Monday 7/08

Aporia

Readings

(none for today)

Synopsis

We began today by reviewing the syllabus and discussing the mechanics of the course. The requirements are simple: At least six times, and perhaps more, we will take time out from class to write an essay. I'll provide the prompt and the paper. The best five of these in-class essays will count for your semester grade. I'll aim for eight, but it's unclear we'll have the time.

There are a few other requirements, most notably the 'no screens!' policy.

Now, as I was thinking about how to run this course, I thought back to all the times I've taught it and realized I was never very happy with how it went. Then I thought all the way back to when I took Intro to Philosophy and realized with horror that I couldn't remember it. At all. Not a bit of it.

Something is amiss, and I think the problem has to do with how we think about philosophy. To wit, thinking of historical or topical surveys as appropriate for an introductory philosophy course is a mistake--elementary and common, perhaps, but a mistake nonetheless.

It's technically a category mistake, like asking to see the U.S. after driving through all fifty states, as if the U.S. were the same kind of thing as (or in the same category as--hence "category mistake") just another state.

You see, despite the fact that the University is organized according to various disciplines like Biology, Theater, Chemistry, English, Mathematics, Philosophy, Education, Business, and so on, putting Philosophy on the grand list of disciplines is like thinking of the U.S. as just another state like Texas or Delaware.

Philosophy, I would argue, is not a distinct discipline in the same way Biology is a distinct discipline from English with its own subject matter and its own history. Fundamentally, the subject matter of philosophy is the subject matter of every discipline; the history of philosophy is the history of every discipline.

Yet if philosophy has neither its own set of topics nor its own history, what, then, is philosophy?

I think in this at least Wittgenstein was right: Philosophy, he said, is an activity. It is something you do.

Think about riding a bicycle. We're not going to study bicycle mechanics. We're not going to learn about famous cyclists. We're not going to study the history of cycling, or memorize who won what race when.

We're going to get on bicycles and ride.

Some of you will pick it up quickly. You'll be zooming around the room in no time.

Others will fall, a lot.

Eventually, though, we should all be up and riding.

Just don't try to explain to anyone else what you're doing in Intro to Philosophy. Make something up. It doesn't matter what.

It may get bumpy at times, but I hope that, unlike me, you'll remember your introduction to philosophy. If Wittgenstein was right, you will.

The upshot of all this is that this semester, we won't study philosophy or philosophers, we will do philosophy, as best we can.

Today we began at the very beginning, so to speak, considering the case of (let's say) Caveman Thog and his buddy Og:

You see, Thog is hanging out in his cave one day when he sees Og coming from down the valley to visit. Just as Og waves back at Thog, a great bolt of lightning strikes Og, killing him dead on the spot. Thog, stunned and terrified, retreats back into the safety of his cave to ponder Og's dramatic demise.

"Surely," he says to himself, "Og must have offended the Gods! Knowing Og, he likely didn't sacrifice enough to the Gods, saving a bit more of the kill for himself and the family than the Gods approved. Angered and vengeful, the Gods struck Og down."

"Og," Thog mutters, "deserved their divine and just retribution. I, however, shall not make the same mistake!"

Thog dutifully proceeds to make a great sacrifice to the Gods, so as to ensure they well know that he, at least, should be in their favor.

Thog, note, seeks to explain Og's sudden death so as to use that explanation and control what will happen to him.

To be sure, Thog relies on a supernatural explanation, but notice that the rationale for the appeal to the supernatural or the religious is, I argued, exactly the same as the appeal to science. We appeal to science so that we can explain and predict, and we use those explanations in developing technologies which enable us to exert control over our environment.

What, then, is the difference between the supernatural explanation and the scientific explanation?

We have historically sought to tell stories about the world to explain the world. It is much easier to explain that lightning is Zeus being belligerent than telling the full, complicated, and surprisingly incomplete story of fulminology, the science of lightning. Thus by attributing agency to phenomena, we at once believe ourselves to have a better understanding of them while we feel ourselves better able to control them.

As I say, these twin desires, understanding and control, are expressed in modern terms as science and technology. If I'm right, the impulse that originally led us to religion is precisely the same impulse that now leads us to science.

Yet science springs from a very different assumption than religion. Science rejects religion's appeal to the supernatural in explanation. That is, natural phenomena can only be explained by other natural phenomena for an explanation to count as scientific. We call this principle 'naturalism'. It asserts that the natural world is explanatorily closed, barring any appeal to a supernatural world in explanation.

The reason for naturalism, of course, is that appealing to the supernatural (gods, demons, spirits, souls, ghosts, or what have you) in explaining a natural event begs the explanatory question. After all, if what explains Og's death is God, what explains God? Since we cannot explain anything about the supernatural world--it being inaccessible to us, if it exists--we are left with a mystery. Put another way, we try to explain a sudden, puzzling event (Og's demise) by appeal to something even more mysterious, God in this case. Necessarily lacking any explanation for God, our explanation of Og's death by lightning strike by appeal to God may make Thog feel better, but he's none the wiser for it.

