(urth) barrington interview

[Adam Thornton]

The Continuum Hypothesis (more or less, there are no infinite sets larger
than the set of integers and smaller than the set of reals) is independent
of ZFC (Zermelo-Fraenkel axioms adjoined to the Axiom of Choice, which
together give something that seems to be coterminous with the standard
model of mathematical reality).  Actual mathematicians (at least in certain
fields) deal with this sort of question all the time, and following the
logic can take you to some very strange--but, if you believe your axioms,
true--places.

http://mathworld.wolfram.com/ContinuumHypothesis.html is a pretty decent
nontechnical overview.

This argument is orthogonal to the Lakoff-Nunez argument that the
conceptualization of mathematics is embedded in our anatomy and sensory
perception.

Adam



On Thu, Oct 9, 2014 at 11:55 AM, Brendon Fuhs <brendon.fuhs at gmail.com>
wrote:

> "A theoretical mathematician may feel he/she is working purely in the
> realm of symbolic logic and reason but it cannot be so."
>
> This is one of those wild statements that calls for an example. If
> mathematicians are not working with symbolic logic, but merely expressing
> some imperfect brain mechanics, and brains and thinking differ from
> person-to-person then surely there should be some mathematical statements
> that different groups of mathematicians are convinced have been
> demonstrated to be true, while others are convinced they have been
> demonstrated to be false, and are unable to come to an agreement on the
> matter.
>
> It is also a statement that represents a difficult (or impossible) place
> for drawing the line between the subjective and the objective. Math, the
> concept, is viewed as a material construct, rather than something which
> accesses objective truths and falsehoods. Why not go all the way and say
> that true and false are constructions? After all, the notion of truth and
> falseness is fundamentally mathematical, prior to being empirical.
>
> Or are you saying that it's possible for there to be a universe so alien
> to our own, epistemologically, that even its logic is unimaginable to us?
> Different not just in physical laws but in a deeper way that demonstrates
> that logic is only universal and not multiversal? Like there's some sort of
> logical ether in which our universe lives that could be different?
>
> That is interesting, but not falsifiable.
>
>
>
>
> On Thu, Oct 9, 2014 at 9:40 AM, Lee <severiansola at hotmail.com> wrote:
>
>> >Antonio Marques: And so you illustrate the point: physics comes from
>>
>> >observing the universe, whereas math comes from reason. Our reason
>>
>> >could be different. There is no such thing as multiplication outside our
>>
>> >minds.
>>
>>
>> I could generally, theoretically agree with this, though in the real
>> world,
>>
>> I question the idea of "pure reason". How can a human mind possibly
>>
>> reason if it had been deprived of all external sensory input since
>>
>> birth/conception of the person in question. I don't think we are
>>
>> built to function that way.
>>
>>
>> >Rick Norwood:  In a universe with different physical laws, we would have
>>
>> >different physics, but the same math.  Math is the knowledge that can
>>
>> >be arrived at by pure reason.
>>
>>
>>
>> Again, I question this concept of "pure reason" as a real world item.
>>
>> How could a human mind ever engage in "pure reason", unpolluted
>>
>> by any real world experience or perception?
>>
>>
>>
>>  I submit that math was, in its original conception and in its
>>
>> continued use, the combination  of real world perception and experience
>>
>> and internal logic/reason, like everything else in our brains.
>>
>>
>>
>> And this is the essential reason I question the universality of math.
>> Because
>>
>> math is inextricably tied to the human, real world experience on planet
>> earth,
>>
>> and thus is inherently limited by it.
>>
>>
>>
>> A theoretical mathematician may feel he/she is working purely in the realm
>>
>> of symbolic logic and reason but it cannot be so.  The adult human brain
>> is a
>>
>> product of millions of years of evolution on planet earth combined with
>> decades
>>
>> of personal experience and perceptual input from the person's life.
>>
>>
>>
>> The suggestion that the human brain can somehow  decide to operate
>> independently
>>
>> from its evolution and the personal experience which molded it is like
>> saying a
>>
>> automobile could suddenly, spontaneously reject its engineering and
>> construction and
>>
>> start running on nuclear fusion power technology. I don't see how it can
>> possibly make
>>
>> sense.
>>
>>
>>
>> (is suggesting a car can't spontaneously become a nuclear fusion device
>> an example
>>
>> of "Genetic Fallacy"?)
>>
>>
>>
>> Even if, maybe, by some wild random chance, humanity, in math, actually
>> did stumble
>>
>> upon the one universal describing system, that all possible intelligences
>> must agree upon.
>>
>> I still don't see how we could possibly know that. How are in the
>> position to make that
>>
>> judgment?
>>
>>
>>
>>  Human beings are not universal.  All we know is our own intelligence and
>> what we can "see"
>>
>>  from our own planet.. To me it seems the height of hubris to think the
>> system we invented
>>
>> here a few thousand years ago applies everywhere, to everything and every
>> form of intelligence.
>>
>>
>>
>> (A little voice in my head is saying someone will argue that we didn't
>> invent math; it is
>>
>> something we discovered. If so I'll just say "I disagree" and leave it at
>> that)
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