Friday, 25 November 2016

The Problem with Multiverses

In The Multiverse & You (& You & You & You…), Sam Harris talks about multiverses with Max 'Mad Max' Tegmark.  Sadly, Harris didn't take the opportunity to ask Tegmark about his foundation, Foundational Questions Institute (FQXi), being funded by Templeton.  To be fair, the FQXi website has a page on their finance arrangements which make huge efforts to distance the Institute from their financiers.  Even so, they are playing with Templeton money which is always disappointing when proper science is involved.

But this is about multiverses.  In their discussion Harris and Tegmark (although possibly more so Harris) make much about the idea that if there is a multiverse, noting that they only got to Level 2 Multiverses, then there will be an infinite number of Harrises and Tegmarks doing slightly different versions of the podcast.  At one point the googolplex is mentioned, a number which although not infinite is officially considered to be very big - 10 to the power of 10100.  Apparently, someone worked out that the number of possible arrangements of the original particles in the universe is in the order of a googolplex.  Not quite infinity but, you know, a lot.  The idea is that out of those arrangements, even if a relatively small fraction of them would result in us, that would still be a lot of arrangements with beings indistinguishable from us in them.

Take that one step further and say there is the possibility that there were more or fewer particles in the initial arrangement of the universe, then you get a huge number of googolplexes of possibilities.  Within that suite of possibilities, there would again be a lot of arrangements with beings indistinguishable from us in them. Then there's the possibility of duplication - which brings us to the possibility of an infinite number of replications of us in existence.  There might not only be an infinite number of universes which are very, very similar to our own, but also an infinite number of universes (albeit a "smaller infinity") that are exactly the same.

So, it's true enough that, if Tegmark is correct about multiverses, that there are an infinite number of Tegmarks and Harrises who has a discussion that was turned into a podcast.  And it's true that there is an infinite number of Tegmarks and Harrises who had very similar, but slightly different, discussions that either did or didn't get turned into a podcast.  And it's true that this infinity of variations might include discussions in which Harris suddenly began talking in Hungarian.

What concerns me, however, is that either by accident or design, the presentation of multiverses was staggeringly arrogant.  They failed to mention that there was an infinite number of universes in which their discussion didn't take place even within the infinite number of universes which contain a Max Tegmark and a Sam Harris.  It's a bit like a series of matryoshka dolls, each of which is infinite in size but, because the rubberiness of infinity, can be ranked:

The infinite number of universes in which the Harris-Tegmark discussion happened precisely as it did in ours which is a subset of:

The infinite number of universes in which the Harris-Tegmark discussion took place which is a subset of:

The infinite number of universes in which Harris and Tegmark met each other which is a subset of:

The infinite number of universes in which both Harris and Tegmark exist which is a subset of:

The infinite number of universes in which humans exist which is a subset of:

The infinite number of universes in which intelligent life is possible which is a subset of:

The infinite number of universes in which there is something rather than nothing:

The infinite number of possible universes.

Tegmark himself points out that human endeavours have been plagued by a sense of arrogance – this, our village, is the only village.  No?  But this land is the only land.  No?  But this continent is the only continent.  No? But this planet is the only planet.  No?  But this solar system is the only solar system.  No?  But this galaxy is the only galaxy.  No?  Well, the universe that we can see is certainly the only universe.  Perhaps we’ll soon be trying on “this is the only multiverse” for size.

The arrogance is inherent in the contemplation of what we are doing (right now) and the imagining of what would be changed if things were very slightly different, as if our activities were some sort of focal point for the universe.

But I think it gets a bit worse, as least in so far as the discussion that Harris and Tegmark actually did have, in our universe.  They were discussing how there could arguably be an infinite number of universes such that anything that is possible does actually happen.  Think about that for a moment.  Anything that is possible happens in some universe or another.  Really?

Is there a universe in which an analogue of me (clearly not actually me, because I live in this universe, but a version of me that would think precisely the same as me except that this other version …) buys a lottery ticket every week and wins the jackpot every time?  This is very highly unlikely, to be sure, but it's not strictly impossible.  Oh Grand Pixie, why oh why am I not that version of me?

It gets worse.  Harris and Tegmark touch on how the brain (and the suite of the processes within the brain) interacts with the outside world, implying that the common ground is mathematics.  My concern isn't so much with that, but with the concept that there are things go on inside our brains that are interpreted as interactions with an external world that really aren't.  Usually these are minor hiccups and most of us resolve them and carry on.  Some however are constantly plagued by voices in their heads and other delusions.  It's highly unlikely that we could all be affected by chemical states in our neurology that results in coherent voices that all tell us that a god is real.  But it's not strictly impossible.  And it's not strictly impossible that cloud formations could take on the appearance of an old man in the sky (or an old woman in slightly less politically incorrect alternate universes).

