Wednesday, 2 November 2016

Getty Gettier Gettiest

The Gettier problem is about epistemology, the philosophical consideration of knowledge and belief.  Apparently, this problem skewers understandings of knowledge justified true belief by pointing out possible holes in the notion of justifying of true beliefs.  Gettier's actual examples are quite complicated (we'll get to them in a moment), but something close to Saul Kripke's version of the problem illustrates the principle well enough to be starting with:

Say that Fred is travelling through the countryside in his car.  He looks up and sees what appears to be a barn in a field and thinks to himself, "There's a barn in that field."  However, what he saw was merely a very convincing mock-up of a barn in the middle of a field, only an inch thick, similar to what might be seen on a movie set.  Nevertheless, further back in the field, obscured by the mock-up of the barn there is in fact a real barn that Fred did not see.

Fred will believe that there is a barn in the field, he will be correct in that there actually is a barn in the field and he will have justification for this belief because he did see what he thought was a barn, even if it was a fake barn.  But that justification is false and thus, despite being right about there being a barn in the field, it would appear that his belief, in this case, could not be thought of as constituting knowledge – despite being "justified true belief" (note that this link, at the time of writing, refers to Gettier as a "significant setback").

This problem has exercised epistemologists for decades, but it's difficult to understand why (at least for someone who is not an epistemologist).  Consider an alternative scenario:

Fred is contacted on-line by someone who is asking for assistance in fencing gold.  He decides to start small, with only a couple of bars of bullion.  He is met at a foreign airport by the Magical Mr Solomon who places a briefcase on the ground between them.  Mr Solomon hands Fred two gold bars to inspect, then waves the bars in the air before tapping rapidly on the briefcase with his foot.  When Fred looks back up, the gold bars are gone from Mr Solomon's hands and he is assured that two gold bars are now in the briefcase.  Fred is not silly, he picks up the briefcase to check its weight and finds it to be convincingly heavy.  Fred then wanders off, gets picked up immediately by airport security and spends the next few hours being questioned as to why he has gold bullion bars in his briefcase.

Note that there are gold bars in the briefcase, but Mr Solomon didn't magically put the bars in the briefcase by means of tapping it with his foot.  That tapping just distracted Fred while the gold bars that Solomon was holding were slipped into a pouch behind his back.  Fred has been fooled into believing that there are gold bars in the briefcase.

The same applies with the barn.  Fred was fooled into believing there was a barn in the field and we know it (because, as "ideal observers", we know everything that is relevant to the scenario) – so we know that he does not have sufficient justification to believe what he believes, even if he may feel that he does.

The idea that the fact that the justification is insufficient and negates any associated claim to knowledge, even if the content of that claimed knowledge may in fact be true, aligns with Nozick's suggested solution to the Gettier problem – even if Nozick doesn't appear (in his paper on the issue) to have raised this particular objection.

It also aligns very well with my own epistemological position.

I believe that it may be the case that I know some things, but I do not believe that it is possible for me to reliably distinguish between things that I know to be true and those that I only believe to be true.  Until I looked at the Gettier problem in more detail, this position was predicated on my vantage point as a non-ideal observer, having no direct access to the truth value of the thing in question.   I only have access to my considered opinion on the truth value of that thing.  (This considered opinion is inclusive of received opinion and anything that I have available and consider to be relevant as evidence with respect to that thing, together with any methodology I may choose to employ in order to arrive at the opinion.)

These considerations have solidified my position somewhat, and extended its scope to include the notion that not only do I not have direct access to the truth value of the thing in question, but I may also be unable to objectively assess the validity of my justification in believing the truth of the thing in question.  For this reason, I should be sceptical about any claims to knowledge on two counts – except where it is clearly understood that "knowledge" is understood to be less than absolute.  This all said, I don't tend to talk in terms of what I know, but rather what I hold to be true.

So far as I know, no-one can reasonably argue that being fooled provides sufficient justification for believing a thing to be true (even if that thing was, by mere coincidence, actually true) – at least not to the extent that that belief could be considered to be proper knowledge.  We do talk in loose terms about people in the past "knowing" that the Earth was flat, but this is never justified true belief knowledge, merely received wisdom or general consensus knowledge.

We can, however, go a little further beyond questioning the validity of someone's belief justification and ask "What does Fred actually think he knows?  What does he actually believe?"  Is he really justified in believing a transferrable general statement to be true based on evidence in support of a specific statement?  In other words, is it meaningful to strip back what Fred believes to no more "there is a barn in that field" or "there are gold bars in the briefcase"?  I don't think so.

