Definition of mathematical object

  • #26
23
0
Wow, replying to me 4 months later. Thats cool.

Anyway, I would argue that as 'our understanding' expands, what we understand also changes, and it can hardly be claimed that we are understanding the same thing pre and post expansion. If you make a claim about some elaborated kind of proof, you cant infer anything about a proof was prior to your elaboration. Or better said, you are now using the word 'proof' in a different way than how you had been before you choose to elaborate into what a proof is.

And I would say the same about what Math is. We define the word math, not math itself, and no definition of the word will fully capture all the ways the word is used.

As a side note, I have since studied a bit of proof theory in the last 4 months, and I find it interesting.
 
  • #27
...And "mathematical existence." Do these phrases have accepted definitions? Back when Dedekind was rejecting Cantor's transfinite ideas, could there have been a definition Cantor would refer to and say definitively "my (infinite) sets have mathematical existence because the criteria of the definition of mathematical object are satisfied"?

There are many examples of mathematical objects. All structures are mathematical objects:
http://math.chapman.edu/cgi-bin/structures?HomePage [Broken]

A proof is also a mathematical object.

Sets and categories are mathematical objects.

Any formal system is a mathematical object.

What is the common thread?

Not being of a philosophical disposition I would define a mathematical object as any object studied in a mathematical way by a mathematician.
 
Last edited by a moderator:

Related Threads on Definition of mathematical object

  • Last Post
Replies
16
Views
4K
  • Last Post
Replies
1
Views
3K
  • Last Post
2
Replies
30
Views
9K
Replies
61
Views
6K
Replies
12
Views
884
Replies
4
Views
4K
Replies
68
Views
2K
  • Last Post
Replies
3
Views
3K
Replies
5
Views
2K
Top