Philosophy in 3 Minutes

Just ran across these little gems on YouTube — overviews of important philosophers done in three minutes, with excellently bad animation!

Here’s one on Aristotle that’s good (although it’s almost four minutes long, tsk tsk):

And one on Locke:

And a good one on Kant’s ethics:

SHRDLU on Film

The glory days of Artificial Intelligence — those heady days when researchers thought genuine intelligence and perhaps even consciousness would transcend the bonds of human brains and sit comfortably on computer hardware — well, it was a fun time to be alive. And check out this gem:

http://www.csail.mit.edu/videoarchive/history/aifilms

An awesome historical collection of AI videos housed at MIT.

This one’s my favorite:

 

A silent, grainy, low-res film of Terry Winograd’s awesome SHRDLU in action. For those of you youngsters out there, SHRDLU was really quite a remarkable achievement in computer programming. And the fact that Winograd’s first release of the software was in 1968 makes it all the more remarkable. The idea was to create a program that could parse real English sentences and respond intelligently to them. Winograd realized that he couldn’t tackle the problem in an unlimited domain (that is, his program wasn’t going to be able to talk about everything a human might be able to), so he limited the program’s world to a virtual table top with some blocks on it, and a virtual robotic arm that could pick up and move those blocks. Within this tiny domain, SHRDLU was really very impressive. Frankly, I’m still impressed by the program today, even though it’s more than 40 years old.

Here’s a sample excerpt from a human-SHRDLU interaction:

Person: WHAT DID THE RED CUBE SUPPORT BEFORE YOU STARTED TO CLEAN IT OFF?
Computer: THE GREEN PYRAMID.
Person: THERE WERE FIVE BLOCKS TO THE LEFT OF THE BOX THEN.
Computer: NO, ONLY FOUR OF THEM: THE RED CUBE, TWO LARGE GREEN CUBES AND A LARGE RED BLOCK.
Person: PUT THE BLUE PYRAMID ON THE BLOCK IN THE BOX.
Computer: OK. (does it)
Person: IS THERE ANYTHING WHICH IS BIGGER THAN EVERY PYRAMID BUT IS NOT AS WIDE AS THE THING THAT SUPPORTS IT?
Computer: YES, THE BLUE BLOCK.
Person: DOES A STEEPLE
Computer interrupting: SORRY, I DON’T KNOW THE WORD “STEEPLE”.
Person: A “STEEPLE” IS A STACK WHICH CONTAINS TWO GREEN CUBES AND A PYRAMID.
Computer: I UNDERSTAND.
Person: ARE THERE ANY STEEPLES NOW?
Computer: NO.
Person: BUILD ONE.
Computer: OK. (does it)
Person: CALL THE BIGGEST BLOCK “SUPERBLOCK”.
Computer: OK.
Person: HAVE YOU PICKED SUPERBLOCK UP SINCE WE BEGAN?
Computer: YES.
Person: WHY DID YOU DROP IT?
Computer: BY “IT”, I ASSUME YOU MEAN THE SUPERBLOCK.

Really impressive language processing.

AI researchers (and philosophers) at the time were a little too impressed with SHRDLU, and thought that genuinely intelligent computers were surely close at hand. In fact, Winograd himself, after wrestling for years with SHRDLU and computational language processing, came to the conclusion that AI researchers were generally far too optimistic about their achievements, at least as regarded the actual supposed intelligence of their creations. Winograd wrote:

“Most current computational models of cognition are vastly underconstrained and ad hoc; they are contrivances assembled to mimic arbitrary pieces of behavior, with insufficient concern for explicating the principles in virtue of which such behavior is exhibited and with little regard for a precise understanding.” [Winograd, 1987]

This was a cold shower for a lot of optimistic AI researchers, and a bolster to philosophers who opposed functionalism. But this is a topic for another post.

Happy AI film viewing!

Quandary Corner: Baby Hitler

Quandary Corner: In this new topic section, Alec and I will each discuss a particular ethical quandary and how we would deal with it, based on whatever ethical theory we take to be applicable at that time or in that situation. Will there be consistency across quandaries? Hahahahahahaha! Good question.

Today’s ethical quandary is an oldie but a goodie: A scientist has created a time machine that can take you back in time to when Adolf Hitler was a baby (let’s say at five months old). You will be sent to his nursery at a time that baby Hitler is alone. The nature of the time machine is such that you are only there for a maximum of two minutes. You cannot bring baby Hitler back to the future with you. You can, however, kill him. Ignoring the question of whether it is possible to change the past or not, should you kill Hitler when he was a baby or not?


