[I seem to have taken a long vacation from blogging. It’s time to get back into the swing.]
I’ve posted before about my dislike for the view that knowledge is justified true belief. I have recently seen a couple of blog posts that are related, so I’ll comment about those.
Infinite worlds
The first is:
The author begins with:
In an infinite universe we would be absolutely ignorant, if my calculation is right.
The author does not give an argument to support that assertion. He seems to take it as self-evident. And I guess I’m not quite sure what he means by “absolute” here, as that qualifier does not seem to fit. I presume him to be going by the assumption that knowledge is justified true belief. And, with that assumption, presumably knowledge of an infinite world would require infinitely many beliefs.
My response is mathematics. The world of mathematics is an infinite world. If the author’s assertion is correct, then mathematical knowledge would seem to be impossible. Yet many knowledgeable mathematicians would disagree.
Education
My second example is a blog post on the conservative view of education:
In that post, the author writes:
If the central goal of education is the transmission of information, then the success of that education can be measured by a simple paper-n-pencil test. This is an idea that resonates with lots of people.
I don’t agree with that as the central goal, nor does the author of that post. But “transmission of information” does fit with “justified true belief.” As I commented on that blog post, if that were a correct account of education, then you would not need schools. Books, or radio or television or the Internet would be sufficient. Yet the evidence is that those are poor substitutes for what schools actually do.
Mathematical knowledge
Back to mathematics.
I have often heard mathematicians complain about students who “regurgitate” the lectures or the text book. Yet, if knowledge is justified true belief, then regurgitation should be a clear demonstration of knowledge. So there seems to be a widespread rejection of the idea of justified true belief among mathematicians, at least with respect to knowledge of mathematics.
The problem with justified true belief is that, while there is believing, the “knowing” could still be missing. And it is that knowing that should matter for knowledge.
I don’t have any objection to philosophers studying justified true belief. It’s just that I think something is missing in that account of knowledge. And philosophy ought to be studying what it is that is missing.