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I don't quite understand the nature of "going back to things themselves". How does Husserl break away from Kant?

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The broader question is answered under In what fundamental ways, if any, does Husserl break with Kant?

As for the title question, the answer is that we can not. Husserl's "things themselves" are nothing like Kant's "things in themselves". Although the two philosophies are incommensurable, to the extent that we can compare them the "things themselves" are Kant's appearances in their least contaminated form, phenomena as they come. This is why Husserl calls his philosophy transcendental phenomenology. Husserl's motto "back to things themselves" was a play on Helmholtz's earlier motto "back to Kant", which in turn was a reaction against the dominance of Hegel-styled speculations about rarefied abstractions in the German philosophical scene of the first half of 19-th century. Back to things themselves meant back to phenomena, and away from the German idealism.

Husserl considers the notion of Kant's "thing in itself", and of unperceivable things generally, to be "countersensical" or "materially nonsensical" (Widersinn, as opposed to Unsinn, logically nonsensical). While logically coherent it involves a vain attempt to imagine perceiving what is at the same time is asserted to be in principle unable to ever enter the imagined situation. Here is from Ideas I:

"The hypothetical assumption of something real outside this world is, of course, ‘‘logically’’ possible; obviously it involves no formal contradiction. But when we ask about the essential condition on which its validity would depend, about the mode of demonstration demanded by its sense... we recognize that something transcendent necessarily must be experiencable... as a demonstrable unity relative to its concatenations of experience... If there are any worlds, any real physical things whatever, then the experienced motivations constituting them must be able to extend into my experience and into that of each Ego."

In fact, Kant himself characterizes application of the categories of experience (such as "thing") beyond any possible experience as "transcendental illusion", so he appears to agree that "thing in itself" is "countersensical". Already Fichte pointed out that on Kantian terms we should not even be saying that "thing in itself" is unknowable, we should not be making this combination of words at all, let alone putting it into sentences. The usual response is that Kant only uses it analogically and metaphorically, to allude to the limits of experience and knowledge.

There is another possible interpretation. One response to the charge that unexperiencable experience is countersensical is that while we can never perceive things in question we can conceive of an intellect that can do so, and this is enough (e.g. it can be God, but it need not be a god of any known religion, and it need not exist, only be possible). In §§76-77 of Critique of Judgment Kant admits the conceivability of such a non-discursive intellect, intellectus archetypus as he calls it, but proceeds to argue that neither we nor anything like us possesses anything like it, see Did Kant come to believe that we have access to things-in-themselves after all?

In fact our Understanding has the property of proceeding in its cognition, e.g. of the cause of a product, from the analytical-universal (concepts) to the particular (the given empirical intuition)... We can however think an Understanding which, being, not like ours, discursive, but intuitive, proceeds from the synthetical-universal (the intuition of a whole as such) to the particular, i.e. from the whole to the parts. The contingency of the combination of the parts, in order that a definite form of the whole shall be possible, is not implied by such an Understanding and its representation of the whole. Our Understanding requires this because it must proceed from the parts as universally conceived grounds to different forms possible to be subsumed under them, as consequences."

Still, this means presumably that the "thing-in-itself" is perceivable to something conceivable to us, which would give it a shadow of sense, however tenuous. And Kant was of course a devout Christian, who, in his own words, had to "limit reason to make room for the faith".

Perhaps the most detailed discussion of meanings and shades of meaning of Kant's "phenomenon", "appearance", "noumenon" and "thing in itself" is Palmquist's Two Perspectives on the Object of Knowledge.

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    "...we recognize that something transcendent necessarily must be experiencable." This is where he goes wrong in my opinion. . To know the transcendent we would have transcend the experience-experiencer distinction. Only in this way can Kant's 'thing-in-itself' be known. There is nothing nonsensical about this. It is orthodox stuff in philosophy.outside the walls of Plato's Academy. . – PeterJ Sep 14 '17 at 11:29
  • transcendent is what's there outside of experience about it. Therefore it is an object. Object cannot be without any knowledge about it. Therefore there is no ground to postulate any thing in itself as something that can appear to itself in any private manner different from how it appears to us. For phenomenology thus, there is no things behind things how they appear to us (phenomena). – ttnphns Sep 15 '17 at 6:41
  • @ttnphns. "...there is no things behind things how they appear to us..." What is the significance of they? Why not call them things-in-themselves? As Kant said, it doesn't make sense to speak of appearances without there being something that they are the appearances of, and there are also no grounds for jumping to the conclusion that they must be the same as their appearances. – user3017 Sep 15 '17 at 10:40
  • @PédeLeão, For Kant, being of a thing "precedes" the appearance of a thing. You are right in that. For Husserl, all thing in its appearance, there is no appearance of. Rather, the assumption that there is "another" being behind the appearance itself is secondary (and not necessary). It doesn't mean that there is no being, of course, only that it is "in" the thing-as-it-appears, not behind it like some known essense or unknowable essense "in itself". – ttnphns Sep 15 '17 at 10:56
  • @PeterJ I think Husserl and Kant are talking about the "transcendent" of Western metaphysics, which tended to turn a negative, that which is not phenomena, into a positive, a metaphysical story of aphenomenal which is nonetheless modeled on phenomena. It is such "transcendent" that is countersensical and a transcendental illusion. Nagarjuna would say things like "We do not assert “empty.” We do not assert “nonempty.” We neither assert both nor neither", and negative theology is similar, but that is not how "transcendent" metaphysics was done in the West. – Conifold Sep 17 '17 at 20:03

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