Mathematical Creation in Frege’s Grundgesetze

We discuss a passage from Grundgesetze der Arithmetik that raises doubts regarding Frege’s attitude towards platonism. First, we motivate a platonist interpretation of Frege’s mature philosophy of mathematics and outline his conception of the aims of definition. We then present the passage which prima facie raises doubts about a platonist interpretation of his logicism. We then survey and discuss readings of this passage by other interpreters. Finally, we present an interpretation that renders the passage compatible with a platonist interpretation of Frege and offers an explanation of Frege’s rather uncharacteristic concessive attitude in the passage.

Mathematical Enargeia: The Rhetoric of Early Modern Mathematical Notation

This article proposes and explicates a rhetorical model for the function of notational writing in sixteenth- and seventeenth-century European mathematics. Drawing on enargeia's requirement that both author and reader contribute to the full realization of a text, mathematical enargeia enables the transformation of images of mathematical imagination resulting from an encounter with mathematical writing into further written acts of mathematical creation. Mathematical enargeia provides readers with an ability to understand a text as if they created it themselves. Within the period's dominant reading of classical geometry as a synthetic presentation that suppressed, hid, or obscured analytic mathematical reality, notational mathematics found favor as a rhetorically unmediated expression of mathematical truth. Consequently, mathematical enargeia creates an operational and presentational link between mathematics' past and its future.

Have You Read …?

If most people were to be asked whether intuition has a role to play in mathematics, they would give a negative reply. The author of this article has placed intuition in mathematics in what seems to me its proper perspective. He says, “I would go so far as to say that, without it, mathematical creation would well-nigh cease, aud modern methods of teaching would be difficult to justify.”