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''This article is about philosophy of logic and philosophical logic

Following the developments in Formal logic with symbolic logic in the late nineteenth century and mathematical logic in the twentieth, topics traditionally treated by logic not being part of formal logic have tended to termed either philosophy of logic or philosophical logic if no longer simply logic.

This article outlines issues in both philosophy of logic and philosophical logic or provides links to relevant articles or both. The terms being of recent coinage (compared to the history of logic) the demarcation between philosophy of logic and philosophical logic is not always entirely clear. Characterisations include


 * Philosophy of logic the arena of philosophy devoted to examining the scope and nature of logic. {{
 * Philosophical logic is the branch of logic concerning aspects other than or outside of formal logic.{{Fact|date=February 2009}}
 * Philosophical logic is the application of formal logical techniques to philosophical problems. {{Fact|date=February 2009}}

Introduction
This article makes use the following terms and concepts:


 * Type-token distinction
 * Use–mention distinction

Truthbearers, Truth and Meaning
Logic uses such terms as true, false, inconsistent, valid, and self-contradictory. Questions arise as Stebbing writes "(a) when we use these words of logical appraisal, what is it exactly that we are appraising? and (b) how does logical appraisal become possible?"

Terminology and examples sentences used in this article
We begin by making some distinctions based on Wolfram 1989, (Chapter 2 Section1), and introduce some terminology as used in this article. It should be understood that the terminology used is not always used in the way described below, and is introduced solely for the purposes of discussion in this article. Use is made of the type-token and use-mention distinctions.

Examples sentences used in this article

 * A: This toucan can catch a can.
 * B: If you have a bucket, then you have a pail.
 * C: I promise to be good.
 * D: He is grnd.
 * E: Are you happy?
 * F: Cats blows the wind
 * G: This stone is thinking about Vienna
 * H: This circle is square
 * I: The author of Waverly is dead
 * J: The author of Ivanhoe is dead
 * K: I am less than six foot tall
 * L: I am over six foot tall
 * M: The conductor is a bachelor
 * N: The conductor is married
 * O: The conductor is an unmarried man.
 * P: I'm Spartacus.
 * Q: I'm Spartacus.
 * R: Spartacus sum.
 * I: He's Spartacus.
 * J: Spartacus did not eat all spinach in London on Feb 11th 2009.

Terminology used in this article
It should be understood that the terminology described below is not always used in the ways set out, and are it is introduced solely for the purposes of discussion in this article.

Characters
By character we will mean a typographic character (printed or written), a unit of speech, a phoneme, a series of dots and dashes (as sounds, magnetic pulses, printed or written), a flag or stick held at a certain angle, a gesture, a sign as use in sign language, a pattern or raised indentations (as in brail) etc. in other words the sort of things that are commonly described as the elements of an alphabet.

Words
Word-tokens and word-types and word-meanings.

Word-tokens

A word-token is a pattern of characters.

The pattern of characters A (above) contains five word-tokens

The pattern of characters D (above) contains three word-tokens

Meaningful-word-tokens

A meaningful word-token is a meaningful-word-token. grnd in D is not meaningful.

Word-types

A word-type is an identical pattern of characters (or units of speech).

The pattern of characters A (above) contains four word-types (the word-token can occurring twice)

Word-meanings

Two word-tokens which mean the same are of the same word-meaning. Only those word-tokens which are meaningful-word-tokens can have the same meaning as another word-token. The pattern of characters A (above) contains four word-meanings.

Although it contains only four word-types, the two occurrences of the word-token can have different meanings.

Consider the pattern of characters labelled B above.

On the assumption that bucket and spade mean the same, B contains ten word-tokens, seven word-types, and six word-meanings.

Sentences
In grammar a sentence can be a declaration, an explanation, a question, a command. In logic a declarative sentence is considered to be a sentence that can be used to communicate truth. Some sentences which are grammatically declarative are not logically so.

Meaningful Declarative-sentences

Sentence-tokens

A sentence-token is a pattern of word-tokens.

The pattern of characters D (above) is a sentence-token because grnd is a word-token (albeit not a meaningful word-token.)

Meaningful-Sentence-tokens

A meaningful-sentence-token is a meaningful sentence-token or a meaningful pattern of meaningful-word-tokens.

The pattern of characters D (above) is not a sentence-token because grnd is not a meaningful word-token.

Sentence-types1

Two sentence-tokens are of the same sentence-type1 if they are identical patterns of meaningful word-tokens characters, e.g. the sentence-tokens P and Q above are of the same sentence-type1.

Declarative-sentence-tokens

A declarative-sentence-token is a sentence-token which that can be used to communicate truth or convey information. The pattern of characters E (above) is not a declarative-sentence-token because it interrogative not declarative.

Meaningful-declarative-sentence-tokens

A meaningful-declarative-sentence-token is a meaningful declarative-sentence-token.

