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We define a notion of difference-making for partial grounds of a fact in rough analogy to existing notions of difference-making for causes of an event. Using orthodox assumptions about ground, we show that it induces a non-trivial division with examples of partial grounds on both sides. We then demonstrate the theoretical fruitfulness of the notion by applying it to the analysis of a certain kind of putative counter-example to the transitivity of ground recently described by Jonathan Schaffer. First, we show (...) |
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In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...) |
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Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”. |
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Bayesians standardly identify irrelevance with probabilistic irrelevance. However, there are cases where e is probabilistically irrelevant to h but intuitively e is relevant to h. For instance, ‘Die A came up 1 and die B came up 1, 3, 5 or 6’ is probabilistically irrelevant to ‘Die A came up odd and die B came up even’, yet, intuitively, it is not, irrelevant to that claim, in the sense that ‘Sydney has a harbour Bridge’ is irrelevant to it. In the (...) |
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N. Tennant; XI*—Entailment and Proofs, Proceedings of the Aristotelian Society, Volume 79, Issue 1, 1 June 1979, Pages 167–190, https://doi.org/10.1093/aristote. |
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This paper treats entailment as a subrelation of classical consequence and deducibility. Working with a Gentzen set-sequent system, we define an entailment as a substitution instance of a valid sequent all of whose premisses and conclusions are necessary for its classical validity. We also define a sequent Proof as one in which there are no applications of cut or dilution. The main result is that the entailments are exactly the Provable sequents. There are several important corollaries. Every unsatisfiable set is (...) |
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This chapter explains an approach to relevantization of logical reasoning that seeks to maximize epistemic gain. It does so by retaining Disjunctive Syllogism and making admissible only a restricted rule of Cut. The virtue of this approach is that one can show that the resulting relevant logic is adequate for mathematics and science. In the course of explaining this kind of relevant logic, we compare and contrast our approach with the Anderson-Belnap tradition. |
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We suggest two precise abstract definitions of the notion of ‘relevance logic’ which are both independent of any proof system or semantics. We show that according to the simpler one, R → source is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second definition, while all fragments of linear logic are not. |
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The rules for Core Logic are stated, and various important results about the system are summarized. We describe its relationship to other systems, such as Classical Logic, Intuitionistic Logic, Minimal Logic, and the Anderson–Belnap relevance logicR. A precise, positive explication is offered of what it is for the premises of a proof to connect relevantly with its conclusion. This characterization exploits the notion of positive and negative occurrences of atoms in sentences. It is shown that all Core proofs are relevant (...) |
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T. J. Smiley; XII.—Entailment and Deducibility, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 233–254, https://doi.org/10.1093. |
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On one important notion of irrelevance, evidence that is irrelevant in an inquiry may rationally be discarded, and attempts to obtain evidence amount to a waste of resources if they are directed at irrelevant evidence. The familiar Bayesian criterion of irrelevance, whatever its merits, is not adequate with respect to this notion. I show that a modification of the criterion due to Ken Gemes, though a significant improvement, still has highly implausible consequences. To make progress, I argue, we need to (...) |
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In this paper we present a logic that determines when implications in a classical logic context express a relevant connection between antecedent and consequent. In contrast with logics in the relevance logic literature, we leave classical negation intact—in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. On the other hand, we give up the requirement that our theory of relevance should be able to (...) |
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