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…

———————————————————

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.)

=======

At a guess, us Brits are trying to stay somewhat true to Russell’s intentions when he introduced the term ‘philosophical logic’, and Russell’s notion doesn’t seem to fit neatly into either JC’s B or C (though both B and C both outstrip Russell’s notion greatly).

In his comment over at logicandlangauge.net Ole Thomassen Hjortland has suggested calling these nomenclature conventions “the JC standard”. Incidentally, I see from his website that Ole’s supervisor is my old logic teacher from when I was an undergraduate – Stephen Read.

The usage suggested here doesn’t seem fully consistent with what David Lewis meant by “Philosophical Logic”. The essays in his

Papers in Philosophical Logicare not exclusively concerned with providing a formal account of consequence—the essence of philosophical logic according to C. Since Lewis was Lewis, his usage carries considerable authority—both in terms of reflecting actual usage and in recommending how the expression ought to be used. So I’d hesitate before revising the meaning of the label in the way JC suggests.Following the title of Grayling’s book (An introduction to Philosophical Logic), there seems to be a use of ‘philosophical logic’ which is broader than any of the above. In fact, Grayling’s subject matter seems to inflate JC’s C. But, as JC, I’m not at all comfortable with that use.

On the other hand, the three classic “textbooks” on

philosophy of logic(Quine, Putnam, Haack) all appear to confirm more or less with C. In addition, I think it’s important that JC’s C captures contemporary use of formal methods to philosophical problems (e.g., forcing techniques in epistemology, category theory in foundations of math (structuralism), proof-theory in semantics, etc.).These sound fine. But how to understand people who list AOS/AOC’s in “formal logic” or “logic” simpliciter? Should we just stop using those terms in that context (though actually JC mentions them in describing what philosophical/formal logic is)? Or is there a natural understanding of those within an extended JC standard?

By the way, now I’m puzzling over which bits of my work are philosophy of logic, and which bits are philosophical logic. I guess one issue I’m having is that philosophical logic strikes me as a tool to be used within broader projects (metaphysics, philosophy of logic/language, etc). If you like, philosophical logic is what you might typically use to do

formalphilosophy of logic (as JC mentions, you can also do non-formal philosophy of logic).The basic problem with any attempt to sort out what counts as logic, philosophy of logic, etc., is that the author presumably has something in mind that they think they’re up to: is “On denoting” a contribution to understanding how descriptions in natural language work (then it’s philosophy of language, I would say)? or is it an application of quantificational devices to some data (philosophical logic maybe)? is it about the contact between natural language and formal specifications of some of their correlates (philosophy of logic, sort of)? And what if Russell boiled the whole thing down to the familiar cluster of “there is at least blah-blah-blah” form in, like, two pages, and sent it off to the Annals of Mathematics—-would that paper be philosophical mathematics? And then would “On denoting” look more like less-formal philosophical mathematics? Very tangled.

I suspect we are inclined to sort older work in terms of the impact they had, so “On denoting” counts as philosophy of language and not epistemology, going by who reads the paper today. Which suggests that the right sorting of current work will have to await impact, influence, and history. (Maybe if philosophers come to have the influence in the academy mathematicians have, we can take logic back, and start to describe work more properly: set theory, metalogic, quantification theory, etc.)

By the way, my first post. Hello.