I’ve been exploring Kant recently, so happy to give it a shot, FWIW...

Unity (universal) describes quantity in existence perceived as if one - treated together.
Totality (singular) describes quantity in existence perceived as the only one.
Plurality (particular) describes quantity in existence perceived as one of.

Infinite describes quality in existence perceived as impossible to measure or calculate. Zero has an infinite quality, for example, being neither affirmative nor negative in itself, but rather describing a limitation.

Inherence (categorical) describes relation in existence perceived as an essence, or the purpose itself.
Cause & Effect (hypothetical) describes relation in existence perceived as contingent or potential (if/then).
Community (disjunctive) describes relation in existence perceived as possible or arbitrary.

Aristotle’s category ‘relative’ is different to Kant’s category of ‘relation’ in that the latter describes the type of relation, but the former describes an existence as relative to another. This also differs from ‘having’, which describes the existence as a result of being acted upon.

That's brilliant!

It seems to me that "having" has mostly to do with the Prime mover then, whether or not this is impersonal or personal. I wonder what a relation would be in the Kantian world which was not cause and effect

It seems to me that "having" has mostly to do with the Prime mover then, whether or not this is impersonal or personal. — Gregory

I wouldn’t say that. ‘Having’ refers to the result of being acted upon by any agent, including itself. The agent is irrelevant, the description is of existence as an observable result. Examples Aristotle gave included ‘shod’ or ‘armed’.

The main difference I see between these sets of categories is that Aristotle describes an observation/measurement, whereas Kant describes an appearance of quantity, quality, relation or modality in existence, without necessarily assuming existence (let alone knowledge) of a thing-in-itself. For me, it demonstrates an evolution of dimensional awareness.

I wonder what a relation would be in the Kantian world which was not cause and effect — Gregory

In Kant’s Critique of the Faculty of Judgement he argues that one’s pleasure exists in necessary relation to an appearance of aesthetic beauty.

Aristotle describes an observation/measurement, — Possibility

Aristotle in a phrase! I think anyone who can understand these 4 or 5 words has a handle on Aristotle, the rest just detail.

In Kant’s Critique of the Faculty of Judgement he argues that one’s pleasure exists in necessary relation to an appearance of aesthetic beauty. — Possibility

I haven't got through his third critique - and may never get through his third critique. Question: by "necessary relation" do you - did he - mean also necessary condition? If you've got page numbers I could look it up....

“...Categories are conceptions which prescribe laws a priori to phenomena, consequently to nature as the complex of all phenomena (natura materialiter spectata). And now the question arises—inasmuch as these categories are not derived from nature, and do not regulate themselves according to her as their model, for in that case they would be empirical, how it is conceivable that nature must regulate herself according to them, in other words, how the categories can determine a priori the synthesis of the manifold of nature, and yet not derive their origin from her?....”
(CPR B163)

I might suggest starting with “Of the Schematism of the Pure Conceptions of the Understanding“, A137/B176, not so much to know how the categories arise, but rather, what is contained in them. Some of them, anyway. He says you’re supposed to be able to “easily” fill in the rest, if only you had “the proper ontological texts”, and because I have no idea what those texts would be, I never did fill them in.

The category of substance, for instance, has conceptions contained in it, such that the schema, the group of all relevant conceptions, of substance, is the permanence of the real in time. For some of the others, the schema of possibility is the accordance of the synthesis of different representations with the conditions of time in general, the schema of reality is existence in a determined time, the schema of necessity is the existence of an object in all time.

Anyway.....have fun with it.

On this point he’s admittedly referring to its modality, but his explanation of relation in aesthetics is not as clear (he talks about a form of purposiveness without purpose).

In Section 18: “I can say of every representation that it is at least possible that (as a cognition) it should be bound up with a pleasure. Of a representation that I call pleasant I say that it actually excites pleasure in me. But the beautiful we think as having a necessary reference to satisfaction. Now this necessity is of a peculiar kind. It is not a theoretical objective necessity; in which case it would be cognised a priori that every one will feel this satisfaction in the object called beautiful by me. It is not a practical necessity; in which case, by concepts of a pure rational will serving as a rule for freely acting beings, the satisfaction is the necessary result of an objective law and only indicates that we absolutely (without any further design) ought to act in a certain way. But the necessity which is thought in an aesthetical judgement can only be called exemplary; i.e. a necessity of the assent of all to a judgement which is regarded as the example of a universal rule that we cannot state. Since an aesthetical judgement is not an objective cognitive judgement, this necessity cannot be derived from definite concepts, and is therefore not apodictic. Still less can it be inferred from the universality of experience (of a complete agreement of judgements as to the beauty of a certain object). For not only would experience hardly furnish sufficiently numerous vouchers for this; but also, on empirical judgements we can base no concept of the necessity of these judgements.”

Christianity makes karma relative thru the mercy principle. You might say the "relational" trumps the absolute in their world view. The world, however, is absolute for them ( which I would agree with) and God's nature is too (I disagree). The world may or not be contingent (being understood thru "practical knowledge" ), and Aristotle 's categories may be compatible with Kant. However karma for a Kantian like myself is absolute. It is the only absolute discovered by speculation. Lastly, if it's possible for completely corrupted people to enjoy things, I wouldn't simply say with the Bible "the sun shines on the good and evil" . It seems they must be accounted for thievery of the universe, by the universe. Christians (among whom Kant was not one) are willing to believe with certainty that they are sinners BECAUSE they have a remedy before them in the cross of Jesus. If you take away atonement, they would ask the "what have I truly done wrong". All that can be said to them at that point is that justice rules over us all. That is absolute

However karma for a Kantian like myself is absolute. It is the only absolute discovered by speculation. — Gregory

Is this referring to passages in Kant?

Thank you; I'm impressed!

What I get from it is that there is an ought. But that the reason(s) for the ought do not qualify as forcing or imperative in any sense (being exemplary). It's as if to to say that, in the presence of the beautiful, in which presence I actually did experience (appropriate) pleasure, I should have, ought to have, done so.

I suppose the underpinning reason is a piece of bootstrapping that in essence says that the thing was beautiful; I appreciate the beautiful; that appreciation is in part a pleasure; I experienced that pleasure; and I should have and now I know why. Kant appears to escape the circularity by acknowledging that he does not know the why of the why - clever man! I accept correction on this.

But circularity or bootstrapping is not a disqualification as a reason. It is simply a qualification as to the kind of reason, and a distinguishing from other kinds of reason.

Is this referring to passages in Kant? — Kevin

Kant believed that the only speculative absolute was moral rules (citation needed). I don't believe moral rules are objective though. I think karma alone is absolute, each person having to learn their own conscience and how it works on their own

I agree - I think Kant takes us to a certain point and then appeals to the ‘soul’ as a source of knowledge - we just ‘know’ that it’s beautiful, and ought to appreciate it as such, without being concerned with the why.

As regards the relation category of ‘inherence’ in particular, Kant argues for a representation or form of ‘purposiveness’ in the relation to existence, without presupposing an end or purpose by which the existence is taken to satisfy. Inherence refers more to essence than to necessity (my mistake there) - that it is the very relation (or relational structure) that is the reason/purpose.

My own view is that we can take this further - that Kant was on the right track, but that his essentialism was holding him back, in a way. Modern neuroscience and QM can help with the paradigm shift Kant was looking for - once we recognise that two consecutive ‘Copernican turns’ were needed from his position; the first offered courtesy of Darwin. But that may be another discussion.