Recovering a Kantian Analytic/Synthetic Distinction through Incompatibility
My dissertation seeks to recover a viable analytic/synthetic distinction that retains a distinctly Kantian heritage. It is formulated with distinctly metametaphysical intent, to be part of another philosophical project that Kant initiated: the critique of metaphysics. My account is formulated specifically with regard to its potential fruitfulness in future metametaphysical work delimiting the bounds of metaphysics, which itself can serve as a basis for advancing a philosophical proposal for avoiding metaphysics. To this end, the account of the divide I offer seeks to remain metaphysically agnostic: it attempts to stay neutral vis-à-vis competing metaphysical viewpoints and anti-metaphysical viewpoints so that it can form part of a mutually-acceptable portrait of the bounds of metaphysics to friends and foes of metaphysics alike. In my view, to take or treat a claim as analytic is to, at least implicitly, undertake a commitment to its being deducible merely from our commitments about object-general, non-localized incompatibility and entailments claims; to treat a claim as synthetic is, at least implicitly, to undertake an implicit commitment to its not being so deducible.
My account of the analytic is strongly tied to Kant’s original idea of conceptual containment and exclusion: incompatibilities articulate material and modally-robust relationships of mutual exclusion among claims, and incompatibility relations can also be used to define entailments, which articulate modally-robust and material relations of inclusion or containment. Furthermore, my account harkens back to a long neglected aspect of Kant’s divide between the analytic and synthetic. For Kant, concepts are irreducibly general or universal representations: there are no concepts of particulars or individuals; that role instead falls to intuitions. In my account just as in Kant’s, since the analytic tracks relations of conceptual containment and exclusion—relations which are modally robust—the analytic/synthetic division thus tracks this divide between general and particular sorts of representations. It is the characteristic sort of modally-robust generality (in contrast with particularity) that I take to be distinctive of the analytic. In contrast, the synthetic takes on distinctive aspects of Kant’s understanding of intuitions—in my view their localization or essential appeal to some “third thing” outside of conceptual relations of containment and exclusion. By emphasizing the semantic distinction between the modally robust generality and universality of the analytic as opposed to the particularity and locality of the synthetic, my account thus highlights a historical aspect of Kant’s divide that has regrettably been overlooked by the dominant tradition, especially when compared to the efforts devoted to understanding the divide in terms of the epistemological distinction, roughly, between (justification based on) interrogating our concepts versus interrogating the world, or the metaphysical distinction, roughly, between truth in virtue of meaning alone and truth in virtue of both meaning and the broader world.
The account of the analytic/synthetic divide I provide is cleaved in terms of alethically modal concepts which, traditionally, have been seen as metaphysically-loaded and hence problematic for my metametaphysical purposes. This is because the dominant philosophical tradition for understanding alethic modality rests its account on the metaphysically and epistemically fraught notion of a continuum of inter-accessible possible worlds. To avoid this, my account draws on resources found in Robert Brandom’s incompatibility semantics, which offers an alternative account of necessity and possibility in terms of the less-problematic notion of incompatibility. My appropriation of Brandom’s incompatibility semantics incorporates several changes. First, I reinterpret Brandom’s semantics using an intensional notion of schematic generality (as opposed to set theoretic and quantificational concepts), which helps me to clarify the semantic interdependence of general and particular therein and resolve several epistemological and methodological concerns. I also discuss the complicating factor of nonmonotonicity of inferences by reference to the Michael Thompson’s work on “natural-historical judgments,” showing how the generality and modality expressed in nonmonotonic, modally-sophisticated claims can fit within my revised understanding of incompatibility semantics and the analytic/synthetic divide. Finally, I modify Brandom’s incompatibility semantics by formally extending it to equal the expressive power of Kripke Semantics for modal logical systems, thereby rectifying formal and intuitive impoverishments of Brandom’s formalism. I do so by incorporating an analog of accessibility relations therein. I provide an interpretation of what accessibility relations, transposed into incompatibility semantics, can be taken to mean by invoking a broadly logical notion of meta-compatibility, and I provide a pragmatic explication of what linguistic practitioners must do in order to take or treat matters as meta-compatible.
 Object-general claims are those that are not objectless but rather are object indiscriminate: they hold of any objects within a certain class or range in a modally robust way but regardless of which particular object therein.
 For a claim to be localized is for its semantics to rest upon indexical, deixic, or otherwise non-object-general reference.
 As Robert Brandom shows in his book, Between Saying and Doing: Towards an Analytic Pragmatism, (Oxford: Oxford University Press, 2008).
 Michael Thompson, Life and Action: Elementary Structures of Practice and Practical Thought, (Cambridge, MA: Harvard University Press, 2008).