Q&A: Negation of Possible Knowledge
Originally published:
This is an English translation (via GPT-5.4). Read the original Hebrew version.
Negation of Possible Knowledge
Question
With God's help,
Hello Rabbi,
Sorry for the bother, but I have a question: according to the rules of logic, can one infer that:
Let us assume the premise (which you don't like so much):
A. If you know -> you cannot be mistaken.
And by negation, then:
B. If you can be mistaken -> you do not know.
Can B be derived from A?
Answer
Absolutely. This is the rule of denying the consequent (MT – modus tollens). See, for example, Column 402 and onward.
Discussion on Answer
See the column I sent you. There are ways of calculating that there.
Okay, thank you very much!
That is indeed what I thought it should be.
If so, the philosophers who identify knowledge with truth are actually claiming that:
if you know -> then it is true.
But from this it only follows that if it is not true, then you do not know. As they indeed assume (and not like you).
But it does not follow that if you are uncertain that you know—for example because you could be mistaken (denying the antecedent)—> then it is not true (denying the consequent).
But in any case, is there a way to quantify by how many "percentages" denying the antecedent denies the consequent? If at all?