A theory of the transfinite Tarskian hierarchy of languages is outlined and compared to a notion of partial truth by Kripke. It is shown that the hierarchy can be embedded into Kripke's minimal fixed point model. From this results on the expressive power of both approaches are obtained.

We consider a language containing partial predicates for subjective knowability and truth. For this language, inductive hierarchy rules are proposed which build up the extension and anti-extension of these partial predicates in stages. The logical interaction between the extension of the truth predicate and the anti-extension of the knowability predicate is investigated.

This paper responds to criticism of the Kripkean account of logical truth in first-order modal logic. The criticism, largely ignored in the literature, claims that when the box and diamond are interpreted as the logical modality operators, the Kripkean account is extensionally incorrect because it fails to reflect the fact that all sentences stating truths about what is logically possible are themselves logically necessary. I defend the Kripkean account by arguing that some true sentences about logical (...) possibility are not logically necessary. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

In the addenda to his Naming and Necessity, Kripke provides an account of how necessary aposteriori statements are possible. In such a case, there is an apriori general principle telling us that it is necessary if true at all. Though straightforward in its broad compass, this account faces two obvious questions in its application: in each case of necessary aposteriori statements, what is the underlying principle and how is it established apriori? I treat these questions with respect to theoretical identity (...) statements concerning chemical substances, such as ‘water is H2OH2O’. I argue that the general principle underlying the necessity of the statements is that if a chemical substance has a certain chemical composition, then it could not have had any other chemical composition. Then I defend the view that the principle is a conceptual truth by providing a novel derivation of it from the theoretical concept of chemical substance with a sufficient level of formal rigor. The logical principles required for the derivation will also be stated and defended. (shrink)

This paper is an attempt to present a Kripkean (Causal) picture of Reference where the cognitive content in fixing reference plays a vital role. It also points out that Kripke is not a pure causal theorist. By introducing Thomas Kuhn and his theory on vulnerability of the rigid designation, I have shown that there is a danger for causal theory of reference. However Kuhn’s argument fails to have an impact if a Knowledge aspect is augmented to Kripkean theory (...) of reference. This new causal theory of reference preserves the truth of the referential term in spite of the vulnerability of the rigid designation and problem of reference change. It can also adequately answer the question of theoretical terms reference failure. (shrink)

The article discusses Saul Kripke’s influential theories of a posteriori necessary truths and natural kinds. With respect to the statements of identity involving proper names, it is argued that although their truth is a posteriori and necessary in the specific sense of counterfactual invariance, this is of no significance for substantial philosophical issues beyond the philosophy of language, because this counterfactual invariance is a trivial consequence of the use of proper names as rigid designators. The case is made that (...) the expansion of the realm of necessary a posteriori truths to the statements of theoretical identity that involve “natural kind terms”, as well as the Kripkean essentialist theory of natural kinds, have no weighty argumentative support and fit badly both with science and language practice. This sets the stage for the development of an appropriately sophisticated “descriptivist” account of meaning and reference that would be better suited for a widened range of Kripke-Putnam style thought experiments. The general outlines of such a descriptivist account are provided. (shrink)

In this paper, the author shows how one can independently prove, within the theory of abstract objects, some of the most significant claims, hypotheses, and background assumptions found in Kripke's logical and philosophical work. Moreover, many of the semantic features of theory of abstract objects are consistent with Kripke's views — the successful representation, in the system, of the truth conditions and entailments of philosophically puzzling sentences of natural language validates certain Kripkean semantic claims about natural language.

By the lights of a central logical positivist thesis in modal epistemology, for every necessary truth that we know, we know it a priori and for every contingent truth that we know, we know it a posteriori. Kripke attacks on both flanks, arguing that we know necessary a posteriori truths and that we probably know contingent a priori truths. In a reflection of Kripke's confidence in his own arguments, the first of these Kripkean claims is far more (...) widely accepted than the second. Contrary to received opinion, the paper argues, the considerations Kripke adduces concerning truths purported to be necessary a posteriori do not disprove the logical positivist thesis that necessary truth and a priori truth are co-extensive. (shrink)

