I’ve been back a week and the papers blog still isn’t done and this blog isn’t moving far either. I have excuses (snow, campus visits, snow, start of semester, snow, etc) but overall must do better. And we will soon!

In the meantime, I was wondering if anyone knew where I should look for what later Wittgenstein might have written on the synthetic a priori. I’m, to say the least, no Wittgenstein scholar, but it turns out I need to know what Wittgenstein thought about the synthetic a priori for something I’m writing, and I really don’t know where to begin to look. So any help would be more than appreciated!

(The title, by the way, is a by-now-familiar-in-the-blogtropolis shortening of “blog beg”.)

14 Replies to “Bleg”

  1. Have you tried Wittgenstein’s Tractus Props 6.53, 6.54, and 5? I will admit that I have not read it, but I do remember Popper citing some of his work in ‘Conjectures and Refutations’. I hope this helps!


  2. The likes of Norman Malcolm may no longer be around, but you could try asking your colleague Richard Miller, or Carl Ginet if he’s in town.

  3. I don’t have texts handy, but I would point toward On Certainty. Pretty much all of it, but especially his use of the riverbed and scaffold metaphors.

  4. Brian,

    I mentioned your inquiry to my colleague, Larry Wright, who sent this email message:


    A number of sympathetic commentators have taken Wittgenstein to simply be “finishing off” the Kantian project. These include at least Garver, Schwyzer, and Monk. He (Witt) several times in the corpus refers explicitly to Kant, saying that what he’s been about is, he thinks, what Kant meant by synthetic apriori, especially in arithmetic (he twice uses Kant’s example of 5 + 7 = 12, and at least once uses Kant’s example of the expansion of pi). From the context, I think it’s clear that what he means is that Kant was on to the irreducibly human (agental) component of language, and of the normative aspect of rule-following in general. This, following Putnam and Floyd, is essentially the Godel result (the concept of number has an irreducibly non-formal component) and what Kripke got excited about in trying to distinguish the “plus” rule from the “quus” rule.

    Hope this helps,

  5. You could begin to look in the Philosophical Investigations for sure and probably Remarks on the Foundations of mathematics. I don’t recall Wittgenstein actually mentioning synthetic a priori, but I have seen it as part of an out reading of early portions of the PI. Michael Forster spends a bit of time on this in Wittgenstein on the Arbitrariness of Grammar.

  6. I don’t have the book w/ me, but in part 4 of Remarks on the Foundations of Mathematics, Wittgenstein says that ‘“Bismarck” contains 8 letters’ is an example of a syntehtic a priori statement; he also mentions statements about the distribution of primes as providing further examples. Its not clear how seriously he intends these remarks.


  7. Although Wittgenstein may have read Kant in his POW days, he didn’t quite work with the analytic/synthetic or a priori / a posteriori distinction. So there is no simple answer to the question.

    One place where he explicitly discusses the synthetic a priori is in his conversations with the Vienna Circle (Wittgenstein and the Vienna Circle, Waismann). You’ll find it in the section entitled ‘Anti-Husserl’. Wittgenstein clearly rejects the idea, and you find similar remarks about the ‘arbitrariness of grammar’(without the reference to the synthetic apriori) in the PI.

    Wittgenstein seems to have thought of necessary claims such as those relating to colour exclusion as grammatical rules (perhaps the non-cognitive analogue of analyticity) and as such not themselves open to rational questioning or justification, although for such rules (where ‘rule’ is understood very broadly) to have their point and content in actual practice a range of empirical and social facts must often be true of speakers; these facts however do not ground the rules or form part of their content. So Blackburn understandably (and controversially) can see Wittgenstein as something of a precursor to his quasi-realism.

  8. Drury, in the Rhees collection (p. 118), says in a conversation with W which he dates “1930(?)”: “I think in your recent lectures you have been directly concerned with Kant’s problem: how are synthetic a priori propositions possible? W: Yes, you could say that. I am concerned with the synthetic a priori.” Those lecture notes are published by G.E. Moore (in P.O.) and Desmond Lee.

  9. (1) There are searchable versions of Wittgenstein’s works easily available through the library here — probably also at Cornell. Search for “synthetic” and “a priori”. You’ll easily find the passages from the Remarks on the Foundations of Mathematics, etc., mentioned above, in this way. Also look for “intuition” as in the Tractatus 6.233: The question whether intuition is needed for the solution of mathematical problems must be given the answer that in this case language itself provides the necessary intuition.

    (2) Wittgenstein’s Notebook entry for 1.6.15 reads:
    The great problem round which everything that I write turns is: Is there an order in the world a priori, and if so what does it consist in?
    You are looking into fog and for that reason persuade yourself that the goal is already close. But the fog disperses and the goal is not yet in sight.

    (3) Peter Sullivan has argued in various papers that Wittgenstein in the Tractatus was particularly aiming to reject the idea of the synthetic a priori (as when he says that all necessity is logical necessity — remember Kant’s link between the necessary and the a priori). Here’s one reference: “The truth in solipsism, and Wittgenstein’s rejection of the a priori.” European Journal of Philosophy 4 (1996), 195-219.

    (I find Sullivan’s work on the Tractatus very valuable, even if I don’t agree with all of it.)

  10. Brian, I don’t know how good your German is, but as I was looking for something else stuff just now on Phil Index, I came across the following:
    TI: Synthese a priori bei Wittgenstein
    AU: Hinzen,-Wolfram
    SO: Zeitschrift-fuer-philosophische-Forschung. Ja-Mr 04; 58(1): 1-28

  11. The Bismarck comment reported by Eli above is Remarks on the Foundations of Mathematics, section IV, paragraph 39. It’s on p245 of the Blackwell edition. The follow-up comment about prime numbers is the same section, paragraph 43. Page 246 in the same edition. It looks like he there explicitly endorses the synthetic a priori character of the propositions of maths, but the parenthetical remark (‘in this sense’) in the latter paragraph looks like it’ll be important to understanding these comments.

    See you next week.

  12. Oh, and Peter Railton’s essay in Boghossian and Peacocke’s New Essay’s on the A Priori is a really excellent account of what Philosophical Investigations might have to say about the apriority of logic. Highly recommended.

  13. Remarks on the Foundations of Mathematics; Lectures on the Foundations of Mathematics; Ludwig Wittgenstein and the Vienna Circle.
    Wittgenstein wants to say that a distinction between the ‘analytic a priori’ and the ‘synthetic a priori’ is spurious. He certainly does not want to say that there is an a priori that is empirical. The thought that there might be a synthetic a priori arises when we realise that logic extends beyond that of the logical constants.He only admits a ‘synthetic a priori’ in a very special sense, which is not that of Kant or Husserl

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