Truth-bearer


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

Introduction

Some distinctions and terminology as used in this article, based on Wolfram 1989
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.
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 character is a typographic character etc.
A word-token is a pattern of characters.
A word-type
is an identical pattern of characters.
A meaningful-word-token
is a meaningful pattern of characters.
Two word-tokens which mean the same are of the same word-meaning
A sentence-token is a pattern of word-tokens.
A meaningful-sentence-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 characters
A declarative-sentence-token is a sentence-token which that can be used to communicate truth or convey information.
A meaningful-declarative-sentence-token is a meaningful declarative-sentence-token
Two meaningful-declarative-sentence-tokens are of the same meaningful-declarative-sentence-type
if they are identical patterns of word-tokens.
A nonsense-declarative-sentence-token
is a declarative-sentence-token which is not a meaningful-declarative-sentence-token.
A meaningful-declarative-sentence-token-use
occurs when and only when a meaningful-declarative-sentence-token is used declaratively.
A referring-expression
is expression that can be used to pick out or refer to particular entity.
A referential success
is a referring-expression's success in identifying a particular entity.
A referential failure
is a referring-expression's failure to identify a particular entity.
A referentially-successful-meaningful-declarative-sentence-token-use
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 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, in liar-paradox sentences such as "This sentence is false", 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.
Revision to Theory 1a, by making a distinction between type and token.
To escape the time, place and person dependent criticism the theory can be revised, making use or the type–token distinction, as follows
Theory 1b:

All and only meaningful-declarative-sentence-tokens are truth-bearers

Quine argued that the primary truth-bearers are utterances

Having now recognised in a general way that what are true are sentences, we must turn to certain refinements. What are best seen as primarily true or false are not sentences but events of utterances. If a man utters the words 'It is raining' in the rain, or the words 'I am hungry' while hungry, his verbal performance counts as true. Obviously one utterance of a sentence may be true and another utterance of the same sentence be false.

Source: Quine 1970, page 13
Criticisms of theory 1b
Theory 1b prevents sentences which are meaningful-declarative-sentence-types from being truth-bearers. If all meaningful-declarative-sentence-types typographically identical to "The whole is greater than the part" are true then it surely follows that the meaningful-declarative-sentence-type "The whole is greater than the part" is true Some meaningful-declarative-sentences-tokens will be both truth and false, or neither, contrary to our definition of truth-bearer. E.g. A token, t, of the meaningful-declarative-sentence-type ‘P: I'm Spartacus’, written on a placard. The token t would be true when used by Spartacus, false when used by Bertrand Russell, neither true nor false when mentioned by Spartacus or when being neither used nor mentioned.
Theory 1b.1

All meaningful-declarative-sentence-token-uses are truth-bearers; some meaningful-declarative-sentence-types are truth-bearers

To allow that at least some meaningful-declarative-sentence-types can be truth-bearers, Quine allowed so-called "eternal sentences" to be truth-bearers.

In Peirces's terminology, utterances and inscriptions are tokens of the sentence or other linguistic expression concerned; and this linguistic expression is the type of those utterances and inscriptions. In Frege's terminology, truth and falsity are the two truth values. Succinctly then, an eternal sentence is a sentence whose tokens have the same truth values.... What are best regarded as true and false are not propositions but sentence tokens, or sentences if they are eternal

Quine 1970 pages 13–14
Theory 1c

All and only meaningful-declarative-sentence-token-uses are truth-bearers

Arguments for theory 1c
By respecting the use–mention distinction, Theory 1c avoids criticism of Theory 1b.
Criticisms of theory 1c
Theory 1c does not avoid criticism of Theory 1b. meaningful-declarative-sentence-token-uses are events and entail a user. This implies that nothing exists and hence nothing is true anytime anywhere nothing exists and hence nothing is true in the absence of a user. This implies that nothing was true before the evolution of users capable of using meaningful-declarative-sentence-tokens and nothing is true except when being used by a user. Intuitively the truth of ‘The tree continues to be in the quad’ continues in the absence of an agent to asset it.
Referential Failure
A problem of some antiquity is the status of sentences such as
U: The King of France is bald
V: The highest prime has no factors
W: Pegasus did not exist
Such sentences purport to refer to entitles which do not exist. They are said to suffer from referential failure. We are obliged to choose either That they are not truth-bearers and consequently neither true nor false or That they are truth-bearers and per se are either true or false.
Theory 1d

All and only referentially-successful-meaningful-declarative-sentence-token-uses are truth-bearers.

Theory 1d takes option above by declaring that meaningful-declarative-sentence-token-uses that fail referentially are not truth-bearers.
Theory 1e

All referentially-successful-meaningful-declarative-sentence-token-uses are truth-bearers; some meaningful-declarative-sentence-types are truth-bearers

Arguments for theory 1e
Theory 1e has the same advantages as Theory 1d. Theory 1e allows for the existence of truth-bearers in the absence of users and between uses. If for any x, where x is a use of a referentially successful token of a meaningful-declarative-sentence-type y x is a truth-bearer then y is a truth-bearer otherwise y is not a truth bearer. E.g. If all uses of all referentially successful tokens of the meaningful-declarative-sentence-type ‘The whole is greater than the part’ are truth-bearers then the meaningful-declarative-sentence-type ‘The whole is greater than the part’ is a truth-bearer. If some but not all uses of some referentially successful tokens of the meaningful-declarative-sentence-type ‘I am Spartacus’ are true then the meaningful-declarative-sentence-type ‘I am Spartacus’ is not a truth-bearer.
Criticisms of theory 1e
Theory 1e makes implicit use of the concept of an agent or user capable of using a referentially-successful-meaningful-declarative-sentence-token. Although Theory 1e does not depend on the actual existence of such users, it does depend on the possibility and cogency of their existence. Consequently, the concept of truth-bearer under Theory 1e is dependent upon giving an account of the concept of a ‘user’. In so far as referentially-successful-meaningful-declarative-sentence-tokens are particulars the definition of truth-bearer just in terms of referentially-successful-meaningful-declarative-sentence is attractive to those who are nominalists. The introduction of ‘use’ and ‘users’ threatens the introduction of intentions, attitudes, minds &c. as less-than welcome ontological baggage.