On the Substitutional Characterization of First-Order Logical Truth

McKeon, Matthew

doi:10.1080/01445340310001642093

Cited by 6 publications

(6 citation statements)

References 16 publications

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“…One line of criticism, voiced by Tarski (1936Tarski ( /1983 (against Carnap (1934(against Carnap ( /2000) and by Hinman, Kim and Stich (1968) (against Quine (1936(against Quine ( /76, 1954, is that a substitutional approach will count an intuitively invalid sentence as valid if there is a sufficient shortage in the stock of terms that we may substitute into the sentence. A simple example from McKeon (2004): we'll end up counting as valid the sentence '∀x∀y(FxMFy)' if all the predicates in our language, 'F' and all the rest, apply to everything; a substitution instance falsifying that sentence requires a predicate that applies to just some things.…”

Section: Technical Issues With Substitutional (And Interpretational) mentioning

confidence: 99%

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Why Is a Valid Inference a Good Inference?

Dogramaci

2015

Philos Phenomenol Research

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True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truthpreserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of 'case', and hence of 'validity': (i) the orthodox definition given in terms of interpretations or models, (ii) a metaphysical definition given in terms of possible worlds, and (iii) a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference.

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Section: Technical Issues With Substitutional (And Interpretational) mentioning

confidence: 99%

“…A solution is proposed by Berlinski and Gallin (1969) and McKeon (2004). They describe the same basic idea.…”

Section: Technical Issues With Substitutional (And Interpretational) mentioning

confidence: 99%

Why Is a Valid Inference a Good Inference?

Dogramaci

2015

Philos Phenomenol Research

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“…As it is not exactly clear what formal theory Quine had in mind for his account-if he had any-the discussion of his account of logical validity is complicated and entangled with sophisticated historical points. Many have attacked him [15,4,8,13], and some have tried to defend him, or at least to soothe the critics [2,19,7].It is common to view the substitutional account as an alternative to the model theoretic account, and yet when it comes to make it precise, people have often used model theory. For example, [2] developed one of the best versions of the substitutional account, which however is framed in model theory.…”

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confidence: 99%

Substitutional Validity for Modal Logic

Grossi

2023

Notre Dame J. Formal Logic

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In the substitutional framework, validity is truth under all substitutions of the non logical vocabulary. I develop a theory where the □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition. Philosophical Backbone and Context of this Work1.1 Simple truth vs truth in a model According to the substitutional account of logical consequence, an argument is logically valid if it preserves truth under all uniform substitutions of the non logical vocabulary. The substitutional account has a longstanding pedigree. 1 Quine is probably the main modern proponent and the target of most of the contemporary discussion, especially in his 'Philosophy of Logic'. As it is not exactly clear what formal theory Quine had in mind for his account-if he had any-the discussion of his account of logical validity is complicated and entangled with sophisticated historical points. Many have attacked him [15,4,8,13], and some have tried to defend him, or at least to soothe the critics [2,19,7].It is common to view the substitutional account as an alternative to the model theoretic account, and yet when it comes to make it precise, people have often used model theory. For example, [2] developed one of the best versions of the substitutional account, which however is framed in model theory. First, they argue that Quine's definition of logical truth is incomplete 'since "truth" must be relative to an interpreted language'. Then, they consider one specific model-what they call a 'Quine model'-and define a sentence to be logically true when true in that model, under all substitutions. Whilst their account answers many questions others have raised, it neglects the fact that the substitutional account does not need the scaffolding of model theory to work: it is really a genuine alternative. In their system, on the other hand, the substitutional account is not very different from model theory: all the semantic work is done exactly in the same way, what changes is only the definition of validity.What is the point of developing an alternative to model theory to frame substitutional validity? In model theory we define the concept of truth in a model. However,

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“…Williamson [31] and others have defended the view that these sentences are logical truths. McKeon [19] discusses the problem for Quine's account of substitutional validity. See also Wagner [30].…”

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confidence: 99%

Formal Notes on the Substitutional Analysis of Logical Consequence

Halbach¹

2020

Notre Dame J. Formal Logic

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Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: An argument is defined to be logically valid iff there is no substitution instance with true premisses and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: Logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or not. It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and thus model-theoretic consequence. Every modeltheoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely the homophonic interpretation that does not substitute anything. Applications to free logic, second-order logic, and theories and languages other than set theory are sketched.

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On the Substitutional Characterization of First-Order Logical Truth

Cited by 6 publications

References 16 publications

Why Is a Valid Inference a Good Inference?

Why Is a Valid Inference a Good Inference?

Substitutional Validity for Modal Logic

Formal Notes on the Substitutional Analysis of Logical Consequence

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