Contemplation of the existence of mathematical entities for very apparent reasons generates a mental cycling of arguments dealing with the nature of mathematical truth, meaning in mathematics, and the obviously related question of which of these two problems should be solved first. The problem of the existence of mathematical entities dates from the first thoughts and ideas of a mathematical nature. The problem of existence in mathematics is fundamental to the domain of speculation and research on the foundations of mathematics. When we try to put ourselves in the place of those philosophers who first explored this problem we must realize that it sprang from the apparent or obvious discrepancy between the truths of mathematics and the entities to which these truths refer. The problem appears to be that the truths of mathematics belong to those elements of human knowledge to which we ascribe the highest degree of certainty; but we search vainly in the world of human experience, for entities which have properties described by these truths.
Alberda, Willis, "Existence in Mathematics" (1977). ACMS Conference Proceedings 1977. 4.
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