What I'm suggesting here is that, at least in the rather light touch on multiverses discussed by Harris and Tegmark, the odds are that in some universe there will be all the evidence that anyone could ever need to prove the existence of a god.  The vast majority of prayers would be answered in such a universe (merely on the basis of coincidence, but the supplicants don't know that).  Everyone would get visitations from what appear to be divine agents (or rather have internally generated experiences of such visitations, purely due to random chemical reactions in their brains).

Remember that we are talking about infinity here, not just a very big number.  Even if the likelihood of an apparently god-infested universe is infinitesimally remote, if there is an infinite number of universes, then there is at least one universe like that, and possibly even an infinite number of them.

Would Harris and Tegmark agree with this, as a possibility?

Either way, it seems that multiverse predictions do tell us something about the likelihood of there being a god.

Consider the difference between 1) a great being which exists and for whose existence there is clear evidence and 2) another great being for which there is no compelling evidence of its existence.  Which is the greatest?  Unless hiddenness is defined as a strength (which seems unlikely since we are repeatedly told that the god of the theists wants to have a relationship with us), the evidence based god is superior.  Some theists will argue that it's not possible to have evidence of their god.  But what multiverse theory seems to be telling us is that it actually is possible to have overwhelming evidence of a god, even their specific god, and that that applies even if such a god does not exist.  But clearly you and I don't live in a universe in which there is overwhelming evidence of anything of the sort.

On the contrary, we live in one of the universes in which it is not only possible but entirely reasonable to reject the notion of a god.  The question therefore is this: How do theists who buy into multiverses and subscribe to some sort of mandatory divine hiddenness get around this issue?

Monday, 7 November 2016

Xavier and the Queen of Hearts

Xavier sits at a card table, across from Derren Brown.  Xavier has been asked to bring with him a brand new deck of cards, which has placed on the table.  Derren opens the pack, removes the jokers, and begins shuffling the deck.  Then he hands over the deck to Xavier and encourages him to inspect it to make sure that it's the same deck he brought and that it's a fair deck, with 52 different cards in it.

Xavier confirms that it's a fair deck.  Derren then asks Xavier to continue shuffling the pack, face down until he is happy that it's thoroughly blended.  Then Xavier is asked to cut the deck, and deal himself two cards, one face up and one face down.  Xavier is instructed to throw the rest of the deck behind him, away from the table, which he does.  Derren clarified that any card on the table or in Xavier's possession belongs to Xavier.

The card that is face up is the Queen of Hearts.  Call this Card A, and the face down card Card B.

Derren asks Xavier whether he believes that he owns the Queen of Hearts, to which Xavier says "yes".  When asked why, Xavier points to Card A and says "because I can see it right there - Card A is the Queen of Hearts".

Derren then asks Xavier to flip Card A over so it is face down, he points out that the cards on the table belong and asks whether he believes that he owns a Hearts card.  Xavier says "yes" and when asked why, says "because the Queen of Hearts is a Hearts card and Card A is the Queen of Hearts.  It's just there!"

Derren pulls his sleeves up, revealing his forearms, and asks Xavier to watch very carefully.  Then he takes a piece of wrapping paper, slips it carefully under Card B, making sure not to touch it with his fingers.  Then he gets some tape and asks Xavier to fold the wrapping paper over the card.  A few folds later and the card is securely wrapped.  Neither Darren nor Xavier has no idea what the face value of Card B is and the wrapping paper is thick enough to prevent either from seeing though it.

Derren now scoops up Card B, leans over and deposits it in Xavier's top pocket.  So, Card A is on the table and Card B is in Xavier's pocket.  Xavier owns both cards.

Now Derren asks whether Xavier believes that he owns a royal card.  Xavier says "yes" and when asked why, clarifies that the Queen of Hearts is a royal card and Card A (right there) is the Queen of Hearts.

At this point, Derren casually flips over Card A, revealing that it isn't the Queen of Hearts after all, but rather the Seven of Clubs.


This article is about a question of belief.

My position is that Xavier believed that he had the Queen of Hearts.  When prompted he assented to the notion that he believed that he owned a Hearts card, however, he didn't simply believe that he owned any old Hearts card, he believed that he owned the Queen of Hearts, which happens to be a Hearts card.  When asked about owning a royal card, he responded in the affirmative, but in reality he believed that he owned the Queen of Hearts, which happens to be a royal card.

Derren used the distraction, while putting Card B into Xavier's top pocket, to switch out the Queen of Hearts with the Four of Clubs which he had palmed earlier, during the initial shuffle.

