Chris and Ravi, (01)
JFS>> Practicing mathematicians -- people who actually solve problems
>> that other people pay somebody to solve -- dismiss the study of
>> foundations as *irrelevant*. (02)
CM> I don't think they dismiss it so much as ignore it... (03)
I think we agree about what working mathematicians do, and the only
difference is in word choice. I have no preference for either
'dismiss' or 'ignore'. In any case, I like the following quotation: (04)
Friend of CM> "Most working mathematicians would rather not think
> about foundational issues, just as most meat-eaters would rather
> not think about how the animals are slaughtered." (05)
That supports my point that foundational issues are "irrelevant"
to the way that mathematicians think and discover their theorems. (06)
RS> But our readers do not want to acknowledge that mathematics is
> as old as the metaphysics (5000 years +) that gave us numbers
> and decimals and zero and infinity as I have translated before
> in this forum. (07)
By ignoring history, people tend to get an exaggerated sense of
"progress". The fields of AI and and Chomskyan linguistics were
notorious for making claims of progress by citing their colleagues
for insights that were thoroughly analyzed by Aristotle. But
Aristotle and Plato discussed many of their predecessors, especially
Heraclitus -- who happened to live in Anatolia on the end of the
Silk Road that brought merchants, soldiers, and philosophers from
as far away as China. (08)
People who speculate about human development used to talk about
the so-called "Great Leap Forward" about 40,000 BC of the first
cave paintings that indicated the "origin" of symbolic thinking. (09)
But now -- surprise, surprise -- archaeologists discovered a
carving of a stone python 6 meters long in a cave in Botswana.
That is not, by itself, surprising because the modern San people
who live in that area believe that humans are descended from
pythons. But upon digging deeper in that same cave, they
discovered fragments from the carving that were buried at a
level that corresponded to 70,000 BC. Furthermore, those
fragments were mixed with stone tools that exactly matched
the style of tools used elsewhere around that time. See (010)
http://www.sciencedaily.com/releases/2006/11/061130081347.htm
World's Oldest Ritual Discovered (011)
I wonder if that's the same snake that tempted Eve? (012)
Another study discovered that ice-age people around 25,000 BC
were wearing woven clothing, not just bear skins: (013)
http://www.sciencedaily.com/releases/2000/02/000203074853.htm
Ice Age Clothing Said To Be More Advanced Than Previously Thought (014)
RS> Is it not right to state that axioms have roots in metaphysics
> or philosophy and need not address reality as is in the many
> other branches of mathematics? What is the a priori basis of
> universality? (015)
I would say that the universal basis for human thinking is language
plus imagery -- and with analogy as the basic method of reasoning.
The idea of using formal axioms and formal rules of inference is
an important special case of using analogy. But you don't need
axioms to hunt deer, grow potatoes, build civilization, wage wars,
worship pythons, or think about, talk about, and reason about
such things. (016)
John (017)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (018)
|