Eric asked:

Returning to what mathematical logic is:

When I say "for all..." or "if ..then..." may I be assuming something that is false?

(I guess there are certain hidden assumptions in the above statements, at the most aggregate level
the assumption of space and time.)

May the conclusion that I come up with be wrong as I begin with false assumptions during working
with any type of mathematical logic? The question is: Has there been an effort to generate a
representation that is free of space, or, time; or both space and time-related assumptions?

Can you recommend me any reference where I can read more about such representations, if they
exist of course?

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In answer to the first question: yes, of course you can be assuming something false. 'If cows had no
tails, then they couldn't swat flies'. A true statement starting with a false assumption, leading to a
wrong (but true, given the logic) conclusion.

(In answer to your second question... yes, there are, at least according to some people. Read: Lakoff,
G., and R.E. Nez. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics
into Being.New York, NY: Basic Books, 2000.)

In answer to question 3: do false assumptions give wrong conclusions? See1.

4. Yes. But what you're really asking is whether the effort has been successful. Most logicians would
consider your question trivial, and answer that of course, any logic is free of those 'assumptions' (a
bad term on your part; they aren't assumptions; they're underlying structures). But given what Lakoff
and Nunez say, that they are metaphors which are basically built into the way we think, roughly
speaking, some cognitive linguists would say that humans cannot escape those structures. Kant
would say the same thing.

Read the Lakoff/ Nunez book for an argument that they cannot exist.

Steven Ravett Brown