Kant showed that mathematics was synthetic a priori. For example the laws of arithmetic or of euclidean geometry, and noted that this had escaped the notice of previous thinkers, they had assumed them to be analytic a priori.

Can the Russelian campaign be seen as an attempt to refound mathematics analytically - that is solely on the laws of logic - by excluding the synthetic excess and retaining an analytic core?

  • What a great question! I'm gonna have to think about it but my immediate reaction was: yes, if you are talking about the bad Kant taught by First Critique Kantians. So I really think it is interesting to consider what comes of this interpretation. Commented Feb 18, 2013 at 4:31
  • Thanks. What do you mean by Bad Kant and the First Critique Kantians? Commented Feb 18, 2013 at 4:41
  • Referring to about 90% of scholarship on Kant, which is a wise teacher told me is a "waste of good trees." People who don't read or take seriously his Third Critique, who ignorantly dismiss what Kant says he is actually doing. As Cassirer showed in his terrific intellectual biography, Kant has an entire critical philosophy worked out! It is organic and way bolder than anything we teach undergrads. The back-pocket Kant we're all taught in school is not even half the story. He is so deep as Rudolph Maakkreel (the best-selling author on Kant) states Kant's "teleological ideas can project Commented Feb 18, 2013 at 5:02
  • a variety of purposive systems--organic, social, and cultural." He argues we have not even seen the authentic interpretative power of the transcendental move yet, but it will be possible in the future. I think this may be correct once one reads Gadamer and Rorty, but that is a different matter. You really should look at his book, Imagination and Interpretation in Kant. Commented Feb 18, 2013 at 5:04
  • Ohh my bad, I just remembered that I wrote on this in another question you asked about the use of transcendent in Kant (if you recall?). So please go there for further elaboration. You ask good questions, at least about what I'm interested in, thanks! Commented Feb 18, 2013 at 5:10

1 Answer 1


The answer to the main question asked is trivially yes; Russell was well aware of Kant's views on mathematics and was influenced by them. Kant, Frege and many others were forerunners to Russell's views on mathematics in a very general sense.

The answer to the more interesting question in the body of the text - whether Russell's conception of mathematics is analytic - is definitely no. Russell held that mathematics and logic are both synthetic. Kant on the other hand held that logic is separate from mathematics; logic is analytic and mathematics is synthetic. As Russell says:

Kant never doubted for a moment that the propositions of logic are analytic, whereas he rightly perceived that those of mathematics are synthetic. It has since appeared that logic is as synthetic as all other kinds of truth...

The Principles of Mathematics, section 434

I would add that when you say Kant 'showed' mathematics is synthetic a priori, you seem to imply this was definitively done, but Kant's, Frege's and Russell's conceptions of mathematics and logic have been disputed by Quine, Wittgenstein and others.

  • I think you nailed it. Well put. Commented Feb 18, 2013 at 6:14
  • While I think this answer is very good (and upvoted it), I think that saying Russell definitely thought that mathematics and logic were synthetic is a bit of an oversimplification. Russell held just about every possible position on every topic in philosophy and so pointing to a single reference from 1903 is by no means sufficient to show that this was the Russellian position. In fact, Principles of Mathematics was written before Russell knew of the paradoxes of set theory and represents the last of his period of confidence following meeting Peano.
    – Dennis
    Commented Feb 18, 2013 at 6:19
  • I'm going to try to dig up some references from later works that show a different side, but my main point here is just that Russell is far too complex and shifting of a figure to admit of such a definite answer regarding his views here.
    – Dennis
    Commented Feb 18, 2013 at 6:21
  • If Russell held both mathematics and logic to be synthetic then what, if anything, did he propose was analytic? Commented Feb 18, 2013 at 7:59
  • 1
    @Dennis You're right, he did indeed change his views after reading the Tractatus. He came to agree with W that logical propositions are tautologies, and therefore analytic. The question was asking about Russell's earlier views on the foundations of mathematics though.
    – adrianos
    Commented Feb 18, 2013 at 13:03

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