The Modal and Epistemic Arguments against the Invariance Criterion for Logical Terms

Sagi, Gil

doi:10.5840/jphil201511239

Cited by 6 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This creates a disconnect between adherents and critics. For discussions see, e.g., McGee (1996), Feferman (1999), Sagi (2015) and Griffiths and Paseau (2016).…”

Section: IVmentioning

confidence: 99%

Invariance as a basis for necessity and laws

Sher

2021

Philos Stud

View full text Add to dashboard Cite

Many philosophers are baffled by necessity. Humeans, in particular, are deeply disturbed by the idea of necessary laws of nature. In this paper I offer a systematic yet down to earth explanation of necessity and laws in terms of invariance. The type of invariance I employ for this purpose generalizes an invariance used in meta-logic. The main idea is that properties and relations in general have certain degrees of invariance, and some properties/relations have a stronger degree of invariance than others. The degrees of invariance of highly-invariant properties are associated with high degrees of necessity of laws governing/describing these properties, and this explains the necessity of such laws both in logic and in science. This non-mysterious explanation has rich ramifications for both fields, including the formality of logic and mathematics, the apparent conflict between the contingency of science and the necessity of its laws, the difference between logical-mathematical, physical, and biological laws/principles, the abstract character of laws, the applicability of logic and mathematics to science, scientific realism, and logical-mathematical realism.

show abstract

“…This creates a disconnect between adherents and critics. For discussions see, e.g., McGee (1996), Feferman (1999), Sagi (2015) and Griffiths and Paseau (2016).…”

Section: IVmentioning

confidence: 99%

Invariance as a basis for necessity and laws

Sher

2021

Philos Stud

View full text Add to dashboard Cite

show abstract

“…It is certainly not logically necessary, as we saw in Section 2.2, since the truth of CH requires the existence of sets that do not exist of logical necessity, but let's allow that it's mathematically necessary. 22 Hence:…”

Section: The Indeterminacy Of Chmentioning

confidence: 99%

“…In contrast, faced with cases such as unicorn-negation, it is open to the proponent of isomorphism invariance to emphasise the extensional nature of their project; unicorn-negation, after all, is coextensional with negation tout court. Gil Sagi [22] has recently taken this line: her strategy is to bite the bullet and defend the logical truth of U . One reason to deny the logical truth of U is its apparent contingency.…”

mentioning

confidence: 99%

Isomorphism Invariance and Overgeneration

Griffiths¹,

Paseau²

2016

Bull. symb. log

View full text Add to dashboard Cite

Abstract. The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of 'logical constant' which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider five possible precisifications of the overgeneration argument and find them all unconvincing.The standard approach to logical consequence in the modern literature is the post-Tarskian model-theoretic conception. On this conception, a sentence φ is a logical consequence of some set of sentences Γ just if every model of Γ is a model of φ. A model consists of a nonempty domain of objects and a valuation function that assigns semantic values to the nonlogical expressions of the language. As such, the standard approach relies on a distinction between logical and nonlogical expressions. It is striking, then, that there is little agreement over how this crucial distinction should be drawn. We defend the most natural supplement to the model-theoretic definition: isomorphism invariance.The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thoughts that logic is distinctively general or topic-neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of 'logical constant' which respects the intuitively clear cases, namely identity, the Boolean connectives and the universal and existential quantifiers-the logical constants of first-order logic with identity.Despite its attractions, isomorphism invariance faces a major recurring objection in the literature.

show abstract

“…Gil Sagi, in recent work, has criticized these arguments (Sagi 2015). Although Sagi's criticisms of this argument are instructive, there is nonetheless a way to understand McCarthy's and in particular,to understand (3)-that avoids Sagi's objections and which is compelling against versions of the invariance criterion (Sections 2.1, 4).…”

mentioning

confidence: 99%

Characterizing Invariance

Woods¹

2017

Ergo, an Open Access Journal of Philosophy

View full text Add to dashboard Cite

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.

show abstract

The Modal and Epistemic Arguments against the Invariance Criterion for Logical Terms

Cited by 6 publications

References 0 publications

Invariance as a basis for necessity and laws

Invariance as a basis for necessity and laws

Isomorphism Invariance and Overgeneration

Characterizing Invariance

Contact Info

Product

Resources

About