Truthbearer

Truthbearer is a term used 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, ^[1] or seek to avoid addressing their distinction, or do not clarify it.^[2]

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-sentences (MDS) itself; sometimes it is used to mean what is asserted by a meaningful-declarative-sentences. It is not always clear in which sense the word is used. This provides two possible definitions for the purposes of discussion as below.

The concept of a statement was introduced by Strawson in the 1950s. ^[3],^[4],^[5]

Consider the following:

• 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

On the assumption that the same person wrote Waverly and Ivanhoe, the two distinct patterns of characters (MDS) I: and J make the same statement but express different propositions.
The pairs of (MDS) (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 may have been asserted about different conductors.

What these 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. (Strawson, P.F. (1952)^[5])

This suggests:

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

Theory S1

All and only statements are a {meaningful-declarative-sentences.

Theory S2

All and only meaningful-declarative-sentences 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 meaningful-declarative-sentences." is either a stipulative definition or a descriptive definition. If the former the stipulation is useful or it is not; if the latter either the decriptive definition correctly describes English usage 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 meaningful-declarative-sentences are statements, as advanced by Theory S1, then the terms are synonymous and we can just as well speak of the meaningful-declarative-sentences themselves as the truthbearers - there is no distinct concept of statement to consider, and the term statement is literally redundant.

Arguments for Theory S2

Propositions

Many authors^[6] 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. ^[7] 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.

(cf Wolfram 1989^[8], p. 21)

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 - 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,^[9] 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^[10]

see also Willard Van Orman Quine, Proposition, The Russell-Myhill Antinomy, also known as the Principles of Mathematics Appendix B Paradox[1]

Sentences

As Aristotle pointed out, since some sentences are questions, commands, or meaningless, not all can be truthbearers. If in the proposal "What makes the sentence Snow is white true is the fact that snow is white" it is assumed that sentences like Snow is white are truthbearers, then it would be more clearly stated as "What makes the mds Snow is white true is the fact that snow is white".

Theory S1:

All and only meaningful-declarative-sentence 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". (see Fisher 2008^[11]) (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 propositional 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. (Kneale, W&M (1962)^[12])

Revision To escape the time, place and person dependent cricism the theory can be revised, making use or the Type-token distinction ^[13], as follows

Theory S2:

All and only token-mds are truthbearers

Criticisms (i) S2 prevents sentences which are mds-types from being truth bearers. If all mds-types typographically identical to "The whole is greater than the part" are true then it surely follow that the mds-type "The whole is greater than the part" is true (just as all Template:Mdsts typographically identical to "The whole is greater than the part" are English entails the Template:Mdstypes "The whole is greater than the part" is English)

Thoughts

Frege (1919) argued that an indicative sentence in which we communicate or state something, contains both a thought and an assertion, it expresses the thought, and the thought is the sense of the sentence. ^[14]

Notes

References

1. ^ eg
   • "In symbolic logic, a statement (also called a proposition) is a complete declarative sentence, which is either true or false." Vignette 17 Logic, Truth and Language
   • "A statement is just that; it is a declaration about something—anything—a declaration which can be evaluated as either true or false. "I am reading this sentence" is a statement, and if indeed you have looked at it and comprehended its meaning, then it is safe to say that that statement can be evaluated as true."Fundamental Logic Concepts: Statement
2. ^ eg * "Some philosophers claim that declarative sentences of natural language have underlying logical forms and that these forms are displayed by formulas of a formal language. Other writers hold that (successful) declarative sentences express propositions; and formulas of formal languages somehow display the forms of these propositions." Shapiro, Stewart (2008). Edward N. Zalta. ed. "Classical Logic" in The Stanford Encyclopedia of Philosophy (Fall 2008 ed.). http://plato.stanford.edu/entries/logic-classical/#1. 
3. ^ Strawson, PF (1950). "On referring". Mind 9.  reprinted in Strawson 1971 and elsewhere
4. ^ Strawson, PF (1957). "Propositions, Concepts and Logical Truths". The Philosophical Quarterly 7.  reprinted in Strawson, P.F. (1971). Logico-Linguistic Papers. Methuen. 
5. ^ ^{a b} Strawson, P.F. (1952). Introduction to Logical Theory. Methuen: London. pp. 4. 
6. ^ eg Russell, Wittgenstein
7. ^ "Philosopher's tolerance towards propositions has been encouraged partly by ambiguity in the term 'proposition'. The term often is used simply for the sentences themselves, declarative sentences; and then some writers who do use the term for meanings of sentences are careless about the distinction between sentences and their meanings" Quine 1970, p. 2
8. ^ Wolfram, Sybil (1989). Routledge. 
9. ^ i.e. when expressed by a token-mds made by Spartacus, and when expressed by somebody other than Spartacus
10. ^ "Philosophers who favor propositions have said that propositions are needed because truth only of propositions, not of sentences [read meaningful-declarative-sentences Ed], is intelligible. An unsympathetic answer is that we can explain truth of sentences to be propositional in their own terms: sentences are true whose meanings are true propositions. Any failure of intelligibilty here is already his own fault." Quine 1970 page 10
11. ^ Fisher (2008). Philosophy of Logic. 
12. ^ Kneale, W&M (1962). The development of logic. Oxford.  page 593
13. ^ see Wolfram, Sybil (1989) generally on the application of type-token distinction
14. ^ Frege (1919) Die Gedanke trans AM and Marcelle Quinton in Frege, G (1956). "The thought: A logical Enquiry". Mind 65.  reprinted in Strawson 1967.