What is the difference between philosophical logic and the philosophy of logic?

Question

Is there a difference between philosophical logic and the philosophy of logic? If so, can someone elucidate the distinction between the two? Also, what are some references on the philosophy of logic?

Answer 1

The term 'philosophical logic' is used in different ways by different authors. Often it is used to mean the application of logic to addressing problems in philosophy. The multi-volume Handbook of Philosophical Logic, edited by Dov Gabbay and others, has articles on many different subjects covering aspects of logic. Just because the subject is described as 'philosophical' does not mean it is not highly technical. For example, modal logic tends to be of more interest to philosophers than to mathematicians, so you will find articles on it in the Handbook of Philosophical Logic, but not in the Handbook of Mathematical Logic.

In the same vein, there is a Journal of Philosophical Logic, which "... invites papers in all of the traditional areas of philosophical logic, including but not limited to: various versions of modal, temporal, epistemic, and deontic logic; constructive logics; relevance and other sub-classical logics; many-valued logics; logics of conditionals; quantum logic; decision theory, inductive logic, logics of belief change, and formal epistemology; defeasible and nonmonotonic logics; formal philosophy of language; vagueness; and theories of truth and validity."

Some authors use 'philosophical logic' to refer to the study of logico-linguistic issues surrounding the study of logic. For example, A.C. Grayling's textbook, An Introduction to Philosophical Logic has chapters covering propositions; necessity, analyticity and the a priori; existence; truth; meaning and reference; realism and antirealism. There is no actual logic in the book, but a good coverage of some of the philosophical issues that the use of logic gives rise to.

'Philosophy of logic' is usually used to describe the task of philosophising about logic. It stands to logic as philosophy of science stands to science, or the philosophy of language stands to language. It is concerned with general questions about the nature of logic, incuding such issues as the relationship between logic and metaphysics, the epistemology of logic, logical pluralism, the boundary between logic and non-logic, the nature of logical validity, the formality of logic, the normativity of logic, the relationship between logic and computation, the relation between logic and cognitive psychology, etc.

Here are some books on the philosophy of logic:

• Beall and Restall. Logical Pluralism.
• Cohnitz and Estrada-Gonzalez. An Introduction to the Philosophy of Logic.
• John Etchemendy. The Concept of Logical Consequence.
• Susan Haack. Philosophy of Logics.
• Matthew McKeon. The Concept of Logical Consequence.
• W.V. Quine. Philosophy of Logic.
• Stephen Read. Thinking about Logic.
• Ian Rumfitt. Boundary Stones of Thought.
• Penelope Rush. The Metaphysics of Logic.
• Graham Priest. Doubt Truth to be a Liar.