The pattern of characters F (above) (Cats blows the wind) is not a meaningful-declarative-sentence-token because it is grammatically ill-formed

The pattern of characters G above (This stone is thinking about Vienna) is not a meaningful-declarative-sentence-token because thinking cannot be predicated of a stone

The pattern of characters H (above) (This circle is square) is not a meaningful-declarative-sentence-token because it is internally inconsistent

The pattern of characters D (above) is not a meaningful-declarative-sentence-token because it contaions a word-token (grnd) which is not a meaningful-word-token

Meaningful-declarative-sentence-types Two meaningful-declarative-sentence-tokens are of the same meaningful-declarative-sentence-type if they mean the same.

The patterns of characters M and O are meaningful-declarative-sentence-tokens of the same meaningful-declarative-sentence-type becasue they mean the same.

Nonsense-declarative-sentence-token

A nonsense-declarative-sentence-token is a declarative-sentence-token which is not a meaningful-declarative-sentence-token.

The patterns of characters F, G & H above are nonsense-declarative-sentence-tokens because they are declarative-sentence-tokens but not meaningful-declarative-sentence-tokens

Meaningful-declarative-sentence-token-uses

A meaningful-declarative-sentence-token-use occurs when and only when a meaningful-declarative-sentence-token is used declaratively.

The pattern of characters  J, Spartacus did not eat all spinach in London on Feb 11th 2009. is meaningful-declarative-sentence-token but, in all probabilty, it has never be used declaratively and thus there have been no meaningful-declarative-sentence-token-uses of J.  A meaningful-declarative-sentence-token may be used zero to many times. Two meaningful-declarative-sentence-token-uses of the same meaningful-declarative-sentence-token are identical if and only if they are identical events in time and space with identical users.

Truthbearers
Truthbearer is a term to designate entities that are either true or false and nothing else. The acceptance that some things are true while others are false raises the question of the nature of such things. Since there is no agreement on the matter, the term truthbearer is used to be neutral among the various theories. Candidates truthbearers include propositions, sentences, sentence-tokens, statements, ideas, beliefs, thoughts, intuitions, utterances, and judgments but different writers exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous, or seek to avoid addressing their distinction, or do not clarify it. A brief outline of some various theories and their criticisms follows

Statements
Many authors use the term statement as truthbearers. There is no single definition or usage. Sometimes it is used to mean a meaningful declarative sentence itself; sometimes it is used to mean what is asserted by a meaningful declarative sentence. It is not always clear i which sense the word is used. This provides two possible definitions for the purposes of discussion as below (wherein mds is written as shorthand for meaningful declarative sentence).

The concept of a statement was introduced by John Stebbing in the 1950s.

Two meaningful-declarative-sentence-tokens which say the same thing of the same object(s) make the same statement.

On the assumption that the same person wrote Waverly and Ivanhoe, the two patterns of characters I: (The author of Waverly is dead) and J (The author of Ivanhoe is dead) make the same statement but express different propositions.

The pairs of sentence-tokens (K, L) & (M, N) have different meanings, but they are not necessarily contradictory, since  K& L may have been asserted by different people, and M & N nay have been asserted about different conductors.

What there examples show is that we cannot identify that which is true or false (the statement) with the sentence used in making it; for the same sentence may be used to make different statements, some of them true and some of them false.

Theory S1 All and only statements are a mds. Theory S2 All and only token-mds can be used to make statements It should be noted that statement is not always used in one or other of these ways. Arguments for Theory S1
 * "All and only statements are a mds." is either a stipulative definition or a descriptive definition. If the former the stiplation is useful or it is not; if the latter either the decriptive definition correct describes  English uisage or it does not. In either case no arguments as such are applicable

Criticisms of Theory S1


 * If the term statement is synonymous with the term meaningful declarative sentence, then the applicable criticisms are the same as those outlined under sentence below
 * If all and only mdss are statements, as advanced by Theory S1, then the terms are synonymous and we can just as well speak of the mdss themselves as the truthbearers[ and there is no distinct concept of statement to consider, and the term statement is literally redundant.

Arguments for Theory S2

Propositions
Many authors use the term proposition as truthbearers. There is no single definition or usage. Sometimes it is used to mean a meaningful declarative sentence itself; sometimes it is used to mean the meaning of a meaningful declarative sentence. This provides two possible definitions for the purposes of discussion as below (wherein mds is written as shorthand for meaningful declarative sentence).

Theory P1: All and only mdss are propositions Theory P2: A token-mds expresses a proposition; two token-mdss which have the same meaning express the same proposition; two token-mdss with different meanings express different propositions. It should be noted that proposition is not always used in one or other of these ways.

Criticisms of Theory P1.
 * If all and only mdss are propositions, as advanced by Theory P1, then the terms are synonymous and we can just as well speak of the mdss themselves as the truthbearers[ and there is no distinct concept of proposition to consider, and the term proposition is literally redundant.

