Truth-bearer

This article is about a term used in philosophy, logic and philosophy of logic.

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, or seek to avoid addressing their distinction, or do not clarify it.

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-sentence. 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.,,

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))

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 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.

(cf Wolfram 1989, 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, 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[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) (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))

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-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 mds-tokens typographically identical to "The whole is greater than the part" are English entails the mds-types "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.

Glossary of Terms used in this article

Some distinctions and terminology as used in this article, based on Wolfram 1989, Chapter 2 Section1) follows. It should be understood that the terminology described is not always used in the ways set out, and are it is introduced solely for the purposes of discussion in this article. Use is made of the type-token and use-mention distinctions.

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

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.

• Word-tokens

A word-token is a pattern of characters.
The pattern of characters A (above) contains six 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 five 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 six word-meanings.
Although it contains only five word-types, the two occurrences of the word-token can have different meanings.
On the assumption that bucket and pail mean the same, the pattern of characters B (above) 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.

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.

• 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 mds 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 mds-type is a meaningful declarative-sentence-token.
The pattern of characters F (above) is not a token-mds because it is grammatically ill-formed
The pattern of characters G (above) is not a token-mds because thinking cannot be predicated of a stone
The pattern of characters H (above) is not a token-mds because it is internally inconsistent
The pattern of characters D (above) is not a token-mds because it contains a word-token (grnd) which is not a meaningful-word-token

• Meaningful-declarative-sentence-types

Two mds-tokens are of the same mds-type if they mean the same.
The patterns of characters M and O are token-mdss/meaningful-declarative-sentence-tokens/ of the same meaningful-declarative-sentence-type because 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. The pattern of characters D (above) is not a nonsense-declarative-sentence-token because it is not a declarative-sentence-token because it contains a word-token (grnd) which is not a meaningful-word-token.

• Meaningful-declarative-sentence-token-uses

A mds-token-use occurs when and only when a mds-token is used declaratively, rather than, say, mentioned.
The pattern of characters J (above) is a mds-token but, in all probability, it has never be used declaratively and thus there have been no mds-token-uses of J. A mds-token be used zero to many times. Two mds-tokens-uses of the same {mds-token are identical if and only if they are identical events in time and space with identical users.