The grounds for the model-theoretic account of the logical properties. (original) (raw)
Related papers
Some Arguments for the Operational Reading of Truth Expressions
Analiza i Egzystencja, 2013
The main question of our article is: What is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents to the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is the fact that it adequately represents how the words “true” and “truth” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths, and explains why they seem to be—in some sense—necessary sentences. Moreover, our operational reading of truth
Some Arguments For the Operational Reading of Truth Expressions (co-author: Jan Wawrzyniak)
The main question of our article is: what is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents of the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is the fact that it adequately represents how words “true” and “truth” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths and explains why they seem to be – in some sense – necessary sentences. Moreover, our operational reading of truth expressions dissolves problems arising from the belief that there is some specific property – truth. The fact that we reject that truth is a certain property does not mean that we deny that the concept of truth plays a very important role in our language, and hence in our life. We indicate that the concept of truth is inseparable from the concept of sentence and vice versa – it is impossible to explicate one of these concepts without an appeal to the other. Analiza i Egzystencja, 24 (2013), pp. 61-86
More Truths about Generic Truth∗
Genericity, 2012
In Pelletier and Asher (1997) we presented a modal conditional analysis of the semantic interpretation of characterizing generics (in the terminology of Krifka et al. 1995). Since that time there have been a number of advances to our understanding of this area:
Classical logic counts sentences such as ‘Alice is identical with Alice’ as logically true. A standard objection to classical logic is that Alice’s self-identity, for instance, is not a matter of logic because the identity of particular objects is not a matter of logic. For this reason, many philosophers argue that classical logic is not the right logic, and that it should be abandoned in favour of free logic — logic free of existential commitments with respect to singular terms. In most standard free log- ics, sentences such as ‘Alice is identical with Alice’ are not logically true. This paper argues that this objection from existential commitments is some- what superficial and that there is a deeper reason why ‘Alice is identical with Alice’ should not be considered a logical truth. Indeed, a key fundamental thought about the nature of logic is that a logical truth is true in virtue of its logical form. The fundamental problem I raise is that a sentence such as ‘Alice is identical with Alice’ appears to not even be true in virtue of its logical form. Thus this paper argues that given that such a sentence is not true in virtue of its logical form, it should not be counted as logically true. It moreover argues, on the same grounds, that even the sentences which free logicians regard as logically true shouldn’t be regarded as logically true. So in this sense free logic is no repair to classical logic.
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.
Quantificational Accounts and the Problem of Logical Consequence I
"Substitutional and interpretational accounts of logical consequence explicate it as truth-preservation in all cases, cases being construed either as admissible substitutional variants or admissible semantic interpretations. This series of three connected studies aims to examine the merits and demerits of “quantificational accounts” of this sort, focusing on seminal contributions of Bolzano, Russell, Tarski, Carnap, Quine and the standard model-theoretic approach. Though extremely influential in the tradition, quantificational accounts have received much critical attention, especially in the wake of Etchemendy 1990. I reconstruct the main objections, arguing that the model-theoretic account appears as the most promising of quantificational accounts vis-à-vis them. Finally, by way of responding to one allegedly devastating objection due to Kneale and Etchemendy, I explain that quantificational slogans do not by themselves capture all there is to logical properties, if not backed up by a plausible account of semantic structure and the specific contribution of logical elements to it. But proponents of the interpretational approach in model-theoretic style need not be paralysed, since they have such a semantic story at their disposal. This, in a nutshell, is my overall agenda. In the present study, I focus on the beginning of systematic theorizing of consequence in Aristotle‘s work, which contains the rudiments of both modal and quantificational accounts of logical consequence. It is pointed out, inter alia, that (1) there is no evidence for the claim that Aristotle would have subscribed to the reductionist spirit of the latter, and that (2) for a full-fledged quantificational approach we need to turn to Bolzano’s substitutional approach, whose motivation, structure and problems are explained in the second part of this study. "
Truth without Standard Models: some conceptual problems reloaded.
Journal of Applied Non-Classical Logics.
A theory of truth is usually demanded to be consistent, but ω- consistency is less frequently requested. Recently, Yatabe [21] has argued in favor of ω-inconsistent first-order theories, minimizing their odd consequences. In view of this fact, in this paper we present five arguments against ω-inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known ω-inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth based on L ukasiewicz infinitely-valued logic: PALT.
This concluding study devoted to quantificational accounts of consequence and related logical properties deals with the model-theoretic account (MTA). In response to objections questioning its intuitive adequacy, it is argued that MTA does not aim to analyse “the” alleged intuitive notion of consequence, but aims to formally reconstruct one specific semantic account, according to which valid arguments preserve truth in virtue of their logico-semantic structure and irrespectively of particular semantic values of the non-logical vocabulary. So conceived, MTA is arguably superior to any other quantificational account, being based on a principled account of the semantic structure and the specific contribution of logical elements to it.
Quantificational Accounts of Logical Consequence II: In the Footsteps of Bolzano
Quantificational accounts of logical consequence account for it in terms of truth-preservation in all cases – be it admissible substitutional variants or interpretations with respect to non-logical terms. In this second of my three connected studies devoted to the quantificational tradition, I set out to reconstruct the seminal contributions of Russell, Carnap, Tarski and Quine and evaluate them vis-à-vis some of the most pressing objections. This study also prepares the ground for my discussion of the standard model-theoretic account of consequence to be found in the concluding study.