The Modal and Epistemic Arguments against the Invariance Criterion for Logical Terms (original) (raw)

The Modal and Epistemic Arguments Against the Invariance Criterion for Logical Terms (penultimate)

Journal of Philosophy, 2015

The essay discusses a recurrent criticism of the isomorphism-invariance criterion for logical terms, according to which the criterion pertains only to the extension of logical terms, and neglects the meaning, or the way the extension is fixed. A term, so claim the critics, can be invariant under isomorphisms and yet involve a contingent or a posteriori component in its meaning, thus compromising the necessity or apriority of logical truth and logical consequence. This essay shows that the arguments underlying the criticism are flawed since they rely on an invalid inference from the modal or epistemic status of statements in the metalanguage to that of statements in the object-language. The essay focuses on McCarthy’s version of the argument, but refers to Hanson and McGee’s versions as well.

The grounds for the model-theoretic account of the logical properties.

Notre Dame Journal of …, 1992

Quantificational accounts of logical truth and logical consequence aim to reduce these modal concepts to the nonmodal one of generality. A logical truth, for example, is said to be an instance of a "maximally general" statement, a statement whose terms other than variables are "logical constants." These accounts used to be the objects of severe criticism by philosophers like Ramsey and Wittgenstein. In recent work, Etchemendy has claimed that the currently standard model-theoretic account of the logical properties is a quantificational account and that it fails for reasons similar to the ones provided by Ramsey and Wittgenstein. He claims that it would fail even if it were propped up by a sensible account of what makes a term a logical constant. In this paper I examine to what extent the model-theoretic account is a quantificational one, and I defend it against Etchemendy's criticisms.

The undergeneration of permutation invariance as a criterion for logicality

Permutation invariance is often presented as the correct criterion for logicality. The basic idea is that one can demarcate the realm of logic by isolating specific entities -logical notions or constants -and that permutation invariance would provide a philosophically motivated and technically sophisticated criterion for what counts as a logical notion. The thesis of permutation invariance as a criterion for logicality has received considerable attention in the literature in recent decades, and much of the debate is developed against the background of ideas put forth by Tarski in a 1966 lecture (Tarski 1966/86). But as noted by Tarski himself in the lecture, the permutation invariance criterion yields a class of putative 'logical constants' that are essentially only sensitive to the number of elements in classes of individuals. Thus, to hold the permutation invariance thesis essentially amounts to limiting the scope of logic to quantificational phenomena, which is controversial at best and possibly simply wrong. In this paper, I argue that permutation invariance is a misguided approach to the nature of logic because it is not an adequate formal explanans for the informal notion of the generality of logic. In particular, I discuss some cases of undergeneration of the criterion, i.e. the fact that it excludes from the realm of logic operators that we have good reason to regard as logical, in particular some modal operators. approaches in this debate is based on the concept of permutation invariance. The main idea is that one can demarcate the realm of logic by isolating specific entities -logical notions/constants -and that permutation invariance would provide a philosophically motivated and technically sophisticated, precise criterion for what counts as a logical notion/constant. Thus, it has been argued that permutation invariance is the correct formal account of logicality. The debate has involved authors such as

Reassessing logical hylomorphism and the demarcation of logical constants

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions.

Logicality and Meaning

Review of Symbolic Logic, 2018

In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers.

Stalnaker on the Interaction of Modality with Quantification and Identity

Thomson and Byrne, 2006

0. Logic is sometimes conceived as metaphysically neutral, so that nothing controversial in metaphysics is logically valid. That conception devastates logic. Just about every putative principle of logic has been contested on metaphysical grounds. According to some, future contingencies violate the law of excluded middle; according to others, the set of all sets that are not members of themselves makes a contradiction true. Even the structural principle that chaining together valid arguments yields a valid argument has been rejected in response ...

Disagreement about logic (Inquiry, preprint)

Inquiry, 2019

What do we disagree about when we disagree about logic? On the face of it, classical and nonclassical logicians disagree about the laws of logic and the nature of logical properties. Yet, sometimes the parties are accused of talking past each other. The worry is that if the parties to the dispute do not mean the same thing with 'if', 'or', and 'not', they fail to have genuine disagreement about the laws in question. After the work of Quine, this objection against genuine disagreement about logic has been called the meaning-variance thesis. We argue that the meaning-variance thesis can be endorsed without blocking genuine disagreement. In fact, even the type of revisionism and nonapriorism championed by Quine turns out to be compatible with meaning-variance.

Some Clearer Reactions: Gauker on the Validity of Universal Instantiation

It is part of the logical orthodoxy that quantifiers are interdefinable and that the rules of Universal Instantiation (UI) and Existential Generalization (EG) hold or fail together. Christopher Gauker has presented some cases which seemingly undermine the validity of UI but nonetheless leave EG untouched, and has developed a very sophisticated theory to explain why this is so. In the process, he has rejected several attempts to explain the asymmetry, especially those aiming at saving the logical orthodoxy by showing what is wrong with the counterexamples to UI. In this paper I argue that some of those proposals are better grounded than Gauker thinks and that ultimately they should be preferred over his since they explain satisfactorily the apparent counterexamples.