Mathematical logic notation. That there exists a member of set A for which a proposition is true does not imply that it is true for all members of set A. It’s a formal statement of the fallacy of overgeneralization.
Set theory and logic concern formal properties, not generalizations. ‘All uncles are brothers to a father’ is a formal statement reducible to logic as is ‘my uncle is left-handed’. The latter does not imply that all uncles are left-handed.
But the important thing for non-formal reality is that no one would ever believe that this is true outside of logic in the first place. It’s like the Sorites Parodox. It doesn’t deal with generalization. Only logic. In reality, only the bald man has problems discerning whether or not he’s bald.
So overall, there’s a very good reason no one in their right mind would apply the axioms of set theory to history or anthropology. The relationship between uncles and left-handedness or the numbers of hairs on a head and baldness has actually troubled nobody. The relationship between, say, a normal person and a group has troubled many.
Ok, I’m lost on this one.
Mathematical logic notation. That there exists a member of set A for which a proposition is true does not imply that it is true for all members of set A. It’s a formal statement of the fallacy of overgeneralization.
There are known knowns, and unknown knowns and unknowable unknowns which have not yet been revealed.
Set theory and logic concern formal properties, not generalizations. ‘All uncles are brothers to a father’ is a formal statement reducible to logic as is ‘my uncle is left-handed’. The latter does not imply that all uncles are left-handed.
But the important thing for non-formal reality is that no one would ever believe that this is true outside of logic in the first place. It’s like the Sorites Parodox. It doesn’t deal with generalization. Only logic. In reality, only the bald man has problems discerning whether or not he’s bald.
So overall, there’s a very good reason no one in their right mind would apply the axioms of set theory to history or anthropology. The relationship between uncles and left-handedness or the numbers of hairs on a head and baldness has actually troubled nobody. The relationship between, say, a normal person and a group has troubled many.
“It’s a formal statement of the fallacy of overgeneralization.”
Thanks, that’s the part I wasn’t getting.