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Carnap on the Foundations of Logic and Mathematics
by Peter Koellner
Overview
I'm writing these notes because it seems clear to me before getting into Koellner's paper that we have opposite view on the merits of Carnap's position, possibly because we have different views on what those positions were. What I want to do as I read the paper, is to clarify my own position in the light of the criticisms of Carnap offered by Koellner (bearing in mind that I usually consider myself and describe myself as substantially in sympathy with Carnap in these areas, at least in principle of not in detail.)
1. Three Central Theses
In this section Koellner identifies three principle theses of "Logical Syntax" and gives textual support for them.
2. Technical Results
3. Critique
4. Foundations of Logic and Mathematics
5. Conception of Philosophy
1. Three Central Theses
In this section Koellner identifies three principle theses of "Logical Syntax" and gives textual support for them.
The Three Theses

Koellner identifies the following three central theses from Carnap's "Logical Syntax of Language".

  1. the truths of logic and mathematics are analytic and hence without content and purely formal
  2. radical pluralism, viz. that: distinct systems of mathematics are all equally justified, the choice between them is one of "mere expedience".
  3. that most of the traditional questions of philosophy are pseudo-questions and the proper task of philosophy is the study of the logic of science

2.

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