Friday, January 19, 2018

Turri's Maxwell's Car

When Maxwell arrives at work in the morning, he always parks in one of two spots: C8 or D8. Half the time he parks in C8, and half the time he parks in D8. Today Maxwell parked in C8. It’s lunchtime at work. Maxwell and his assistant are up in the archives room searching for a particular document. Maxwell says, “I might have left the document in my car.” The assistant asks, “Mr. Maxwell, is your car parked in space C8? It’s not unheard of for cars to be stolen.” Maxwell thinks carefully for a moment and then responds, “No, my car has not been stolen. It is parked in C8.”
With that example began John Turri's "Epistemic closure and folk epistemology," where he went on to add that:
The epistemic closure principle says, roughly, that if one knows that P, and one knows that if P then Q, and one infers Q, then one knows Q.
Maxwell may have been misapplying logic, when he thought carefully: he recalled that he had parked in C8, rather than D8, and so he thought that his car was in C8 (unless it had, as his assistant noted, been stolen), from which he may have concluded that it was not stolen (unless it was). (But perhaps he took the low chance of his car having been stolen to be reason enough to think that it had not been stolen. And for all we know the archive's windows looked down on C8.)

Most people think that Maxwell knew that his car was parked in C8 (assuming that it had not been stolen), but not that it had not been stolen, which contradicts Epistemic Closure: if Maxwell knows that his car is in C8, and he knows that if his car is in C8 then it has not been stolen, which he seemed to know, because he did seem to infer, from it being in C8, that it had not been stolen, then Closure says that Maxwell did know that his car had not been stolen.

What I find interesting is how logical it seems, to go from Maxwell knowing that his car was in C8 rather than D8 (which I think he did know), to Maxwell knowing that his car was in C8 (which most people think he did know), to Maxwell knowing that his car was still in C8, to Maxwell knowing that his car had not been taken out of C8 (which most people think he did not know). Were that sequence formalized, would we be further from the dark?

Thursday, January 18, 2018

50 meanings for "know"

To say that you know something is, basically, to say that you are certain of it; in effect you are promising the truth of what you say. Knowledge is important because we want, as a society, bodies of knowledge that can be relied upon. That is why, when cause for doubt is shown to us by skeptical scenarios, our natural reaction is to doubt that we had knowledge. But of course, academics cannot conclude that they know nothing. At the other end of the scale, consider a boy, sitting an exam, who is not sure of an answer but puts it down anyway, and it is the right answer: we say that he did know the answer. There are a range of uses of the word "know." In between those two are all the sciences, and all their applications, and we might expect that such varied uses of "know" might give it a certain inconsistency. That would explain why the Analytical philosophical analysis of "know" remains an on-going opportunity in modern epistemology. Continental philosophers may notice that you can only ever really know what you have yourself made up, however, because the paradigm case of knowledge is, as it has always been, that of a God: proposition P is known by subject S when S's justification for believing P guarantees that P is true. How close you have to get to that ideal, for what you believe to count as knowledge, depends upon the kind of knowledge that it is, the use that you are going to make of it, and so on. We pick up on the use of "know" as we learn English, and I for one have found that good claims to knowledge can be gambles, akin to promises, even though knowledge stands opposed to epistemic luck. More generally, we might disagree about the meaning of "know" without any of us being wrong.

Wednesday, January 17, 2018

Gettier's Smith's Job

Smith applies for a job, as does X. Smith thinks that X will get the job, and knows that X has 10 coins in his pocket, so Smith thinks that the man who gets the job will have 10 coins in his pocket. As it turns out, Smith gets the job, and also has 10 coins in his pocket, and so his italicized belief was true. Since Smith was justified in thinking that X would get the job (his new boss had told him that X would get the job) his italicized belief was also justified; but, it was not knowledge, according to Gettier.

One problem with all of that is that it is a bit obscure what exactly is going on: there was a bit of inferring going on, and as a rule we cannot rely on such things as, for example, epistemic closure: If you know that P, and also that P implies Q, then even if you infer Q, you do not necessarily know Q (there was a good example by John Turri at Certain Doubts). Still, one thing is obvious: Smith's reasons for believing the italicized belief were no part of the reasons why it was true, and so it was not knowledge.

However, because those reasons turned out not to be that good (X did not get the job), there is also a question mark over whether they really were good enough to count as justification in the sense required for knowledge (only a question mark). A statement known to be false was always a statement that could have been false (that really could, not just could theoretically). When we think of knowledge we think of statements that can be relied upon, that are justified in ways that basically guarantee their truth.

Monday, January 15, 2018

A lot of very high credence is Not belief

The Lockean assumption that belief is sufficiently high credence became very popular in analytic philosophy, but it seems to be refuted by a lot of our quotidian beliefs:

Consider the view from any familiar window, for example. You already know the kind of view that you would probably have, although the chance of any particular arrangement of people, cars, leaves and so forth is extremely low. Consequently you have a very high tacit (or implicit) credence that you will not have that particular view. Still, your view will probably be unsurprising: you do not believe that you will not have that particular view.

