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By Sylvester J.J.

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But, if more is being asked than this, what can the question mean? If it is allowed that there may be no contradiction in postulating the existence of large cardinals of that type, but held that there still remains a question whether there really are such cardinals, what could determine the answer to such a question? It is not, surely, a matter of whether God chose to create such cardinals. Kronecker told us that the existence of any mathematical objects other than the natural numbers is the work of man.

If we were, we should assume that there is an absolutely determinate totality of mathematical objects, as determinate as the totality of molecules in a particular glass of water or of monkeys in a certain jungle at a given time. In such a case, it would be enough, in order to specify a domain of quantification, to select a concept under which some mathematical objects fall and others do not; for then reality could decide whether any given object fell under the concept as well as we can, once the object is given to us.

To believe is in this case to feel an immediate impression of the senses, or a repetition of that impression in the memory. ’Tis merely the force and liveliness of the perception, which constitutes the first act of the judgment, and lays the foundation of that reasoning, which we build upon it, when we trace the relation of cause and effect. (p. 86) 11 40 P ATRICK S UPPES As in many things, Hume puts his finger on the central problem, how indeed do we distinguish a belief from a fancy or an idle thought?

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Collected mathematical papers, volume 1 by Sylvester J.J.


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