I am debating with my friend and want to quote some statements I disagreed with him about. Please try to give an unbiased answer because I feel like there is a lot of misunderstanding or dissonance between the words we use speak to each other and the definition that we both imagine them to have. I might be right, he might be right and we are both confident therefore I suggested we take it to people who have studied philosophy and mathematics (or either).
A is logical
B is proven to be logical
Are both A and B correct?
This is what my friend says
What I tell him is that A being logically possible doesn't make it true whereas B being proven logically true makes it true.
What I meant by that (and I might be wrong so again please be unbiased in telling us who is right) was that saying something is logical isn't enough. You have to say whether you mean it is logically possible or logically proven to be true since I argued that these two things are NOT the same thing.
He says, “No, I said A is logical not A is logically possible”, which confuses me since it is an unfinished sentence or statement (according to my perspective on things of course).
Second quick question regarding the academic fields of logic compared to mathematics. I told my friend, "All of maths is logic but not all of logic is maths” and my friend disagreed saying, “All of logic is maths and all of maths is logic”. I don't want to comment on what my friend meant but what I meant by my statement: that maths is a subset of logic but logic is not in its entirety a subset of maths, hence all of maths is logic but not all of logic is maths.