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In Kant's famous division between a priori vs a postriori, and synthetic vs analytic, Kant's example for a priori analytic proposition is:

All bodies are extended.

Without immediately delving into the proposition itself, I'd like to ask why (if at all) Kant considers extendedness to be an a priori trait. I'll give a bit more context-

In later chapters Kant discuss one of the only a priori metaphysical objects (or subject?) - space (spatiality? Not sure about the proper English term). The proposition is quite simple: in order to think of anything we'd first need to contain it inside something, no matter if it's a thought or "physical" object (not sure if Kant would agree exactly to that sentencing, as it's more of a Spinozanian metaphysical space) - we always "imagine" it contained within some container, and even if we try to "get out" of that container -- we're simply ending up in a bigger container.

After taking space as an a priori metaphysical object, we need to discuss if extendedness (the ontology of physique, or "being in space") is also a priori metaphysical or a postriori (or maybe more precisely, analytic a priori or synthetic a priori). If we go to the direction that says extendedness is analytic a priori, I think it takes us more to a Leibnizian metaphysics rather than Kantian, so I'd have to assume Kant take extendedness to be synthetic a priori. But if extendedness is synthetic a priori, what does it mean to the quote above, as Kant gives it as analytic a priori? Or maybe the judgment itself on the link between body and extendedness is analytic a priori, but extendedness itself is really synthetic a priori?

I hope this isn't too convoluted.

Yechiam Weiss
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  • Bodies are extended by definition - hence its analytic. Where does Kant actually say this proposition is *a priori*? – Mozibur Ullah Jul 08 '18 at 11:44
  • @MoziburUllah correct, Kant doesn't specify the proposition by its a priori-ty, only by its analyticity. But when Kant define the 4 possible combinations of analytic-synthetic and a priori-a postriori, it's quite obvious that the proposition falls under "analytic a priori". – Yechiam Weiss Jul 08 '18 at 15:54
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    Kant isn’t saying that ‘body’ or ‘extended’ is an a priori representation, he’s saying that the proposition ‘all bodies are extended’ is true by definition, i.e. independently of experience. The empty example here is ‘A is A.’ Subject A already contains predicate A, hence is true by definition, independent of confirmation or confutation by experience. The representation ‘body’ comes from experience, but the analytic proposition involved simply draws out what is implicit in the representation in accordance with the principle of contradiction. Because we cannot conceive of an unextended body. – WolandBarthes Jul 08 '18 at 16:10
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    @WolandBarthes agreed until the last couple lines. And this is where I'm not sure about my wordings and I get a bit convoluted. If Kant considers "space" to be metaphysically a priori, is "extendedness" a synthetic or analytic a priori (or even a postriori?) term in relation to "space"? – Yechiam Weiss Jul 08 '18 at 16:13
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    In what way do space and extendedness relate? Space is an a priori presentation, that is, a pure form of intuition. The application of space as an a priori presentation is a precondition for our perception of objects at all: objects appear in time and space. We recognize an object as extended definitionally, because we can perceive objects—and we are able to perceive objects in the first place only because we structure them in space-time as a condition of perception. This is my understanding, at least: we are in very difficult territory now. – WolandBarthes Jul 08 '18 at 17:07
  • @WolandBarthes now you're using extendedness as a post-definition term, which is fine, but not the way I used it. What you're saying as "the application of space", "objects *appear* in time and space" -- these are the definitions of "extendedness" for me (and so I presumed Kant uses it). – Yechiam Weiss Jul 08 '18 at 19:16
  • @Yechiam Weiss: It's not at all obvious to me that it's *a priori*; it's obvious to me that it's true by definition. Since actual existing bodies are things we experience then it seems to me that this is an *a posteriori* proposition. – Mozibur Ullah Jul 08 '18 at 20:53
  • @MoziburUllah interesting, that's a reply I didn't expect to receive. Yet it seems that without the "extendedness" feature being a priori, we wouldn't have anything to connect (perceptually) between the object and it's "materialized" form (it'd need some kind of "bootstrapping" in order to do so, which may be the case, but I don't think Kant would approve of this approach). – Yechiam Weiss Jul 09 '18 at 03:27
  • Only propositions, not concepts, can be analytic or synthetic, this just depends on how they are established. Establishing a synthetic proposition requires synthesis in intuition, while analytic ones can be obtained by merely inspecting and clarifying concepts ("definitions"), which is the case with bodies and extension. Geometric propositions involving extension would of course require synthesis in intuition. I do not know what "a priori metaphysical" means, and whatever it is comparing Kant's and Leibniz's "metaphysics" is highly misleading, Kant has no metaphysics in Leibniz's sense. – Conifold Jul 09 '18 at 23:53
  • @Conifold what would you consider Kant's transcendental inquiry into "space", if not recognizing it as a metaphysical a priori concept? Also (although it isn't really related to the question but it's interesting), why do you so "Kant has no metaphysics in Leibniz's sense"? – Yechiam Weiss Jul 10 '18 at 03:22
  • @Conifold and, are you saying that analytic-synthetic divide is only for propositions, but a priori-a postriori is for both propositions and concepts, or both distinctions are only for propositions? Because if you say the latter then I don't know how to read Kant this way, as he uses at least one of those distinctions (a priori-a postriori) for concepts too, or at least that's how I understand it. – Yechiam Weiss Jul 10 '18 at 03:43
  • Kant's metaphysics in Leibniz's, or any other old metaphysician's sense, begins and ends with "the thing in itself", and he somewhat breaks his own rules to say even that. Metaphysics as the science of true being is not only impossible but unintelligible for Kant, space is just one of our own cognitive faculties. A priori is sometimes applied to concepts, in the sense of innateness, but this is different from propositions, where it refers to mode of justification, and reading it into Kant is dubious. Arguably for him they are all *acquired* from experience and "*without intuitions are empty*". – Conifold Jul 10 '18 at 04:05

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