Alec

My students, following my example, don’t take long before offering up “Hitler and the Nazis” whenever I ask for an example of great moral evil. Indeed, if there were a prohibition on mentioning Hitler, I’m not quite sure what I’d do, pedagogically. I suppose I’d have to resort to fictional super-villains. (Maybe I should anyway. It’s not as depressing to talk about Lex Luther.)

So, faced with the opportunity to wipe out the source of perhaps the greatest evil perpetrated in the last couple of centuries, what would I do?

Utilitarianism

My initial thought is: Of course I would kill baby Hitler. But there are some mitigating ideas that cross my mind soon after.

For one thing, Hitler was not alone in carrying out the Holocaust, and perhaps it would have happened regardless of his existence. It could well be that social forces were pointing Germany in that direction, and that another figurehead would’ve stepped into Hitler’s place, if Hitler hadn’t been available. If we’ve learned anything from time travel movies it’s that the whole thing is very unpredictable. But let’s put this worry aside for the time being, and address my feeling that the baby Hitler should be killed.

I imagine that this is the popular intuition here. But what is the basis for this intuition? Well, I can see two probable bases: utilitarianism, and righteous vengeance.

Utilitarianism is the philosophical stance that ethical decisions should be made strictly on the basis of weighing the possible good and bad outcomes of your actions. Famously, utilitarianism says that, other things being equal, ten lives are more valuable than one life, and so an action that kills one person in order to save ten is ethically justified. (We’ll save the finer points of this theory for another post. Utilitarianism is not, as you might imagine, free from problems.) Well, if you can save ten lives by killing one, just imagine the scenario where you can save millions by killing one. That’s the scenario we’ve been tasked to analyze here. By killing the baby Hitler, we are ostensibly saving millions of lives that will eventually die at his command.

Virtue Ethics

Another thing that makes me pause, when thinking about killing baby Hitler, is that I’m tremendously squeamish about death, and the idea of killing a baby (even an evil one) makes me blanch.

Gregory Peck, confronting a moral dilemma.

Gregory Peck, confronting a moral dilemma.

Now, psychological squeamishness, one could argue, has no place in ethics. If something is the right thing to do, and I don’t want to do it, I’m just wrong about that, despite whatever my superego is telling me.

But there is an aspect of this squeamishness that is actually philosophically relevant, and it revolves around the issue of virtue. Most theories of ethics are action-based. Utilitarianism, for instance, is supposed to tell you what to do in any given situation. Virtue ethics (Aristotle is most often credited as its founder) is based more on the idea of developing a good character — the idea is that if you are a generally virtuous person, you’ll generally make the right decisions when faced with moral dilemmas.

Well, it is reasonable to argue that it’s the sign of a virtuous character to be squeamish about killing a baby. And so perhaps killing the baby Hitler is the wrong thing to do, if we are to take virtue ethics seriously. Of course, it’s also the sign of a virtuous character to save millions of lives if you can, and so virtue ethics sends us mixed signals on this one.

The Right Thing To Do

In the end, I think that killing the baby Hitler is the right thing to do. And if you try to justify sparing his life, on the basis of virtuous squeamishness, you’re probably displaying the unvirtuous trait of cowardice.

There are some philosophers who argue that utilitarianism goes wrong in cases of human death, because it’s just wrong (and impossible) to weigh a life. But I say there’s something wrong with a theory of ethics that tells us we can’t weigh one life against millions.


Jim

Alec makes some good points in his write-up of the issue. I think that baby Hitler should also be killed, but I am not sure that it is for the same reasons. Let’s see.

What should we do if we have the chance to save a life, and we can do so at little to no peril to our own life? We should save the life. Few people would argue that point. Well, I might argue that point. I am not entirely convinced that life, least of all human life, is always worth saving, and that is not even based on the character or worth of the (human) life. That is a matter for another post though, perhaps. Here, I am content to go with the status quo and agree that life should be preserved.

If you see a person about to cross the street, but he does not see an oncoming car, you should alert the person to the danger, grabbing him if necessary (and, again, if it does not immediately imperil your own life). Should we save life if the only way that is available to us is to end the life of another? Whew. Good question. Do we have time left for this? We do? Dammit.

