I might have rushed into this and have insufficient knowledge about logic, however i have yet to see anything online go against this. Though i am not foolish enough to believe I have 'broken' logic, I am merely curious as to where I am being confused.
I realised i havent really posted a question so i'll have to do that:
I don't understand how false implies true, I'll try to explain below
People seem to be okay with making normal sentences out of A -> B.
If i have a cold, then my nose is runny.
I have a cold.
My nose is runny.
A = i have a cold
B = Nose is runny
If A then B
So far so good, this seems perfectly reasonable.
Also, false implies true exists. "If the sun is green then the grass is yellow". This statement is true. This is(almost) fine, since i can never prove nor disprove it since the sun will never be green. The only contention i have is that logic assumes that false implies true. False would(in my and some other peoples heads) imply:
"We dont know anything if false, the IF statement says something about it if it is true, not false". If the sun is green THEN the grass is yellow, we dont know anything about it if the sun is not green, the statement does not say anything about that.
It is an axiom of convenience that (False implies true) the grass is yellow is true. Logic needed that to function as far as i understood it, or it was much more convenient this way, and this leads me to my confusion, because now logic cannot be applied to statements about real life anymore.
What i mean is:
A -> B
If a is false, then B is true, which also means:
A = I have a cold
B = I have a runny nose
So if A is false then B is true. This means i have a runny nose... which is not necessarily true
The thing i could be missing would be that i can actually disprove this case of If A then B if we assume that A is cold and B is runny nose. I could disprove it just by saying I don't have a cold and my nose is not runny.
Is the precondition then that B will always be true only if A can never be true?
Which would mean that "if the sun is green then the grass is yellow" is true but "if i have a cold then my nose is runny" is not necessarily true, in which case i am satisfied.
Thanks for reading, any commens or answers are highly appriciated!
Also i am just reading wiki articles and other questions about logic but it seems like i am making slow progress in understanding anything. If anyone has suggestions as to where a good place/course to further my knowledge would be, that would also be highly appriciated.
Edit: Edited the question so that it actually points to what i am wondering about, not just 'read my text please'.
Edit 2: My confusion was this: If the sun is green then the cows are chickens. This statement is true in logic. My contention was that if we have a false statement first(The sun is green) then the second part would be true(Cows are chickens). I Thought i could use this format to make a false statement first(i do not have a cold) and then make another statement(my nose is runny) and i thought this would be true. However as far as i understand it, i can only make such statements if the first premise(i do not have a cold) is ALWAYS false and "i do not have a cold" is not always false, however, "the sun is green" is always false. So because "the sun is green" is always false, then the following statement: "Cows are chickens" is true, because we cannot possibly disprove it(because the sun is green can never happen, we may never know if cows are chickens if the sun indeed was green and therefore cannot disprove it), and in logic, if we cannot disprove something we assume it to be true. Anyways this was a silly question and i figured it out earlier when talking to someone, but either way thanks to you all for your answers!