|Frege||Affirmation by Dooyeweerd||Critique by Dooyeweerd|
Frege was a mathematician, and wanted to explore the foundations of mathematics. |
He rejected the Kantian tendency to ground mathematics in geometry.
Instead, he tried to ground it in logic.
We might expect a focus on the quantitative aspect. |
Mathematics cannot be grounded in geometry, despite the close association between them, because the quantitative aspect is distinct from the spatial.
But it is also distinct from the analytic aspect, so Frege was likely to find problems - as indeed proved to be the case.
|Sense is difference from reference|
|That 'The Morning Star is a planet' expresses a different sense from 'The Evening Star is a planet' is a linguistic fact, not a logical one. [p.30]. (Both are the planet Venus.)||Lingual and analytic aspects cannot be reduced to each other.|
|Frege does not tell us what sense is. "'What is the sense of a name?' There is no such answer to be found in Frege. What is to be found is a theory of logic and language, in which the notion of sense has an important role to play." [p.26]||
1. Notice how even such a carefully-logical thinker like Frege must, at some points, fall back on notions whose meaning derive from intuition or some other pre-theoretical belief. This is precisely what Dooyeweerd would predict, because logic is never absolute. |
2. Frege absolutizes the analytic aspect. Because he does, things outwith its sphere have no meaning for him. Being honest, he attempts to find a way to reduce their meaning to that of the absolutized aspect - but ultimately fails to find a way to do so.
Copyright (c) 2004 Andrew Basden. But you may use this material subject to conditions.
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Created: 9 February 2008 Last updated: