) |
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In virtue of what are we justified in employing the rule of inference Modus Ponens? One tempting approach to answering this question is to claim that we are justified in employing Modus Ponens purely in virtue of facts concerning meaning or concept-possession. In this paper, we argue that such meaning-based accounts cannot be accepted as the fundamental account of our justification. |
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In this paper, we evaluate Button’s claim that knot is a nasty connective. Knot’s nastiness is due to the fact that, when one extends the set \ with knot, the connective provides counterexamples to a number of classically valid operational rules in a sequent calculus proof system. We show that just as going non-transitive diminishes tonk’s nastiness, knot’s nastiness can also be reduced by dropping Reflexivity, a different structural rule. Since doing so restores all other rules in the system as (...) No categories |
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We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the (...) |
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This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ?inferential definitions? of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a semantic foundation for (...) |
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In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulas. Such systems lend themselves to an inferentialist story about how truth-conditional content of connectives can be determined by inference rules. In particular, for classical logic there is a bilateral proof system which has a property that Carnap in 1943 called categoricity. We show that categorical systems can be given for any finite many-valued logic using $n$-sided sequent calculus. These systems are understood as a further development (...) |
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Karl Popper developed a theory of deductive logic in the late 1940s. In his approach, logic is a metalinguistic theory of deducibility relations that are based on certain purely structural rules. Logical constants are then characterized in terms of deducibility relations. Characterizations of this kind are also called inferential definitions by Popper. In this paper, we expound his theory and elaborate some of his ideas and results that in some cases were only sketched by him. Our focus is on Popper's (...) |
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This is not a normal book. It is a collection of transcripts of talks that I gave between the year 2003 and now. I gave most of these talks on the spur of the moment, without making notes ahead of time. (“Impromptu” is the usual term for that dangerous way of speaking.) One of the “talks” is not a transcript, but a set of notes for a talk I never gave. Any organization or order in the talks is purely coincidental—or (...) |
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Recent attempts to answer ontological questions through conceptual analysis have been controversial. Still, it seems reasonable to assume that if the existence of certain things analytically follows from sentences we already accept, then there is no further ontological commitment involved in affirming the existence of those things. More generally, it is plausible that whenever a sentence analytically entails another, the conjunction of those sentences requires nothing more of the world for its truth than the former sentence alone. In his ‘Analyticity (...) |
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What is the relationship between logic and thought? One view is that logic merely describes how people think. But this view – called 'psychologism' – cannot be quite right. Logic cannot describe how people reason, because although people can reason well, they can also reason badly. The obvious response is to say that logic does not describe how people do think, but rather prescribes how they ought to think. If logic describes how people ought to reason, then if the premises (...) |
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Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis has also (...) |
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