I'm reading Kant's Critique of Pure Reason and I understand that he thought that "Mathematical Judgements are all synthetic". I would like to know where does this debate lies or if it is of interest nowadays.


  • Pure mathematics is ultimately a game using invented symbols and invented rules to combine these symbols. It is purely synthetic. You can even invent your own set of symbols and rules. The ones we use now have been carefully chosen to avoid problems, but it's possible problems still exist. – barrycarter Jul 2 '18 at 16:56
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    The interest is rather "academic" but within its narrow bounds the debate is still lively - a survey of the field at the end of the SER article plato.stanford.edu/entries/kant-mathematics . Jaakko Hintikka is still the inevitable ref. Quine fans may claim that the distinction an./sy. has been dissolved but logicists still have not succeeded to present mathematics as logic. – sand1 Jul 2 '18 at 18:21
  • After the revision of logic at the end of 19th century Kant's distinction is of historical interest only, see What is the philosophical ground for distinguishing logic and mathematics? What he called "synthetic" is roughly what requires multi-place predicate calculus with quantifiers to be derived, whereas for "analytic" Aristotelian syllogistic (the only logic known to Kant) suffices, in modern terminology both are called "analytic". The Hintikka-Parsons debate described by SEP is a debate over interpreting Kant, not over mathematics. – Conifold Jul 3 '18 at 21:35
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  • Can you provide the cite to "Mathematical Judgements are all synthetic"? The cite will give the quote a context and let readers be more specific in their answers. – Mark Andrews Jul 4 '18 at 0:58

In this 2002 article, I defended Kant, and argued that arithmetic and geometry are synthetic. In my view, the best arguments for this conclusion come from post-Kantian logic and mathematics. https://dash.harvard.edu/bitstream/handle/1/4725028/suber_synth.htm

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