***You can not say that "something" comes to existence before math.***
When I say 'before' I am talking in terms of your sequence (i.e., (1) "something" exists and is labelled 1 or 0 if not "something"), (2) boolean logic comes from 1 and 0, (3) math arises from boolean logic).
***By other words, at some moment in time objects appear and only few seconds later (or few billion years later) those objects gained ability to be labeled (or counted).***
Here you seem to be contradicting yourself. You seem to be saying that "something" exists as mathematical, and only later do we come along and label this "something" as mathematical. Then there is only one step as to why "something" is mathematical which is because it is. That is:
(1) "something" exists (S1) and has the property of being mathematical
(2) S1 evolves mathematically into S2
(3) observers evolve in S2
(4) observers label S2 as mathematical
(5) In 2002, Alex labels S1 as mathematical too
In (4) and (5) your label has nothing to do with S1 or S2 being mathematical. They are already mathematical in (1) and hence (2).
***As soon as anything "appear" it ALREADY is mathematical object - it can be labeled as "1" or "yes", or you may call it "existing", objects can be added (if more than one object can be counted), multiplied, etc.***
So, (1) is a correct interpretation of your scheme? Then why is it that mathematics is a hierarchial structure? That is, one theorem (T1) is true, hence (T2) is true. If S1 is mathematical as an inherent property, then why is that property built in a hierarchial structure? One theorem is dependent on a previous theorem being true.
Also, why is S1 contain all of mathematical truthfulness, however if we trace all of this hierarchy back to its most simplist roots that we arrive at simple axioms as being true? How can S1 be the most fundamental structure existing when there are a list of a few dozen axioms that incorporate all of which follows?
***So, by your logic math indeed exists BEFORE anything else comes to existence, and from this point of view is MORE FUNDAMENTAL than universes or any other "stuff".***
So, S1 is purely immaterial - not physical, right? This is idealism (i.e., the world can be reduced to immaterial properties).
***But I feel that word like "before" is not accurate word here because math may describe objects existing without time or without space.
"More fundamental" probably is better. Math indeed is more fundamental than anything wich has property "to exist".***
Why don't we agree that we are not talking in temporal terms - just in terms of sequence (or fundamental as you say). I understand that you are not referring to spatio-temporal terms.
Warm regards, Harv