Criticisms of Theory P2
 * Theory P2 entails that if all token-mdss typographically identical to say, "I am Spartacus" have the same meaning then they (i) express the same proposition (ii) that proposition is both true and false, contrary to the definition of truthbearer.
 * The concept of a proposition in this theory rests upon the concept of meaning as applied to mdss, in a word synonymy among mdss. Quine 1970 argues that the concept of synonymy among mdss cannot be sustained or made clear, consequently the concepts of "propositions" and "meanings of sentences" are, in effect, vacuous and superfluous

see also Willard Van Orman Quine, Proposition, The Russell-Myhill Antinomy, also known as the Principles of Mathematics Appendix B Paradox

Sentences
As Aristotle pointed out, some sentences are questions, commands, or meaningless not all can be truthbearers. The proposal "What makes the sentence Snow is white true is the fact that snow is white"  implies that it is sentences like Snow is white that are truthbearers. The theory would be restricted to meaningful declarative sentences (mdss). Restricting sentences to meaningful declaratative sentences gives the theory, where mds is written as shorthand for meaningful declarative sentence

Theory S1: All and only mdss are truthbearers

Criticisms Some mdss will be both truth and false, contrary to our definition of truthbearer, e.g. (i) the liar-paradox sentences such as "This sentence is false". (ii) Time, place and person dependent sentences e.g "It is noon". "This is London", "I'm Spartacus"

''Anyone may ..ascribe truth and falsity to the deterministic propoitional signs we here call utterances. But if he takes this line, he must, like Leibniz, recognise that truth cannot be an affair soely of actual utterances, since it makes sense to talk of the discovery of previously un-formulated truths.''ref name="Kneale 1962"> page 593

Revision To escape the time, place and person dependent cricism the theory can be revised, making use or the Type-token distinction, as follows

Theory S2: All and only token-mdss are truthbearers Criticisms (i) S2 prevents sentences which are type-mdss from being truth bearers. If all token-mdss typographically identical to "The whole is greater than the part" are true then it surely follow that the type-mds "The whole is greater than the part" is true (just as all token-mdss typographically identical to "The whole is greater than the part" are English entails the type-mds "The whole is greater than the part" is English)

Thoughts
Frege argued that an indicative sentence in which we communicate or state something, contains a thought and an assertion, it expresses the thought, and the thought is the sense of the sentence.

Truth
Aristotle said To say that that which is is not or that which is not is, is a falsehood; and to say that which is is and that which is not is not, is true

This apparent truism has not proved unproblematic.

Logical Truth
See also Proposition

What is and is not considered a logical truth (also called an analytic truth or a necessary truth) has been a matter for clarification, even up to the early part of the 20th Century.

A logical truth was considered by Ludwig Wittgenstein to be a statement which is true in all possible worlds. This is contrasted with synthetic claim (or fact) which is only true in this world as it has historically unfolded.

Later, with the rise of formal logic a logical truth was considered to be a statement which is true under all possible interpretations.

Logical truths are necessarily true. A proposition such as “If p and q, then p.” and the proposition “All husbands are married.” are considered to be logical truths because they are true because of their meanings and not because of any facts of the world. They are such that they could not be untrue.

Logic is concerned with the patterns in reason that can help tell us if a proposition is true or not. However, logic does not deal with truth in the absolute sense, as for instance a metaphysician does. Logicians use formal languages to express the truths which they are concerned with, and as such there is only truth under some interpretation or truth within some logical system.

Are Logical Truths a priori or a posteriori knowledge? Synthetic or Analytic
See Is logic empirical?

The analytic/synthetic distinction
see
 * Willard Van Orman Quine: Rejection of the analytic-synthetic distinction
 * Analytic-synthetic distinction

Leibniz's Law
see Identity of indiscernibles

Do predicates have properties?
See Second-order logic

Realism
see Platonic realism, Philosophical realism

The Law of Excluded Middle
see Law of excluded middle

The problem of the material conditional
see Material conditional

Important figures
Important figures in the philosophy of logic include (but are not limited to):


 * Aristotle
 * George Boole
 * George Boolos
 * Rudolf Carnap
 * Alonzo Church
 * Augustus De Morgan
 * W V Quine


 * Michael Dummett
 * Gottlob Frege
 * Kurt Gödel
 * Georg Hegel
 * Immanuel Kant
 * Gottfried Leibniz
 * David Lewis
 * Wittgenstein
 * Gordon Clark


 * John Stuart Mill
 * Charles Peirce
 * Alvin Plantinga
 * Arthur Prior
 * Willard Van Orman Quine
 * Bertrand Russell
 * Alfred Tarski

Resources

 * Haack, Susan. 1978.  Philosophy of Logics.  Cambridge University Press.  (ISBN 0-521-29329-4)
 * Quine, W. V. O. 2004.  Philosophy of Logic.  2nd ed.  Harvard University Press.  (ISBN 0-674-66563-5)

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.
 * Quine, Willard Van Orman, 1970. Philosophy Of Logic. Prentice Hall: New Jersey USA.
 * Wolfram, Sybil, 1989. Philosophical Logic: An Introduction. London: Routledge. 290 pages. ISBN 0415023181, 9780415023184
 * Journal of Philosophical Logic, Springer SBM
 * Fisher J, On the Philosophy of Logic, Thomson Wadworth, 2008, ISBN 13 978-0-495-00888-0