The question revolves around Card B.  Nobody knows what that card is, not even Derren.  It could be a royal card.  If it is a royal card, noting that Xavier owns it, does this make his assent to the notion "Xavier owns a royal card" a true belief, if when asked he no longer owns the Queen of Hearts?

I don't think so, because I don't think that Xavier ever has a partially formed belief that he owns a royal card.  He very specifically believes that he owns the Queen of Hearts, which is a royal card.

Strangely enough, some people don't think this way.  They think that if Card B was, say, the Queen of Spades, then Xavier would have had a true belief that he owned a royal card, despite having a false belief that he owned the Queen of Hearts.

What do you believe?

Thursday, 3 November 2016

A Warrant Against the Gettiest of Gettiers

In Getty Gettier Gettiest, I wrote about how the Gettier problems that I have seen don't present a problem to the notion of justified true belief, because they all involve fooling the subject into false believing something specific, having that subject infer something general from the false belief and then having the general inference proved to be true.

I want to expand a little in this article, having discussed the issue over at CraigLand in terms of "warrant" (more of "warrant" a bit later).

It's generally understood that to have knowledge, one must have justified true belief.  In other words, in order to know something, you must have sufficiently good reasons for believing something that is true.  What is built into this model, but apparently overlooked, is the idea that you can have good reasons for believing something that is not true.  So, you can have justified false belief.  Let's revisit the scenario of the faux-barns as an explanation (slightly complicated per Goldman 1976, as taken from EIP).

The fake barns (Goldman 1976). Henry is driving in the countryside, looking at objects in fields. He sees what looks exactly like a barn. Accordingly, he thinks that he is seeing a barn. Now, that is indeed what he is doing. But what he does not realize is that the neighborhood contains many fake barns - mere barn facades that look like real barns when viewed from the road. And if he had been looking at one of them, he would have been deceived into believing that he was seeing a barn. Luckily, he was not doing this. Consequently, his belief is justified and true.

So what we have here is an observer, Henry, whose eyes have received a configuration of photons which is consistent with having seen a barn.  The problem is that he could have received a functionally identical configuration of photons without having seen a barn, if he had been looking at a fake barn, rather than a real one.

So the question is, given that he could just as easily as been deceived as having been correctly informed about a barn in the field, does this constitute knowledge?  My instinct tells me that it does.  Henry has a good reason to believe that there's a barn there, there is a barn there and he believes that there's a barn there.

Those arguing that there is a problem will raise a few other related scenarios.

First, Henry looks into another field and receives a configuration of photons that is consistent with there being a barn in that field and as a consequence believes that there is a barn in the field.  However, it's not a barn, it's a faux-barn.  I don't think that this introduces a problem.  Henry merely has a justified false belief; he's made a completely understandable error and this does not constitute knowledge.

Second, say that when looking into the first field, Henry is actually aware that in the region it is reasonably common for fields to have fake barns in them.  He sees what looks like a barn, it is actually a barn, but now he does not know that there is a barn there.  This seems strange.  He's been given more information about the situation but the apparent effect of that is to make less knowledge available to him.  The reduction of available knowledge, however, is not real - the total knowledge has increased but is differently distributed.  Henry now has knowledge about other things that look like barns in fields and as a consequence of having that knowledge, he now will not form a belief that what he sees is necessarily a barn.  Instead, he's forced to believe something more general, that what he is seeing is something that looks like a barn - which constitutes knowledge because it's a justified true belief.  However, this more generalised knowledge will apply when he looks in other fields.  Note that without this information about fake barns, Henry would otherwise have held false beliefs about barns when he saw faux-barns and thus had no knowledge at all.

Third, say that Henry is looking in a third field, not knowing about fake barns despite looking right at one.  Hidden behind that barn, and thus not seen by him, is a real barn.  This is a scenario that I covered in Getty Gettier Gettiest and, per that article, my position is that Henry is being fooled into believing that there is a barn in the field.  He might actually be right in the general claim that there is "a barn" in the field, but believing that to be so is not justified by the information that is available to him.  He could know that he is looking at something that looks like a barn.  If he could justify believing that he is looking at a fake barn, then he could know that there is a fake barn in the field.  But there is no relevant justification for him to believe that there is an actual barn in the field.  The fact that there actually is a barn in the field is only "serendipitously" true.

Now, in Getty Gettier Gettiest, I raised the issue of sliding between specifics and generalities.  Henry saw what he thought to be a specific barn and in order for there to be a problem with justified true belief, it would have to be valid to make an inference from a specific false belief to a general true belief.  That's not logically sound.

