The main application of canonical models are completeness proofs. Properties of the canonical model of K immediately imply completeness of K with respect to the class of all Kripke frames. This argument does not work for arbitrary L, because there is no guarantee that the underlying frame of the canonical model satisfies the frame conditions of L. We say that a formula or a set X of formulas is canonical with respect to a property P of Kripke frames, if X is valid in every frame which satisfies P, for any normal modal logic L which contains X, the underlying frame of the canonical model of L satisfies P. A union of canonical sets of formulas is itself canonical. It follows from the preceding discussion that any logic axiomatized by a canonical set of formulas is Kripke complete, and compact.
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Published: December 19, John P. Burgess, Kripke, Polity, , pp. The discussions of Kripke on modal epistemology, on Wittgenstein on rules, and on a posteriori necessities involving natural kinds -- to mention just three topics -- will be read with interest by anyone working in the relevant areas. The chapters concern, in order: names, necessity, identity, rules, belief and the mind. And although undeniably an admirer of Kripke, Burgess is also forthright in his criticisms, showing, for example, where the arguments in the published work are incomplete and require further elaboration.
There are, however, several cases where Burgess tracks a trend that reassesses the conventional Kripkean wisdom.
A particular area where this is so -- where Burgess says more than strictly needs to be said again, without necessarily endorsing a position -- is in the area of proper names and the semantics of belief.
Indeed, Jerrold Katz claimed that such a sentence is analytic, and argued on this basis that its sense structure contains a metalinguistic sense. These intuitions notwithstanding, metalinguistic theories have not fared well in responding to the modal argument.
I will set these approaches aside here, as Burgess omits discussion of them. Rather, I will consider a descendent of the "actualized descriptions" approach, due to Ora Matushansky While Burgess stops short of endorsing this approach, he takes seriously the suggestion that it provides a genuine alternative to the view, still dominant among philosophers if not linguists , that names are semantically simple expressions, lacking descriptive content.
One intriguing aspect of his proposal is that, while it provides a descriptivist alternative to the direct reference theory -- an approach that, although not endorsed by Kripke, provides the most natural implementation of his overall approach -- it also incorporates an important Kripkean element: namely, that the reference of a name is partly determined by its causal-historical pedigree.
One way to address the problem concerning modal profiles is to rigidify the description. This seems bizarre. The actualized-descriptions view assigns a proposition to the that-clause that we can assume to have the correct modal profile setting aside for the moment concerns about the uniqueness of the implied descriptions.
But this is deeply implausible. As Burgess notes, metalinguisticism thus forfeits any advantage it might have over the direct reference theory. To get the right truth conditions for 1 , the advocate of the metalinguistic approach would seem forced to resort to a direct-reference analysis, namely: 2 Consider on the one hand Hesperus, i. Here, the analysis is de re with respect to the "traditions of usage" of the two names. On HPN, sentences containing names in subject position make implicit, contextually-determined reference to a naming convention.
While not a decisive consideration against the proposal, it is certainly worth noting. A more pressing concern relates to the fact that the description piggybacks on a pre-existing naming convention.
It is hard to see how this could be so without the relevant name functioning as a name. Why is this a problem? To incorporate that convention into what is said seems to mislocate the relevant phenomenon. Moreover, one might ask: If linguistic conventions are part of the content here, why not elsewhere?
Since it is obvious that they do not, we need an answer to the question of why they enter into the analysis only of proper names. By the middle of the twentieth century the question of the mystery of modality had been re-conceived: the most pressing cases of putative synthetic a priori knowledge -- that is, the truths of arithmetic -- were reclassified as analytic.
All else was either analytic and thus a priori or synthetic a posteriori. Moreover, the analytic itself had been rendered entirely un-mysterious, since these were truths known on the basis of linguistic convention. This latter move was coupled with the assimilation of the necessary to the a priori, so that at one stroke the mysteries of necessity and a priority were solved. According to Kripke, the whole line of thought from Kant to Frege to Carnap went wrong at its very first step" 6.
