[lbo-talk] The Ontology of Two Chairs

[ravi]

joanna bujes wrote:
> Jon Johanning wrote:
> 
>>>-- What kind of mathematics will result if the reality of a number is 
>>>given simply by our ability to represent something as a possible 
>>>number. For example, what kind of number is x in the equation x = the 
>>>square root of (-1)? Is it a number like 1, 2, 3 .... is a number?
>>
>>It's i, a perfectly good number in the mathematics we have. Look, 
>>Joanna, I appreciate your efforts, but you haven't come up with an 
>>alternative to mathematics, because there is *only* mathematics. I 
>>have to run now, so catch you later. 
>
> You may accept integer arithmetic as a subset of mathematics, but I am 
> saying that there were philosophers who rejected the superset you call 
> mathematics as mathematics.
>

not just philosophers. greek mathematicians did not have a zero because
it made no sense to them (or they weren't uptospeed with arab/eastern
math yet). mathematicians of the day had problems with 'i', infinity,
transfinite numbers, counting to infinity proofs, and a host of other
things. intuitionism in mathematics, while far from its 1900s peak, can
still be found (i believe) in current technical literature.

w.r.t "coming up with alternatives to mathematics", aren't there already
many kinds of mathematics, some inconsistent with others? further, if
the wiring of the human mind causes us to perceive and describe the
universe in a particular way, that could be a limitation of the mind,
could it not?

	--ravi