Seoyeon Park

A sentence is logically true just in case it is true under every interpretation of its non-logical vocabulary. This account can be conceptually adequate only if its underlying conception of interpretation exhaustively ranges over all legitimate interpretations. I argue that neither the standard model-theoretic conception nor Volker Halbach's refined substitutional conception meets this demand. Models are restricted to set-sized domains, so they fail to secure interpretations too large to form a set. Halbach's substitutions deserve a more careful discussion. While it is far more difficult to pinpoint which interpretation they omit, two considerations tell against their exhaustiveness. First, a certain class of interpretations is not ensured to fall within the range of substitutions, as one of Halbach's own predicates furnishes an example. Second, any attempt to generalize over all substitutions runs into a Russell-style paradox, to which Halbach's response is unsatisfactory. This prompts a search for an alternative conception free of the restrictions borne by models and substitutions. I suggest that Tarski's early work supplies one.

Logical anti-realism is the view that logical truths answer to no features of mind-and-language-independent reality. Treating logical truths as fundamentally unlike ordinary and scientific truths, logical anti-realism requires a dualist metasemantics, where the meanings of logical expressions are grounded entirely in rules internal to language while those of others are grounded in causal connections to the external world. I develop what I call the Interlocking Problem: a dualist metasemantics is untenable whenever its two components are not both complete and coherent, failing to ensure that all meaningful expressions receive a cogent metasemantic account. I illustrate the problem by showing how it arises for Jared Warren’s conventionalist version of logical anti-realism. His systematic dualist metasemantics combines inferentialist metasemantics for logical terms with a causal metasemantics for empirical terms. Yet the Interlocking Problem undermines Warren’s dualism. First, it fails completeness since the meanings of some significant metaphysical terms remain underdetermined by either component. Second, it fails coherence in cases of overdetermination where its two components assign incompatible meanings to a single expression. I conclude by noting that the problems Warren faces are instances of a general structural worry for dualist metasemantics, and so represent a salient obstacle that any similar logical anti-realist view would have to overcome.

Kripke’s ‘The Question of Logic’ ignited a surge of interest in the Adoption Problem, a challenge to the coherence of adopting a special subset of logical principles. However, from an exegetical standpoint the fixation on the Adoption Problem risks overlooking the central message of Kripke’s paper. His text contains broad and unusually forceful commitments about the nature of logic that cannot be justified by any lesson one could draw from the Adoption Problem. Partly on this basis, I argue that Kripke in fact presents two distinct challenges: the well-known Adoption Problem and what I call the Interpretation Problem. The Interpretation Problem suggests that the idea of adopting a logic by choosing one among several formal systems is ultimately incoherent. In particular, Kripke provides reasons to think that one cannot so much as interpret formal systems of logic, in the sense that one cannot specify how the formal systems can guide reasoning, unless engaging in reasoning that prejudges matters in favor of a system conforming to that reasoning. It turns out that the Interpretation Problem has extensive implications for the nature of logic that provide support for Kripke’s strongest claims about it.

I argue that Kant’s conception of logic provides constructive justifications for Kripke’s bold claims about the nature of logic. Their shared view of logic sharply differs from Quinean Anti-Exceptionalism, which treats logic as part of our web of belief. Arguing against the Quinean view, Kripke adds two bold claims: (i) in logic informal thinking is indispensable; and (ii) logic is unique. Both claims remain unjustified since Kripke does not offer a constructive conception of logic. The missing justifications can be supplied by Kant’s conception of logic as a science of the form of thought. On this view, logic aims to articulate the constitutive rules for knowledge. Then informal thinking is indispensable because no formal system can even count as logical without being interpreted in light of informal thinking we have already employed, and logic cannot tolerate plurality because a different set of rules could not constitute knowledgeable thought as such.

My goal is to clarify Kant's conception of logic as self-knowledge of the understanding as to the mere form of thought, considering its methodological consequence: logic develops through mere reflection. Reflection is a function of the understanding that results in the concept of a common feature of various representations. I first examine what it means that logic is the science of the mere form of thought as such. There are two forms of thought that render thoughts with different types of unity. The first is the synthetic form that determines how a thought ought to relate to its object. The second is the analytic form that constitutes the way a thought ought to be related to each other. I propose that Kant’s logic employs the reflection on higher-order representations about thoughts, which are themselves representations of objects, with respect to their forms. Referring to Jäsche Logic, I outline the process of this higher-order reflection for logic. Reflection as to the synthetic form generates transcendental logic, and reflection as to the analytic form yields pure general logic. My account will reveal that these two kinds of reflection correspond to transcendental reflection and logical reflection presented in Amphiboly.