# Logic & Philosophy of Mathematics **URL:** https://www.thephilosophyforum.com/c/logic-philosophy-of-mathematics/12.md [Latest](https://www.thephilosophyforum.com/latest.md) · [Categories](https://www.thephilosophyforum.com/categories.md) · [Tags](https://www.thephilosophyforum.com/tags.md) --- ## [About the Logic & Philosophy of Mathematics category](https://www.thephilosophyforum.com/t/about-the-logic-philosophy-of-mathematics-category/15)
**Author:** [@Jamal](https://www.thephilosophyforum.com/u/Jamal)\ **Replies:** 0\ **Last updated:** [November 13, 2025, 10:46am UTC](https://www.thephilosophyforum.com/t/about-the-logic-philosophy-of-mathematics-category/15 "2025-11-13T10:46:45Z")
Were logic and mathematics invented or discovered? Can reason be reduced to formal logic? Are there true contradictions? --- ## [The panic in mathematics](https://www.thephilosophyforum.com/t/the-panic-in-mathematics/1005)
**Author:** [@Banno](https://www.thephilosophyforum.com/u/Banno)\ **Replies:** 132\ **Last updated:** [October 19, 2026, 2:15am UTC](https://www.thephilosophyforum.com/t/the-panic-in-mathematics/1005 "2026-10-19T02:15:31Z")
There’s a bit of anxiety setting in amongst our mathematical cousins, it seems. Please, have a read of this Scientific American article to get an idea of why. At Secret Math Meeting, Researchers Struggle to Outsmart AI … --- ## [How do we know which logic describes the real world? ](https://www.thephilosophyforum.com/t/how-do-we-know-which-logic-describes-the-real-world/3476)
**Author:** [@Cserax](https://www.thephilosophyforum.com/u/Cserax)\ **Replies:** 107\ **Last updated:** [October 17, 2026, 9:22pm UTC](https://www.thephilosophyforum.com/t/how-do-we-know-which-logic-describes-the-real-world/3476 "2026-10-17T21:22:06Z")
Hi everyone! I don’t have a background in philosophy, so I might have made a major flaw in my reasoning, and I apologize in advance for that. Recently, I decided to look into Godel’s incompleteness theorems, and I was di… --- ## [Morton's fork, fallacious/not?](https://www.thephilosophyforum.com/t/mortons-fork-fallacious-not/2609)
**Author:** [@Scorpion](https://www.thephilosophyforum.com/u/Scorpion)\ **Replies:** 53\ **Last updated:** [October 7, 2026, 9:58am UTC](https://www.thephilosophyforum.com/t/mortons-fork-fallacious-not/2609 "2026-10-07T09:58:05Z")
Morton’s fork is the tax dilemma. If you’re poor you’ve saved money. If you’re rich you have money to spare. Either way you have to pay taxes. The Wikipage claims this is a false dilemma. I thought it might be of intere… --- ## [The Pythagoreans](https://www.thephilosophyforum.com/t/the-pythagoreans/3092)
**Author:** [@VerticalOntology](https://www.thephilosophyforum.com/u/VerticalOntology)\ **Replies:** 11\ **Last updated:** [September 29, 2026, 7:06am UTC](https://www.thephilosophyforum.com/t/the-pythagoreans/3092 "2026-09-29T07:06:53Z")
From the standpoint of the naïve logic of modern positivism, Pythagoras’ philosophy may not appear particularly profound, and his reflections may seem little more than childish games with numbers. Yet at the foundation o… --- ## [The Liar's Paradox](https://www.thephilosophyforum.com/t/the-liars-paradox/447)
**Author:** [@Porge0](https://www.thephilosophyforum.com/u/Porge0)\ **Replies:** 106\ **Last updated:** [September 22, 2026, 5:29pm UTC](https://www.thephilosophyforum.com/t/the-liars-paradox/447 "2026-09-22T17:29:51Z")
This is a paradox that, as I, a logic purist (If such a label exists anywhere) have read, troubles me, for it seems to strike a jab at one of the three most foundational laws of logic, which is that of noncontradiction (… --- ## [Godel's Incompleteness theorems implication](https://www.thephilosophyforum.com/t/godels-incompleteness-theorems-implication/2991)
