A Solution to the Gettier Problem (JTB+ #1)

Some thoughts on epistemology

The classic formulation of knowledge, until Gettier came around and knocked it down, was Justified True Belief (henceforth JTB). At first glance it seems reasonable enough. I look at an apple on my table, I see that it is an apple (justification), there is in fact an apple on my table (truth), and I believe that the thing on my table is an apple (belief), so we say I know that there is an apple on my table.

Great. Then Gettier rolls up and says “well okay, but what about cases like this?” And now we call such cases Gettier cases.

Example, lifted from Wikipedia: “Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition: (d) Jones is the man who will get the job, and Jones has ten coins in his pocket.

Smith's evidence for (d) might be that the president of the company assured him that Jones would, in the end, be selected and that he, Smith, had counted the coins in Jones's pocket ten minutes ago. Proposition (d) entails: (e) The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is true, though proposition (d), from which Smith inferred (e), is false. In our example, then, all of the following are true: (i) (e) is true, (ii) Smith believes that (e) is true, and (iii) Smith is justified in believing that (e) is true. But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith's pocket, while Smith does not know how many coins are in his pocket, and bases his belief in (e) on a count of the coins in Jones's pocket, whom he falsely believes to be the man who will get the job.”

So Smith has a true justified belief that it seems very strange to call knowledge. Cases like these are Gettier cases. And you can construct all sorts of examples of this type, Gettier cases where you have a true justified belief but through happenstance the subject seems to be missing some important element of knowledge.

The classic bandaid solution to this example is to throw in a fourth element to our definition of knowledge. Instead of JTB we’ll require that knowledge be JTB and, in addition, that the belief not be derived from any false lemmas. Call this formulation JTB+. This does fix the Smith/Jones example, as Smith’s JTB is derived from the false lemma that Jones will get the job. However, it’s not so clear that JTB+ is sufficient to solve all Gettier cases.

Example: I see a thing on my lawn that looks like a deer. I am therefore justified in believing there is a deer on my lawn. Unbeknownst to me the deer is a fake, a plush replica deer. However, outside my field of vision there is in fact a deer on my lawn. So in this case we have a justified true belief, but it seems to be true only by happenstance, and it seems strange to say that I know there’s a deer on the lawn even though I don’t know about the actual deer. Moreover, it’s not immediately obvious that I have inferred my belief from any false suppositions or lemmas. Rather the argument has been made that my belief is a purely sensory perception. My eyeballs perceive a deer. At first glance it doesn’t seem like there’s any logic at all going on there, let alone logic based on false lemmas. This has been widely regarded as the death knell for the JTB+ approach.

I propose the following remedy to salvage it. I claim that there is in fact logic happening subconsciously and that it is in fact based on false premises in our deer scenario (and indeed in any Gettier case). The causal chain of “look at a deer—>belief it’s a deer” seems ironclad in its lack of logic. And yet it can’t be a purely perceptual matter because babies don’t look at a deer and immediately believe “that’s a deer”. Rather as we develop we see examples of objects we are told are deer by fiat and gradually we learn there is a particular set of traits comprising “deer-ness” and that an object having a sufficient number of those traits is a deer. Four legs, brown fur, white tails, etc. I claim that subconsciously, under the hood, our brains are playing this matching game whenever we see something and categorize it. Take the following example: I see a furry four-legged mammal from behind and I don’t know what it is, but I have at the ready a handful of categories of furry four-legged mammals to which it could belong. If someone asked me what it was I might say “it could be a dog, or it could be a cat.” I’ve begun to play the matching game. Then the animal turns to face me and I see its snout and its wet nose and its floppy ears. Then I’ve matched enough traits to be sure, and I tell the person, “it’s a dog.”

You might object that this doesn’t salvage JTB+ just yet, and I think you’d be right. After all, I matched a lot of traits in our deer example, and still it fell through. What gives?

The crux of my perceptional-logical model of categorization is the following principle: it’s context sensitive. I claim we have a set S of all the traits of a given category, and depending on context, we select some subset S’ of S with which to play our matching game. After all, if I really want to be sure it’s a deer I’m looking at, I ought to genetically sequence it. But in practice we accept much lower standards of evidence for claiming “x belongs to category C”. It may be sufficient in most cases to check only a handful of traits.

But by contrast there may be cases in which we have reason to believe we are being deceived where S’ is a rather large subset. Suppose for example that someone shows you a real deer and a very lifelike synthetic, animatronic deer without telling you which is which and asks you to identify the real one. Now in this case the animatronic deer has most of the traits of deer-ness, and so we are inclined to use a larger subset S’. It’s not enough to just look at both of them and see that they are furry four-legged mammals with brown fur and white tails anymore.

If we accept my perceptive-logical model of categorization and we accept that S’ is context sensitive, I claim this is sufficient to repair JTB+. In the deer example we were not expecting to be deceived and so were subconsciously using too lax a set S’. In other words, subconsciously we did have a false lemma, and that lemma was something like this: “In this context C, an object with the traits in the set S’ is a deer.” Which turns out not to be true.

Did I manage to save JTB+ from the tyranny of Gettier? Let me know what you think in the comments.