Upshots for Other Debates

This chapter explores and draws out the consequences of both the dualist view of rationality defended in Part I and the theory of structural rationality defended in Part II for a series of standing debates in (meta)ethics and epistemology—including debates about moral rationalism, rational choice theory, higher-order evidence, the normativity of logic, epistemic permissivism, and conditionalization. It also considers and criticizes some popular ways of trying to account for the existence and force of coherence requirements in the formally inclined philosophical literature—namely, Dutch book and money pump arguments and accuracy dominance arguments.

Logical aliens and where to find them

This paper is concerned with Frege’s logical aliens argument against psychologism in logic. The paper argues that this argument becomes too radical in the context of current philosophy in logic. The possible answer to Frege’s argument could be inspirited by the philosophical ideas of later Wittgenstein: we play different language games, and some of them are logical games. However, different people have different criteria of certainty and not all of them can play logical games. This gives new comprehension of the normativity of logic that shows that there are no logical aliens in absolute sense. This view can give in turn a new understanding of what rationality is and show why logic and psychology should interact.

Logical Conventionalism

This chapter argues that logical truth, validity, and necessity in any language can be fully explained in terms of the language’s linguistic conventions. More particularly, it is demonstrated that unrestricted logical inferentialism is a version of logical conventionalism by arguing for conventionalism in detail and answering various objections involving the role of metasemantic principles and semantic completeness in the conventionalist argument. The chapter then discusses how this account relates to the deflationist accounts offered by Field and others, before turning to the metaphysics and normativity of logic, which it discusses on conventionalist grounds. Overall, this chapter shows that conventionalism leads to a naturalistically acceptable and philosophically plausible theory of logic.

The Collapse Argument Reconsidered

According to Beall and Restall’s logical pluralism, classical logic, relevant logic, and intuitionistic logic are all correct. On this version of logical pluralism, logic is considered to be normative, in the sense that someone who accepts the truth of the premises of a valid argument, is bound to accept the conclusion. So-called collapse arguments are designed to show the incompatibility of the simultaneous acceptance of logical pluralism and the normativity of logic. Caret, however, by proposing logical contextualism, and Blake-Turner and Russell by proposing telic pluralism, have sought to nullify the collapse problem. In the present article, after setting out these two approaches to the collapse problem, we argue that by using the concept of the ‘rationality of beliefs’ in order to frame the canonical purpose of logic, it can be demonstrated that if logical contextualism and telic pluralism are considered as philosophically significant logical pluralisms, a refined version of the collapse argument is still a threat for both of these kinds of logical pluralism.

Non-Normative Logical Pluralism and the Revenge of the Normativity Objection

Logical pluralism is the view that there is more than one correct logic. Most logical pluralists think that logic is normative in the sense that you make a mistake if you accept the premisses of a valid argument but reject its conclusion. Some authors have argued that this combination is self-undermining: Suppose that $\mathcal {L}_{1}$ and $\mathcal {L}_{2}$ are correct logics that coincide except for the argument from Γ to ϕ, which is valid in $\mathcal {L}_{1}$ but invalid in $\mathcal {L}_{2}$. If you accept all sentences in Γ, then, by normativity, you make a mistake if you reject ϕ. In order to avoid mistakes, you should accept ϕ or suspend judgment about ϕ. Both options are problematic for pluralism. Can pluralists avoid this worry by rejecting the normativity of logic? I argue that they cannot. All else being equal, the argument goes through even if logic is not normative.