Originally posted by ErtaiNaGia
IT is both, actually.... because we can actually observe the world to check the veracity of the statement.
The thing is: your axiom is mathematical, despite you saying it is not.
Check here:
en.wikipedia.org...
A mathematical axiom is something that can be concluded without the use of observation. It is universally correct, regardless of subjective experience
because of its redundancy. Scientific study uses observation to try and conclude results of our Universe.
From what I am interpreting, you are trying to use this reflexive axiom as a representation of reality. Basically saying that "reality is reality",
which is true but is also a logical and philosophical statement. What science is doing is trying to prove the absolution of objects within this
reality. However, we can not prove that reality is subjective or objective but more evidence leads to reality being subjective, still neither are
falsifiable.
The reason I say that reality being subjective is more likely is because of the philosophical ideals of solipsism, which can be summed up in one
question. Can your prove that anything outside of your own mind exists?
A few other questions for thought:
Can we prove that this is not a dream? Can we prove that we are not in a coma? Can we prove that our mentality has broken down so much that we are now
manifesting a different reality than the one our true self exists in physically?
We can not prove either of these things.
So, under that assumption that reality is subjective, we will take your representation of it in the form of a mathematical axiom.
Reality is reality, A = A. This is true.
Now let's
observe the objects within reality. We will look at objects 1, 2, and 3.
We could say that 1 = 1, 2 = 2, and 3 = 3. Remember, these are realistic objects, not mathematical numbers. We are representing reality with numbers,
but they do not necessarily hold the same numerical values as math.
Since reality is subjective, we can not really prove that 1, 2, or 3, in fact, exists. What we can prove exists is our mind and the reality it
creates, i.e "A".
Now everything would have to be a reflection (reflexion) of A.
Which we would then conclude that:
1 = A
2 = A
3 = A
because 1, 2, and 3 is our reality(A), which would mean that 1 =/= (does not equal) 1 universally.
This is because I can prove my reality, but I can not prove yours, and you can prove your reality, but can not prove mine. Which would conclude that I
have a reality, and you have a reality, from each of our own perspectives. This would result in my reality(A) and your reality(B).
The conclusions would be the same for you:
1 = B
2 = B
3 = B
And since A =/= B, but both A and B govern the object 1, we can say that 1 =/= 1 in an objective sense from a subjective reality.
However, as I stated, neither subjective reality nor objective reality are falsifiable so it comes down to a matter of perspective.
In any event, your axiom is still mathematical logic. Not science.