In answer to someone's question regarding Kant's idealist view of space vs. modern science, someone referred to the dichotomy between a cup as normally perceived and a cup as a collection of atoms. If we also admit the notion of the cup itself we then have a "trichotomy". I wonder if anyone holds that the cup-in- itself is just a collection of atoms. Could we say that atoms are not phenomena but mathematical entities; that things themselves are fundamentally mathematical? I imagine though that Kant sees mathematics as a human construct.

  • 2
    If possible, please provide some reference (e.g. a link) to the question and answer you mention in your first sentence.
    – user2953
    Dec 31, 2014 at 10:02
  • FWIW I was explicitly told in sci realism class that NO ONE SAYS THIS :) IIRC since then I found someone who did, but he wasn't very fashionable anyway haha
    – user6917
    Jan 1, 2015 at 5:40
  • You are wrong that mathematics is not a phenomena itself. Mathematics is same thing as hamburger, or red shorts. You just have never (not so many times) "seen" it. That is why we regard mathematics and thinking as more ideal. If the world will be filled with mathematical facts all over the place then in that world Pythagoras theorem or Atomism will be as dull as are red shorts in ours. Are red short actually dull? Hm. Ps: Comparison.
    – Asphir Dom
    Jan 2, 2015 at 17:59

3 Answers 3


Regarding the thing itself...

I'm sure there are people who hold the thing in itself is the fundamental construct of matter (probably subatomic particles rather than atoms). In fact, isn't this the materialist position?

However, if we look at the cup-in-itself as noumenon in the Kantian sense, then I don't think atoms qualify. Noumenon are unknowable. Atoms on the other hand are (at best) indirectly knowable through their effects, or are (at worst) mathematical abstractions that help us model certain things.

Regarding whether the thing itself is mathematical...

Are things fundamentally mathematical? Well, cosmologist Max Tegmark has put forward his Mathematical Universe Hypothesis and wrote a book called Our Mathematical Universe in which those views are presented.

I also recall an author who made a half-facetious argument that we all believe mathematics is the fundamental ontology. His argument went something like this. Put 1 ball into an empty box. Now put another ball into that same box. Now count the number of balls in the box. If there aren't 2 balls, then we'd look for holes in the box, physical anomalies, and even doubt our very senses. Yet the one thing we would not do is doubt that 1+1 = 2.

This raises all sorts of fascinating questions. What does it mean for something to be a mathematical structure, as opposed to a physical one? Are mathematical structures things that lack any properties and consist purely of relations? If we go down to the smallest substrate of matter, would there be any properties? Would properties imply parts? At that point, would we be in an area where our traditional thinking simply cannot cope (although some would argue that we got there with Quantum Mechanics)?

  • Thanks so much for the great answer and welcome to Philosophy! :)
    – Joseph Weissman
    Dec 31, 2014 at 15:42
  • @R. Barzell. Thanks, that was very clarifying. I suppose some would argue that things in themselves are in fact knowable. Didn't Kant posit the unknowableness of things in themselves to deal with the problem of perception. We can now account for the redness of a cup in terms of it's property of reflecting a certain wavelength of light. Thus appearance is explained in terms of something which is not an appearance and which is knowable.
    – Marek
    Jan 2, 2015 at 6:02
  • @R. Barzell I actually hope Kant is right. It would be terrible to think that he was obsolete!
    – Marek
    Jan 2, 2015 at 6:04
  • @Marek Well, for an interesting view of the opposite regarding perception, I recommend checking out Bundle Theory, and especially Berkeley. Even if Kant were wrong, engaging with his ideas is powerful, for it clarifies our own. In broad views, Kant is worth thinking about. In fact, I found it useful not just to think about Kant's views, but to introspect on my own reactions to them. That inevitably clarifies my own views, or reveals them to be muddled (that too is a clarification I suppose :)).
    – R. Barzell
    Jan 2, 2015 at 13:12
  • 1
    @Marek To argue that "things in themselves are in fact knowable" is to disagree with Kant. In that case, using the same terms as him, just to use them contrarily, seems to make no sense to me. The thing is itself is not knowable. The question then is if there is a dichotomy like that. But I'd say phrasing your question like you did makes things rather obscure.
    – iphigenie
    Jan 2, 2015 at 14:44

A collection of atoms is something that can be captured by our intellect. According to Kant, the thing in itself is the thing as it exists before being captured by our intellect. The collection of atoms won't do, nor any scientific theory.

Sellars' distinction between the 'manifest image' and the 'scientific image' of the world better express the dichotomy you are referring at.

For Kant, mathematics correspond to the prerequisite of understanding. Mathematics is the tool which allow us to put phenomena into shape so our intellect can capture it. Saying that the 'things in itself' is mathematical is thus far from Kant's philosophy.

  • @quentin What about energy to which atoms are reducible. Is that just something that can be captured by our intellect? To Schopenhauer Will was the thing in itself. I have heard it suggested that he should have called it energy.
    – Marek
    Jun 19, 2015 at 7:02
  • Well yes, if we have a word for it and it enters in equations... Jun 20, 2015 at 5:02
  • The question is not what captures Kant's philosphy.The question is whether Kant's idea of the unknowable noumenon is undercut by the idea that things in themselves are particles. I hope that it is not since I like mystery. Does anyone strongly argue that things in themselves are acutally particles or configurations of energy? Any suggestions as to the literature?
    – Marek
    Apr 11, 2020 at 8:39
  • Maybe mathematics is univeral. One cannot imagine aliens having different mahematics. It is synthetic a priori, univerally.
    – Marek
    Apr 11, 2020 at 8:44
  • @Marek I would object to the locution "things in themselves" since for most philosophers this refers to Kant's conception. But putting aside questions of vocabulary, if your question is something like: do some people believe that reality is just particles or fields (in opposition to Kant's idea that it is fundamentally unknowable), then the answer is yes. The position is known as physicalism. I'm not sure where to point in the literature (you can look up "realism" in Stanford's encyclopedia maybe since it's more general than physicalism, and still opposed to Kant). Apr 14, 2020 at 3:11

I have just looked at Max Tegmark's book. He is widely quoted online as saying that the ding an sich is unnowable. Actually this position is one that he categorizes as meaningless. It seems I have to accept his view that reality is ultimately mathematical. Sad, because I like mystery. Anyway we still have the mystery of affective consciousness.Apologies for not being able to direct my comments to exactly the right correspondants. Sorry Quentin.

  • @quentin Thanks Quentin, I will have to mull over the distinction between unversal conditions of understanding and the thing in itself. It seems you have got to the crux of the matter.
    – Marek
    Apr 15, 2020 at 7:57

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.