Mathematics has no foundations

[ladyjane]

The Australian philosopher colin leslie dean argues mathematics has no
foundations

http://gamahucherpress.yellowgum.com/books/philosophy/Absurd_math_science4.pdf

The absurdities or meaninglessness of mathematics and science: paradoxes and contradiction in mathematics and science which makes them meaningless, mathematics and science are examples of mythical thought, case study of the meaninglessness of all views

Moeblee states

http://www.talkaboutscience.com/group/sci.logic/messages/203462.html

Granted, we use an informal version of that logic to prove the consistency of the formal version of that logic (or we use a formal version at the meta level to prove the consistency of the formal version of the object level). But such would be the case for ANY logic that is foundational

Mathematics uses logic
but
it needs to prove this logic is consistent
before it has a foundation for its mathematics

if you use logic to prove logic is consistent then you are just begging
the question and being circular -and that is not a proof
or
2)
you use another system as Moeblee says

Granted, we use an informal version of that logic to prove the consistency of the formal version of that logic

(or we use a formal version at the meta level to prove the consistency of the formal version of the object level). But such would be the case for ANY logic that is foundational

then you must prove the logic that is used to prove the consistency of the
formal version to be consistent

or
you must prove the formal version at the meta level is consistent

here you just end in an infinite regress
thus there can be and is no foundation to mathematics

thus Godel etc have not proved anything as there is no foundation upon
which to base the proofs

[Faust]

Mathematics rests upon a handful of axioms and assumptions.

Which every mathematician already knows.

This does not render mathematics meaningless, it merely removes mathematics as a source of certainty. Which all but a few rationalists have known for a long time.

Old news.

[ladyjane]

Mathematics rests upon a handful of axioms and assumptions.

manipulated by rules of logic
that logic cannot be proven consistent without
circularity
or getting into an infinite regress
thus with out proof of the consistency of the rules that manipulate the axioms assumptions of math
mathematics has no foundations

[Wonderer]

@ladyjane

Mathematics rests upon a handful of axioms and assumptions.

manipulated by rules of logic
that logic cannot be proven consistent without
circularity
or getting into an infinite regress
thus with out proof of the consistency of the rules that manipulate the axioms assumptions of math
mathematics has no foundations

the logic which you use to point this out suffers from the same attack on logic.

logic is something we all agree on, not something we say is absolute.

your attack on math is just as meaningles as the math itself if you choose to disregard logic.

[Faust]

Yes, logic is “circular”. As a method. This is never an objection to a logical argument. What is objectionable is what is known as “vicious” circularity. Which may be in the eye of the beholder. But this has to do with the premises, and not with logic itself.

ladyjane - it’s really time to get over your heartbreak.

Life is uncertain. We must live it, nonetheless.

I am quite certain that if you bought something from me that costs 75 dollars, and paid for it with a hundred dollar bill, you would be quite certain that I owed you twenty-five dollars in change.

If this is not true, then I would like to sell you something.

Anything.

[Anthem]

Reported.

Seriously, can’t we ban him?

[bike_seat]

what has he/she done wrong?

[Anthem]

This is probably his tenth post on the exact same subject.