Philosophy Now Forum

Under common ontological notions, you obviously cannot describe a class that doesn't already exist, since they all exist as abstract objects as soon as they are classes. Also a class didn't come into existence. It exists independently of time since it is neither a physical nor a mental object. So y...

But note that "All axioms are invented" is still false. After you described a class of axiomatic systems, you may discover them without any inventing. How do you describe a class that doesn't already exist? How did this class came into existence without the axioms which define it? Under c...

... That's a really long-winded way to go about it. All axioms are invented. All consequences thereof (theorems) are discovered. This is going in a better direction. But note that "All axioms are invented" is still false. After you described a class of axiomatic systems, you may discover ...

There are four types of mindsets when it comes to religion: 1. gnostic theist: "I know that my god(s) is/are real." 2. agnostic theist: "I believe that my god(s) is/are real, but I am aware to not know this for certain." 3. gnostic atheist: "I know that no gods are real.&quo...

Without going into detail, this cannot be an argument in any way for P != NP, because what really matters is _how_ hard problems are to solve, not that they are merely "harder". So any argument would have to include corresponding calculations of boundaries . For instance, the LLM wrote pot...

I fully agree with godelian throughout this thread up to this point, if I correctly understood the points made. Moreover, I am convinced (partly due to numerous interactions with such people) that people who oppose the axiom of infinity and advocate constructivism (as a philosophy of mathematics) si...