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This morning I'm pondering some early influences on my thinking that I don't talk about so much: Quine's 'Two Dogmas of Empiricism' and the later Wittgenstein, especially On Certainty. These instilled a methodological skepticism regarding theories of meaning that served me well.
I've since developed a more positive methodological position, and the outlines of a theory of meaning proper (engaging even with formal semantics), but much as with my position on metaphysics, taking skeptical concerns seriously was a very important part of getting here.
If I was to some up the influence of Wittgenstein and Quine on my thinking in two claims, I'd say: 1) that meaning is use, and 2) that there's a porous boundary between the semantic and the epistemic. I was attracted to Brandom's work by his precise elaboration of these ideas.
To say something more about how these ideas have been tempered in my thinking, it's worth considering the meaning of 'meaning' from the perspective of how it is used. This gives us insight into the pragmatics of the boundary between semantic and epistemic that Quine overlooked.
In particular, we shouldn't just look at the difference between definitional assertions (analytic judgments) and informative assertions (synthetic judgments), but at the questions that elicit them, and the role they play in calibrating communication and meaningful disagreement.
There's an important distinction between questions of the form 'What are mitochondria?' and 'What does 'mitochondria' mean?'. The former invite disagreements that push all the way out to the edge of scientific inquiry, while the latter clarify the conditions of such disagreement.
This reveals a pragmatic distinction between meaning and essence tells against both Quine & Davidson's attempt to collapse the latter into the former, and Kripke & Putnam's attempt to collapse the former into the latter. We must grasp both to have an effective theory of meaning.
I've written a bit more about the wider history of this issue in my thread on the concept [concept]: https://twitter.com/deontologistics/status/1357987175179157504?s=20
But I'd like to keep this thread more tightly focused on the analytic/synthetic distinction, and how I understand it given my original sensitivity to Quine's concerns and my eventual fidelity to Kant's account of it. There are two key issues here: mathematics and identity.
Unsurprisingly, any discussion of these two issues must be prefaced by linking to my pick for the most under-read and under-appreciated paper in the Analytic tradition, Per Martin-Löf's 'Analytic and Synthetic Judgments in Type Theory': https://github.com/michaelt/martin-lof/blob/master/pdfs/Martin-Lof-Analytic-and-Synthetic-Judgements-in-Type-Theory.pdf
I think Martin-Löf more or less definitively proves Kant's point that mathematics is synthetic a priori, by showing that in this context the analytic/synthetic distinction encodes an asymmetry between the effort required to discover a proof and the effort required to check it.
If you understand the type definitions in terms of which ranges of mathematical objects (e.g., natural numbers), and the identities between them (e.g., 1 = succ(0)) are specified, then you can understand conjectures made about them, and even verify proofs of these conjectures.
But you don't thereby have everything you need to find a proof of every conjecture you can understand, or rather, to answer every question you can pose. Examples such as '5 + 7 = 12' are deceptive compared to 'there are infinitely many prime numbers' or Goldbach's conjecture.
There are some further questions here regarding judgments that are as easy to prove as check (e.g., 5 + 7 = 12) and those whose proofs require new types to check (e.g., Fermat's last theorem), but I want to move from the mathematical (a priori) to the empirical (a posteriori).
Martin-Löf makes Kant's account of the distinction between the analytic and synthetic a priori formally compelling, but Quine's worries about analyticity are more squarely aimed at the analytic a posteriori, a category which Kripke's essentialism eventually rehabilitates.
Quine thinks that there's a fundamental difference between conventional terms such as 'bachelor' whose meaning can be treated as stipulated, and full blooded empirical terms such as 'uranium' whose meaning cannot be adequately fenced off from scientific revision.
The crucial point to make concerning Kant's position here is that he does not think that analytic judgments are unrevisable. Kant's anti-Aristotelianism is predicated on the idea that the genus-species hierarchies through which individuals are typed are not simply given to us.
The judgments that 'cats are felines', 'felines are mammals', 'mammals are animals', etc. are in some sense presupposed by the judgment 'Chairman Meow is a cat', but these systems that organise individuation and inference can evolve in response to the pressures of experience.
Whereas an Aristotelian such as Kripke would say that a judgments such as 'water is H2O' and 'whales are mammals' are always analytic a posteriori, Kant would most likely maintain that these are initially informative claims (synthetic) that become definitional (analytic).
This is the action of faculty of reason upon the faculty of understanding, revising the system of principles (or concepts/types) contained therein. The dialectical dynamics that reconfigure the boundaries of the analytic and synthetic. These are the pragmatics discussed above.
It's worth adding one more thinker into the mix here. Despite his view that mathematics is analytic, the concerns about informative identity judgments that motivated Frege's distinction between sense and reference are directly relevant to all this.
To be clear, even by Frege's own lights a mathematical identity judgment such as '5 + 7 = 12' can be informative. The senses of the two expressions '5 + 7' and '12' are distinct, even if it's as easy to prove they refer to the same object as it is to check such a proof.
This is still work that needs to be done, which one can be saved from doing by having the result communicated to you by a trusted source. How many bother to check Ramanujan's claim that '1729 is the smallest number expressible as the sum of two cubes in two different ways'?
But the judgment that 'Hesperus is Phospherus' is quite different. The information received therein cannot be checked simply by virtue of understanding the types to which these terms belong (once 'star' and eventually 'planet' as the system of individuation was revised).
If we are to maintain, with Kant and against Quine, that judgements such as 'planets are heavenly bodies' are analytic, then we must understand the role of those judgments in a manner that is fundamentally different from 'triangles are three sided polygons'.
Here is my position then: the role of analytic a posteriori judgments is not in checking proofs of synthetic judgments, but in testing the communication channels along which such information can be communicated. They make for useful questions, rather than informative answers.
'You know cats are mammals, right?' is a reasonably good question to ask anyone you might want to take care of Chairman Meow, because you're not going to be able to communicate anything informative if they've got no grip on the system through which your cat is individuated.
Such questions test for the minimal agreement on the basis of which meaningful disagreement is predicated, assessing the degree of semantic competence needed to engage in dialogue open to epistemic inquiry. It makes perfect sense to ask a student 'You know water is H2O, right?'.
This is because it is entirely possible to learn a coherent set of linguistic behaviours for using 'water' in context without thereby knowing anything about chemistry per se. The analytic judgment here articulates a connection between relatively independent 'language games'.
The pragmatic distinction between questions of meaning and essence, along with Brandom's account of de dicto and de re vocabulary, enable us to pinpoint these behavioural boundaries within our linguistic practices, articulating local regimes of semantic/epistemic competence.
This is where my attempts to explore how 'meaning' is used have lead me in thinking about the idea that meaning is use. To push beyond the question of what 'meaning' means in the direction of what meaning is. I could say more about where this goes, but I'll stop here for now.
If you want a some more thoughts on the semantic difference between the mathematical and the empirical, I recommend this post: https://deontologistics.co/2019/12/27/tfe-varieties-of-rule-following/
If you want a slightly more detailed version of my speculations inspired by Martin-Löf, check out the more technical secret sections I cut out of Transcendental Blues: https://deontologistics.files.wordpress.com/2017/12/transcendental-blues-secret-sections.pdf
Til next time, solidarity in calibrating your communication channels.