Superbad

Hitler was a bad, bad, superbad, person. If anyone ever deserved to die, it was Hitler. Perhaps, as Alec suggested above, Hitler was not the sole person responsible for all the evil attributed to his movement, but he was close enough to the sole person. Would most of it still have happened had Hitler not have been? While that is an interesting question, I don’t see that it matters much here. Baby Hitler is, as a baby (philosopher-speak: qua baby), is not evil, has not committed evil, and does not, in any modern understanding, exhibit evil tendencies or character. We are going to kill baby Hitler for what adult Hitler will bring about.

This is an interesting sense of justice: we are trying to balance a wrong that has yet to happen, but will certainly happen. The ‘balancing’ act however, is such that it will ensure the evil never occur. If that is so, then our act is unjust. If we do not do this act though, then great evil will result and that seems to make not committing the act unjust as well. There is a true dilemma here, and each horn is going to do whatever you think would make for the least possible cliche here.

This is not a true dilemma of the ordinary sort as we know what will happen if we do not act. We are 100% positive (Mel Gibson’s father aside) about what will occur if Hitler is not killed as a baby. Hence, I suggest that all the time travel does for this scenario is modify our verbs in a way that bothers us. In a justice sense, baby Hitler has to die for what we know adult Hitler will do.

Squeamishness, Utility, and the Right Thing

As for the squeamish factor that Alec notes above, I think I agree, but only as an interesting artifact. Can we trust squeamishness as a guide to morality? No, but nor does Alec think so. It is a suggestion or a clue at best.

Would I feel squeamish about killing baby Hitler? I would like to say no, because of the greater good I would be serving, but that would be a lie. I would be a little squeamish; he is a baby after all. Were I to look at his little mustache and think for even a moment about the evil commands that would march out, albeit much later, from beneath it, however, I would full on vomit with squeamishness were I not to kill him.

Lives will certainly be saved by killing baby Hitler and an enormous evil will be excised from the world. Will some other evil fill that void? More than likely, as the world seemingly sucks. Will that substitute evil be more evil than Hitler? Who can say? Baby Hitler should be killed because more lives will be saved, including infant lives, than will be lost by the singular act of killing baby Hitler, and this we can be remarkably certain of given our futuristic knowledge.

And if it turns out we were wrong, surely we would appear to ourselves in the past to stop us before it is too late. Right?

The Teleportation Debate

Arguing Over Nothing: A regular feature on the blog where we argue over something of little consequence, as if it were of major consequence. Arguing is philosophy’s raison d’être, and the beauty of an argument is often as much in its form as its content.

Today, we argue about the rough points of personal identity in Star Trek style teleportation cases. Given that the debate is essentially one about personal identity, the argument isn’t really over nothing; but the fact that teleportation is impossible makes the debate one that skirts around the edges of nothing.

Each philosopher is granted up to a 500-750 words to state his/her case as well as up to 250-500 words for rebuttal. The winner will be decided by a poll of the readers (or whoever happens to have admin privileges at the appropriate time).


Alec: I Am On Venus

So the standard teleportation scene in sci-fi goes something like this: You step into the teleportation chamber here on Earth, the technician presses a few buttons, a beam sweeps over you, and moments later you materialize in a teleportation chamber on Venus (a lovely vacation destination; bring your sunscreen).

Of course, sci-fi is not science, so it can gloss over the finer points of how this might work. Philosophers (bless them) parading as scientists have given us a couple of options regarding these finer points. (Scientists have stayed away from the issue because of it being “impossible” or some-such. Such negative nancys.)

Option 1: Each particle of you is converted to energy and actually beamed through space to be reconstituted into matter on Venus.

Option 2: Each particle of you is scanned, and the teleportation chamber on Venus pulls particles from a pile of carbon and constitutes them one by one to match the original you on Earth.

The first option is “cleaner”, in that the you on Venus is pretty incontrovertibly you. It’s all of the same particles, in the exact same configuration, after all. The messy part is in the details of how exactly you could survive being ripped apart into atoms and rebuilt. Imagine your brain being deconstructed, particle by particle. At some point your identity will be in question, as your brain will be half gone.

The second option is more interesting, and seems (to this non-scientist) to be the more likely scenario. Your physical structure is essentially computed (analyzed in the minutest detail), and rebuilt as a perfect replica. Once the replica is created, it will be atom-for-atom identical with you, and so how could it fail to have the exact same memories and thoughts as you? How could it, in other words, fail to be you?

