Hey love your channel and may I ask a question: If in set theory, I can create a relation which takes a set of elements which are propositions (like set a is a subset of set b) and map it to a set of elements containing “true” and “false”, then why is it said that set theory itself can’t make truth valuations? I ask this because somebody told me recently that “set theory cannot make truth valuations” Is this because I cannot do what I say above? Or because truth valuations happen via deductive systems and not by say first order set theory ?
Glad you pointed this out. The word valid is unfortunately used in more than one way, even within the context of logic. The definition you are thinking of, which is also the one I was introduced to first, is the major one given at the Wikipedia page for Validity in logic: en.wikipedia.org/wiki/Validity_(logic). So, no doubt you are right. But if you scroll down that page to the section that says "Valid formula" you'll see the meaning I'm using in these videos.
Great explanation, thanks a lot!
Hey love your channel and may I ask a question:
If in set theory, I can create a relation which takes a set of elements which are propositions (like set a is a subset of set b) and map it to a set of elements containing “true” and “false”, then why is it said that set theory itself can’t make truth valuations?
I ask this because somebody told me recently that “set theory cannot make truth valuations” Is this because I cannot do what I say above? Or because truth valuations happen via deductive systems and not by say first order set theory ?
Theorems well explained
Well explained
I thought valid means if the premises is true then the conclusion must be true
Glad you pointed this out. The word valid is unfortunately used in more than one way, even within the context of logic. The definition you are thinking of, which is also the one I was introduced to first, is the major one given at the Wikipedia page for Validity in logic: en.wikipedia.org/wiki/Validity_(logic). So, no doubt you are right. But if you scroll down that page to the section that says "Valid formula" you'll see the meaning I'm using in these videos.
Good stuff.
"cuz val is not the problem" lol