From: Chuck Roghair (ctr@pacificpartssales.com)
Date: Wed Nov 17 2004 - 19:04:05 GMT
-----Original Message-----
From: owner-moq_discuss@venus.co.uk [mailto:owner-moq_discuss@venus.co.uk]
On Behalf Of Mark Steven Heyman
Sent: Tuesday, November 16, 2004 10:12 PM
Hello:
msh:
I think I would say that mathematics is rooted in empiricism and
blossoms through reason, and thus cuddles snugly with my rational-
empiricist interpretation of the MOQ. I've forgotten more set
theory than I remember, but I'm pretty sure that our conception of
numbers derives from our sense experience of collections. We see a
box containing a turnip, a radish and a carrot, and another box with
an orange, an orange, and an orange, and abstract the commonality as
the number three. Similarly the other base 10 digits, including,
maybe, an empty box for zero. We then start combining the elements
of the various boxes in various ways, and suddenly we have an
abstract "sense" of addition and subtraction, and are well on our way
to deriving a base-10 mathematics.
Chuck comments:
Isn't our 10-base mathematics derivitive of our 10-base digits?
Sense-perceptionally speaking, I imagine an infant noticingng his own hands
for the first time, smiling in awe at wiggling fingers.
That's raw empericism, I think.
Best regards,
Chuck
To: moq_discuss@moq.org
Subject: RE: MD Empiricism
Scott, DMB,
I should probably jump back in here for this portion of your
discussion, which I've been enjoying from the sidelines. I'd meant
to address Scott's claim that math is not empirical in nature, but
didn't get around to it in a timely manner, so maybe now's my chance.
I think I would say that mathematics is rooted in empiricism and
blossoms through reason, and thus cuddles snugly with my rational-
empiricist interpretation of the MOQ. I've forgotten more set
theory than I remember, but I'm pretty sure that our conception of
numbers derives from our sense experience of collections. We see a
box containing a turnip, a radish and a carrot, and another box with
an orange, an orange, and an orange, and abstract the commonality as
the number three. Similarly the other base 10 digits, including,
maybe, an empty box for zero. We then start combining the elements
of the various boxes in various ways, and suddenly we have an
abstract "sense" of addition and subtraction, and are well on our way
to deriving a base-10 mathematics.
If this doesn't convince you, then I think another way to arrive at
the fundamental empirical nature of mathematics is to try to imagine
what sort of numeric reasoning a person who is sense-deprived from
birth might develop. In fact, it's difficult to understand how ANY
kind of sustained thought process might occur under such
circumstances. So what on earth can we mean by the phrase non-
empirical consciousness?
A few comments interspersed below....
On 16 Nov 2004 at 7:48, Scott Roberts wrote:
>dmb:
> In any case, to take your counter-example for example, its clear
> that you have not noticed what this expanded empiricism means. As
> MSH has pointed out, mental experience counts as experience within
> rational empiricism. Unlike the most narrow kind of empiricism,
> where only sensory exprience counts, rational empiricism would most
> definately say that mathematical is an entirely empirical reality.
scott:
That's not what Pirsig said. He said "The MOQ denies this. (That
Reason perceives truths which are incapable of verification in
sense-experience."
msh says:
Can you provide a page or chapter reference for this? We might need
to see it in context.
scott:
Mathematical truths are not verified in sense-experience. They are
verified through reason,
msh says:
But they are rooted in sense-experience; the verification is the
rational blossom... see above.
scott:
so if you now say that the rational verification process is itself
experience,
msh:
The rational verification process is secondary to experience...
scott:
in order to keep with the next sentence: "Reason grows out of
experience and is never independent from it."
msh says:
I would say reason without experience is impossible...
scott:
... then you are saying that, in the case of mathematics, reason
grows out of reason.
msh says:
I don't follow your reasoning here, empirical or otherwise. I would
say what I said in the beginning: math is rooted in experience and
flowers through reason. No roots, no reason.
scott:
What is clear from this is that the way you want to extend
"empirical" to include reason makes the word "empirical" lose any
distinctive value it might have.
msh says:
I'm not sure what DMB would say here, but I'm not extending
"empirical" to include reason. I'm saying that any sentient deprived
of sensual input from birth will, upon emerging from his SD
environment, be INCAPABLE of reasoning for a mensurable amount of
time.
Thanks. I'll let you guys work out the details.
Best,
Mark Steven Heyman (msh)
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