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Now sometimes it is said that knowledge is primarily knowledge-that, i.e. some elementary epistemic operator is a propositional operator/"attitude report". Or at least there is an invoked distinction between descriptive knowledge and knowledge-by-acquaintance, where the formerly is roughly propositional (or at least perhaps covers the obtaining of states of affairs).

At any rate, in English, I think I almost always see the concept of beauty applied as a predicate on objects, as in, "This painting is beautiful," and I can't recall a clear instance of this application being a propositional attitude report, as in, "It is beautiful that this painting exists/has the content it does" (or whatever). Just the same, the grammatical construction "beautiful that..." is permissible, and we do more often say comparable things like, "It's wonderful that..." or, "It's splendid that..."

Now, as far as my judgment of Kant goes, he uses cognition (or rather its German cognate) the way we (if "we" are "analytic philosophers") tend to use proposition. For example, we say that propositions are the primary bearers of truth-values, Kant says that truth is "the accordance of a cognition with its object." When Kant speaks of conceptions and intuitions as objective cognitions, he seems to contrast the apprehensive mode of intuition ("bare sensation") from a sentential mode (an intuition as an apprehension not of individual concept-applications, but of a sentential array of these applications).

And so he has an intricately intellectualized theory of aesthetics, one grounded in the "faculty of judgment," where for him, judgments are broadly equivalent to, or a possible subset of, cognitions. Not that he commits us to a doctrine of aesthetic cognition straightforwarldy, only that the source of cognition, in the faculty of judgment, also has this weird side-output, aesthetic representation, which is at least para-cognitive (so to say). As we (again, "analytic philosophers") are often tempted to emphasize knowledge-that over "smaller" term knowledge, is Kant implicitly committed to representing beauty (and sublimity) in terms of "beautiful-that" more than as a predicate on object terms? At the very least, the SEP article on Kant's aesthetics says:

More strongly, judgments of beauty are not to be understood as predicating the concept beauty of their objects: as he puts it later, “beauty is not a concept of the object” (§38, 290).

EDIT: Insofar as Kant holds that, "I think," accompanies all our representations(?), he does have a generic propositional (or cognitive, or whatever) operator that would perforce range over our aesthetic judgments. This doesn't "prove my point" (since, "I think that it is beautiful that..." is not inferrable from the bare apperception operation, of course), but I do wonder if a "beautiful-that" moment could be construed as a (non-factive) second-order propositional attitude report, applying to, "I imagine (that...)," here, then. Admittedly, "I think that I imagine that it is beautiful that..." doesn't sound at all like what Kant was trying to get across, though.

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    I think he denies that beauty can be predicated of an object not because he thinks it is more propositional, i.e. should instead be predicated of a proposition, but because he thinks it is less so. It is not even subsumption of an object under a concept:"we do not use understanding to refer the presentation to the object so as to give rise to cognition; rather, we use imagination... to refer the presentation to the subject and his feeling of pleasure and displeasure." There is definitely an attitude there, but not a propositional one, more like evaluative attitude of expressivism.
    – Conifold
    Aug 8, 2022 at 13:00
  • We should think of judgment as performing, generally speaking, a 3-place relation between object, predicate and subject. In cognitive judgments dependence on the latter mostly vanishes, so we get 2-place predication, but not in aesthetic judgments. See Matherne, Kant on Aesthetic Autonomy on Kant's affinity to aesthetic expressivism.
    – Conifold
    Aug 8, 2022 at 13:14
  • Beaty/the sublime is more of a feeling that arises from the free play of the faculties, ie. imagination and judgement finding ever more forms and possible cognitions in the same object that cannot be subsumed under any proposition/concept that would fully reflect it. Thus, in a sense, it is a predicate of the intuition, or even more precise the process of its cognition. That being said, Kant uses accordance of a representation (Vorstellung) with its object as definition of truth. Cognition is a bad/misleading translation IMHO.
    – Philip Klöcking
    Aug 8, 2022 at 20:59
  • @PhilipKlöcking, first, Meiklejohn strikes again I guess, argh! Now, how far apart are a non-factive aesthetic propositional operator that only "correctly" applies to propositions about the subject and the imagination (in the relevant way), and an expressivist aesthetic term? Or rather, how difficult would it be to translate the language of the operator into the language of the term? OTOH, I don't have a lot riding on this idea (as far as my beliefs about Kant go, anyway), so if such a translation should seem unlikely or implausible, I hope that my thesis goes down without a fight. Aug 9, 2022 at 0:21
  • @Conifold, I know you more than likely already know what I mean by "non-factive," but I'll just throw in the definition for other possible readers: BT does not imply T, "It is beautiful that X," does not mean, "It is true that X." Aug 9, 2022 at 0:23

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Cognition for Kant is a term which names both judgements and concepts, i.e. spontaneous acts of the understanding. Kant even sometimes calls judgements concepts due to this similarity in their nature. The definition you quote, of the notion of truth, encapsulates the essence of what a cognition is for Kant, i.e. objectivity, reference to object, the ability to compare it with the object (Is it true to its concept? Does it agree with what the judgement says? etc.). Indeed, these Kantian notions - concept and judgement respectively - correspond to the concepts of classificatory content (intension) and propositional content (proposition).

The reason why aesthetic judgements cannot be seen as predicating beauty of their object is because this would mean they're judgements about beauty, i.e. theoretical cognitions pertaining to objective necessity which just have as their object beauty (aesthetic judgements have subjective, not objective necessity, i.e. their validity cannot be explained by reference to object being as the cognition says it is, only by a feature of the subject independent of the truth of the cognition - because objectivity means nothing but the necessary agreement of the judging with what is judged, i.e. the judging's being explained by what is judged, the propositional content; the ground here is the feeling of pleasure, not any determinate proposition holding true). Furthermore, any judgement that predicates of its subject a concept is a determinate judgement whereas aesthetic judgements - that's the whole point of discussing them for Kant - are not determinate, but reflective, judgements. "Reflection" would be, in modern terms, "abduction".

However, the notion of an object for Kant should not be equated with what is nowadays called an object, i.e. a particular. Whenever we speak of an object of some discourse, for example, we mean its topic, the content. That's the way Kant uses the term in the definition you cite. Therefore the very same objections which make it impossible to consider aesthetic judgement as determinately predicating of an object a concept apply also to the notion that beauty is predicated of a state of affairs.

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