Knowledge as Absolute Impossibility of Mistake

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.  
  

Comments

[Leo Carton Mollica]

Thanks for the post.

Might not Dr. Jones' remark be parsed as "ceteris paribus, I shall be teaching philosophy at Whatsamatta U. next year"? Taken that way, which seems plausible, we avoid the aporia your argument otherwise forces upon us, since winning the lottery is surely among the possibilities ceteris paribus clauses are meant to exclude.

[Sean M]

Does Butchvarov's view run the risk of making the standard of knowledge too high? Does it allow for instance a version of Cartesian skepticism to arise (this is borrowed from John Greco): Note that in 1 below, I would take the discriminating from all relevant possibilities to be equivalent to the impossibility of being mistaken.

1. S can know that p is true on the basis of evidence E only if E discriminates p’s being true from all relevant possibilities that are inconsistent with p’s being true.
 
2. My evidence for my belief that I am sitting by the fire is my sensory experience.
 
3. It is a relevant possibility that I am not sitting by the fire but only dreaming that I am.
 
4. Therefore, I can know that I am sitting by the fire only if my sensory experience discriminates my sitting by the fire from my only dreaming that I am. (1, 2, 3)
 
5. But my sensory experience does not discriminate these possibilities for my sitting by the fire.
 
6. Therefore I do not know that I am sitting by the fire.
 

And if this is the case, then this type of infallibilist approach to knowledge should lead us to skepticism.

[Ethan]

But why adopt such a view of knowledge? If we do, then we have to say there is no knowledge at all. Some say mathematical "knowledge" is real "knowledge" because you can prove things and be certain about them, but one can simply be mistaken about it. So no knowledge there either. Under this view, we have to conclude that there has been no advance in human knowledge in the last 100 years, or 1000 years, or ever.

[Ethan]

Also, if we adopt this view of knowledge, then we must reconsider how we test students. Tests should determine how well the student knows the subject. But since it is possible for the student to be mistaken on a question, he merits a zero. For, no matter how correctly he answered the question, he has not demonstrated that he knows anything.

[Kevin Ringeisen]

My question is on (2) "Jones knows that if he wins the lottery, then he will not be teaching philosophy next year."

Isn't there possibility that this, too, isn't knowledge under his definition? As far as I'm aware, predictability is pretty slim when applied to the future. A number of situations (of which he can't be aware of) might arise where he both wins the lottery and continues teaching (a change in heart etc)? Also, are we talking teaching in a literal sense, as in, at the university? It's also arguable that teaching, in a sense, will not stop when he becomes an independent scholar (he does after all interact with others, publication of studies "teaches" people also). If these are both false, would they not then be contradictory but just lead to a non sequitur and invalidate the argument?

@Ethan, I see your point and agree that the hardness of this argument amounts to (at least) a negative view of knowledge in general. However, I disagree with the argument that Tests determine a student's knowledge for a variety of reasons:

1.) If a student is absent, he may receive a zero, contrary to his knowledge base.
2.) Grading uses averages (which are intrinsically non-resilient)so the student who doesn't turn in things on time (even once) has his grade influenced much more than if the teacher used the median (which is resilient). The forgetful student would have a higher "grade" with the latter. Thus, the only true grading scheme would have to include a complete statistical package complete with confidence levels et al.
3.) In relation to the above, a students "knowledge" then, is actually based on the relative distances between the scores, rather than their absolute quantities. Straight addition would fix this issue as zeros would amount not to lack of knowledge, but unproven knowledge. But then you run into the problem of a student taking more tests than others and the retesting of material.
3.) This applies mainly to multiple choice questions and mathematics. Write-out answers, or the subjective nature of an english class, also add to the difficulty as portraying tests as accurate assessments of knowledge.

In other words, instead of stating that "Tests show knowledge of students" and arguing that as a premise that this view of knowledge might be flawed (or at least pessimistic) because it always nets in 0, I would argue the opposite: "Test's don't show the knowledge of students" in which case your reasoning ends. It's not perfect system, but as the saying goes "It's good enough for government work."

[Ethan]

Very well, then, about the tests. Concerning mathematics we have to say that nobody knows if the four-color theorem has been proved, even though it has been. Similarly nobody knows that 2+2=4; we may have been mistaken about it all along.

[Ethan]

Testing aside, all students should get zero, no matter what they do, because they know nothing. Why should someone who knows nothing get an A?