A simpler (but non-quotidian) example for explicit belief: consider a die with a very large number of faces. You can roll the die around in your hand, giving each face a cursory glance and think, of each face, that it is very unlikely to end up on top when you roll the die, but that it might. For each face, you have a very high credence in the proposition that it will not end up on top, but you do not believe that it will not end up on top, because you will not be at all surprised when one of them does.

Sunday, January 14, 2018

Most Knowledge is Epistemic Luck

In a recent post (linked to here) I noted how we seem to simply assume that we can refer directly to the things around us: we cannot know that their substances are not changing in ways that leave their properties the same, because we can only know their properties. Were their substances changing, reference to them would keep failing (assuming that reference is direct).
     And similarly, we cannot rule out that we are Brains In Vats: all of our evidence is compatible with our brains having been harvested by aliens (in a real world where such aliens are common) and put into high-tech vats that simulate worldly experiences. While we are unlikely to have been harvested recently (as recently noted) it is not unlikely that there are such aliens (what is strange is that we see no aliens).
     But of course, we can and do simply assume that there are not such aliens, that we are not currently asleep in our beds and dreaming, that all of our particles are not always being switched with identical particles, and so forth. It is upon such foundations that our knowledge of the external world is built. And of course, we are not BIVs, we are not dreaming, and so on; or at least, I do assume not. And so we do have knowledge of the external world. But, because those are assumptions, such knowledge is epistemic luck.

Saturday, January 13, 2018

Something like Fake Barns

What is adequate justification for holding a belief? It depends on one's context. A true belief that was well-justified when it was formed might cease to count as knowledge within a stricter setting, such as a court-room or a laboratory. And the famous Fake Barns involve unusual contexts. And of course, one needs to be sufficiently rational. Suppose that I see a red car, in a normal road (no fake cars), for example, and so form the belief that there is a red car. But, I also have a lot of irrational beliefs that there are various objects. When there is a red car, I believe that there is, and I am unlikely to have the belief that there is a red car if there is not a red car, although I am quite likely to have some belief that there is something when there is nothing. (It is easy to think of other examples of true beliefs that might seem at first glance to be justified but which do not count as knowledge because they are held by someone who is in some way unqualified.)

Friday, January 12, 2018

UK Gender Pay Gap

What is the Gender Pay Gap in the UK?
Progress has stalled on closing the gender pay gap, which now stands at 14.1% according to the Office for National Statistics, with no movement on the figure in the last three years. At the current rate of change it will take 100 years to close the male-female gap in pay.
     According to the ONS, older women face the greatest discrimination, with women in their 50s paid on average 18.6% less than their male colleagues. While the gap among younger women had almost been eliminated, in the last six years there was a notable increase, from 1.1% in 2011 to 5.5% this year.
     The gap is highest in London (20.7%), followed by the south-east at 16.3%. It is lowest in Wales, at 8.3%, and the north-east, at 10.2%. The gap is higher in the private sector, at 17.1%. But it has fallen by 4.3% points since 2011, while in the public sector it has plateaued at just above 14%.
The Guardian, 10 November 2017
     A Populist might think: Clearly there is sexism in how people are paid, and clearly it is worse in London. But London is a relatively progressive place, so why would there be so much more sexism in London? Well, there are more foreigners in London, and a lot of foreign countries are more sexist than we are. Could the solution to the problem of the Gender Pay Gap therefore be immigration limitation? Of course, that's silly; so the question arises: should we blame sexism? If sexism is not the whole story, then we may well go wrong if we do. Equal Pay legislation has been around for a while, so there must be more to the Gender Pay Gap than men getting paid more than women for doing the same job, even if there are occasional instances of illegality.
     The key to unlocking the meaning of any statistics is lateral thinking, because we need, of course, the full range of possibilities to examine, if we are not to go wrong in our analyses. I shall run through a few possibilities below, but I am not a statistician; I cannot aim for completeness. My point is the logical point that when we are given statistics by professionals we also need to be given, not just links to where the numbers came from, but also a list of a broad range of factors that might have given rise to them, and some argument that that range is complete. Professionals should be able to do that, because statistics have also been around for a while.
     A large part of the Gender Pay Gap comes from the most highly paid (who tend to be older, and to work in London), so the question arises: is that part mostly due to men getting paid, on average, more than women for doing the same sort of top jobs, or to men getting, on average, better paid top jobs than women? The former should be dealt with by the courts; regarding the latter, individuals at high levels of pay are often paid for what they seem to be offering as that individual. Consequently it matters, not so much what colleagues are getting, as how much the individual could get elsewhere. And so if men are, on average, more mobile than women, then that could lead to a Gender Pay Gap, because being able to choose from a greater range of jobs would tend to increase the pay of the highest paid job. Note that people do tend to move to London to get jobs and promotions.
     Men might be more mobile. At the other end of the pay scale, a proposed solution to the pay gap has indeed been to improve the availability of child care. And just as childcare is a factor because women have wombs, so men may, perhaps, be more likely to work in order to show off (which could tend to make them more mobile). Such displays may well have been part of our biological differences earlier in our evolution, and in the modern economy men might therefore be statistically more suited to such areas as sport, gaming, banking and so forth, areas that tend to have very high pay at the top, and which tend to be in the private sector. There might even be an element of danger-money in such areas. Overall, life-expectancy is a few years less for men than it is for women (a gap that is also no longer shrinking), and according to HSE:
In 2016/17, 133 (97%) of all worker fatalities were to male workers, a similar proportion to earlier years.
Since most of those were in low-paid work, that might go some way towards explaining that part of the Gender Pay Gap (note that there would be greater numbers of injured, and so forth).
     The most obvious biological factor, though, is that men tend to be taller than women, on average, so that there are a lot more men than women among the tallest people. That is a possible factor in the Gender Pay Gap because people do naturally tend to look up (pun intended) to tall people, so that being tall has long been known to be a desirable quality in management. Note that it is not so much whether tall people do make better leaders, as whether recruiters think that other people will think more highly of tall people, and give them better results. (Note that this factor might be exacerbated by taller boys tending to think of themselves as natural leaders, while taller girls tend towards shyness to some extent, for just one example of an exacerbating factor.)
     The question is: what are the other factors? Why has a complete list not figured in the recent political debates (e.g. those recently sparked by Carrie Gracie)?
     What other factors can you think of?

