Date of Degree
Epistemology | Logic and Foundations of Mathematics | Metaphysics | Philosophy of Language
logical monism, philosophy of logic, philosophy of language, logical consequence, metaphysics, logic
This material in this dissertation will be divided into two parts. The first part is a preliminary discussion of vicious regress arguments in the philosophy of logic in the 20th century. The second part will focus on three different versions of logical pluralism, i.e., the view that there are many correct logics. In each case an argument will be developed to show that these versions of logical pluralism result in a vicious regress.
The material in part one will be divided into three chapters, and there are a few reasons for having a preliminary discussion of vicious regress arguments in philosophy of logic. Many vicious regress arguments have been raised in the past with the aim of making some kind of point in the philosophy of logic. Looking at some of these historical examples will serve multiple purposes. Primarily it will provide an opportunity to think carefully about the structure of vicious regress arguments. Vicious regress arguments can be distinguished in terms of what their underlying assumptions are and what they ultimately aim to demonstrate. The successfulness of a vicious regress argument will always be a function of these two things. But thinking about the structure of vicious regress arguments will also be beneficial for another reason. It will provide for a useful comparison to see how and in what way my own arguments relate to or differ from previous vicious regress arguments. Having cases to compare and contrast will help to clarify what assumptions I am making and where it will be important to reply to objections.
In chapter one, I'll look at a vicious regress that unfolds in Lewis Carroll's dialogue "What the Tortoise Said to Achilles?" (1895). I'll look at a few different ways that people have tried to extract a moral from Carroll's text, and I'll argue that our thinking about the moral should be guided by a prior question about how to understand the nature of the regress. I'll look at some different interpretations of the regress in Carroll, and I'll comment on why some interpretations may be more plausible than others.
Chapter two focuses on a vicious regress argument that is developed in Willard Van Orman Quine's "Truth by Convention" (1936). In some ways, it is easier to see what the intended moral of Quine's vicious regress argument is because he explicitly characterizes the view he aims to criticize. He aims to criticize a conventionalist thesis about logic where logical truths are fully explained in terms of linguistic conventions for logical connectives. I'll assume that Quine took himself to be criticizing a view held by Rudolph Carnap (1934/37). (I'll also note some views that challenge this assumption.) I won't focus on the exegetical question of whether Quine's interpretation of Carnap is accurate, but I will look at a few passages from the Carnap material that Quine cited in his critique. Whatever the case may be with Carnap's actual view, Quine distinguished between two forms of conventionalism about logic. He only intended his regress argument to apply to a version of conventionalism about logic where conventions are understood as being somehow explicit. Quine developed a separate argument for a version of the conventionalist thesis about logic where conventions are understood as implicit. I'll discuss both of these arguments and the operative notions of convention. Much of the discussion in this chapter will concern the nature of Quine's regress argument and the extent to which its successfulness depends on the notion of convention at play. Quine saw his regress argument as based on the same kind of considerations in Carroll's dialogue. I'll note that there are both epistemic and non-epistemic interpretations of Quine's regress argument, and I'll argue that there are reasons to prefer a non-epistemic reading. I'll also look at a view from Jared Warren who develops an implicit convention version of the conventionalist thesis about logic. Warren responds to the critique of implicit conventionalism about logic from Quine, and I'll provide some reasons for thinking that Warren's response isn't successful. I'll end the chapter by making two observations about versions of conventionalism about logic that employ a conception of conventions where they are understood as implicit. I'll suggest that these views don't obviously avoid vicious regress worries, and that they also face worries concerning underdetermination (although I'll discuss these latter two points in more detail in chapter five).
In chapter three, I'll look at an argument from Saul Kripke (1974a/74b) that is also supposed to be inspired by the regress considerations in Carroll's dialogue. Kripke's argument is directed towards Quine's own views regarding the idea that logical hypotheses can be empirically revised. I'll explain Quine's view about the empirical revision of logical hypotheses and Kripke's criticism. I'll also comment on some of the similarities and differences between Kripke's argument against Quine and Quine's argument against Carnap (largely to argue that they are based on the same kind of underlying point). I'll also argue that there are some reasons for thinking that Kripke's argument may be based on a misinterpretation of Quine. I'll look at the interpretation that is needed in order for Kripke's challenge to be successful, and I'll criticize some arguments in support of this interpretation from Romina Padro (2015).
