A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories. Truth-bearer candidates include propositions, sentences, sentence-tokens, statements, beliefs, thoughts, intuitions, utterances, and judgements but different authors 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,e.g. "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 or seek to avoid addressing their distinction or do not clarify it.e.g. * "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."
Introduction Some distinctions and terminology as used in this article, based on Wolfram 1989 (Chapter 2 Section1) follow. It should be understood that the terminology described is not always used in the ways set out, and it is introduced solely for the purposes of discussion in this article. Use is made of the type–token and use–mention distinctions. Reflection on occurrences of numerals might be helpful.Occurrences of numerals 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.
A characterCharacter A character is 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. is a typographic character (printed or written) etc.
A word-tokenWord-token A word-token is a pattern of characters. The pattern of characters A This toucan can catch a can contains six word-tokens The pattern of characters D He is grnd contains three word-tokens is a pattern of characters. A word-typeWord-type A word-type is an identical pattern of characters, . The pattern of characters A: This toucan can catch a can. contains five word-types (the word-token can occurring twice) is an identical pattern of characters. A meaningful-word-tokenMeaningful-word-token A meaningful-word-token is a meaningful word-token. grnd in D He is grnd. is not meaningful. is a meaningful pattern of characters. Two word-tokens which mean the same are of the same word-meaningWord-meaning 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: This toucan can catch a can. 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: If you have a bucket, then you have a pail contains ten word-tokens, seven word-types, and six word-meanings.
A sentence-tokenSentence-token A sentence-token is a pattern of word-tokens. The pattern of characters D: He is grnd is a sentence-token because grnd is a word-token (albeit not a meaningful word-token.) is a pattern of word-tokens. A meaningful-sentence-tokenMeaningful-sentence-token A meaningful-sentence-token is a meaningful sentence-token or a meaningful pattern of meaningful-word-tokens. The pattern of characters D: He is grnd is not a sentence-token because grnd is not a meaningful word-token. is a meaningful sentence-token or a meaningful pattern of meaningful-word-tokens. Two sentence-tokens are of the same sentence-type if they are identical patterns of word-tokens charactersSentence-type Two sentence-tokens are of the same sentence-type if they are identical patterns of word-tokens characters, e.g. the sentence-tokens P: I'm Spartacus and Q: I'm Spartacus are of the same sentence-type. A declarative-sentence-token is a sentence-token which that can be used to communicate truth or convey information.Declarative-sentence-token A declarative-sentence-token is a sentence-token which that can be used to communicate truth or convey information. The pattern of characters E: Are you happy? is not a declarative-sentence-token because it interrogative not declarative. A meaningful-declarative-sentence-token is a meaningful declarative-sentence-tokenMeaningful-declarative-sentence-tokens A meaningful-declarative-sentence-token is a meaningful declarative-sentence-token. The pattern of characters F: Cats blows the wind is not a meaningful-declarative-sentence-token because it is grammatically ill-formed The pattern of characters G: 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: This circle is square is not a meaningful-declarative-sentence-token because it is internally inconsistent The pattern of characters D: He is grnd is not a meaningful-declarative-sentence-token because it contains a word-token (grnd) which is not a meaningful-word-token Two meaningful-declarative-sentence-tokens are of the same meaningful-declarative-sentence-typeMeaningful-declarative-sentence-types Two meaningful-declarative-sentence-tokens are of the same meaningful-declarative-sentence-type if they are identical patterns of word-tokens characters, e.g. the sentence-tokens P: I'm Spartacus and Q: I'm Spartacus are of the same meaningful-declarative-sentence-type. In other words a sentence-type is a meaningful-declarative-sentence-type if all tokens of which are meaningful-declarative-sentence-tokens if they are identical patterns of word-tokens. A nonsense-declarative-sentence-tokenNonsense-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: Cats blows the wind, G: This stone is thinking about Vienna and H: This circle is square are nonsense-declarative-sentence-tokens because they are declarative-sentence-tokens but not meaningful-declarative-sentence-tokens. The pattern of characters D: He is grnd 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. is a declarative-sentence-token which is not a meaningful-declarative-sentence-token. A meaningful-declarative-sentence-token-useMeaningful-declarative-sentence-token-use A meaningful-declarative-sentence-token-use occurs when and only when a meaningful-declarative-sentence-token is used declaratively, rather than, say, mentioned. The pattern of characters T: Spartacus did not eat all his spinach in London on Feb 11th 2009 is a meaningful-declarative-sentence-token but, in all probability, it has never been used declaratively and thus there have been no meaningful-declarative-sentence-token-uses of T. A meaningful-declarative-sentence-token can be used zero to many times. Two meaningful-declarative-sentence-tokens-uses of the same meaningful-declarative-sentence-type are identical if and only if they are identical events in time and space with identical users. occurs when and only when a meaningful-declarative-sentence-token is used declaratively.
A referring-expressionReferring-expression An expression that can be used to pick out or refer to particular entity, such as definite descriptions and proper names is expression that can be used to pick out or refer to particular entity. A referential successReferential success a referring-expression’s success in identifying a particular entity OR a meaningful-declarative-sentence-token-use’s containing one or more referring-expression all of which succeed in identifying a particular entity is a referring-expression's success in identifying a particular entity. A referential failureReferential failure a referring-expression’s failure to identify a particular entity is referentially successful OR a meaningful-declarative-sentence-token-use’s containing one or more referring-expression that fail to identify a particular entity. is a referring-expression's failure to identify a particular entity. A referentially-successful-meaningful-declarative-sentence-token-useReferentially-successful-meaningful-declarative-sentence-token-use A meaningful-declarative-sentence-token-use containing no referring-expression that fails to identify a particular entity. A use of a token of the meaningful-declarative-sentence-type U: The King of France is bald is a referentially-successful-meaningful-declarative-sentence-token-use if (and only if) the embedded referring-expression ‘The King of France’ is referentially successful. No use of a token of the meaningful-declarative-sentence-type V: The highest prime has no factors other than itself and 1 is not a referentially-successful-meaningful-declarative-sentence-token-use since the embedded referring-expression The highest prime is always a referential failure. is a meaningful-declarative-sentence-token-use containing no referring-expression that fails to identify a particular entity.
Sentences in natural languages As Aristotle pointed out, since some sentences are questions, commands, or meaningless, not all can be truth-bearers. 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 truth-bearers, then it would be more clearly stated as "What makes the meaningful-declarative-sentence Snow is white true is the fact that snow is white".
Theory 1a: All and only meaningful-declarative-sentence-types*Meaningful-declarative-sentence-types Two meaningful-declarative-sentence-tokens are of the same meaningful-declarative-sentence-type if they are identical patterns of word-tokens characters, e.g. the sentence-tokens P and Q above are of the same meaningful-declarative-sentence-type. In other words a sentence-type is a meaningful-declarative-sentence-type if its tokens of are meaningful-declarative-sentence-tokens are truth-bearers
Criticisms of theory 1a
Some meaningful-declarative-sentence-types will be both truth and false, contrary to our definition of truth-bearer, for example, (i) in liar-paradox sentences such as "This sentence is false", (see Fisher 2008) (ii) and in time, place, and person-dependent sentences such as "It is noon", "This is London", and "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 solely of actual utterances, since it makes sense to talk of the discovery of previously un-formulated truths. (Kneale, W&M (1962)) page 593
Revision to Theory 1a, by making a distinction between type and token.