As Burgess argues, this raises a mystery of its own. The question now is: "How is a posteriori knowledge of necessity possible? The "a posteriori" part is learning that the theorem is true via testimony. There thus remains a crucial, if diminished, role for a priori knowledge to play.
The remaining mystery is to discover the a priori principles at work here. There is little to go on here, beyond what has already been quoted. Burgess conjectures that Kripke had in mind that the principles are "analytic, ultimately resting on rules of language" 77 , basing this interpretation on the fact that, for Kripke, "philosophical analysis" ultimately grounds our ability to detect the sort of truth conditions that mathematical statements have — i.
However, it seems to me doubtful, given his general hostility to conventionalist views, that Kripke would invoke linguistic rules at this point. This, after all, would be a significant, and surprising, concession to the Carnapian. The setup of the paradox is swift and includes a subtle discussion of the nature of the meaning-constituting fact that is at the heart of the paradox. If there is such a fact, it is somehow determined by my past usage.
The problem here is that representing the rule involves other concepts -- counting, combining, and so on. I will here focus on ii. The standard objection to the dispositionalist analysis of meaning is that it fails to reflect the normativity of meaning. I should, at least in principle, be able to derive how I ought to respond from how I have responded. If so, the dispositional fact fails to ground the normativity constraint.
The summary of the skeptical solution is also crisp. The transition from discussion of the problem to discussion of the solution involves the recognition that the case of meaning ascription is not somehow special. This requires a "whole new theory of meaning", to which he then turns. To keep things manageable, Burgess considers the lineaments of such a theory only in application to meaning ascription. The rough idea is that meaning ascriptions no longer are seen as depicting or representing facts.
Rather, "an account of the meaning of a declarative sentence should include an account of its assertability conditions and its application" Burgess is not satisfied with this "solution". As he writes: the language-game of meaning ascriptions that has been given so far is too crude and only amounts to a first approximation. Recall that the dispositional account fails the normativity constraint, since I am unable to justify my answer to the above question based on an appeal to the truths characterizing my dispositions.
Whether or not one accepts this response, it is an important move in the overall dialectic. The fact that the move depends essentially on a Kripkean innovation however unrelated would make it worth mentioning in this context, if only to show the power of the insight. I have also omitted entirely, for reasons of space, discussion of the final chapter, on the philosophy of mind. While Kripke is not a systematic philosopher in the standard sense of that term, his writings are nonetheless illuminated by the careful, systematic exposition provided here.
Situations and Attitudes. Cambridge: MIT Press. Dummett, Michael. Frege: Philosophy of Language. London: Duckworth. Katz, Jerrold. Names without Bearers. Philosophical Review. Kripke, Saul.
Naming and Necessity. Cambridge: Harvard University Press. Wittgenstein on Rules and Private Language. Matushansky, Ora On the Linguistic Complexity of Proper Names.
Soames, Scott. In Ali A. Kazmi, ed. Meaning and Reference. Canadian Journal of Philosophy, Supplementary vol. Beyond Rigidity. New York: Oxford University Press. Wittgenstein, L. Philosophical Investigations, Trans. Oxford: Basil Blackwell. The typo in the statement of the formula on p. Matushansky makes use of a wealth of cross-linguistic data in arguing for this claim.
Recall that Kripke has us suppose that Peter, unaware that his beliefs concern a single person, believes that Paderewski the pianist is musically gifted but that Paderewski the statesman is not. Thus i and ii are both true: i. Peter believes that Paderewski is musically gifted. Peter disbelieves that Paderewski is musically gifted.
The main application of canonical models are completeness proofs. Properties of the canonical model of K immediately imply completeness of K with respect to the class of all Kripke frames. This argument does not work for arbitrary L, because there is no guarantee that the underlying frame of the canonical model satisfies the frame conditions of L. We say that a formula or a set X of formulas is canonical with respect to a property P of Kripke frames, if X is valid in every frame that satisfies P, for any normal modal logic L that contains X, the underlying frame of the canonical model of L satisfies P.