I have one nagging question about things in themselves being outside of space and time. How do we locate objects in space and time? Why are some objects in our vicinity and others far away? The objects could be anywhere in space and time. They have no "label". Why is my glass of beer in front of me, and the moon so far away? I have never seen any reference to this question. I hope someone can help me.
You seem to think that the thing-in-itself was "the real thing" and our representation is just a bad similacrum. That is simply wrong.
The real world, that which counts, is the world of representations in Kant. In it, objects just do have spatial properties and stand in spatial relations. And that is the basis of all knowledge proper.
The only reason he speaks of "things-in-themselves" at all, as a figure of speech instead of being about any metaphysical statement, is that if we understand that whatever input there may be and wherever that comes from is mediated by our understanding, this naturally leads to the possibility of different ways of understanding that does not mediate in the same way. And the common gound would be that the same "something" that produces our sensual input would be the source of their knowledge.
That is also why Kant posthumously wrote that the thing-in-itself is not even a thing proper, since "thing" (as opposed to object) is a category that only makes sense for our way of understanding.
Thus, your question is based on an essentialist misunderstanding. It's not like Kant ever stated that noumenal objects indeed had any properties we perceive so that we could say 'if we perceive spatial properties, we should be able to state at the very least that there is something space-like about noumenal objects and, put backwards, if we say there is nothing space-like about noumenal objects, how could we ever perceive spatial properties of them?' This is, interestingly, exactly the Sellarsian reinterpretation of Kant where the noumenal becomes the real object of which we gradually get a better picture through scientific inquiry.
But for Kant, this is not true. He radically rejects any characterisation of the noumenal in conceptual - representational - terms. He would not even state that noumena were outside of space and time, rather that we simply don't know what to say about noumena at all and because of that (see his logic) even to say they exist would be dubious. Kant rather speaks of thing-in-themselves to gain reality (Wirklichkeit) through transcendental necessity but this is how ideas become real in his system, not things, so this is not the same understanding of reality as it pertains to empirical objects. We don't "perceive properties of noumena" in Kant. We perceive (apprehend) properties of representations. Full stop. The very talk of 'properties' and, indeed even 'objects' already produces a category error if applied to the noumenal. Kant deliberately left the step from the noumenal to the manifold of intuition (the raw sensual data in a sense) out as explicitly inexplicable. The thing-in-itself does not "exist" in a meaningful way, it is basically something we posit to make sense out of the fact that we do not have immediate access to the fabric of reality.
The main takeaway from Kant should be "That which we cannot know about we should not speak about as if we did. Therefore, we should make very clear to ourselves what we actually can know anything about and questions beyond that are meaningless".
Kantian things in themselves not in space or time. How do we locate them? (...) How do we locate objects in space and time?
The Kantian idea is that space and time are pure a priori forms of sensible intuition, not properties of things in some real world that would exist outside our mind. According to this, we locate objects in space and time because the objects and their location in space and time is actually part of our sensible intuition, not something real outside our mind. Thus, the real world we think we perceive and believe exists outside our mind is really an idea, inside our mind.
This does not seek to explain how come we have this idea. Rather, it seeks to make clear what we really know, namely, our intuition, and what we don't, for example how the things we believe exist outside our intuition really are.
This also does not deny that there is a real world outside our mind, only that whatever there is, we don't know what it is because we only know the contents of our own mind, so to speak.
- How do we locate objects in space and time?
We locate objects in space by measuring their distance from a given point.
We locate events in time by measuring the time period between a given point in time and the point in time when the event happens.
Note: We do not locate objects, but events in time. Further questions about the possibility of distinguished positions or time periods as well as questions about the relativity of distances and time periods are the subject of physics, in particular of the Theory of Relativity.
These considerations do not apply to things in themselves, as taken according to Kant’s Critique of Pure Reason. We do not have direct access to things in themselves. In particular, we cannot measure them. Even more: We cannot even apply our common concepts to them.
All we can do is to hypothesize that things in themselves exist and affect our senses. Subsequently our senses and our mind generate some corresponding experience.
We can't. We can't even assume that they exist, or that a thing-in-itself corresponds to a thing-as-it-appears (therefore, every atom-as-it-appears would correspond to one atom-in-itself... what???).
In we take such assumptions, we know something about the thing-in-itself, which is by definition contradictory.
What we locate are the things-as-they-appear, which do exist in time and space.
My understanding of this is that for Kant space and time are "the pure forms of intuition" whereas things are representations. Kant says in hist first Critique, if I remember correctly, that in order for there to be representations there must be "something" which is represented. He sees a logical requirement that there must be "things in themselves" which give rise, along with our cognitive faculties; our conceptual categories of judgement, to the representations we call "things".
I would say that basic to our capacity to conceptualize space and time is our capacity to perceive differences,similarities, repetitions and patterns. This capacity also enables us to conceptualize things as entities, each with their own unique identity.
So my question to Kant would be as to why, if we think things in themselves, we should not think space in itself and time in itself. Things are as they are for us, as they are perceived and understood by us, so why should not space and time, which are also as they are for us, as they are conceived and understood by us, not lead to a notion of space and time in themselves?
What provides us with representations of spatial locations? This is not a complete answer, but it at least suggests there is a question. https://plato.stanford.edu/entries/kant-spacetime/notes.html This passage:
One of the clearest recent discussions of intuition, sensation and the representation of space in the first Critique can be found in Allais 2009. She argues that intuition provides us with representations of particulars - of things with spatial locations - independently of concepts, urging that we distinguish this claim about representation from the famous Kantian thought that we cannot achieve cognition without both intuitions and concepts (Allais 2009, 390).
According to Allais it is intuition that presents us with the locations of things.
Unfortunately, I cannot access Allais's paper, and I don't see how intuition can actually provide the locations.
Perhaps the answer to the problem of the spatiotemporal location of objects lies in Kant's notion of the Transcendental Subject. It seems to be the regulator of empirical reality. "Kant's view of subjectivity implies a twofold consideration of the idea of subject. On one hand, there is the empirical self, and on the other hand, there stands the transcendental subject as the principle of the unity of experience, and therefore, as the principle of the existence of the empirical self. Kant's transcendental subject is an effort to suggest a theory of subjectivity, which is impersonal and non-atomistic, that is to say a model that intends to exclude individualism. Yet, this model fails to constitute the factually existing person as subject. Kant's theory of transcendental subject is rooted in his subjectivist idealist philosophy; the transcendental subject appears to be another type of the idea of absolute."