Topic

# Conditional proof

About: Conditional proof is a research topic. Over the lifetime, 18 publications have been published within this topic receiving 424 citations.

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York University

^{1}TL;DR: The theory of conditional proof as discussed by the authors is based on a set of pragmatic principles that govern how an if sentence is likely to be interpreted in context, and it is defined by a lexical entry that defines the information about if in semantic memory.

Abstract: The theory has 3 parts: (a) A lexical entry defines the information about if in semantic memory; its core comprises 2 inferences schemas, Modus Ponens and a schema for Conditional Proof; the latter operates under a constraint that explains differences between if and the material conditional of standard logic. (b) A propositional-logic reasoning program specifies a routine for reasoning from information as interpreted to a conclusion. (c) A set of pragmatic principles governs how an if sentence is likely to be interpreted in context

302 citations

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01 Jan 2017TL;DR: In formal logic, an argument is a set of one or more interlinked premiss-illative-conclusion sequences as discussed by the authors, which can be expressed either in language or by visual images or physically.

Abstract: Informal logic studies the identification, analysis, evaluation, criticism and construction of arguments. An argument is a set of one or more interlinked premiss-illative-conclusion sequences. Premisses are assertives, not necessarily asserted by anyone. Conclusions can be assertives, directives, declaratives, commissives or expressives. Each can be expressed either in language or by visual images or physically. Two arguments can be linked either by having a conclusion of one as a premiss of the other or by having one as a premiss of the other. A box-arrow system for diagramming arguments thus conceived is illustrated with reference to three expressed arguments; the diagrams show that the diagramming system can handle conditional proof, argument about an arbitrary instance as a proof of a universal generalization, argument by cases, and reductio ad absurdum. A final section lists issues in informal logic and gives some indication of the range of positions taken on these issues.

41 citations

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TL;DR: This chapter attempts to make some sense of the competing claims concerning conditional-reasoning competence, and concludes that the appropriate assessment of formal operational competency with conditionals appears to concern performances in judging universally quantified conditionals.

Abstract: Publisher Summary This chapter attempts to make some sense of the competing claims concerning conditional-reasoning competence. The competence model is based on the natural deduction approach to standard logic; modus ponens and the schema for conditional proof provide inference rules for simple conditionals and, together with the recognition of the constraints imposed by universal quantification, they provide a model for reasoning with universally quantified conditionals. Piaget's account of conditional reasoning is inadequate on logical grounds, that is, it confuses simple and quantified conditionals, but it is possible to make fairly clear empirical predictions when quantifiers are assumed. Ennis and Brainerd have argued that Piaget's account of formal operational thought is wrong because children have some ability to evaluate conditional syllogisms correctly. However, Piaget argued that successful performances on many conditional reasoning tasks can be obtained without a formal operational appreciation of the conditional. Given that the class-inclusion logic structure of concrete operational thought should be sufficient for reasoning with simple conditionals; this does not appear to be a warranted dismissal of the theoretical expectations. Rather, the appropriate assessment of formal operational competency with conditionals appears to concern performances in judging universally quantified conditionals.

31 citations

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TL;DR: It would still be an exercise in relevance logic to formulate a deductive system free of the fallacies of relevance in deductive form even if this were done in a language whose only connectives were, say, &, ∨ and ∼.

Abstract: Relevance logic began in an attempt to avoid the so-called fallacies of relevance. These fallacies can be in implicational form or in deductive form. For example, Lewis's first paradox can beset a system in implicational form, in that the system contains as a theorem the formula (A & ∼A) → B; or it can beset it in deductive form, in that the system allows one to deduce B from the premisses A, ∼A. Relevance logic in the tradition of Anderson and Belnap has been almost exclusively concerned with characterizing a relevant conditional. Thus it has attacked the problem of relevance in its implicational form. Accordingly for a relevant conditional → one would not have as a theorem the formula (A & ∼A) → B. Other theorems even of minimal logic would also be lacking. Perhaps most important among these is the formula (A → (B → A)). It is also a well-known feature of their system R that it lacks the intuitionistically valid formula ((A ∨ B) & ∼A) → B (disjunctive syllogism). But it is not the case that any relevance logic worth the title even has to concern itself with the conditional, and hence with the problem in its implicational form. The problem arises even for a system without the conditional primitive. It would still be an exercise in relevance logic, broadly construed, to formulate a deductive system free of the fallacies of relevance in deductive form even if this were done in a language whose only connectives were, say, &, ∨ and ∼. Solving the problem of relevance in this more basic deductive form is arguably a precondition for solving it for the conditional, if we suppose (as is reasonable) that the relevant conditional is to be governed by anything like the rule of conditional proof.

26 citations

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TL;DR: There appears to be no good reason to doubt thatif is transitive, that the antecedent of a conditional can be strengthened, and that the contrapositive can be inferred, and the rule of conditional proof does seem to capture a commonly accepted form of argument in support ofif-then statements.

Abstract: The paper has sought to show two things. One is that the apparent variety of Stalnaker and Lewis's counterexamples is misleading. Several of their examples are quite unsatisfactory because they depend on unguarded language behavior. There is in fact only one type of counterexample that is worth serious discussion, and that has the form of Barense's. For Barense's example, I try to show that it fails as a counterexample to transitivity because one of the premisses is false within the context of the example. However, Barense's example is problematic for the Stalnaker-Lewis analysis, since their device for avoiding transitivity (rejecting the rule of conditional proof) does not in fact eliminate anomalous conclusions that can be drawn when both the premisses are taken as true. In sum, there appears to be no good reason to doubt thatif is transitive, that the antecedent of a conditional can be strengthened, and that the contrapositive can be inferred. And the rule of conditional proof does seem to capture a commonly accepted form of argument in support ofif-then statements.

9 citations