The Concept of Logical Consequence

Hanson, William H.

doi:10.2307/2998398

Cited by 76 publications

(30 citation statements)

References 17 publications

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“…One might reply that even if an existent infinity of individuals is metaphysically necessary, it is nevertheless logically possible for there to be finitely many individuals and in such a case what is conditionally valid and what is intuitively valid will diverge. But this suffices to show that conditional accounts miss the modal feature of validity only if conjoined with some story about logical possibility according to which even though an existent infinity is metaphysically necessary, the world could logically have turned out so that there were just n individuals, for each n. But Etchemendy does not provide such a story, and it is rejected by other critics of conditional accounts (e.g., Hanson 1997). That Etchemendy's case for premise (2) is incomplete at best and problematic at worse is not reason for thinking that premise (2) is false.…”

Section: A Criticism Of Conditional Accounts Of Validitymentioning

confidence: 91%

“…This view is not uncommon. 4 The rationale behind premise (2) can be drawn from Etchemendy's view that because the extensions of the ordinary, informal logical concepts are not determined 2 Critics of the model-theoretic account qua conditional account include Kneale (1961), Field (1989Field ( , 1991, and Hanson (1997), among others. 3 This borrows from W.D.…”

Section: A Criticism Of Conditional Accounts Of Validitymentioning

confidence: 99%

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A plea for logical objects

McKeon

2008

Synthese

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An account of validity that makes what is invalid conditional on how many individuals there are is what I call a conditional account of validity. Here I defend conditional accounts against a criticism derived from Etchemendy's well-known criticism of the model-theoretic analysis of validity. The criticism is essentially that knowledge of the size of the universe is non-logical and so by making knowledge of the extension of validity depend on knowledge of how many individuals there are, conditional accounts fail to reflect that the former knowledge is basic, i.e., independent of knowledge derived from other sciences. Appealing to Russell's pre-Principia logic, I defend conditional accounts against this criticism by sketching a rationale for thinking that there are infinitely many logical objects.

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Section: A Criticism Of Conditional Accounts Of Validitymentioning

confidence: 91%

Section: A Criticism Of Conditional Accounts Of Validitymentioning

confidence: 99%

A plea for logical objects

McKeon

2008

Synthese

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“…Timothy McCarthy (1981) and William Hanson (1997) have offered compelling arguments along these lines against the invariance criterion when used as an account of the logicality of expressions (in the way described above).…”

Section: Invariance and Meaningmentioning

confidence: 99%

“…Logical expressions, intuitively and traditionally, should yield truths which are necessary (Hanson 1997). The necessity of logical truths is, presumably, supposed to be a consequence of the insensitivity of logical expressions to the natures of objects they are applied to.…”

Section: Contingency and Invariancementioning

confidence: 99%

Characterizing Invariance

Woods¹

2017

Ergo, an Open Access Journal of Philosophy

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I argue that in order to apply the most common type of criteria for logicality, invariance criteria, to natural language, we need to consider both invariance of content-modeled by functions from contexts into extensions-and invariance of character-modeled, à la Kaplan, by functions from contexts of use into contents. Logical expressions should be invariant in both senses. If we do not require this, then old objections due to Timothy McCarthy and William Hanson, suitably modified, demonstrate that content invariant expressions can display intuitive marks of non-logicality. If we do require this, we neatly avoid these objections while also managing to demonstrate desirable connections of logicality to necessity. The resulting view is more adequate as a demarcation of the logical expressions of natural language.

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“…From the point of view of the present foundational project, whose focus is theoretical, whose concerns are epistemic, and whose interest is in the construction of a logical system fulfilling certain theoretical epistemic roles, these criticisms are largely irrelevant.38 38From other perspectives, of course, they might be relevant. For examples of criticisms in which linguistic intuitions play a significant role, see, e.g., Hanson [1997] and Gómez-Torrente [2002]. For responses see Sher [2001], [2003].…”

Section: Preservation Of Truthmentioning

confidence: 99%

The foundational problem of logic

Sher¹

2013

Bull. symb. log

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Abstract. The construction of a systematic philosophical foundation for logic is a notoriously difficult problem. In Part One I suggest that the problem is in large part methodological, having to do with the common philosophical conception of "providing a foundation". I offer an alternative to the common methodology which combines a strong foundational requirement (veridical justification) with the use of non-traditional, holistic tools to achieve this result. In Part Two I delineate an outline of a foundation for logic, employing the new methodology. The outline is based on an investigation of why logic requires a veridical justification, i.e., a justification which involves the world and not just the mind, and what features or aspect of the world logic is grounded in. Logic, the investigation suggests, is grounded in the formal aspect of reality, and the outline proposes an account of this aspect, the way it both constrains and enables logic (gives rise to logical truths and consequences), logic's role in our overall system of knowledge, the relation between logic and mathematics, the normativity of logic, the characteristic traits of logic, and error and revision in logic. Association for Symbolic LogicIt is an interesting fact that, with a small number of exceptions, a systematic philosophical foundation for logic, a foundation for logic rather than for mathematics or language, has rarely been attempted.1 In this essay I aim to understand why this is the case, utilize this understanding to develop an appropriate foundational methodology, and use this methodology to construct an outline of a philosophical foundation for logic. The notion of a philosophical foundation will be clear to some readers, but due to the diverse readership of this journal it would be useful to briefly spell out and motivate the kind of philosophical foundation I have in mind.Received October 8, 2010. Acknowledgments: An earlier version of this paper was presented at a meeting of the Southern California History and Philosophy of Logic and Mathematics Group. I would like to thank the participants for stimulating comments. I am also very thankful to anonymous reviewers of this journal. Special thanks are due to two editors of the journal for extremely helpful comments that led to a considerable improvement of the paper. Finally, I am greatly thankful to Peter Sher for important suggestions and support.*One recent exception is Maddy [2007, Part III], which differs from the present attempt in being thoroughly naturalistic. Another psychologically oriented attempt is Hanna [2006]. Due to limitations of space and in accordance with my constructive goal, I will limit comparisons and polemics to a minimum. 14...

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The Concept of Logical Consequence

Cited by 76 publications

References 17 publications

A plea for logical objects

A plea for logical objects

Characterizing Invariance

The foundational problem of logic

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