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It is generally assumed that rigidity plays a key role in explaining the necessary a posteriori status of identity statements, both between proper names and between natural kind terms. However, while the notion of rigid designation is well defined for singular terms, there is no generally accepted definition of what it is for a general term to be rigid. In this paper I argue that the most common view, according to which rigid general terms are the ones which designate the same kind in all possible worlds, fails to deliver a posteriori necessities. I also present an alternative view, on which the work of explaining a posteriori necessities is not done by rigidity, but by a related metasemantic notion, which I call actuality - dependence.

We think that Kripke’s arguments that there are contingent a priori truths and that there are necessary a posteriori truths about named and essentially described entities fail. They fail for the reasons that there are ambiguities in each of the three eases. In the first ease, what is known apriori is not what is contingent. In the latter two cases, what is necessary or essential is not what is known a posteriori.

I present and defend a unified, non-reductive analysis of the a priori and a posteriori. It is a mistake to remove all epistemic conditions from the analysis of the a priori (as, for example, Alvin Goldman has recently suggested doing). We can keep epistemic conditions (like unrevisability) in the analysis as long as we insist that a priori and a posteriori justification admit of degrees. I recommend making the degree to which a belief’s justification is a priori or a posteriori solely dependent on the revisability relations that obtain among the faculties that deliver the belief and all other faculties.

The terms "a priori" and "a posteriori" refer primarily to how or on what basis a proposition might be known. A proposition is knowable a priori if it is knowable independently of experience. A proposition is knowable a posteriori if it is knowable on the basis of experience. The a priori/a posteriori distinction is epistemological and should not be confused with the metaphysical distinction between the necessary and the contingent or the semantical or logical distinction between the analytic and the synthetic. Two aspects of the a priori/a posteriori distinction require clarification: the conception of experience on which the distinction turns; and the sense in which a priori knowledge is independent of such experience. The latter gives rise to important questions regarding the positive basis of a priori knowledge.

I undertake a metaphysical investigation of Saul Kripke's modern classic, Naming and Necessity (1980). The general problem of my study may be expressed as follows: What is the metaphysical justification of the validity and existence of the pertinent classes of truths, the necessary a posteriori and the contingent a priori, according to the Kripke Paradigm? My approach is meant to disclose the logical and ontological principles underlying Kripke's arguments for the necessary a posteriori and the contingent a priori respectively. The results of my study are to a certain extent negative: They attempt to show that the classes of the necessary a posteriori and the contingent a priori statements cannot possibly be valid. If the general argument of this thesis is sound, then, on this ground, the realist conception of metaphysical essentialism is rejected. The positive thesis of this study is the articulation of certain ways to frame the necessary a posteriori and the contingent a priori which avoid the problems of realistic essentialism and which suggest a certain transcendental reading of modality. According to the Kripke Paradigm, any de dicto modal status (of a statement) derives ultimately from the de re modality inherent in the object designated, as the object is characterised by contingent and necessary properties on the ontological level. Thus, the Kripke Paradigm is primarily a thesis in de re realist essentialism. The final verdict in this study is that the Kripke Paradigm cannot sustain the realistic conception of de re metaphysical essentialism. If we should adopt a transcendental reading of modality, then certain portions of the Kripke Paradigm are valid. I do not delineate or possess the details of a comprehensive doctrine of transcendental metaphysic. Nevertheless, the observations I make should suffice to bring about the rough orientation of how I conceive the notion of transcendental modality.

The “scientific essentialist” doctrine asserts that the following are examples of a posteriori necessary identities: water is H2O; gold is the element with atomic number 79; and heat is the motion of molecules. Evidence in support of this assertion, however, is difficult to find. Both Hilary Putnam and Saul Kripke have argued convincingly for the existence of a posteriori necessities. Furthermore, Kripke has argued for the existence of a posteriori necessary identities in regard to a particular class of statements involving proper names. Neither Kripke nor Putnam, however, has argued convincingly that sentences containing syntactically complex terms or descriptive phrases can express a posteriori necessary identities. I will argue by way of a hypothetical example that ‘water is H2O’ does not express a necessary identity. My argument is unique in that it attacks the relevant sufficiency claim needed to underwrite this putative necessary identity.1 That is, even if we grant that water is necessarily composed of H2O, we should not accept that H2O necessarily forms water.

The New Semantics (NS) introduced by Kripke and Putnam is often thought to block antiphysicalist arguments that involve an inference from an explanatory gap to a failure of supervenience. But this “NS Rebuttal” depends upon two assumptions that are shown to be dubious. First, it assumes that mental-kind terms are among the kinds of terms to which NS analysis is properly applied. However, there are important differences in this regard between the behavior of notions like ‘pain’ and notions like ‘water’, as Kripke himself has argued. Second, even on the assumption that NS analysis is appropriate to mental-kind terms, it is further assumed that this would block the anti-physicalist premise that an abiding and principled explanatory gap would entail a failure of metaphysical supervenience. But the paradigm examples of NS analysis show nothing of the sort. What they show is that there are a posteriori necessities (e.g., “water contains hydrogen”) that cannot be inferred from the sense of natural kind terms. But they do not show that such necessities cannot be derived from an adequate scientific understanding of the phenomena in question. Indeed, such derivations are often available with kinds like water, but seem unavailable with mental kinds like ‘pain’ and ‘belief’.

David Chalmers' conceivability argument against physicalism relies on the entailment from a priori conceivability to metaphysical possibility. The a posteriori physicalist rejects this premise, but is consequently committed to psychophysical strong necessities. These don't fit into the Kripkean model of the necessary a posteriori, and they are therefore, according to Chalmers, problematic. But given semantic assumptions that are essential to the conceivability argument, there is reason to believe in microphysical strong necessities. This means that some of Chalmers' criticism is unwarranted, and the rest equally afflicts the dualist. Moreover, given that these assumptions are independently plausible, there's a general case to be made for the existence of strong necessities outside the psychophysical domain.

The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning , and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.

In this paper I will offer a novel understanding of a priori knowledge. My claim is that the sharp distinction that is usually made between a priori and a posteriori knowledge is groundless. It will be argued that a plausible understanding of a priori and a posteriori knowledge has to acknowledge that they are in a constant bootstrapping relationship. It is also crucial that we distinguish between a priori propositions that hold in the actual world and merely possible, non-actual a priori propositions, as we will see when considering cases like Euclidean geometry. Furthermore, contrary to what Kripke seems to suggest, a priori knowledge is intimately connected with metaphysical modality, indeed, grounded in it. The task of a priori reasoning, according to this account, is to delimit the space of metaphysically possible worlds in order for us to be able to determine what is actual.