Timeline for How do you prove mathematical induction without the notion of a set?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23 at 4:41 | answer | added | lee pappas | timeline score: 0 | |
| Jun 20 at 18:03 | history | edited | lee pappas | CC BY-SA 4.0 |
added 9 characters in body
|
| Jun 20 at 14:07 | history | edited | lee pappas | CC BY-SA 4.0 |
added 1 character in body
|
| Jun 20 at 13:53 | history | edited | lee pappas | CC BY-SA 4.0 |
added 309 characters in body
|
| Jun 18 at 22:46 | comment | added | lee pappas | @MichaelCarey, the proof is not mine. I regard it as a heuristic argument, that's why I'm seeking a rigorous one. | |
| Jun 18 at 16:47 | comment | added | Michael Carey | The proposed proof, in your post is also a bit strange. It uses an infinitely long proof, - infinitely many modus ponens arguments. Proofs are typically required to be finite. | |
| Jun 18 at 16:04 | answer | added | gnasher729 | timeline score: 2 | |
| Jun 18 at 11:26 | comment | added | lee pappas | @MichaelCarey, I simply want to avoid the set theoretic proof. That's what I meant by don't use sets in the proof. To state the axiom you need the elementhood symbol, but not more. And the notion of infinity is not required to state the principle. You will need the assumption let k denote an arbitrary natural number. But that doesn't necessitate the notion of set | |
| Jun 18 at 11:10 | answer | added | Mikhail Katz | timeline score: 3 | |
| Jun 18 at 10:33 | answer | added | user21820 | timeline score: 3 | |
| Jun 16 at 18:23 | comment | added | Michael Carey | I don't understand your question. The principle of induction as you stated it, uses the notion of set and infinity. How as any theory without a notion of set and infinity supposed to prove it? Even just stating the principle uses the notions which you want to exclude. Maybe, you can rephrase the principle to some context you have in mind which isn't talking about sets or infinity? | |
| Jun 16 at 18:11 | review | Close votes | |||
| Jun 23 at 3:05 | |||||
| Jun 16 at 17:55 | comment | added | David Gudeman | And, in any case, this is yet another example of you using this forum as a way to get people to discuss your own ideas. That is an improper use of the site. Please stop. There are plenty of philosophy sites that allow for open discussion. This is not one of them. | |
| Jun 16 at 17:53 | comment | added | David Gudeman | Your proof implicitly uses mathematical induction to prove mathematical induction. | |
| Jun 16 at 14:08 | comment | added | Matteo | In order to obtain the principle of induction, you need equivalent or stronger mathematical principles. It is possible to obtain induction from an axiom known as Hume’s principle, and there is a school of thought (Logicism) that argues that this principle is purely logical and not mathematical. | |
| Jun 16 at 12:01 | comment | added | Mauro ALLEGRANZA | You can prove it in set theory, type theory, second-order logic. All them have stronger principles that first-order logic dos not have. | |
| Jun 16 at 10:52 | history | asked | lee pappas | CC BY-SA 4.0 |