I don't get that, if there is no unambiguous link of cause and effect, what is there left to describe, or even observe ?
I think that if someone is completely unable to justify an observed truth to others, then it might not be a truth at all.
I think that if someone is completely unable to justify an observed truth to others, then it might not be a truth at all.
Veritasium has a nice video on Godel’s incompleteness theorem. It’s quite ironic that it was mathematically provable that analytic systems can never be complete, and can’t be provably coherent.
https://m.youtube.com/watch?v=HeQX2HjkcNo&pp=ygUUdmVyaXRhc2l...
If you somehow find an unprovable theorem (quite rare), you can always try with a different set of axioms. Mathematics are not about proving absolute truths of the universe but rather of pushing reasoning over a set of axioms the furthest possible.
Also as a nitpick, analytic systems that don't contain arithmetic can be complete and proven coherent.
As for the real world, facts that can neither be proven true nor false (existence of an immaterial soul for example), I think should be left at that. It is useless speculating about things we can't ever know of. I leave that to religion/spirituality.
And how do you know which things we can know of and which we cannot? Trusting your gut instinct on that isn't scientific. And why is speculating about immaterial things useless? I'm sure many great mathematicians heard some form of "what you're doing is useless and has no use or relation in the real world" especially in the realm of pure mathematics.
You bring up the soul which is a convenient example, but let's instead use a concept which YOU know exists for yourself which is consciousness. Can we ever know anything more about the mystery of consciousness or life or why any of this world and universe exists? Are those unknowable? Should we not talk about them? Should we only try to apply the lens of science here and for some reason not try to advance our understanding using philosophy even though it might not be as formal and unambiguous as math?
Imagine reality as the problem space of all things that could exist within the constraints of physics. The problem with observational evidence that it is only providing a tiny window into what is possible, really only the most probable are going to be what you see for the most part. Philosophy gives a means of meta views of systems and simplified system views that allow us to find otherwise unreachable islands of what can exist in our reality.
As for the other questions you mentioned, I still haven't found any reason to believe their answers are unkowable.
If anyone disproves my first reasoning, I will have to consider the question of the soul as worth pursuing again.
Just like in mathematics, if you have sufficient proof that a theorem is unprovable, it is useless trying to prove it!
So no, I don't trust my gut feeling about wether or not to seek the answer to something.
Not death of logic, since logic is still consistent. Gödel didn't say math was wrong, just incomplete.
So philosophy might step into the space beyond where a current logical set of axioms can reach. To explore something un-provable and maybe find a new set of axioms that were not reachable through logic built on the previous axioms.
What if the observed truth that someone is trying to communicate is paradoxical and hard to communicate in and of itself? What if the truth is ambiguous? What constitutes ambiguous or unambiguous?
At the end of the day ambiguity is a real concept, so is a paradox, therefore there will exist things that are ambiguous and paradoxical and pointing that out does have value.
Being hard to communicate is precisely why it's important to communicate rigorously and formally.
How can you try to explore the ego, consciousness, unconsciousness, dreams, suffering, life's purpose, subjective beauty, symbolism, truth, religion, god, ethics and whatever else that is not easily formalized? We might very well arrive at a formal and unambiguous description of these sometime in the far future, so are we not supposed to at least try to talk about these concepts now? You use different tools for different concepts, and science and philosophy is just 2 of those tools. At the end of the day philosophy undeniably changed the world, so there is at least some value to it. Philosophy is not anti-logic, it is very much for logic.
It is a practical question. Sometimes we need to have or choose a hard answer to make a decision. It inevitably isn't going to be solved formally.
Any more than what is the dividing line between a chair and not-chair. Many patterns we encounter have fuzzy non-formal edges.
Perfect consensus is impossible, but any consensus is valuable. So we invent and argue about the "best" way to "understand" these things.
These arguments are partly objective, partly subjective, partly emergent, and partly just farmed out to favorite "authorities" or social pressure. But important and unavoidable.
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At the highest level, even how we percieve reality is important. It impacts our values, our motivations, our ethics, how we cope with events, etc. Trickling down to every day choices.
"What is real?" ends up being an important question, no matter how lacking in formal rigor the answers we each have are.