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.