The second part begins with chapter four where I will look at a version of logical pluralism from Jc Beall and Greg Restall (2006). Beall and Restall's version of logical pluralism is based on a case-theoretic analysis of logical validity. I'll give an exegesis of their view, and then I'll argue that it results in a vicious regress. I'll spend some time talking about how I understand the nature of vicious regresses in this chapter, and the discussion of vicious regresses will be informed by a view from John Passmore (1961). I'll give an exegesis of Passmore's view, and I'll also devote quite a bit of space to an objection and reply section. Part of the objection and reply section will contribute to making a case for the claim that the vicious regress point is a consideration in favor of logical monism. In particular, I'll respond to an objection claiming that there is an analogous regress for logical monism. Without responding to an objection like this, the ultimate objective of my thesis would be incomplete (since there is only a consideration in favor of logical monism if it doesn't face an analogous puzzle). Chapter four will end with a discussion of a view from Colin Caret (2017). Caret develops a view where the details of Beall and Restall's theory are articulated in terms of an indexical contextualist semantic theory for expressions like "logicaly valid". In chapters four and six, my use of theoretical labels like "indexical contextualist", "non-indexical contextualist", and "assessment sensitive" will follow the usage of MacFarlane (2014). Shapiro (2014) cites MacFarlane when explaining his usage of these technical terms, and Caret's view fits the definition of indexical contextualism that is given by MacFarlane (although Caret cites other sources when developing his view). I'll argue that a vicious regress can still be developed for a view like Caret's where the details of Beall and Restall's theory are understood in this way.
In the fifth chapter, I'll look at a version of logical pluralism from Hartry Field. Field's logical pluralism is developed by conjoining a normative conception of logical validity with a relativistic conception of normativity. I'll devote a good deal of space to explaining Field's normative conception of validity and how his form of relativism is understood. The main upshot of combining these two components is that it results in a view where validity attributions are understood as being somehow relative to policies. I'll argue that Field's view also results in a vicious regress, and I'll look at a few objections to my argument. The objections will mostly concern an issue about whether the regress argument only works for certain conceptions of policies (in particular whether they are conceived of as being somehow explicit). So the issues here will be analogous to some of the concerns that are discussed in chapter two regarding Quine's criticism of logical conventionalism. I'll also raise a separate puzzle for Field's view that is based on considerations of underdetermination. The details of this argument are informed by a criticism of dispositional analyses of rule-following from Kripke (1982). So I'll spend some time in this chapter looking at responses to Kripke's criticism from Tomoji Shogenji (1993) and Jared Warren (2018). I'll argue that neither of these accounts will help to dissolve the underdetermination issue. The points in this chapter (concerning regress and underdetermination) are also the ones I mentioned I would come back to in chapter two.
In the sixth chapter, I'll look at Stewart Shapiro's version of logical pluralism (2014). It is also based on a form of relativism, but it is distinctive in that it is developed in terms of considerations in the philosophy of mathematics. I'll provide an exegesis of Shapiro's view, and I'll argue that it also faces a vicious regress puzzle. It's worth noting that Shapiro gives a semantic characterization of his view. He gives a detailed description of his view about the meaning of logical connectives and expressions like "logically valid". He describes his view on the semantics of expressions like "logically valid" as a form of indexical contextualism (although there are some important qualifications to this claim which I'll discuss). I'll argue that a vicious regress can be developed for Shapiro's view even when the details of his indexical contextualist semantic theory are taken into consideration. I'll also argue that Shapiro's view faces an underdetermination puzzle. These points about underdetermination will be similar to what is discussed in the chapter on Field, but the argument will concern details that are specific to Shapiro's semantic theory. A key point of focus will be Shapiro's view of contexts and the role that contexts are supposed to play in his indexical contextualist theory of "logically valid".
Boyd, Daniel, "Logical Pluralism and Vicious Regresses" (2020). CUNY Academic Works.