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Re: 0 = 1
Posted:
Sep 23, 2017 2:47 PM


On Saturday, September 23, 2017 at 10:54:13 AM UTC7, FromTheRafters wrote: > FredJeffries wrote : > > On Saturday, September 23, 2017 at 9:10:59 AM UTC7, 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 notyetformalized 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.



