I incline towards Panayot Butchvarov's notion of knowledge as involving the absolute impossibility of mistake. In *The Concept of Knowledge *(Northwestern UP, 1970), Butchvarov writes that "an epistemic judgment of the form 'I know that p' can be regarded as having the same content as one of the form 'It is absolutely impossible that I am mistaken in believing that p'." (p. 51)

One way to motivate this view is by seeing it as the solution to a certain lottery puzzle.

Suppose Socrates Jones has just secured a teaching job at Whatsamatta U. for the 2011-2012 academic year. Suppose you ask Jones, "Do you know what you will be doing next year?" He replies, "Yes I know; I'll be teaching philosophy." But Jones doesn't like teaching; he prefers the life of the independent scholar. So he plays the lottery, hoping to win big. If you ask Jones whether he knows he isn't going to win, he of course answers in the negative. He doesn't know that he will win, but he doesn't know that won't either. Jones also knows that if he wins the lottery, then he won't work next year at a job he does not like.

On the one hand, Jones claims to know what he will be doing next year, but on the other he also claims to know that if he wins the lottery, then he won't be doing what he claims to know he will be

doing. But there is a contradiction here, which can be set forth as follows.

Let 'K' abbreviate 'knows,' 'a' the name of a person, and 'p' and 'q' propositions. We then have:

1. Kap: Jones knows that he will be teaching philosophy next year.

2. Ka(q -->~p): Jones knows that if he wins the lottery, then he will

not be teaching philosophy next year.

3. ~Ka~q: Jones does not know that he does not win the lottery.

Therefore

4. Ka~q: Jones knows that he does not win the lottery. (From 1 and 2)

But

5. (3) and (4) are contradictories.

Therefore

6. Either (1) or (2) or (3) is false.

Now surely (3) is true, so this leaves (1) and (2). One of these must be rejected to relieve the logical tension. Isn't it obvious that (1) is the stinker, or that it is more of a stinker that (2)? The inference from (1) and (2) to (4) is an instance of the principle that knowledge is closed under known implication: if you know a proposition and you know that it entails some other proposition, then you know that other proposition. This seems right, doesn't it? So why not make the obvious move of rejecting (1)?

Surely Jones does not KNOW that he will be teaching philosophy next year. How could he KNOW such a thing? The poor guy doesn't even KNOW that he will be alive tomorrow let alone have his wits sufficiently about him to conduct philosophy classes. He doesn't KNOW these things since, if we are serious, knowledge implies the impossibility of mistake, and our man can easily be mistaken about what will happen in the future.

Of course, I realize that there is much more to be said on this topic.

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