Tuesday, May 18, 2010


In graduate school, I had to take a class in epistemology, the study of "what is knowledge" and "how do we know what we know." It took one week in this class to realize I didn't know crap, and this course was going to be VERY difficult. VERY.

We slugged our way through "Justified True Beliefs" ... only to blow these beliefs away by Edmund Gettier's problems titled "Is Justified True Belief Knowledge?"
Gettier gave me a headache.

Gettier is famous for his counter-examples that say there are cases of beliefs that are both true and justified, but they are not knowledge. If you need to read his Case I  here it is:

Case I

Smith has applied for a job, but, it is claimed, has a justified belief that "Jones will get the job". He also has a justified belief that "Jones has 10 coins in his pocket". Smith therefore (justifiably) concludes (by the rule of the transitivity of identity) that "the man who will get the job has 10 coins in his pocket".
In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that "the man who will get the job has 10 coins in his pocket" was justified and true. But it does not appear to be knowledge.

Do you have a headache yet?

The whole semester went on and on like this. I questioned my whole life, my knowledge of myself, and even the multiplication table. If I knew 3 x 3 was 9, was it really?

At this same time in my life, I was tutoring a young lad named Seymour, a 3rd grader. Seymour was very weak in math. His skills weren't bad, but his attention span was lousy. Seymour was not going to learn the multiplication table by going through flashcards. Yet he responded to learning how to multiply by building the equations - first on paper, then in his mind. 3 x 3.... hmm, build a line of three blocks three times. Duh, you get nine. And not only did Seymour BELIEVE it was nine, but he had knowledge that it was.

Seymour became so proficient at building his mental multiplication models that I could actually see the blocks being arranged when I stared into his eyes. His brain was piling block upon block, butting them up side to side and top to bottom.

When the day came for his big math test, he aced the multiplication questions. He told me he just looked at a problem, closed his eyes, and pictured the blocks being built. He had the knowledge...
I was sad. All I had was the justified true belief that had been driven into my brain by flashcards. When I was in 3rd grade and took my first multiplication test, I never built blocks in my mind. Instead, I would close my eyes and picture my mother holding up a flashcard, coaxing me to answer correctly.

Maybe epistemology is only as hard as we make it.

Did you know that there is such a thing as Catholic Epistemology? I wonder if they use flashcards or building blocks...


altadenahiker said...

This is related to, though not the same as, syllogisms, is it not? Let me come back to this, because 'tis a meaty topic. I know it is.

BANJO52 said...

Gettier and his kind might make it sound less appealing or less important than it is. If I understand the issue, all we have to do is look at politics, or religion, or the real meaning of currency to realize the difference between knowledge and belief. "I believe this $100 bill has value." In fact, it's a piece of paper that a culture CLAIMS to be valuable. People rob, rape, and kill (to be brief) because they think that what they believe is what they know. Am I hearing the issue correctly?

You baited the hook . . .

Brenda's Arizona said...

But that is the whole point, Banyjomyn. A knowledge has to have belief AND be true to all. Robbing, raping and killing might be a truth or belief to one (or a group), but not to all. Just because you see something or just because you believe something does NOT make it knowledge. You see a cow in a field. Do you knowledge of a cow in that field? No, you have belief that a cow is there, and it might be true, but it is not knowledge...

So, what we are learning is that knowledge is NOT a belief or a truth. It is more. And CULTURE, of all things, influence what is knowledge. Maybe that will Part Two of my post... what I learned is knowledge depending on where the student is 'from'. Or at least, where I thought I had knowledge of his/her being from. Ok, I just had copies of birth certificates, which gave me justified true belief, but now knowledge.

Sigh. My head is hurting again.
I think this is why I taught math and not epistemology.

Thérèse said...

Methodology sounds easier...
I liked reading your example with Seymour.

BANJO52 said...

So what can be known? And if it's limited to one culture, is it worth knowing?

I might be OK with the answers, "nothing" and "no, unless you need to do 'business' with that culture."

I'm not sure I actually buy that (most likely a person or region that's been robbed, raped -- and MAYBE even killed -- KNOWS that something is very different, in a bad way).

But it's easier to accept the notion of knowing nothing than the "I know everything because I say I know it, and my preacher, parents, teacher said so," which I feel I'm hearing more often now than ever, from at least a couple parts of the world.