The problem, of course, with this scenario, is that there are now two of you. In the standard case, the original you is supposed to be anesthetized and killed after the scanning/reconstructing process. The new you (with all of your memories, and the exact molecular structure of you), wakes up on Venus, with no concern about the dead original on Earth. What happens (so asks the thought experiment) if the Earth-side anesthetization goes wrong, and the original you wakes up on Earth before being killed? The technician sheepishly says: “Um, sorry, but you have been successfully replicated on Venus, and you weren’t supposed to wake up here on Earth. I’m gonna get fired if I don’t kill you right now.” Would you be okay with this? Clearly not. And this intuition fuels some philosophers to say that the original you is you, and the replicant you is not you.

But what’s good for the goose is good for the gander. What happens if the technician on Earth has an untimely heart attack, and dies before anesthetizing and killing the original you. Now the technician on Venus says to the replicant you: “Um, sorry, but the original you on Earth hasn’t been successfully killed. There can only be one you, and since you’ve only existed for a few seconds, we figure you should be killed now.” Would the replicant you be okay with this? Of course not. The replicant you has the same memories, feelings, and thoughts as you do, and would not want to be killed by a technician, no matter what the circumstances. So the same intuition that causes some philosophers to say that the original you has sacrosanct rights and is thus clearly the one you, lets us argue that the replicant you also has sacrosanct rights and is also clearly you.

What are we to say about this? Well, I think we have to bite the unpleasant bullet that there are actually two yous in this scenario, each with complete human rights and responsibilities. They almost immediately will diverge, and so the “problem” of personal identity of having two of the “same” person is not really a problem after the initial reconstitution on Venus. In fact, as soon as the replicant you has any new experience, he is effectively a different person. Which one is the real you? It’s an unanswerable (and therefore bogus) question, I think.

Jim’s Reply

Well, first of all, congrats to Alec for presupposing a big objection and then biting that bullet clean in two. I still disagree with him, but such is the nature of a friendship based on unquenchable hate.

Because Alec was kind enough to break his argument into two options, I will respond in kind. Option One is just as I would have described it, and though Alec takes the you-ness of the arrivee as incontrovertible, I controvert it just the same.

What are we to mean when we talk about a person and her identity, when questions of preservation or sameness arise? I tried to address the difficulties of this question over the past few weeks, and hopefully no one solution was seen as much better than any other (I strive for objectivity as much as possible). Let’s see what is going on here.

If you are just your parts, then option one results in you arriving at the destination, and Alec is right. Your parts are deconstituted at pod 1, shot through space in some sort of stream (the mechanics here do not matter), and are reconstituted at pod 2. However, I doubt that anybody else, Alec included, thinks of a person as just the collection of her parts. Should a serial killer dismember an individual and place all those body pieces in a bag, is that person in the bag? Surely not — who among us would say that was the person we once knew instead of saying that is what is left of that person? Were we to sharpen a pencil until all that was left was a pile of wood shavings, graphite, and an eraser, no one would point to that collection and label it as a pencil. Instead, we would all correctly say, that once was part of a pencil. I mention both a person and pencil to show that I am not going to argue for some sort of ineffable soul as the missing piece.

I think it has to be the parts and how those parts are put together, how they function, that makes the person or the object what it is. What does this say for the ‘stream’ of parts as they travel from one place to the other? You are, then you are not, then you are again. But what are we to say of you when you are not? Are you dead, only to return at a later time and different place? Are you merely gone? But to where? And how did you get there?

I am going to guess that Alec is against such a conception, once he thinks about it. Perhaps he will just bite the bullet and say that the stream is you, recognizable or not. Okay. What if we put a reflector dish in front of the receiver at pod 2 so that instead of being put together, you are bounced off into deep space, never to be caught in another receiver? Are you still existing? Do you cease to exist only when the potential for reincorporation ceases to exist? That then puts personal identity into terms of potentiality, of what ifs, of what you would be in the right circumstances. I am what I am because of what I am likely to be? But what an odd conception that seems.

As for the second option, I wholeheartedly agree with Alec. The person at the other end, the one who steps from the transporter, is not you, though it looks as much like you as you ever have and has the same thoughts and desires as you ever have had. It is not you though. You are who you are because of what you do (function) and why you do it (mental states) and what makes that possible (physical states). Those three together, in just the way they are, is what gives rise to you. The movie clone that steps out of the destination pod can only be identical in two of those three requirements (function and, possibly, mental states). Now I just have to hope that Alec does not press me on what proportions of the three above ingredients are necessary for identity to be preserved.

