Q&A: Does Knowledge Automatically Entail Additional Knowledge, and Does Knowing Require Refuting All Possible Alternatives
Does Knowledge Automatically Entail Additional Knowledge, and Does Knowing Require Refuting All Possible Alternatives
Question
With God’s help,
Hello Rabbi,
A. I wanted to ask whether you think that a claim about knowledge that we have of something always entails some other deductive knowledge that is self-evident.
For example, a person can calculate the list of numbers in front of him and know the result (without checking again), and still not know that if someone whom he assumes is better than he is at arithmetic were to claim that the result he got is not the result, then she is mistaken. Or not?
I saw that some say there is a practical implication here: if we do in fact accept this principle of automatic entailment, then in order to know that something is true, one would actually have to rule out all competing hypotheses. But theoretically that is not workable, because it is always possible to come up with an ad hoc hypothesis that will fit all the parameters and explain the conclusion indirectly.
For example, if a person sees green grass, can he know that there really is green grass there without also rejecting the possibility that it is some kind of green polyethylene covering that looks exactly like that in one way or another?
B. What do you think about this specific example (as a metaphor, of course, for our other forms of understanding): what is the source of our understanding and justification that there is green grass before us, and what is that conclusion derived from? (After all, one can imagine something else that created the same impression at the point of our vision.)
Answer
I didn’t understand the question. Are you asking whether a mistake can occur in a mathematical calculation that I do? Obviously yes. That is not a question in logic but in psychology. In a correct calculation where it is clear to me that no mistake was made, anyone else who performs the calculation correctly will of course arrive at the same result as well (even someone smarter than me can make a mistake in calculation). This is just a collection of tautologies, and I do not know what there is to discuss here.
What does that have to do with the question about the grass? There too, if there is no other explanation, then that is the explanation. If there are other explanations, then it is not necessarily the explanation. If there are only N explanations, then once you have ruled out N-1 of them, only the last one remains. What is the discussion about?
If you are asking how we draw conclusions even though there are always additional interpretive possibilities, then I have answered that more than once: our intuition is a kind of non-sensory observation, and it selects the correct explanation (though of course it sometimes makes mistakes).