Reality as if is doubled in relation to language: The one counterpart of reality is within the language as the representation of the other counterpart of reality being outside the language and existing by itself. Both representation and metaphor are called to support the correspondence between the two twins as an \image and simile".
The mechanism of that correspondence and its formal conditions are investigated by the following construction: Language is reduced to an innite countable set (A) of its units of meaning, either words or propositions, or whatever others. It includes all possible meanings, which can be ever expressed in the language rather than the existing till now, which would always a nite set.
The external twin of reality is introduced by another set (B) such that its intersection with the above set of language to be empty. The union of them (C = A8B) exists always so that a one-to-one mapping (f C A) should exist under the condition of the axiom of choice. The mapping (f) produces an image (B(f)) of the latter set (B) within the former set (A). That image (B(f)) serves as the other twin of reality to model the reality within the language as the exact representation of the reality out of language (modeled as the set B). In the model, the necessity and sucient condition of that representation between reality both within and out of the language is just the axiom of choice: If the axiom of choice does not hold, the relation between the sets B(f) and B cannot be dened rigorously as an exact representation but rather as some simile and the vehicle between the two twins can be only metaphor. Furthermore the metaphor can be anyway dened to a set of one-to-one representations of the only similar external twin into a set of internal \twins", each of which is a dierent interpretation of the external \twin" so that a dierent metaphor is generated in each case. The representation seems to be vague, defocused, after which the image is bifurcate and necessary described by some metaphors within the language.
Consequently reality is in an indenite, bifurcate position to language according to the choice formalized in the axiom of choice. If that choice is granted, the language generates an exact image of reality in itself; if not, only some simile can exist expressible within it only by metaphors.
If the axiom of choice does not hold, language and reality converge, e.g. as `ontology': Ontology utilizing metaphors can describe being as an inseparable unity of language and reality within language abandoning representations and the conception of truth as the adequacy of language to reality. Furthermore, those metaphors should coincide with reality (and with physical reality in particular) in virtue of the ontological viewpoint. Furthermore, language can be formally dened by representation after the latter is in turn dened as a one-to-one mapping between two innite sets, one of which is dened as reality and the other, as its image. Language is namely the natural interpretation of that image.
The advantage of that approach is to link the representation of the human being supplied by language to the representation by a machine (e.g. a computer), which should
be formally modeled to be constructed. Another point of interest is the following: That mathematics, which is underlain by the mapping between sets, can be related to language by link of representation.
The mechanism of that correspondence and its formal conditions are investigated by the following construction: Language is reduced to an innite countable set (A) of its units of meaning, either words or propositions, or whatever others. It includes all possible meanings, which can be ever expressed in the language rather than the existing till now, which would always a nite set.
The external twin of reality is introduced by another set (B) such that its intersection with the above set of language to be empty. The union of them (C = A8B) exists always so that a one-to-one mapping (f C A) should exist under the condition of the axiom of choice. The mapping (f) produces an image (B(f)) of the latter set (B) within the former set (A). That image (B(f)) serves as the other twin of reality to model the reality within the language as the exact representation of the reality out of language (modeled as the set B). In the model, the necessity and sucient condition of that representation between reality both within and out of the language is just the axiom of choice: If the axiom of choice does not hold, the relation between the sets B(f) and B cannot be dened rigorously as an exact representation but rather as some simile and the vehicle between the two twins can be only metaphor. Furthermore the metaphor can be anyway dened to a set of one-to-one representations of the only similar external twin into a set of internal \twins", each of which is a dierent interpretation of the external \twin" so that a dierent metaphor is generated in each case. The representation seems to be vague, defocused, after which the image is bifurcate and necessary described by some metaphors within the language.
Consequently reality is in an indenite, bifurcate position to language according to the choice formalized in the axiom of choice. If that choice is granted, the language generates an exact image of reality in itself; if not, only some simile can exist expressible within it only by metaphors.
If the axiom of choice does not hold, language and reality converge, e.g. as `ontology': Ontology utilizing metaphors can describe being as an inseparable unity of language and reality within language abandoning representations and the conception of truth as the adequacy of language to reality. Furthermore, those metaphors should coincide with reality (and with physical reality in particular) in virtue of the ontological viewpoint. Furthermore, language can be formally dened by representation after the latter is in turn dened as a one-to-one mapping between two innite sets, one of which is dened as reality and the other, as its image. Language is namely the natural interpretation of that image.
The advantage of that approach is to link the representation of the human being supplied by language to the representation by a machine (e.g. a computer), which should
be formally modeled to be constructed. Another point of interest is the following: That mathematics, which is underlain by the mapping between sets, can be related to language by link of representation.
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