Our tutorial course in the philosophy of logic focuses on the following question. Is there one correct foundational logic (logical monism) or more than one (logical pluralism)? The material we shall present is largely drawn from Part I of our book One True Logic, to be published by Oxford University Press in spring 2022. The course presupposes logical and philosophical experience but no prior exposure to this particular debate.

There are countless many logics on offer, which can be investigated in a mathematical spirit, in the way that mathematicians investigate many different geometries. A foundational logic, roughly, aims to capture natural-language consequence. Determining what the correct such logic is, or such logics are, is the task of the applied logician. Like the physicist who wishes to investigate which of the many possible geometries, investigated by mathematicians, is the actual one (or which are compatible with the laws of nature), the applied logician wishes to know which of the many available logics is the correct foundational one(s). The question is whether there is one such logic or more than one.

In the first session, we consider the intuitive features of logical consequence. Virtually everyone accepts that logical consequence involves truth-preservation and some further properties. What these further properties are, though, is the subject of much disagreement. The most prominent ones are necessity and formality. We will argue that there is significant disagreement about the importance of these properties for logical consequence. The disagreement only multiplies when we consider other features such as normativity, relevance or a priori knowability. We sketch a way forward in light of this disagreement.

In the second session, we show how to define the notion of a correct foundational logic. This definition makes crucial use of the notion of formalisation, which we clarify. Logical monists claim that there is one such while logical pluralists maintain that there are many. We define all these claims and clarify their relations.

In the third session, we offer a metalogical argument against any version of pluralism proper. If a logical pluralist is to engage in metalogical reasoning, what logic should they use? We shall show that there is no good answer for the logical pluralist.

References

Preliminary Reading

None required, as we will introduce and explain the ideas as we go along. For those who wish to read ahead, the following might be useful.

First Session

> O. Griffiths (2013), ‘Problems for Logical Pluralism’, History and Philosophy of Logic 34, pp. 170–182.

Second Session

> A.C. Paseau (2019), ‘A Measure of Inferential-Role Preservation’, Synthese 196, pp. 2621–42.

> A.C. Paseau (2021), ‘Propositionalism’, The Journal of Philosophy 118, pp. 430–449.

Third Session

> Part I (chapters 1 to 3) of Jc Beall and G. Restall (2006), Logical Pluralism, Oxford University Press.

> O. Griffiths and A.C. Paseau, ‘The Instability of Logical Pluralism’. Please email one of us to get hold of a copy of this ms.