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THE MIRACLE OF UNDERSTANDING
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A proposal is put forward to extend Quine’s criterion of existence (a theory is committed to the existence of bound variables) to mathematical structures. In the spirit of this criterion every mathematical structure can be regarded as a world in which only those entities exist that are necessary for the meaning of the structure. Some of mathematical worlds are used by physicist to model the real world. In such a case, ontology of a given mathematical world is transferred to the physical world or, more prosaically, some mathematical structures are interpreted as structures of the physical world. The miracle of understanding consists in the miracle of this interpretation.
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