I spent some time in the departure lounge of Calgary airport on Friday, with Agustin “the Mexican Multiplier” Rayo and JC Beall, and JC mentioned how annoying he found it that some philosophers used the expressions “philosophical logic” and “philosophy of logic” interchangably. In fact, he thought he might write something up about it and try to get people to take notice. Not being one to stomp on a worthy cause, I asked him whether he’d let me post such a thing to a blog. He agreed, and so I give you JC’s Column (an occasional series?) Reform or perish…

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Terminological Theme: Philosophical Logic, Philosophy of Logic, and Formal Philosophy.

There’s reason to think that confusion exists over the terminology of “philosophical logic” and “philosophy of logic”. It would do the profession — and, perhaps, aspiring graduate students — well to have uniform terminology. While terminological differences certainly exist across the English-speaking countries (e.g., in parts of the UK, “philosophical logic” is often synonymous with “philosophy of logic”, though not so in Oz), here is a fairly standard — though admittedly (perhaps perforce) vague — classification, one that, if broadly adopted, would at least diminish some of the confusion.

A. Formal Philosophy: formal (mathematical) methods used in the service of philosophy.

(This comprises a lot, including philosophical logic, some areas of mathematical logic, decision theory, what Branden calls “formal epistemology”, some areas of foundations of mathematics, some incarnations of philosophy of logic, some incarnations of philosophy of language, and much more. Similarly, some work in metaphysics — particularly, formal ontology, formal mereology, etc. — would certainly fall under this banner. So, this category is perhaps the broadest category, but it’s worth including here. What is crucial is that formal, mathematical methods — as opposed to just using symbols as abbreviations, etc. (!) — is essential.)

B. Philosophical Logic: formal logic (usually, applied maths) in the service of philosophy; in particular, a formal account of **consequence** for some philosophically interesting fragment of discourse.

[If we take Logic to be concerned with **consequence**, then philosophical logic aims to specify — in a formal, precise way — the consequence relation over some philosophically significant fragment of our language. (Usually, this is done by constructing a formal “model language”, and proposing that the logic of the target “real language” is relevantly like **that**.) Usually, philosophical logic overlaps a lot with formal semantics, but may often be motivated more by philosophical concerns than by linguistic data. Work on formal truth theories — i.e., specifying the logic of truth — is a familiar example of work in philosophical logic, as are the familiar modal and many-valued accounts of various expressions, and similarly concerns about ‘absolute generality’ and the **consequence** relation governing such quantification, and much, much else. What is essential, as above, is a specification of a given **consequence** relation for the target, philosophically interesting phenomenon. Whether the consequence relation is specified “semantically”, via models, or proof-theoretically is not critical — although the former might often prove to be heuristically better in philosophy.]

C. Philosophy of Logic: philosophy motivated by Logic; philosophical issues arising out of a given, specified logic (or family of logics).

[While competence in (formal) logic is often a prerequisite of good philosophy of logic, no formal logic or, for that matter, formal methods need be involved in doing philosophy of logic. Of course, philosophy of logic often overlaps with philosophy of language — as with many areas of philosophy. The point is that philosophy of logic, while its target **may** be mathematical or formal, needn’t be an instance of either philosophical logic — which essentially involves formal methods — or, more broadly, formal methods. A lot of work on “nature of truth” might be classified as philosophy of logic (though much of it probably isn’t motivated by logic, and so shouldn’t be so classified), and similarly for “nature of worlds” etc. Whether the classification is appropriate depends, in part, on the given project — e.g., whether, as with Quine and Lewis, one is directly examining the commitments of a particular logical theory, as opposed to merely reflecting on “intuitions” concerning notions that are often thought to be logically significant. The point, again, is just that philosophy of logic is a distinct enterprise from philosophical logic, each requiring very different areas of competence, and each targeted at different aims.]

It would be useful if the profession, in general, but especially **practitioners** adopted terminology along the above lines. Of course, there’s still room for confusion, and the foregoing hardly cuts precise joints. It might be useful to discuss refinements to the above terminological constraints.

One more — just for those who might be wondering:

D. Mathematical Logic: formal logic in the service of (usually classical!) mathematics, as well various subfields of mathematics. (E.g., standard limitative theorems and classical metatheory is mathematical logic, as is reverse mathematics, many aspects of category theory, many aspects of set theory, areas of abstract algebra, areas of recursion theory, and so on. Mathematicians need have no interest in philosophy to engage in such areas, in contrast with the philosophical logician who is driven to use “mathematical methods” in an effort to clarify the consequence relation of some philosophically interesting “discourse”. There’s more to be said here, but this is chiefly a post about A, B, and C.)

- One note: it may well be that anyone talented in B is interested in C, but it hardly follows that one who is talented in B is talented in C. Similarly, one who is talented in C may well have little talent or interest in B. My hunch is that, on the whole, those who do B (or do it well) are usually talented in C. It’s unclear whether those with a talent in D are naturals for B or C — or A, for that matter — but one can think of excellent philosophers who also engaged directly in D. (The obvious such folks were also good at A, B, and C, as well as D. Russell comes to mind, as does Kripke, but there are others.)

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