At CraigLand, that was not precisely the approach that I took.  Instead I pointed out that for justified true belief to constitute knowledge, the justification involved must be relevant and that the belief cannot be merely serendipitously true.  In other words, the truth of the belief cannot be decoupled from the justification for the belief.

While the invalidity of inferring a general true belief from a specific false belief covers all the Gettier problems that I am currently aware of, I think that relevance of justification and absence of serendipity may be key in addressing a more generalised Gettier-like challenge to the notion of justified true belief as a basis for knowledge.


Now, I did say that there would be more on "warrant".  In the discussion I was having at CraigLand, the definition of warrant was:

the quality or property that turns mere true belief into knowledge

This definition is very close to how Plantinga introduces it in Warranted Christian Belief (I have elsewhere challenged what Plantinga thinks warrant is (as opposed to what it is defined as)).

Think about it.  Warrant is being considered almost like an alchemical agent.  Not only that, it would appear that "warrant" only pertains to true beliefs.  Could you have a warranted false belief, if "warrant" is the "the quality or property that turns mere true belief into knowledge"?  Plantinga's theory is a dual plus theory of knowledge, masquerading as a tripartite theory of knowledge.

And, even worse, it's basically a theological approach to knowledge as one of the WLC fans at CraigLand wrote "I would say it has to be an actual interface with God".  Plantinga himself writes about how warrant is related to some sort of "design plan" - a cognitive system "working the way it ought to" (ie as designed).

Anyway, part of the motivation to look towards something like warrant is because some people think that the justified true belief theory of knowledge is somehow threatened by the Gettier problem.  Once it's realised that the Gettier problem doesn't affect justified true belief theory and that, at best, warrant is just a limited form of (relevant) justification for (non-serendiptiously) true belief, the justification for even considering "warrant" quickly dissipates.

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.  For example, 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 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" (even if it is an unpainted real barn, given our caveat that "real barns" are red - we're straying into "No True Scotsman" territory here and I don't want to e'en think aboot let alone ken what Scotsmen keep in their barns).

Finally, I suppose we should return to 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.

Tuesday, 1 November 2016

Another Whack with the Sledgehammer

In The Sledgehammer Approach, I compared theism to believing that a test subject hit an egg with a sledgehammer while blindfolded - in the absence of actual evidence in support of that belief.

There are of course problems with the analogy.

Some theists would say that the nature of god is such that the test subject could not have missed an egg (this is equivalent to the claim that god is necessary, the theological position that it is impossible for god not to exist).  Such theists would argue that I was vague in that I said "give (the test subject) a sledgehammer" and "take some eggs" rather than specifying that the experimental protocol would require either an infinitely large sledgehammer or an infinite number of eggs, thus making it impossible for the test subject to miss.

Some atheists would say that if any eggs were put out, then that would be ignoring the fact that the god in question is logically impossible and cannot exist.  I'd probably agree if we were talking about a specific god, but strictly speaking when we are talking about theism, the god isn’t specified.

Then there is the problem of "prior probability".  If only one very small egg was put out and the sledgehammer's head was tiny (a pinhammer or needlehammer, perhaps), then the prior probability of hitting an egg would be very small.  Alternatively, if a large (but not infinite) number of eggs were put out and the sledgehammer was a monster, then it'd be highly likely that an egg would be hit.  This wasn't really what I was getting at with the article, I wasn't trying to be accurate about the likelihood of a god existing, I was only trying to explain the shading involved with being an atheist - so something like a 50-50 chance of hitting an egg was fine.  This also has the benefit of being a strong-ish version of the theist position.

The size of the sledgehammer's head, however, raises another issue.  Evidence.  The test subject would be justified in assuming a low probability to hitting an egg if the sledgehammer was light (and the head small) and a higher probability if it was heavy (and the head large).  Then there are the sounds and smells involved.  The test protocol only called for a blindfold, but an egg being smashed by a sledgehammer might make a distinguishable noise and the albumen and yolk could possibly release a scent that the test subject could pick up.  Also, the sledgehammer might have been a bit slippery after the strike, if an egg was smashed.  There are enough variations between potential test subjects with respect to their sensitivity that some might smash eggs without noticing while others would believe that they had smashed one when they hadn't.  Their beliefs, therefore, would be subjective - overdetectors would detect smashed eggs when there aren't any, underdetectors would miss a lot of smashed eggs.  (This is equivalent to "agent detection" - some atheists, like myself, reckon that theists have hyperactive agent detection.)

The point in the analogy is that there isn't any conclusive evidence, which is precisely the position that atheists take.  A theist might want to argue that there is conclusive evidence for their god, but the atheist cannot really accept that argument without becoming a theist.