[lit-ideas] Re: Numbers
- From: John Wager <john.wager1@xxxxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Wed, 18 Jan 2006 12:38:56 -0600
Andreas Ramos wrote:
There are only two fundamental numbers. 0 and 1.
In... base 10? Binary? "10" is ten in base 10, but 2 in binary. . . .
Western Civ people tend to think that base 10 is "natural" because we
have ten fingers. I've
heard this many time. But many of our counting systems are actually
base 12. . . . .
Counting systems are fascinating. Understanding them opens up entire
new ways of looking at
things and understanding them.
To get students to start to think about the "concept" of number, I
typically draw a crude picture of myself on the board, and then ask them
what it is. They say "You." I then erase it, and ask if I should be held
for murder for "wiping out" the teacher. Then they say it's just an
IMAGE of me. I then make a "4" on the board and ask what THAT is. They
say "The number 4." I then erase IT and ask if I've killed "4." They
say "Of course not." But I then ask if they COULD "wipe me out" in some
way, and if that's different than what they could do to the number 4:
Can you destroy 4 in the same way you can destroy the teacher? That
gets them started to think about 4 as an idea or concept, not a symbol.
Even if we destroyed all four-legged chairs in the room, "4" would still
shomehow "be there."
I know these are all "arguments" for showing what "4" means, not just
explorations of the concept "4" but the point I was raising is that
there is a great deal of value in just exploring these concepts,
regardless of the "truth value" of the argument. Paying too much
attention to whether the conclusion formally follows from the premise
diverts attention from the fascination with what "4" might mean, really.
Is it something "out there" like the teacher? Is it something that's
permanently real? Is it only in the mind? These things should be
allowed to take root in the mind, and grow a bit, before subjecting them
to an Aristotelean critique of Platonic forms, or a formal analysis of
whether the premise is somehow mis-stated.
I personally don't think that Plato's "allegory of the cave" is a good
approach to either metaphysical or epistemological questions, but I
don't get as far as saying why not in an introductory philosophy class;
I think that students need more time than a single semester to think
about this before accepting or rejecting the "truth" of the concepts.
(And in this one thing alone, perhaps, I am close to Plato, who
suggested that one should spend YEARS doing mathematics before
attempting to do philosophy. The reasons for this, I suspect, are
similar to why I don't try to go too rapidly to formal analysis of
arguments in an introductory philosophy class.)
--
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"Never attribute to malice that which can be
explained by incompetence and ignorance."
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John Wager john.wager1@xxxxxxxxxxx
Lisle, IL, USA
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