Thursday, January 11, 2018

What Do Philosophers Do?

What do you know, for sure? Being sure that you have hands,
for example, could be justified ( you may be using them now,
to operate a phone or a keyboard), but you can hardly rule out
the following scenario, according to which you have no hands:

Your brain was recently harvested by aliens and you are now in a vat
experiencing a detailed simulation; your memories have been altered,
but for you "hand" still refers to things outside the vat. And out there,
those aliens have turned the real world into one enormous brain-farm.

You cannot rule that out,
but you can know that it is unlikely
that your brain was only recently harvested
and so you can, of course, know that you have hands.

Monday, December 18, 2017

Do We Systematically Misunderstand Our Own Language?


Suppose that God had created Adam and also, in an identical space-time, an exact copy of Adam. Such a God could swap Adam with that other person, then swap them back, and do that over and over, and it would make no difference, empirically: they have identical memories and everything. One difference it would make, though, is that any direct reference to Adam in this space-time would keep failing.

And similarly, what if fundamental particles (or other substances) are constantly being replaced by identical particles (substances)? It would make no difference empirically, which is why we cannot rule it out, logically. We can of course assume that it does not occur. Consequently we can assume that reference is direct; but, surely language would work normally even if such replacements were occurring.

Friday, November 03, 2017

The Trouble with Transporters

In Star Trek people are beamed from place to place using transporters (their molecules are converted into energy which is then beamed to another place where it is turned back into the original people), even though logic dictates that if so then people should not eat food, whereas in Star Trek they do eat food. The logic is as follows: When people eat they replace some of their molecules with ones from food, so that we can easily imagine that all their molecules are replaced, with the old ones being crapped out. If that crap was collected and its atoms rearranged into an exact copy of those people, then that would be just that: copies. So, if that is how things are, then transporters would kill people and create copies of them.

Thursday, October 19, 2017

Isserley's Feeling For Snow

The sensation of fresh snow crunching underfoot was deeply satisfying to Isserley. Just the idea of all that water vapour solidifying by the cloudful and fluttering to earth was miraculous. She couldn't quite believe it, even after all these years. It was a phenomenon of stupendous and unjustifiably useless extravagance. Yet here it lay, soft and powdery, edibly pure. Isserley scooped a handful off the ground and ate some. It was delicious.
Michel Faber, Under the Skin, 56

Saturday, September 09, 2017

"Him Who Has Understanding"

222111 is the number of The Royal Mint,
and it equals 1 + 2 + 3 + ... + 666, where
666 = 1 + 2 + 3 + ... + 36 is The Number
Of The Beast, which is Spooky, because
money is the root of all evil. 36 = 1 + 2 +
+ 3 + ... + 8, and 8 = 2 x 2 x 2 x 1 x 1 x 1

Tuesday, February 14, 2017

Easy as 1, 2, 3 (in base 5 + 5)


12 = 3 x 4
56 = 7 x 8
90 = 360/4

      0 + 12 = 3 x 4
      5 + 67 = 8 x 9 = 360/5

(in a minute there's 360/6 = 60 seconds)

4 x 5 x (6 + 6 + 6) = 360 = (5 + 5) x 6 x 6

                    1 + 2 + 3 + 4 = 5 + 5
1 + 2 + 3 + ... + 8 = 9 x 4 = 6 x 6

    1 + 2 + 3 + ... + (5 + 5) = 55
    1 + 2 + 3 + ... + (6 x 6) = 666