Michaela McSweeney

Dissertation Summary

In my dissertation, The Metaphysical Basis of Logic, I explore some territory at the intersection of metaphysics and the philosophy of logic and develop a novel approach to answering what I take to be the central question uniting these two areas of philosophy: Is there something about the world—and, specifically, the mind-independent world—that underpins logic? I argue against what I call logical anti-realism—the view that there is nothing about the mind-independent world that underpins logical truths. I argue for a form of logical realism—the view that there is something about the world, specifically, some logical structure, that underpins logic). But, I argue, our knowledge of this structure is necessarily obscured. We have to adopt a certain kind of epistemic humility about it. I point out, however, that this does not mean that we cannot make many true claims about it. I argue that we should think of our best theories of the world, which contain logic, as surrogates for the ideal fundamental theory of the world (the target theory)—which, I argue, we cannot state or access. Finally, I propose some ways to evaluate how good a candidate surrogate theory is at representing the target theory.

In chapter one, I give an argument against a specific realist view about the metaphysics of logic. The kind of realist view I target is one on which there is fundamental ontology or structure that the logical constants directly reflect. I argue that we can't adopt this view because it faces us with serious redundancy of fundamental ontology or structure, given that there are very small collections of logical constants that have the same expressive power as all the constants combined. I offer an argument against allowing for such redundancy at the fundamental level. Hence, if logical realism is true, it has to be something other than logical structure that resembles the logical constants that underpins our use of logic. I conclude this chapter by suggesting some ways forward for the logical realist, to be picked up again in chapter three.

In chapter two, I discuss a challenge to maintaining both logical anti-realism and metaphysical or scientific realism. Logical anti-realism has traditionally been conceived of as committing us to a more thoroughgoing philosophical anti-realism. I consider an argument that concludes that logical anti-realism leads to deflationism about a large number of metaphysical disputes. I conclude that, while largely successful, the argument has a faulty premise, which says that there are no constraints on the semantics for logical constants except for grammatical consistency and inferential adequacy. I argue that we should reject this premise. But rejecting this premise does not mean we can be full-fledged logical anti-realists. It commits us to something realist—for these constraints have to come from somewhere--but it does not commit us to thinking that the logical constants are either fundamental or referential.

In rejecting the premise, I appeal to the idea that logical vocabulary is special in that it is indispensible to stating our best theories of the world. Hence, there are special constraints placed on the semantics for logical vocabulary that are not true of non-referential (syncategorematic) terms that aren't required for stating our best theories of the world. I argue that these constraints actually put us in a good position with respect to debates over the semantics for logical constants. Inferentialist or proof-theoretic semantics for the constants—according to which the semantic content of the constants is entirely given by their inferential or proof-theoretic role—are appealing for many reasons, but they are a) cast as anti-realist accounts of the constants and b) face a long-familiar problem: what is it that makes constants like '&' meaningful and truth-preserving, but not constants like 'tonk'? I think that we can hold onto something very much like inferentialism for the constants while rejecting anti-realism and solving the tonk problem: by claiming that there are external constraints on the semantics for logical constants (I address the nature of these constraints in chapter four). I conclude by pointing out that all of this is consistent with, and indeed coheres well with, the argument I gave in chapter one.

In chapter three, I argue that we should adopt logical humility. Logical humility does not entail that we can't know anything at all about which of the candidate logical constants “track” reality in the right way. It instead entails that we can't know much about the underlying structure of reality itself. But indispensibility arguments for the logical constants can help us know quite a bit about which collections of logical concepts are better and worse tools for helping characterize reality. The argument I offer in chapter one does not conflict with this--it merely tells us that while various collections of logical constants are all adequate for characterizing reality, none of them 'carves nature at its joints': none of them allows us to represent the world in a way that perfectly mirrors the world itself.

In chapter four, I present an argument for thinking about logical constants in a similar way to that in which measurement theory categorizes quantitative properties like being five grams in mass. I explore how this would pan out in the case of logic. I claim that in both the mass case and the logic case, our best theories surrogatively represent our target (ideal/fundamental) theory: they represent the world well despite their structure not exactly matching the structure of the world. I discuss tools from measurement theory that help us determine, in the case of mass, when our theories are good surrogates. I point out that, while in the case of logic, we lack direct correlates of two keys of measurement theory—representation and uniqueness theorems—there are candidate proxies for them. I lay out some of these proxies for representation and uniqueness theorems.