**Author:** [@Realist](https://www.thephilosophyforum.com/u/Realist)\ **Replies:** 15\ **Last updated:** [September 20, 2026, 1:59pm UTC](https://www.thephilosophyforum.com/t/godels-incompleteness-theorems-implication/2991 "2026-09-20T13:59:50Z")
As far as I can tell Godel proved that if your system is as strong as Peano number theory then it’s not complete, i.e there are assertions that are true but not provable. But then its negation must be false but not refu… --- ## [Mathematics and Phenomenology](https://www.thephilosophyforum.com/t/mathematics-and-phenomenology/3102)
**Author:** [@VerticalOntology](https://www.thephilosophyforum.com/u/VerticalOntology)\ **Replies:** 11\ **Last updated:** [September 17, 2026, 4:04pm UTC](https://www.thephilosophyforum.com/t/mathematics-and-phenomenology/3102 "2026-09-17T16:04:02Z")
Mathematics Begins Not with Proof, but with Vision The stereotypical image of mathematics revolves around proof. But proof belongs to a later layer. What comes first is not a deduction, but a vision. This is precisely wh… --- ## [Expository OP on propositional logic?](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886)
**Author:** [@Maybe-MaybeNot](https://www.thephilosophyforum.com/u/Maybe-MaybeNot)\ **Replies:** 4\ **Last updated:** [September 8, 2026, 12:21am UTC](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886 "2026-09-08T00:21:07Z")
I’m new to TPF. Apologies if this is the wrong category. I’ve been working for some time on a system of propositional logic melding classical 2-valued logic with S5. It’s finally coming together. Now I have the problem… --- ## [AI is Evolution Succeeding](https://www.thephilosophyforum.com/t/ai-is-evolution-succeeding/2607)
**Author:** [@ucarr](https://www.thephilosophyforum.com/u/ucarr)\ **Replies:** 34\ **Last updated:** [August 23, 2026, 7:16pm UTC](https://www.thephilosophyforum.com/t/ai-is-evolution-succeeding/2607 "2026-08-23T19:16:13Z")
If I program an AI to find the most efficient and thorough way to achieve a presumably innocent goal, innocently allowing it robust defenses for protecting the stability and persistence of the results and ramifications o… --- ## [The Halting Problem Problem](https://www.thephilosophyforum.com/t/the-halting-problem-problem/2173)
**Author:** [@j\_j](https://www.thephilosophyforum.com/u/j_j)\ **Replies:** 124\ **Last updated:** [August 13, 2026, 9:31am UTC](https://www.thephilosophyforum.com/t/the-halting-problem-problem/2173 "2026-08-13T09:31:07Z")
“Does a program halt on a given input ?” I would like to react to this question as a sort-of-constructivist. Turing machines are great, but they are one model of computation among many “equivalent” models. It suffices … --- ## [A discussion of "generalized numerals"](https://www.thephilosophyforum.com/t/a-discussion-of-generalized-numerals/1703)
**Author:** [@j\_j](https://www.thephilosophyforum.com/u/j_j)\ **Replies:** 49\ **Last updated:** [July 11, 2026, 4:42pm UTC](https://www.thephilosophyforum.com/t/a-discussion-of-generalized-numerals/1703 "2026-07-11T16:42:04Z")
EDIT : I didn’t realize that “generalized numerals” was already in use for something that I don’t intend here. I thought the phrase was mine — not already taken. What are numbers ? I suggest that we might want to under… --- ## [What’s So Shocking About Incompleteness?](https://www.thephilosophyforum.com/t/what-s-so-shocking-about-incompleteness/1048)
