Skip to main content
Log in

Modality, invariance, and logical truth

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Conclusion

Let us sum up. We began with the question, “What is the interest of a model-theoretic definition of validity?” Model theoretic validity consists in truth under all reinterpretations of non-logical constants. In this paper, we have described for each necessity concept a corresponding modal invariance property. Exemplification of that property by the logical constants of a language leads to an explanation of the necessity, in the corresponding sense, of its valid sentences. I have fixed upon the epistemic modalities in characterizing the logical constants: to be a logical constant in the language of a population is to be invariant over a modality describing complete possible epistemic states of that population (or an idealized analogue thereof). The grounds for this characterization are these: (1) It leads, I believe, to an extensionally reasonable demarcation of the logical constants, including clear cases and excluding clear non-cases. It gives a principled criterion for deciding unclear cases. (2) It provides an analysis of the topic-neutrality of logic. (3) It leads to an explanation of the epistemic necessity of the logical truths in terms of the topic-neutrality of the logical constants.

All the same, it is reasonable to ask, even if the suggested demarcation of logic is extensionally correct, whether it can reasonably be expected to be fundamental. The epistemic invariance of an expression is a rather striking property, one which we should want to explain. What is missing, then, is an explanation of the distinguishing epistemic properties of the constants in terms of more fundamental properties involving their understanding and use. It would be these that properly define the nature, not just the extent, of logic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. McCarthyT.: ‘The Idea of a Logical Constant’, J. Phil. LXXVIII 9 (Sept., 1981): 499–523.

    Google Scholar 

  2. Montague, R.: ‘Pragmatics and Intensional Logic’, Synthese (1970): 68–94.

  3. MostowskiA.: ‘On a Generalization of Quantifiers’, Fundamenta Mathematicae 44 (1957): 12–36.

    Google Scholar 

  4. Tarski, A.: Logic, Semantics, Metamathematics, Oxford, 1956.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

McCarthy, T. Modality, invariance, and logical truth. J Philos Logic 16, 423–443 (1987). https://doi.org/10.1007/BF00431187

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00431187

Keywords

Navigation