Philosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with philosophy of logic, metalogic, and mathematical logic; and since the development of mathematical logic in the late nineteenth century, it has come to include most of those topics traditionally treated by logic in general.^{[citation needed]} It is concerned with characterizing notions like inference, rational thought, truth, and contents of thoughts, in the most fundamental ways possible, and trying to model them using modern formal logic. ^{[citation needed]}

The notions in question include reference, predication, identity, truth, negation, quantification, existence, necessity, definition and entailment. ^{[citation needed]}

Philosophical logic is not concerned with the psychological processes connected with thought, or with emotions, images and the like. It is concerned only with those entities — thoughts, sentences, or propositions — that are capable of being true and false. To this extent, though, it does intersect with philosophy of mind and philosophy of language. Gottlob Frege is regarded by many as the founder of modern philosophical logic. ^{[citation needed]}

Not all philosophical logic, however, applies formal logical techniques. A good amount of it (including Grayling's and Colin McGinn's books cited below) is written in natural language. One definition, popular in Britain, is that philosophical logic is the attempt to solve general philosophical problems that arise when we use or think about formal logic^{[citation needed]}: problems about existence, necessity, analyticity, a prioricity, propositions, identity, predication, truth. Philosophy of logic, on the other hand, would tackle metaphysical and epistemological problems about entailment, validity, and proof. So it could be said that philosophy of logic is a branch of philosophy but philosophical logic belongs to the domain of logic (though logic is itself a branch of philosophy). ^{[citation needed]}

Truth

Theories of truth

The Correspondence Theory

The correspondence theory is the "default" theory of truth. It's the one most people think is obvious. According to the correspondence theory, a claim is true if it corresponds to what is so (the "facts" or "reality") and false if it does not correspond to what is so. Most scientists and many philosophers hold some version of the correspondence theory of truth.

Example: The statement "The opera Aida had its first performance in Cairo" is true just in case the opera Aida had its first performance in Cairo, and false otherwise. "Snow is white" is true just in case snow is white.

Problems: Is the correspondence theory itself true? If so, what does it correspond to?

How do we figure out what is so? This latter question belongs to metaphysics. A metaphysical realist will hold that the reality that "corresponds" is objective and mind-independent. An idealist may hold that it is objective yet not mind-independent.

The Pragmatic Theory

The founder of pragmatism, Charles Sanders Peirce developed the original pragmatic theory of truth. According to Peirce's pragmatism, truth is the (supposed) limit of the beliefs of intelligent inquirers using the scientific method.

Some later versions of pragmatism dropped the hypothesis of the existence of truth. The "pragmatism" of William James and John Dewey was so defective, in the judgment of Charles Sanders Peirce, that Peirce began calling his theory "pragmaticism".

The rest of this section discusses versions of pragmatism that were rejected by Peirce.

According to William James's pragmatic theory, a statement is true if it allows you to interact effectively and efficiently with the cosmos. The less true a belief is, the less it facilitates such interaction. A belief is false if it facilitates no interaction. The originator of this non-Peircian pragmatic theory was the American philosopher William James. A more recent adherent was Richard Rorty.

Example: My belief that inanimate objects do not spontaneously get up and move about is true because it makes my world more predictable and thus easier to live in. It "works."

Problems: Sometimes unreasonable beliefs "work". A tribe might believe that human sacrifice brings their crops back each year. The crops do come back after the human sacrifice, but not because of the human sacrifice.

The pragmatic theory of truth might invite relativism in the case of beliefs that are compatible with all states of affairs, e.g., religious beliefs. (Someone might say the belief "God exists" is true because it "works for me," i.e., it helps this person "interact more effectively with the cosmos.")

The notion of "more effective and efficient interaction with the cosmos" is objectionably vague.

The pragmatic theory of truth invites the notion that there are degrees of truth (some beliefs might be more effective than others), and thus invites us to reject the law of non-contradiction ("a claim is either true or false").^[1]

The Coherence Theory

According to the coherence theory of truth, a statement is true if it is logically consistent with other beliefs that are held to be true. A belief is false if it is inconsistent with (contradicts) other beliefs that are held to be true. We should doubt claims that are currently inconsistent with the rest of our beliefs. Willard Quine is a famous contemporary philosopher who advocates the coherence theory.

Example: we don't believe in solipsism primarily because it contradicts so many of our other beliefs.

Problems: a belief can be consistent with all our other beliefs and yet have no independent supporting evidence. For example, many metaphysical beliefs are consistent with all imaginable states of affairs (e.g., "the universe came into existence five minutes ago complete with historical records and memories").^[2]

Truthbearers

Semantics

Definition

Necessity and analyticity

Presuppositions

Formal and Natural language

Consequence

Conditionals

Probability

Literature

• Goble, Lou, ed., 2001. (The Blackwell Guide to) Philosophical Logic. Oxford: Blackwell. ISBN 0-631-20693-0.
• Grayling, A. C., 1997. An Introduction to Philosophical Logic. 3rd ed. Oxford: Blackwell. ISBN 0-631-19982-9.
• Jacquette, Dale, ed., 2002. A Companion to Philosophical Logic. Oxford Blackwell. ISBN 1-4051-4575-7.
• Sainsbury, Mark, 2001. Logical Forms: An Introduction to Philosophical Logic. 2nd ed. Oxford: Blackwell. ISBN 0-631-21679-0.
• McGinn, Colin. 2000. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press. ISBN 0-19-926263-2.
• Wolfram, Sybil, 1989. Philosophical Logic: An Introduction. London: Routledge.
• Journal of Philosophical Logic, Springer Science+Business Media