We ask, when is a property of a model a logical property? According to the so-called Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to model-theoretic characteristics of abstract logics in which the model class is definable. This results in a graded concept of logicality in the terminology of Sagi [46]. We investigate which characteristics of logics, such as variants of the Löwenheim–Skolem theorem, Completeness theorem, and absoluteness, are relevant from the (...) logicality point of view, continuing earlier work by Bonnay, Feferman, and Sagi. We suggest that a logic is the more logical the closer it is to first order logic. We also offer a refinement of the result of McGee that logical properties of models can be expressed in $L_{\infty \infty }$ if the expression is allowed to depend on the cardinality of the model, based on replacing $L_{\infty \infty }$ by a “tamer” logic. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is (...) often paired with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Dos̆en’s analysis of logical constants as punctuation marks is embraced, it is possible to show that all the modalities in the cube of normal modal logics are indeed logical constants. It will be proved that the display calculus for each displayable modality admits a purely structural presentation based on double-line rules which, following Dos̆en’s analysis, allows us to claim (...) that the corresponding modal operators are logical constants. (shrink)

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. (shrink)

The status of the equality predicate as a logical constant is problematic. In the paper we look at the problem from the proof-theoretic standpoint and survey several ways of treating equality in formal systems of different sorts. In particular, we focus on the framework of sequent calculus and examine equality in the light of criteria of logicality proposed by Hacking and Došen. Both attempts were formulated in terms of sequent calculus rules, although in the case of Došen it has (...) a nonstandard character. It will be shown that equality can be characterised in a way which satisfies Došen’s criteria of logicality. In the case of Hacking’s approach the fully satisfying result can be obtained only for languages with a nonempty, finite set of predicate constants other than equality. Otherwise, cut elimination theorem fails to hold. (shrink)

What is the relationship between syntax and logic? Is the former autonomous and independent of the latter? If it is not, what kind of logic syntax interfaces with? These questions are not unheard of, having been around for quite some time, along with different answers. In the generative tradition, for example, logic cannot provide a model for linguistic behaviour. Conversely, according to the logicality of language hypothesis logical considerations are relevant to syntactic formation and explain the ungrammaticality of certain (...) constructions. This note offers a brief overview of the logicality of language hypothesis and proposes new evidence that seems to indicate that accepting the said hypothesis does not necessarily require assuming a “natural” logic. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

In this paper we focus on the logicality of language, i.e. the idea that the language system contains a deductive device to exclude analytic constructions. Puzzling evidence for the logicality of language comes from acceptable contradictions and tautologies. The standard response in the literature involves assuming that the language system only accesses analyticities that are due to skeletons as opposed to standard logical forms. In this paper we submit evidence in support of alternative accounts of logicality, which (...) reject the stipulation of a natural logic and assume instead the meaning modulation of nonlogical terms. (shrink)

Is there a relation of logical consequence in natural language? Logicality, in the philosophical literature, has been conceived of as a restrictive phenomenon that is at odds with the unbridled richness and complexity of natural language. This article claims that there is a relation of logical consequence in natural language, and moreover, that it is the subject matter of the bulk of current theories of formal semantics. I employ the framework of _semantic constraints_ (Sagi in Log Anal 57(227):259–276, 2014), (...) which generalizes the Tarskian definition of logical consequence. I apply the widely accepted criterion of invariance under isomorphisms (Sher in J. Symb Log 61(2):653–686, 1996) generalized to the framework of semantic constraints (Sagi in Bull Symb Log 28(1):104–132, 2022b), combined with a theory of Glanzberg (in Metasemantics: new essays on the foundations of meaning, 2014) to delineate the relation of logical consequence in natural language. (shrink)

I argue that there is tension in Wittgenstein’s position on trivialities (i.e. tautologies and contradictions) in the Tractatus, as it contains the following claims: (A) sentences are pictures; (B) trivialties are not pictures; (C) trivialities are sentences. A and B follow from the “picture theory” of language which Wittgenstein proposes, while C contradicts it. I discuss a way to resolve this tension in light of Logicality, a hypothesis recently developed in linguistic research. Logicality states that trivialities are excluded (...) by the grammar, and that under the right analysis sentences which look trivial are in fact contingent. The tools necessary to support Logicality, I submit, were not available to Wittgenstein at the time, which explains his commitment to C. I end the paper by commenting on some points of contact between analytic philosophy and the generative enterprise in linguistics which are brought into relief by the discussion. (shrink)

The Editors express their gratitude and appreciation to the indi-viduals listed below who served as referees for Informal Logic for Volumes 31 (2011) and 32 (2012).

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the (...) invariance criterion is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force. (shrink)

Various attempts at demarcating logic were undertaken, many of them based on specific understanding of how logical knowledge is formal and not material. MacFarlane has persuasively shown that general idea of formality of logic can be understood in various ways. I take two of the accounts of formality, namely the requirement of conservativity and the requirement of schematicity of logical vocabulary, into consideration as promising candidates to make the all too unclear notion of formality more precise and study to what (...) degree they could be considered as either necessary or sufficient conditions for logicality of some piece of vocabulary. Finding both notion unsatisfactory, as they stand, I propose combining them and envisage a hierarchy of logicality of expressions of a given language. Such a hierarchy is complicated and not linear, yet still offers a valuable explication of both the range and pragmatic significance of logic, if we combine it with logical expressivism. (shrink)

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality. In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, (...) the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality. (shrink)

Deflationism about truth describes truth as a logical notion. In the present paper, I explore the implication of the alleged logicality of truth from the perspective of axiomatic theories of truth, and argue that the deflationist doctrine of the logicality of truth gives rise to two types of self-undermining arguments against deflationism, which I call the conservativeness argument from logicality and the topic-neutrality argument.

This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a proposal in response to one of those critiques via homomorphism invariance. That has quite divergent characterization results (...) depending on its formulation, one in terms of FOL, the other by Bonnay in terms of L∞,∞, both without equality. From that we move on to a survey of Bonnay’s work on similarity relations between structures and his results that single out invariance with respect to potential isomorphism among all such. Turning to the critique that calls for sameness of meaning of a logical operation across domains, the paper continues with a result showing that the isomorphism invariant operations that are absolutely definable with respect to KPU−Inf are exactly those definable in full FOL; this makes use of an old theorem of Manders. The concluding section is devoted to a critical discussion of the arguments for set-theoretical criteria for logicality. (shrink)

This note follows up an earlier paper in which a possibility of defining logical constants within abstract logical frameworks was discussed, by using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality. In the present note, this approach is applied to the discussion on logicality of generalized quantifiers. It is demonstrated that generalized quantifiers are logical constants by this criterion.

Ontological monists hold that there is only one way of being, while ontological pluralists hold that there are many; for example, concrete objects like tables and chairs exist in a different way from abstract objects like numbers and sets. Correspondingly, the monist will want the familiar existential quantifier as a primitive logical constant, whereas the pluralist will want distinct ones, such as for abstract and concrete existence. In this paper, we consider how the debate between the monist and pluralist relates (...) to the standard test for logicality. We deploy this test and show that it favors the monist. (shrink)