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Topic: 0 = 1
Replies: 1   Last Post: Sep 23, 2017 2:47 PM

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Posts: 1,845
Registered: 11/29/07
Re: 0 = 1
Posted: Sep 23, 2017 2:47 PM
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On Saturday, September 23, 2017 at 10:54:13 AM UTC-7, FromTheRafters wrote:
> FredJeffries wrote :
> > On Saturday, September 23, 2017 at 9:10:59 AM UTC-7, Dan Christensen laid
> > down the law:
> >

> >> If you cannot formally define these concepts of yours purely in terms of the
> >> symbols of logic and set theory (or some equivalent), it isn't mathematics.

> >
> > That's ridiculous. You have just chauvinistically declared the mathematics of
> > thousands of years and hundreds of cultures to be "n[o]t mathematics"; not to
> > mention all of the experimental and not-yet-formalized current research; not
> > to mention all of the checkbook balancing done by millions of people who
> > never saw a "symbol of logic" in their lives.

> Are you saying that all of these thousands of years of mathmematics
> later, these things still can not be broken down to formally defined
> things "like" sets based on first order logic?

No, that is not what I said. Neither did I say the contrary. I have no idea how much of mathematics can be so broken down.

> I thought this was the
> essence of formal mathematical proofs, the ability to 'boil it down' to
> the foundational aspects.

There is more to mathematics than "formal mathematical proofs".

Mathematics has been done for thousands of years. The current fad for "defin[ing] ... concepts ... purely in terms of the symbols of logic and set theory (or some equivalent)" has been around for about a century.

I do not deny that it has proved productive in some areas, but it's not all that there is, even now. Two areas that come to mind are fractals and category theory -- neither have the formalistic foundation you require.

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