Beliefs exist in the context of other related (and correlated) beliefs.  Fred believes that a specific barn (the one he saw) is in a specific position in a specific field ("that field").  He probably also has a range of beliefs that impinge on his beliefs regarding the barn that he saw – barns are thicker than a few centimetres, farmers can't pick up barns and move them around by hand, barns usually contain hay and/or walkers.  Any potential knowledge that he has with respect to the existence of a barn exists in a very specific context, correlated with what he already knows about barns in general.  The error made appears to be in going from the specific to the general – something between a fallacy of composition and a hasty generalisation.

Similarly, Fred is wrong in believing that Mr Solomon magically placed into the briefcase the bars he had been mystically waving about.  Sure, there might be gold bars in the briefcase, but if so they are not the bars that Fred had inspected – this is an unjustified leap from "the specific gold bars, as inspected" to "two gold bars in general".  It might be worth noting that, in order to get this scenario to work, I had to rework a sentence to ensure that it wasn't a direct lie – "When Fred looks back up, the gold bars are gone from Mr Solomon's hands and he is assured that they (the two gold bars) are now in the briefcase".

Some might argue that my stripped-down variant of the Kripke version of the Gettier problem (the fake-barn scenario) might not pass muster so let's look at the actual Gettier problems.

Case I

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 then 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 Smith's 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.

Case II

Let us suppose that Smith has strong evidence for the following proposition:

f.      Jones owns a Ford.

Smith's evidence might be that Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford. Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:

g.    Either Jones owns a Ford, or Brown is in Boston.

h.    Either Jones owns a Ford, or Brown is in Barcelona.

i.      Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (f), and proceeds to accept (g), (h), and (i) on the basis of (f). Smith has correctly inferred (g), (h), and (i) from a proposition for which he has strong evidence. Smith is therefore completely justified in believing each of these three propositions, Smith, of course, has no idea where Brown is.

But imagine now that two further conditions hold. First Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not know that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.

Well, what do you know?!  In Case I, Smith is fooled.  The president of the company told him something that was untrue (deliberate or otherwise, it doesn't matter, Smith was nevertheless fooled into believing something that was untrue).  So he's lacking justification after all, the link to the ten coins in Jones' pocket is an irrelevant coincidence since the key, specific (and false) fact was that Jones was to get the job.

(An analogue that came to mind when walking the dogs is the claim that one of my dogs, which happens to be a desexed male, would almost certainly defecate on the pavement.  I have good reason to believe that was the case because he almost always does, and I carry bags at all times because I know that.  I could go from that fact to a number of generalities: a dog would defecate on the pavement, a male would defecate on the pavement and someone would have bags in their pocket.  How amazed would someone be if I claimed to have successfully predicted the actions of that homeless guy?  Hopefully not at all, since it's a totally spurious claim.)

In Case II, Smith is fooled again – in much the same way as ducks are mistaken on their last day when they get slaughtered rather than being fed as they had expected – having presumed that past events will continue unabated into the future.  Therefore, Smith has insufficient justification with respect to any claim to knowledge related to Jones' car.  (It's actually worse than this, as I explain below/)

This all comes down to a question of scepticism.  How sceptical should we be with respect to anyone's claim to knowledge?  I would suggest that we are talking about the difference between a notional claim to "absolute" knowledge (the sort of knowledge that is only accessible to an ideal observer) and a claim to a high level of confidence with respect to a belief.  As soon as we refer to a very high level of confidence as "knowledge" and accept the possibility, no matter how remote, that our "knowledge" might be false, the whole Gettier problem goes away without, I would argue, introducing unreasonable levels of scepticism.  And anyone suggesting that they might have "absolute" knowledge is likely to run headfirst into problems because they are very much fooling themselves.

---

In Gettier's paper, I think, a major problem lies in this paragraph:

I shall begin by noting two points. First, in that sense of 'justified' in which S's being justified in believing P is a necessary condition of S's knowing that P, it is possible for a person to be justified in believing a proposition that is in fact false.  Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q. Keeping these two points in mind, I shall now present two cases in which the conditions stated in (a) are true for some proposition, though it is at the same time false that the person in question knows that proposition.

It's a bit of a mess when taken out of context, but I'll try to clarify: make S a person, Smith, make P simply "a proposition" and make Q "a fact that follows from the proposition".  If (and only if) Smith is justified in believing a proposition to be true, then Smith is justified in believing any fact that follows from that proposition.   A non-controversial example is that, if Smith is justified in believing that Miss Pootles has many cats, then Smith is also justified in believing that Miss Pootles is a crazy cat lady.

(There is admittedly some subjectivity here, but the extent to which Miss Pootles is a crazy cat lady is directly related to how many cats she has, so long as Smith defines the number of cats Miss Pootles has as "many" then he can be justified in defining Miss Pootles as a crazy cat lady, even if he thinks that two is "many". For some very sad people, one might easily be defined as "(too) many".)

