The identity theory of truth is usually to be represented as a reaction against the correspondent theory. The former can be considered as a particular case of the latter where the correspondence is reduced to identity. Ramsey was who continued that course of thought: if the correspondence is identity, then the concept of truth is redundant for the statement that any A is true is equivalent to ‘A’, and “true” does not add anything to ‘A’.
One can see further that a choice is interpreted differently in the above cases. The correspondent theory chooses whether a mental image or a sign corresponds to some fact of reality. Both identity and redundancy theories choose whether some fact takes place or not. The identity theory conserves anyway the concept of truth as irredundant.
Problem:What should be the meaning of truth in the identity theory? (Ramsey’s step is not done.)
Thesis:
The meaning of truth is a choice usually represented as the choice between ‘false’ and ‘true’ as a predicate for some discussed entity. The identity theory conserves that meaning of truth as choice, but renames or reinterprets ‘false’ as ‘does not take place’, and ‘true’ as ‘takes place’. The redundancy theory conserves implicitly the same interpretation of the choice, but rejects the meaning of truth as choice substituting it with ‘takes place’, i.e. by the one of the selective options. Thus, the identity theory distinguishes ‘truth’ from ‘true’, and the redundancy theory identifies them.
A few comments of the thesis:
One can say the concept of truth in the above three cases can be represented formally as adding a single bit of information to any entity, namely the choice between ‘false’ and ‘true’. The correspondent theory addresses the criterion for that choice. The redundancy theory identifies the entity with the pair of the entity and that additional bit. Then, the identity theory should be sited between the former and the latter: it neglects the correspondence to an external etalon as some criterion, usually constructive, for either ‘false’ or ‘true’ to be chosen, but conserves the meaning of truth as choice and therefore as the complementation of any entity by an additional bit about truth.
Two practical distinctions:
The identity theory neglects the correspondence criterion and thus does not require constructiveness particularly. Therefore, it admits the “pure existence” in a mathematical sense as true or that any entity can be true randomly or occasionally. On the contrary, the correspondent theory suggests certain constancy for the correspondence and has problems due to the “pure existence”.
Utilizing the Gödel encoding, one can ascribe a Gödel number being a positive integer to any entity after it has been described in relevant logical terms, therefore doubling the entity, which is equivalent to adding a bit (digit) more. The encoded entity plus that additional bit cannot be represented by the logical terms relevant for the entity, and thus it is irreducible to the entity, therefore rejecting redundancy.
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