Yet we must not thereby conclude that religion has no role in our lives. The point is rather that the reasons for having religious belief today are different than the reasons we originally had for religious belief. Naturalism recognizes that explanations by appeal to the supernatural merely explain at the cost of inviting far more troubling puzzles and mysteries, which themselves are not open to investigation.

But I digress. Today's discussion was not about supernatural explanation and the transition to natural (aka, scientific) explanation per se. We'll take up those topics later in greater detail. Instead, today what I wanted to do was to identify what gives rise to our desperate search for understanding and control in the first place.

Go back to the home page for a minute and look at the title banner. What does the little man in the painting have in his hands? Where is he sitting? If you look long enough, you come to realize that he is busy examining an impossible object, while he himself is perched on an impossible ledge. How can this be?

This feeling you may have looking carefully at the painting has many names: Bewilderment, puzzlement, perplexity, astonishment, wonderment. The Ancient Greeks had a special term for it: Aporia. Think of aporia as that sense one has of encountering something which is not merely surprising, but astonishing and, seeminly, inexplicable. Seeing Og be devastated by lightning gave Thog a wholly disconcerting sense of aporia. Indeed, aporia is often met with fear. Clearly, when we don't understand something, we've no hope of controlling it. As a result aporia--bewilderment, or wonderment--is often associated with a sense of fear and discomfort. We like thinking we understand; being shown we don't understand what we thought we did is often seen as offensive or disruptive. Need it?

"Philosophy," Aristotle announced, "begins in wonder." Without fear or discomfort, philosophy embraces aporia, finding more of value in the puzzle than in any seemingly satisfactory solution. Philosophy is special in this regard. Where other disciplines seek solutions, philosophy revels in puzzles. Philosophy invites us to wonder and, unflinching, encourages our bewilderment. As we shall see, this is also why philosophy has had a rocky history.

For now, though, I wanted to see if by considering a series of puzzles whether we could find within the class a sense of aporia--a sense, if you will, of 'how can that be?' We only got about half way through the puzzles I had planned. We'll revisit some of these next time. In the meantime, let me briefly here go over some of the puzzles we discussed again.

Aporia 01

Suppose you found yourself on the Island of Knights and Knaves needing to find the Castle, where you will find your eternal and truest love. Knights, you know, always tell the truth; Knaves never do. You also know that a Knight and a Knave guard the way to the Castle at a fork in the road and you can ask only one question to find out which way to go. Unfortunately, there is no way to tell Knights from Knaves by the way they dress or look. Nevertheless, if you are extremely clever there is a question you can ask which will get you to the Castle straightaway to be forever united in bliss with your love.

What one question should you ask? And why should you ask that question?

Point to one guard and ask the other, "Would he tell me left (or right, it doesn't matter which way you ask) is the way to the castle?" Go the opposite direction of whatever you're told.

Since one of the guards is a knight and the other a knave, you're either asking the knight or you're asking the knave this question. If the knight, he will faithfully report what the knave would say, but the knave would lie, so you do the opposite. If the knave, he will lie about what the knight truthfully says, so again you do the opposite.

The solution trades on the fact that a lie truthfully reported is still a lie, while the truth lied about is, again, a lie. No matter what you're told, it will be a lie. Hence the instruction to do the opposite.

Aporia 02

Newcomb's Paradox*

You are confronted with a choice. There are two boxes before you, A and B. You may either open both boxes, or else just open box B. You may keep what is inside any box you open, but you may not keep what is inside any box you do not open. The background is this.

A very powerful being, who has been invariably accurate in his predictions about your behavior in the past, has already acted in the following way:

He has put $1,000.00 in box A.

If he has predicted that you will open just box B, he has in addition put $1,000,000.00 in box B.

If he has predicted that you will open both boxes, he has put nothing in box B.

Should you open both boxes A and B? Or just B? Justify your answer.

*adapted from Sainsbury, R.M., Paradoxes, 2nd ed (Cambridge University Press, 1995).

As we discussed, there are equally good reasons to be a one-boxer as a two-boxer. The one-boxer will say, by choosing to open just box B, I'm doing what the predictor would have predicted, so I'll get the million dollars. The two-boxer says, sure, but the the predictor has already come and gone. Either there is a million and a thousand dollars in the boxes as you stand there wondering whether to open both, or there's not. So you might as well open both.

In this case, we seem to have two equally rational yet incompatible courses of action at hand. Unlike a puzzle, where we can grasp the solution once we discover and demonstrate it, in this case there seems no final solution at hand.

