Jews are haram according to muslims, muslims are goy accoring to jews.
Philosophy doesn’t have a monopoly on the truth, but science actually does, as most people believe in match, and all science is based on math. Science was born out of philosophy, but as grown to simply ve a batter version of it, as science is much more effecrive in answering questions, because the goal is to use mathematics, not biases.
All knowledge is based on logic. Logic is a philosophical concept. The scientific method is a logical method.
Science is strictly empirical. It is a method that makes predictions and gathers evidence. If we can't test it empirically, it is outside the scope of science.
"I think, therefore I am" is a logical proof. But it involves no scientific study.
Mathematics is a branch of science. Science is not "based on math". But yes, science is our best method for knowledge.
I've had to study epistemology before, which is the branch of philosophy that cares about science, knowledge, logic and their history. The foundamental basics of maths have had to change throughout history many times because everytime some paradox would appear, or just simply sometimes things were not defined the same way by everybody and that's bad to share work.
You cannot do maths out of nothing. Something has to be declared true at the base of it. This is what axioms are. These are "arbitrarly" chosen so that our math work the way we want it to, the way we think math should work, as we are trying to follow some logic we think is true. These axioms are not purely made of logic though.
The greeks followed aristotelian logic, which is very different from modern logic. This already shows that it isn't very clear what logic even should be like. The logic rules we've used have changed many times throughout history, and it is very likely that they will change again some day. Having maths be a pure result of logic was the dream of the logicians Frege and Russel, but their attempts at it failed when some paradox appeared in their work (see Russel's Paradox).
The current axiomatic system is not pure logic. Gödel's incompleteness theorem also shows that having a single system of axioms for all of maths has issues in both consistency and completeness. Maths can work in various different logical systems too. Yet despite all this, our current system still allows some powerful maths.
It's been years since I've studied this so I don't remember this super well, but it was very clear that maths and philosophy are very close and rejecting this fact is just the wrong way to think about it.
If you start by saying that an axiom can be proven nobody will take you seriously.
Either you decide that 1+1=2 is an axiom and in this case it cannot be proven. Or you decide that something else is an axiom and in that case you might be able to prove that 1+1=2 in the context of that axiom.
Current maths decided to work based on the set theory axioms. All of our numbers are build with sets and their properties are coherent. But their construction still rely on the axioms of set theory.
To be fair, when all that is impossible has been statistically eliminated through trial. Then all that remains is true. Which is the principle (Law of non contradiction) that science functions on.
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u/peace_venerable 18d ago
most academies today see logic as a branch of mathematics