We present a semantics for a language that includes sentences that can talk about their own probabilities. This semantics applies a fixed point construction to possible world style structures. One feature of the construction is that some sentences only have their probability given as a range of values. We develop a corresponding axiomatic theory and show by a canonical model construction that it is complete in the presence of the ω-rule. By considering this semantics we argue that principles such as (...) introspection, which lead to paradoxical contradictions if naively formulated, should be expressed by using a truth predicate to do the job of quotation and disquotation and observe that in the case of introspection the principle is then consistent. (shrink)

In his influential Naming and Necessity lectures, Saul Kripke made new sense of modal statements: “Kant might have been a bachelor”, “Königsberg is necessarily identical with Kaliningrad”. Many took the notions he introduced-metaphysical necessity and rigid designation -- to herald new metaphysical issues and have important consequences. In fact, the Kripkean insight is at bottom semantic, rather than metaphysical: it is part of how proper names work that they purport to refer to individuals to whom modal properties can be (...) ascribed. We can see this by reflecting on analytic truths that ground modal claims like the two examples above. (shrink)

In this paper, I consider the criticism due to Hartry Field, John Pollack, William Hanson and James Hawthorne that the Kripkean requirement that a logical truth in modal logic be true at all possible worlds in _all quantified model structures is unmotivated and misses some logical truths. These authors do not see the basis for making the logical truth of a modal sentence turn on more than the model structure given by one reading of the modal operator(s) (...) which occur in the sentence. The primary goal here is to motivate the Kripkean requirement. (shrink)

Robert Brandom claims that the theory of meaning he presents in Making It Explicit is expressively complete—i.e., it successfully applies to the language in which the theory of meaning is formulated. He also endorses a broadly Kripkean approach to the liar paradox. I show that these two commitments are incompatible, and I survey several options for resolving the problem.

The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook, Cook, Schlenker, and Tourville and Cook via the addition of intensional operators such as ``is paradoxical''. In this extended framework we are (...) able to characterize the difference between sentences, such as the Liar and the Truth-teller, that receive the same semantic value in minimal fixed points yet seem to involve distinct semantic phenomena. (shrink)

The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap’s Revision Theory of Truth into the formal framework of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. (...) I want to do something similar replacing the Kripkean sets of grounded true sentences with revision-theoretic sets of stable true sentences. This can be done by defining a monotone operator through a variant of van Fraassen’s supervaluation scheme which is simply based on ω-length iterations of the Tarskian operator. Clearly, all virtues of Kripke-style theories are preserved, and we can also prove that the resulting set of “grounded” true sentences shares some nice features with the sets of stable true sentences which are provided by the usual ways of formalising revision. What is expected is that a clearer philosophical content could be associated to this way of doing revision; hopefully, a content directly linked with the insights underlying finite revision processes. (shrink)

We expand on the fixed point semantic approach of Kripke via the addition of two unary intensional operators: a paradoxicality operator Π where Π(Φ) is true at a fixed point if and only if Φ is paradoxical (i.e., if and only if Φ receives the third, non-classical value on all fixed points that extend the current fixed point), and an unbounded truth operator Υ⊤ where Υ⊤(Φ) is true at a fixed point if and only if any fixed point extending (...) the current fixed point can be extended to one on which Φ receives the value true. We prove a generalized version of Kripke’s fixed point theorem guaranteeing the existence of models of this new language, as well as an expressive completeness result. We conclude with an exploration of the significant improvements in expressive power that result from the addition of these new operators, and we precisely identify what still cannot be said on this intensional extension of the Kripkean framework. (shrink)

In Pantsar, an outline for an empirically feasible epistemological theory of arithmetic is presented. According to that theory, arithmetical knowledge is based on biological primitives but in the resulting empirical context develops an essentially a priori character. Such contextual a priori theory of arithmetical knowledge can explain two of the three characteristics that are usually associated with mathematical knowledge: that it appears to be a priori and objective. In this paper it is argued that it can also explain the third (...) one: why arithmetical knowledge appears to be necessary. A Kripkean analysis of necessity is used as an example to show that a proper analysis of the relevant possible worlds can explain arithmetical necessity in a sufficiently strong form. (shrink)