| |
 |
|
|
Science Forum Index » Logic Forum » Calculus vs. Non-contradiction?...
Page 1 of 1
|
| Author |
Message |
| OccasionalFlyer... |
 Posted: Mon Jun 09, 2008 2:32 pm |
|
|
|
Guest
|
I have no background in Calculus but I am convinced that the
principle in logic of Non-Contradiction to be correct. A and Not-A
cannot both be true simultaneously. However, I was recently told by
someone, who is reading some very big, philosophical book on
mathematics, that the proposition of calculus disproves the Law of Non-
Contradiction in logic. Can someone fill me in on how this would
work? Thanks. |
|
|
| Back to top |
|
| OccasionalFlyer... |
| Posted: Tue Jun 10, 2008 2:05 pm |
|
|
|
Guest
|
On Jun 9, 11:46 pm, Rupert <rupertmccal... at (no spam) yahoo.com> wrote:
Quote: On Jun 9, 5:32 pm, OccasionalFlyer <klit... at (no spam) apu.edu> wrote:
I have no background in Calculus but I am convinced that the
principle in logic of Non-Contradiction to be correct. A and Not-A
cannot both be true simultaneously. However, I was recently told by
someone, who is reading some very big, philosophical book on
mathematics, that the proposition of calculus disproves the Law of Non-
Contradiction in logic. Can someone fill me in on how this would
work? Thanks.
Calculus does not disprove the law of non-contradiction.
Perhaps you could tell us which book this person is reading. It's not
Berkeley's "Discourse addressed to an infidel mathematician", is it?
That was written before calculus had rigorous foundations.
The book is _Godel, Escher, Bach_, by Hofstadter. I haven't read it
but apparently the section on Propositional Calculus challenges the a
priori of Non-Contradiction. |
|
|
| Back to top |
|
| MoeBlee... |
| Posted: Tue Jun 10, 2008 2:35 pm |
|
|
|
Guest
|
On Jun 10, 5:05 pm, OccasionalFlyer <klit... at (no spam) apu.edu> wrote:
Quote: On Jun 9, 11:46 pm, Rupert <rupertmccal... at (no spam) yahoo.com> wrote:
On Jun 9, 5:32 pm, OccasionalFlyer <klit... at (no spam) apu.edu> wrote:
I have no background in Calculus but I am convinced that the
principle in logic of Non-Contradiction to be correct. A and Not-A
cannot both be true simultaneously. However, I was recently told by
someone, who is reading some very big, philosophical book on
mathematics, that the proposition of calculus disproves the Law of Non-
Contradiction in logic. Can someone fill me in on how this would
work? Thanks.
Calculus does not disprove the law of non-contradiction.
Perhaps you could tell us which book this person is reading. It's not
Berkeley's "Discourse addressed to an infidel mathematician", is it?
That was written before calculus had rigorous foundations.
The book is _Godel, Escher, Bach_, by Hofstadter. I haven't read it
but apparently the section on Propositional Calculus challenges the a
priori of Non-Contradiction.
It challenges that the law of non-contradiction is known a priori or
it challenges the law of non-contradiction? Since the law of non-
contradiction is a theorem of the classical propositional calculus, I
highly doubt that Hofstader finds the classical propositional calculus
challenging the law of non-contradiction.
MoeBlee |
|
|
| Back to top |
|
| Rupert... |
| Posted: Tue Jun 10, 2008 5:08 pm |
|
|
|
Guest
|
On Jun 10, 5:05 pm, OccasionalFlyer <klit... at (no spam) apu.edu> wrote:
Quote: On Jun 9, 11:46 pm, Rupert <rupertmccal... at (no spam) yahoo.com> wrote:
On Jun 9, 5:32 pm, OccasionalFlyer <klit... at (no spam) apu.edu> wrote:
I have no background in Calculus but I am convinced that the
principle in logic of Non-Contradiction to be correct. A and Not-A
cannot both be true simultaneously. However, I was recently told by
someone, who is reading some very big, philosophical book on
mathematics, that the proposition of calculus disproves the Law of Non-
Contradiction in logic. Can someone fill me in on how this would
work? Thanks.
Calculus does not disprove the law of non-contradiction.
Perhaps you could tell us which book this person is reading. It's not
Berkeley's "Discourse addressed to an infidel mathematician", is it?
That was written before calculus had rigorous foundations.
The book is _Godel, Escher, Bach_, by Hofstadter. I haven't read it
but apparently the section on Propositional Calculus challenges the a
priori of Non-Contradiction.
No, it doesn't. He has a philosophical discussion about the
epistemological significance of a consistency proof of the
propositional calculus. This is nothing to do with calculus in the
sense in which it is ordinarily meant, namely differential and
integral calculus. |
|
|
| Back to top |
|
| |
|
Page 1 of 1
All times are GMT - 5 Hours
The time now is Sun Nov 23, 2008 12:07 pm
|
|