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There was a thought experiment that came to me.

Suppose there would only be a cube, and you as an observer. These are the restrictions.

  • You do not have any knowledge of yourself. i.e. questions about how you perceive the cube etc. are not accessible to your mind.
  • There is only a cube.

What could you be able to know about this cube?

Suppose now a sphere is introduced.

Is there anything you would learn about the cube (positively), by the introduction of the sphere, that you could not have previously known about the cube?

(for example, could you, by the existence of a cube alone learn the concept of an edge, corner, number (amount of edges that a cube has)). Or do you need another object so you would be able to distinguish characteristics and so learn properties of the objects?

*( I am not merely talking about negative attributes of a cube, such as: it is not round, but rather things like: it is straight). (perhaps an additional question related, do you need negative attributes in order to be able to assert positive attributes)

*The answer given to this question would determine whether or not everything that is knowable about an object depends on other objects, or whether everything about an object can be known be simply studying that object. (This is what I mean by epistemological potential).

*The question is about what you COULD know, not necessarily what you would actually know in such a situation.

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  • You have only stated what the observer does not know. This entire thought experiment is heavily dependent upon what the observer does already know. Does he know anything at the onset?
    – JacobIRR
    Mar 2, 2018 at 19:30
  • Thank you, I presume he does not know anything (else) at the onset, since the only object he can have knowledge of is the cube.
    – St.Clair Bij
    Mar 4, 2018 at 12:38

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If you have no knowledge of how you perceive the cube, could you even know that you were presented with a three-dimensional object ? Wouldn't there just be a two-dimensional shape in your visual field ? The same with the sphere : it would appear merely as a circular shape, and still only a circular shape even if it were rotated.

You could gain contrastive knowledge of the kind you indicate. The sphere, even qua circle, presents an object without angles; so you now know about the square (a) that it is not the only shape an object can have and (b) more specifically that there are objects without angles.

You might also gain comparative knowledge. For instance it might occur to you whether the cube has or can have the same volume as the sphere. You would of course need some maths to work this out.

You don't say how much background knowledge the observer has. It's not a criticism but that does limit the range of potential answers. Nice question even so.

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  • thank you very much for your answer. The way I tried to formulate the question, would not involve physical limitations to the perception of the objects. It might even be mental perception instead of visual perception. I like what you said about contrastive and comparative knowledge. You are right I should have clarified the starting knowledge of the observer. I had a tabula rasa in mind with the only existing object being a cube.
    – St.Clair Bij
    Mar 4, 2018 at 12:41
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What does it take for a baby to perceive these things? It starts off not even able to focus eyes. Then a process of development and learning, understanding solid shapes often by putting them in it's mouth, by play, and watching others, then discussion, abstraction, analysis through school.

Implicit to your framing

You do not have any knowledge of yourself

is that all this development is just accidental, not necessary for mentality and thinking. Babies not only fail to thrive and develop without these developments, they die. The philosophical framing, in the Private Language argument, points out meaning is not inherent in signs or objects, like

the concept of an edge, corner, number (amount of edges)

it occurs in languages, social conventions of use that occur through culture and community. Meaning does not exist in the world, but only in minds, in community with each other.

Mathematics and geometry are not just a matter of progressively unpacking axioms. They need a backwards-and-forwards process between minds and the world and between people. From set theory to Incompleteness, the tools and insights occur not as insights of isolated brains, but in dialectics, discussions, in adding to and refining meaning which has context only through our lives and community.

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  • Thanks for the answer! In this case the observer is not necessarily assumed to have eyes, neither to be an infant, nevertheless your analogy of a baby might be helpful in answering the question or understanding the difference between an ideal observer, who knows everything that is knowable about the object, vs. an infant who by means of instruction and language is able to understand concepts. I especially liked what you said about dialectics. However, you can have the internal process of dialectics as well. In either case, dialectics pressuposes at least distinct objects.
    – St.Clair Bij
    Mar 4, 2018 at 12:47
  • You misunderstand me. I think the thought experiment fails to account for the nature of language and mind, so it can't work.
    – CriglCragl
    Mar 5, 2018 at 10:06
  • I think I do not misunderstand. I'm approaching the problem from a realist point of view, while you take a more down to earth, nominalist point of view. To be more specific, this thought experiment is not so much about how the observer would think about the cube, but rather what is knowable about the cube. That which is knowable about a cube I would describe in terms of concepts. concepts/ideas, are or at least can be pre-lingual. One argument for prelingual concepts would be synonyms or same concepts in different language. continued in another comment.
    – St.Clair Bij
    Mar 6, 2018 at 17:06
  • That ofcourse does not prove that a concept can exist without language, I would argue that language encodes a concept. But language is preceded by concept. Ofcourse, language can inform concepts or help give rise to other concepts. (As language, like a cube, can be an object of the mind, so it can give rise to the perception/conception of concepts. As evidenced in meta-linguistics as a simple example).
    – St.Clair Bij
    Mar 6, 2018 at 17:12
  • Yes there are advocates of Universal Grammar. And a solid case can be made for concepts based in shared bodily experience. But even vision like colours, or hunger, are profoundly cultural. Wolf-raised children are indicative of non-linguistic humans, and just wouldn't care about the shapes if they couldn't eat them
    – CriglCragl
    Mar 6, 2018 at 17:41

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