Aporia 03

With a twinge of apprehension such as he had never felt before, an anthropologist named Abercrombie stepped onto the Island of Knights and Knaves. He knew that this island was populated by most perplexing people: knights, who make only true statements, and knaves, who make only false ones. “How,” Abercrombie wondered, “am I ever to learn anything about this island if I can't tell who is lying and who is telling the truth?”

Abercrombie knew that before he could find out anything he would have to make one friend, someone whom he could always trust to tell him the truth. So when he came upon the first group of natives, three people, presumably named Arthur, Bernard, and Charles, Abercrombie thought to himself, “This is my chance to find a knight for myself.” Abercrombie first asked Arthur, “Are Bernard and Charles both knights?” Arthur replied, “Yes.” Abercrombie then asked: “Is Bernard a knight?” To his great surprise, Arthur answered: “No.”

Is Charles a knight or a knave?

Well, what do we know?

  1. Arthur asserts that Bernard and Charles are both knights.
  2. Arthur also asserts that Bernard is not a knight.

Arthur himself must be a knave: Bernard cannot both be a knight and not a knight. Hence Arthur is lying when he makes both of the above assertions.

So it is false that Bernard is not a knight, which entails that he is a knight.

It is also false that Bernard and Charles are both knights. Specifically, Arthur's first assertion is false just in case neither of them are knights or only one of them is a knight.

Yet we've already shown Bernard is a knight since Arthur's second assertion is false. So it must be the case that the Charles is not a knight. He is a knave.

All this was explained neatly and correctly, I thought, by our own Kaitlin. By the way, credit where credit is due: These and other knights and knaves puzzles are adapted from the great logician Raymond Smullyan's "Satan, Cantor, and Infinity".

Aporia 04

Setting a Surprise Exam*

On Friday before the last week of class, the Classical Formal Logic class are told that they are to have a quiz on what they have learned so far this term, particularly Aristotle's 256 logical forms. This is because they are a rather slow and lazy class, teacher adds, offensively. The class are not pleased and start muttering. 'When is it, anyway?' they ask sullenly.

Teacher smirks. 'That is up to me. I may have it at any point between now and next Friday. However, let me assure you of this, when I do have the quiz it will be a surprise!'

After school, Bob and Patricia are discussing the bad news. Bob is very worried as he has a poor memory. 'I could pass, I'm sure,' says, 'if I knew on which day the test would be, then I could learn everything the night before.'

'Don't worry, Bob,' says Patricia, 'I think teacher is having a bit of a joke at our expense - you see, I don't think there can be a quiz!'

And she explains that the test cannot be held next Friday, the last day of the term, because by then the class will know that it must be going to be held, and will therefore quickly memorize the material for the test the night before. That's great" says Bob sarcastically. 'So it's any day between now and Thursday then?'

Patricia explains patiently. 'It can't be Thursday either, because if it can't be on Friday, and it is already Wednesday night, we'd all know it would have to be coming up on Thursday, the next day!'

Bob gets it now. 'Nor could it be Wednesday, nor Tuesday - nor indeed Monday! Hey! What a joke - teacher trying to get us worried! - and now he can't hold the pop quiz without having to back down on the surprise bit. Silly old fool!'

They don't tell the others, who spend ages trying to memorize the 256 aristotelian logical forms and other nonsense, much to Bob and Patricia's secret amusement. Then on Wednesday, teacher comes in and announces the quiz.

'You can't do this!' says Bob.

'Why not?' replies teacher, surprised, but not very.

'Because it's got to be a surprise - and you can only hold the test when we're not expecting it!'

'Yes, but Bob, you're surprised, and I am holding the test' says teacher in a teachery sort of way.

Is there a flaw in Bob and Patricia's reasoning? If not, how was teacher able to surprise them with a pop quiz? If so, what is the mistake in their reasoning?

*adapted from Cohen, M. 1999. 101 Philosophy Problems. London: Routledge.

If there is a flaw in their reasoning, there must be a step in it to which we can point and say, "ah ha! That's where you've gone wrong." Yet as we think about it, where would the step be? We all agree the exam can't be Friday, but since it can't be Friday we know that once Thursday rolls around it won't be a surprise on Thursday. Since it can't be Thursday any more than it could have been Friday, it also can't be Wednesday. Nor Tuesday. Nor Monday. In thinking about it, we see no particular step in the argument where the kids went wrong. Yet here they are, surprised all the same.

Note that all of these are perplexing. Some have solutions we can figure out, but others don't seem to have any obvious solutions. The trouble is, we can't tell in advance which perplexing problems are just hard but ultimately solvable problems and which may admit of no solution whatsoever.

In this class, we will examine a number of deeply perplexing puzzles, all of which give rise to a jarring sense of aporia. I invite you to welcome and maybe relish the feeling; if not relish, then at least allow it. Allow, in short, that we may not know all we claim to know.