**Author:** [@Jamal](https://www.thephilosophyforum.com/u/Jamal)\ **Replies:** 84\ **Last updated:** [July 8, 2026, 4:23am UTC](https://www.thephilosophyforum.com/t/what-s-so-shocking-about-incompleteness/1048 "2026-07-08T04:23:29Z")
I saw this comment on Quanta Magazine from mathematician and logician Jouko Väänänen, contributing to a survey of opinions about the implications of Gödel’s incompleteness theorems: Incompleteness is an unwelcome but u… --- ## [Newcomb's Paradox](https://www.thephilosophyforum.com/t/newcombs-paradox/298)
**Author:** [@AlveK](https://www.thephilosophyforum.com/u/AlveK)\ **Replies:** 900\ **Last updated:** [June 13, 2026, 12:57pm UTC](https://www.thephilosophyforum.com/t/newcombs-paradox/298 "2026-06-13T12:57:47Z")
Veritasium recently posted this video on Newcomb’s Paradox. I also debated the matter with someone in the Shoutbox, and now I felt compelled to make a post on this. I believe that with a little logic, the singular correc… --- ## [Using code for Newcomb's problem](https://www.thephilosophyforum.com/t/using-code-for-newcombs-problem/1183)
**Author:** [@felipec](https://www.thephilosophyforum.com/u/felipec)\ **Replies:** 39\ **Last updated:** [June 12, 2026, 2:38am UTC](https://www.thephilosophyforum.com/t/using-code-for-newcombs-problem/1183 "2026-06-12T02:38:42Z")
Newcomb’s problem has been discussed ad nauseam — in this forum and elsewhere — but after all this discussion little ground has been gained by either side. In an attempt to change this I’m going to use a novel approach: … --- ## [Philosophy and Math](https://www.thephilosophyforum.com/t/philosophy-and-math/1192)
**Author:** [@VerticalOntology](https://www.thephilosophyforum.com/u/VerticalOntology)\ **Replies:** 17\ **Last updated:** [June 2, 2026, 6:26pm UTC](https://www.thephilosophyforum.com/t/philosophy-and-math/1192 "2026-06-02T18:26:57Z")
Recently, one can observe a growing tendency toward a rupture between the scientific and the philosophical worldview. Even major scientists sometimes express the opinion that philosophy is useless for modern science, for… --- ## [Mathematical Platonism and its Critics](https://www.thephilosophyforum.com/t/mathematical-platonism-and-its-critics/1077)
**Author:** [@Wayfarer](https://www.thephilosophyforum.com/u/Wayfarer)\ **Replies:** 134\ **Last updated:** [May 31, 2026, 9:44am UTC](https://www.thephilosophyforum.com/t/mathematical-platonism-and-its-critics/1077 "2026-05-31T09:44:50Z")
Mathematical Platonism and its Critics I’ve long been persuaded by the basic intuition of mathematical Platonism regarding the reality of number and other mathematical entities. It came upon me as a kind of epiphany - th… --- ## [Wittgenstein and the World as Fact](https://www.thephilosophyforum.com/t/wittgenstein-and-the-world-as-fact/1135)
**Author:** [@VerticalOntology](https://www.thephilosophyforum.com/u/VerticalOntology)\ **Replies:** 6\ **Last updated:** [May 27, 2026, 9:41pm UTC](https://www.thephilosophyforum.com/t/wittgenstein-and-the-world-as-fact/1135 "2026-05-27T21:41:57Z")
It can be shown that Wittgenstein’s Tractatus Logico-Philosophicus is not logically neutral, but already contains a hidden metaphysics. The very first sentence — “1.1. The world is the totality of facts, not of things” … --- ## [Zermelo's Theorem is simultaneously intuitive and odd](https://www.thephilosophyforum.com/t/zermelos-theorem-is-simultaneously-intuitive-and-odd/974)
**Author:** [@FlannelJesus](https://www.thephilosophyforum.com/u/FlannelJesus)\ **Replies:** 9\ **Last updated:** [May 11, 2026, 10:00pm UTC](https://www.thephilosophyforum.com/t/zermelos-theorem-is-simultaneously-intuitive-and-odd/974 "2026-05-11T22:00:18Z")
In the game of Tic Tac Toe (knots and crosses for our English brothers out there), it doesn’t take long to learn the strategies to employ so that you can guarantee that you can AT LEAST get a tie in every game, and possi…