Re: hebrew - significant archaeological find

In article <1132149898.286256.98100@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Shlomo Argamon <argamon@xxxxxxxxxxx> wrote:

>Micha Berger wrote:
>> On Wed, 16 Nov 2005 07:17:32 +0000 (UTC), jameshanley39@xxxxxxxxxxx <jameshanley39@xxxxxxxxxxx> wrote:
>> : By the way. Linguistics does not have its own logic. Computer science
>> : does not have its own logic.

>> But both quantum mechanics and halakhah do!

Quantum mechanics does not have an adequate logic. However,
what is observed by any observer satisfies "ordinary" logic.

>> I know, a tangent. But this discussion of what linguistics is threatens
>> to grow into a tangent itself, AND it's off-topic.

>True. To get it slightly more on-topic (have a little patience):
>Mathematical logic is only a small corner, really, of logic (= the
>science of valid reasoning). The program, exemplified by Russell &
>Whitehead's Principia, to establish all of mathematics on the basis of
>formal logic (set theory, more or less) foundered on Goedel's theorems,

Not at all. It is still the case that all of mathematics
is explained by the same logic; it is just that some things
might never be answered. One can add more to get those
answered, but then some others cannot be, etc. If the
assumptions lead to an inconsistency, some assumptions
are scrapped, in the hope that that inconsistency has been
eliminated, but the logic is still kepts. Goedel's theorems
are true in a weaker logic, but the "usual" logic will not
lead to an inconsistency; it is not powerful enough. Set
theory is NOT formal logic; formal logic is only the
framework within which mathematics is done.

>and reasoning in other fields only makes the problem worse. For
>example, the "13 modes of interpretating the Torah" (R. Yishma'el's
>version) are not principles of formal mathematical logic, but rather
>rhetorical principles; even those which are "logical" as opposed to
>"linguistic" in nature, cannot easily (if at all) be placed in a purely
>formal framework.

Rhetorical principles can lead to contradictory results;
the ones above do.

And of course even formal logic comes in many
>varieties, as Micha notes.

Not that many. The weaker ones, adequate for Goedel's
results, are clumsy to use and even unclear. I am
familiar with the attempts to do mathematics with them,
and the problems are too great.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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