James Franklin

MATHEMATICAL NECESSITY AND REALITY.

Australasian Journal of Philosophy. 1989; 67: 286-294

EINSTEIN AND MOST PHILOSOPHERS HAVE THOUGHT THERE CANNOT BE MATHEMATICAL TRUTHS WHICH ARE AT ONCE NECESSARY AND ABOUT REALITY. THE ARTICLE ARGUES AGAINST THIS. "PRIMA FACIE" EXAMPLES SUCH AS "IT IS IMPOSSIBLE TO TILE MY BATHROOM FLOOR WITH (EQUALLY-SIZED) REGULAR PENTAGONAL TILES" ARE GIVEN, AND DEFENDED AGAINST OBJECTIONS SUCH AS THOSE BASED ON THE SUPPOSED PURELY LOGICAL OR HYPOTHETICAL NATURE OF MATHEMATICS.