Nature of Persons and Mathematics

First, let me define 'Person' as anything complex enough to perceive truths about reality in the level that we do.
Now, i'm gonna provide two mutually exclusive options about the nature of persons

1 - The basic concepts of math ( space and number ) and logic have to be common to any person.
Any person ( aliens in sittuations as distant as possible from ours, perhaps of different universes or perhaps even more distant than that ) would end up obtaining the things that are ultimately true for us, namely the truths of classical logic and math ( "2+2=4" considering the usual meaning of '2','+','=','4' , and the fact that there are only five platonic solids ) even if in completely different languages and formalizations. Numbers can be expressed in terms of geometry, or in terms of induction and sets, but in each case the truths of arithmetic are preserved, what is changed is the formalization and the proofs.

2 - There might be completely different kind of persons and for some of them, their ultimate truths would be really different than ours, perhaps even inconsistent. For some, "2+2=4", considering the usual meaning of '2','+','=','4' , would'nt even make any sense at all. Perhaps for them, the idea of a platonic solids would not make any sense.

I know we couldn't know for sure whether 1 or 2 is correct because we are already trapped in the sittuation described by 1.
Nevertheless, I'm interested if there is any nice completely objective argument ( not bringing morality or emotion into picture ), that makes one of them more plausible.
Perhaps, surprisingly, there is an argument that makes 2 really seem more plausible than 1, even if we are trapped by 1.

Or perhaps there isn't any argument and we can't even know which is more plausible and hence taking a position regarding 2 or 1 is futile.

Any good arguments ?

• You can read Quine's "philosophy of logic" on the subject. – Quentin Ruyant Jun 3 '15 at 12:17
• I don't have time for a full answer, but I've read before that some cultures don't bother to develop words for numbers beyond a certain point. That would potentially make mathematical statements like "2+2=4" not something they would have developed or made sense of. – James Kingsbery Jun 3 '15 at 15:36

oh my, that's a good one. Firstly i should mention that i wanted this to be a comment, but anticipate it being longer than a comment can handle.

ok, well, if i am understanding what you are getting at, which i am only partially doing. Not, one hundred percent sure what the platonic solids are. (unless thats the stuff sagan was trying to tell me about euclid... what with the triangles and dodecahedrons n'such?)

I am not sure that they are mutually exclusive. As i think it is a question of context. Think of the metric system vs... the uhhh... not metric system. (forgive my foolish public education) So you have two systems that use the same numeric system in differing and non equal ways. (non equal, like its not a perfect substitution. Like ten "units" from a metric system wont match up with ten of any of the other systems units.)

I think of it in terms of minecraft. Growing up in america i tended to see the world in a decimal sort of system. Which is to say, in orders of tens. Well now after hours of minecrafting, i can now break things down in its terms. where 8 becomes the new 10, as it were. The "stack" becoming the new "100" if ya dig.

In that way of thinking, i haven't changed so much what the numbers mean, so '2','+', and all that still apply, but in a modified sort of way. Firstly, everything was a 10 or was building to a 10, so that i could get it to 100, and so on. But then, the new master unit is 8, with the goal being 64, and then 128, and so on.

Mayhaps, some distant future will reveal some "groundbreaking" new understanding about math and the way we perceive it, but the part about geometry... Everything i understand about math as a "language" or a framework for understanding, quantifying, and measuring things. As taught to me by the movie "mean girls" (gah, i know right... ::shudders::) Was basically that it is "universal." A triangle is always a triangle as there are "three" "angles". The vocabulary may be different. or perhaps the contextual understanding of it. (metric vs m'rican) May differ from our present view of it. But that geometric principle remains.

All of this talk of perception and math gets me thinking of the novella "Flatland." wiki article It's about a 2 dimensional world inhabited by different polygonal forms. Well Square one day meets sphere, and since square had existed entirely in a world of only 2 dimensions. He could not see the sphere for what it is. It originally appears to square as a circle sort of dot thing. that grew to be a larger circle then shrunk back down to the size it started. It was not until square had visited "spaceland" where sphere was from, a land with 3 dimensions. That he could "accurately" perceive the spherical form.

Just because we squares cannot see the spherical forms... doesn't entirely mean that they are not out there. But even in that sense. It would seem to be that it would only be expanding on the mathematics, as we know them. So perhaps some(astrological)day out in the distant future. The most complex and "freaky deaky" maths we know of. Will just be covered in a small section of math textbook nueral data interface whatevers... under the heading "All the ape descendents figured out about math."

Imagine (2) is the case.

You have persons capable of perceiving truth about reality, yet they don't accept that 2+2=4 even though they share our definitions of 2, + and 4.

I think this statement is problematic. 2+2=4 follows from the definition as a matter of logic. If they don't reach the same conclusion, they must have different inference rules, a different logic. But the definitions of 2, + and 4 are logical definitions! How can they have the same definitions if they don't share our logic? We must conclude that these persons are not talking about the same 2, +, 4 as us.

Now consider the following: there exist some persons, capable of perceiving truths about the world, but the very meaning of our numbers doesn't make sense to them, so they'll never reach the conclusion that 2+2=4.

I think the statement is still problematic. If these persons share our logic, then our definition of numbers should be accessible to them. We could just give them the axioms. So these persons must have a different logic that is not translatable into our own. But how are we entitled to call it a logic if it is not even translatable into ours, or accessible to us? There is nothing "logical" in it.

Anyway let us assume we have reasons to call it a different logic. Logic is about inferences that preserve truth. If these persons have different rules for truth preservation, then how are we entitled to call it truth? Isn't it a different concept from our concept of truth?

Now if these persons don't share our concept of truth, why should we still call them persons? Remember a person (as you defined it) is an entity capable of entertaining truth about the world but it's not clear that "persons" with a completely different, untranslatable logic and notion of truth can be said to entertain truth about the world. It's not clear why we should say that they entertain truth rather than vgghjvf (replace with any string you like).

Perhaps we couldn't even say that these "persons" have a language and communicate. Imagine they share signals and act accordingly. If we can see patterns in their behaviour, then probably we can start decoding their language, i.e. we have the begining of a translation, of a "logic". Now if you encounter objects on a planet with signals travelling between them but their behaviour appears completely random and inconsistent with the signals, you'd probably not say that they are intelligent creature: you'd view that as a mere random natural phenomenon, such as clouds in the sky or whatever. You wouldn't call these objects "persons".

So it seems that if not even the begining of a form of communication is possible between us and them (and arguably that would require having a translatable logic for a start), then we'd have no good reasons to call them "persons", because after all, the way we define what a person is comes from our standards, and our logic is embedded into that standards.