Thursday, December 06, 2012

Analytic/Synthetic II

Thinking about some issues raised by Pseudonoma's comments on my previous Kant-and-mereotopology post, one question that keeps coming up is what connection would the account of synthetic judgments require? Kant says (A7):

Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it.

The second clause is synthetic or ampliative judgment. The relevant connection can't be internal definitional relevance, i.e., it can't be the connection of an internal part for the definition, because that would mark an analythic judgment. So it has to be in some way extrinsic to the definition as such. At the same time it's unclear whether, when considering definitions, anything can be relevant to anything else without overlapping it at some level of generality. So something in between seems relevant, and that would suggest something like an overlap. But we seem to have two different kinds of synthetic judgments: those like "The house is red" and those like "The shortest distance between two points is a straight line". The latter seems more obviously to have an overlap than the former. I'm more and more taken with the idea that the difference is that, as far as Kant goes, the former has to do with possible experience, whereas the latter has to do with the possibility of experience. Thus house and red overlap in the sense that they share general features (sensible, for instance) that mean it is possible that they can come together in experience, whereas straight line and shortest distance between two points as Kant understands them overlap in the sense that their sharing something is required for experience (of any sort that we would recognize) at all. But that's a rough characterization that would need more development, and I haven't a clue how it would further relate to Kant's broader question of how we can know synthetic a priori truths.

4 comments:

  1. pseudonoma11:42 PM

    "their sharing something is required for experience (of any sort that we wouldThus house and red overlap in the sense that they share general features (sensible, for instance) that mean it is possible that they can come together in experience, whereas straight line and shortest distance between two points as Kant understands them overlap in the sense that recognize) at all."

    Well formulated....and I believe your formulation gives a clue as to how one might proceed further in considering what bearings the aspect of definitional overlap has on the synthesis of synthetic judgments: the inquiry can proceed, in good Kantian fashion, by reexamining the problematic in terms of a reflection on the sources of knowledge involved. Take, for example, your "instance" of shared general features in a synthetic a posteriori statement ("the house is red"). You cite "the sensible" here as a point of overlap. If we trace this back to the sources of knowledge, it would seem, we are pressed to make a further distinction; if sensible means "able to be sensed, i.e. a potential sensation" then it would seem it can be shared by "house" and "red" only in an equivocal fashion; red alone here offers a proper correlate of sensation, namely of sight. "House" however, can never be sensible in this direct way since it is not quality but a bearer of qualities --it requires the implicit objective synthesis proper to perception or the explicit objective synthesis proper to experience. In the former case, the object intended is the subject of a judgement of perception and is therefore a mere appearance, in the latter case, it is the subject of a judgement of experience and is an object. (I will continue in the next comment)

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  2. pseudonoma4:57 AM

    Both an object qua appearance and an object qua substance are not properly sensible in the sense of a potential sensation, but they are yet still sensible in another strict sense with whose semantic employment Kant alone can be credited. This is of course the sensible of sensibility as the transcendental aesthetic specifies that term, namely in terms of pure intuition. For it is clear that I can neither sense red without space and time nor perceive the appearance of an object such as a house without these. And obviously the same dependencies a fortiori are true of the definition of a line. Sensibility in the second sense is the most material underlying connection of all synthetic judgement, i.e. the most material underlying defintional overlap. Does this different formulation offer anything more than what any reader of the Kritik already knows? Perhaps. Lets revisit your question:

    ... what connection would the account of synthetic judgments require?

    We know that the short answer to this is Anschauung, precisely because it can comprehend both pure and empirical intuition, and so it can exhaust the possibilities of an appeal to something outside the judgment for its connection. But if this is what Kant has in mind by "to be sure it stands in connection with it."
    the question is how does definitional overlap complicate this. It seems clear that the definitional overlap enjoyed by the synthetic a priori propositions of arithmetic or geometry is rooted in the way they have the ground of their judgment in pure intuition, but the possibly intriguing thing about the mereotopological formulation overagainst Kant's is that the connection of definitional relevance can be spoken of in terms only of the concepts being combined in these judgments --we do not have to appeal to intuition to perceive that the line and its two points share as formal intuitions, the connection of being conceived as extensive magnitudes. This relevance of connection can be adduced only from the subject and predicate, despite the fact that it is too weak to ever ground the connection that allows us to discern that a line is not only related to two points (unlike house and red) but that it is the shortest distance between them...

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  3. pseudonoma5:07 AM

    So the result of what I am saying (which seems to be posting in an order which reverses its chronology) is that it is because formal intuitions are constructed out of pure forms of intuition that they can render this further definitional relevance in their concepts alone, without an immediate appeal to intuition. But this does not seem to be true of judgments where transcendental physiology is involved, and thus does not seem to extend to all synthetic a priori statements. For instance, "the heat of the sun causes the rock to rise in temperature"...unless we maintain heat and temperature to bear the same connection of relevance...still hazy but thanks for entertaining these suggestions with me...

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  4. branemrys4:29 PM

    There's a lot I'll have to think about here, but this sounds like we're at least in the vicinity.

    I'm trying out the newer version of Disqus. It has a default ordering for comments that I don't seem to be able to change, but you should be able to change it for your own view by clicking on the little arrow by the Discussion tab.

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