Note that Gettier's argument is based on a logical statement that he explicitly instructs us to kept in mind.  We can present that statement like this:

If JB(P) and P->Q, then JB(Q)

Here JB(x) means "justified belief that x is true", so this could be read as "if there is justified belief that P is true and it follows that Q is true if P is true, then there is justified belief that Q is true".  When we apply this to Gettier's first case we get:

If JB(Jones will get the job) and if follows that (a person with ten coins will get the job) is true if (Jones will get the job) is true, then JB(a person with ten coins will get the job)

We can see immediately that this falls apart.  Jones did not get the job (retrospectively making the statement "Jones will get the job" false), so the fact of his having ten coins is and was completely irrelevant.

In the second case, Gettier appears to totally ignore the requirement that Q follows from P.  Jones' car ownership has no apparent relevance to Brown's current whereabouts.  We simply cannot reasonably get from P (Jones does not own a Ford) to the suggested versions of Q (Brown is in Boston, Barcelona or Breste-Litovsk).  Even is Brown is in fact in Barcelona, Smith cannot from the facts presented, be said to "know" that.  Despite Gettier's claim to the contrary, Smith's belief (if he were to generate one in this fashion) is not at all justified.  Furthermore, there is absolutely nothing suggesting that Jones could not own a Ford while Brown is in Barcelona.  Gettier is simply wrong when he claims that "(e)ach of these propositions is entailed by (the proposition that Jones owns a Ford)".

If we turn to Kripke's example, that of the fake barn, we can see that this equates to:

If JB(a barn was observed) and it follows that (there is a barn) is true if (a barn was observed) is true, then JB(there is a barn)

But as ideal observers we know that a barn was not observed, so the argument falls apart.  Kripke's example actually goes further, including additional information to the effect that only real barns are red.  This would mean that Fred would "know" that he had observed a real barn if he observed what he took to be a red barn, but presumably he would be uncertain if the "barn" he observed was any other colour.

Some see this as "unsettling" because "there is a barn" can be inferred from "there is a red barn", but the more general "there is a barn" (which would apply to barns of all different colours) cannot necessarily be inferred directly from observing a barn.  I think that this is very much an artificial concern.

Roughly speaking, everything that falls into a particular category looks look something in that particular category (I'm going to ignore camouflage and cross-dressing).  Fake-barns and barns both look like barns.  Supposedly fake-barns and barns also look like fake-barns, to a certain extent.  However, at some arbitrarily close level of inspection, you would expect that a fake-barn would no longer look like a barn and only the barn would continue to look like a barn (for example when looked at from the side).  If this weren't the case, you could conceivably keep looking at the barn in more depth and never be able to distinguish between the "fake" barn and a "real" barn.  But if a fake barn and a real barn are indistinguishable in every possible way, then the fake barn is a real barn.  (If you consider provenance to be a distinguishing feature, as in fashion items, then provenance would merely be a feature that you would focus on.  Similarly blood diamonds are blood diamonds because of their provenance, not because of any related physical characteristic.)

I'd suggest that, strictly speaking, we don't know that, when we see things, they are what we might believe them to be.  It would be more accurate and honest to say in the example above that "there is something that looks like a barn" and/or "there is something that looks like a red barn".  The fact that fake-barns cannot be red, despite looking like a barn, would mean that we could immediately infer that something that looks like a red barn has the characteristic of looking like a real barn.  (I am ignoring red houses and horses that, due to strange tricks of the light, might look like barns – and also holograms, I'm ignoring those too.)

If that which looks like a barn is not red, we are left with the claim "there is something that looks like a barn" – which is an acceptable claim to knowledge, since such a claim doesn't stray beyond its jurisdiction, it's true irrespective of whether it's an actual barn that happens not to be painted red, or a fake-barn.  What we cannot reasonably do is make the claim "there is something that looks like a real barn".

Finally, I suppose we should think about Fred and his bullion exploits:

If JB(Mr Solomon [magically] transferred gold into the briefcase) and it follows that (there is gold in the briefcase) is true if (Solomon transferred gold into the briefcase) is true, then JB(there is gold in the briefcase)

Again, there is no justification to the key belief – the belief in Mr Solomon's magical powers – so we don't arrive at justified belief in the existence of gold in the briefcase.  (An additional clause is actually required here: "and it follows that (Mr Solomon transferred gold into the briefcase) is true if (Mr Solomon [magically] transferred gold into the briefcase) is true".)  For all Fred really knew, there could have been ordinary bricks in the briefcase, or lumps of lead.

So, in conclusion, the concerns associated with the Gettier problem do not appear to be justified.  All the examples that I have seen thus far involve fooling of the subject into believing something specific that is not true and the subject inferring something general from that which he or she has been fooled into believing.  I don't see this as presenting any real challenge whatsoever to the principle of justified true belief.


If there is a better instantiation of the Gettier problem, please feel free to present it.

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