Alec’s Rebuttal

That’s a great way to think of the first scenario: “You are, then you are not, then you are again. But what are we to say of you when you are not? Are you dead, only to return at a later time and different place? Are you merely gone?” That observation definitely makes dubious my belief that the you on Venus is the you from Earth. I should’ve picked up on this from my own quote: “The messy part is in the details of how exactly you could survive being ripped apart into atoms and rebuilt. Imagine your brain being deconstructed, particle by particle. At some point your identity will be in question, as your brain will be half gone.” At some intermediate point, indeed your identity will in fact be null and void.

So now the question is whether or not a discontinuity in your identity is enough to call that identity into question. Well, if we take consciousness as central to the question of one’s identity, then, no, a discontinuity is not enough to call that identity into question. A dreamless sleep; an period of unconscious drunkenness; going under general anesthesia for an operation;… all of these put a big discontinuity in our conscious lives, and we still think we’re the same people after such events. But if you take bodily intactness and continuity as the key element in personal identity, then the discontinuity that your body goes through in the first scenario is indeed a big problem. The atoms all scrambled and shooting through space obviously don’t keep your physico-functional form — we can’t say that your particles flying through space are a person, any more than we can say that our pile of pencil parts is a pencil.

Jim wrote: “I think it has to be the parts and how those parts are put together, how they function, that makes the person or the object what it is.” Yes, indeed. The pile of pencil parts is not a pencil, because being a pencil is more than just the sum of its parts — it’s also the functional configuration of those parts. But if you took the pencil parts and were able to thwart the laws of thermodynamics and put all of those parts back together in the exact same configuration as when it was a pencil, then don’t you have the same pencil again? Well, then if you put those human atoms all back together again on Venus, in the exact configuration they were in before, then don’t you have the same person again, on Venus?

In fact, that’s really what this debate boils down to, metaphysically speaking. If you have a thing, and duplicate every last atom of that thing, in terms of function and construction, then don’t you have two of that exact thing? Jim thinks not; I think so. We’ll debate this more closely in a future post on the possibility of making diamonds out of Cheetos. (Seriously.)

Dualism in the Movies

What Is Dualism?

Dualism is the age-old belief that there are two sorts of stuff in the universe: physical stuff (the stuff that constitutes brains and bodies and stones and trees and cats), and mind stuff (or “soul” stuff, if you like). It found it’s most cogent expression in Descartes’ Meditations, where early on he remarks that there is one thing clearly, distinctly, and uniquely possessed by the mind: Thinking.

Thinking is another attribute of the soul; and here I discover what properly belongs to myself. This alone is inseparable from me. I am — I exist: this is certain; but how often? As often as I think; for perhaps it would even happen, if I should wholly cease to think, that I should at the same time altogether cease to be… I am therefore, precisely speaking, only a thinking thing…

Whatever else he might be, it is definitely the case that Descartes is a thinking thing. Go ahead and doubt the existence of what we usually think of as the real world — stones, trees, and cats. Say that it’s all an illusion, or a dream, or that there’s an evil demon deceiving us about the true nature of things. But one thing that’s certain is that if Descartes is being deceived, Descartes is being deceived — even if his mind is being fooled about things, it is his mind that is being fooled.

Well, if the mind has this certain specialness that the rest of the world (if it exists at all) doesn’t, then the mind and the body must be separate sorts of things:

[B]ecause I know that all which I clearly and distinctly conceive can be produced by God exactly as I conceive it, it is sufficient that I am able clearly and distinctly to conceive one thing apart from another, in order to be certain that the one is different from the other, seeing they may at least be made to exist separately, by the omnipotence of God; and it matters not by what power this separation is made, in order to be compelled to judge them different; and, therefore, merely because I know with certitude that I exist, and because, in the meantime, I do not observe that aught necessarily belongs to my nature or essence beyond my being a thinking thing, I rightly conclude that my essence consists only in my being a thinking thing [or a substance whose whole essence or nature is merely thinking]. And although I may, or rather, as I will shortly say, although I certainly do possess a body with which I am very closely conjoined; nevertheless, because, on the one hand, I have a clear and distinct idea of myself, in as far as I am only a thinking and unextended thing, and as, on the other hand, I possess a distinct idea of body, in as far as it is only an extended and unthinking thing, it is certain that I, [that is, my mind, by which I am what I am], is entirely and truly distinct from my body, and may exist without it.

Here is dualism: the idea that mental and physical substances are of an entirely different kind from one another. And, in fact, the idea goes further — mind-stuff is inherently non-physical. It doesn’t exist in space-time (otherwise it would just be a variety of physical stuff), and it doesn’t need the body in order to exist.

Dualism in the Movies

Hollywood, always up for exploiting a good philosophical idea, has a proud history of using dualism to good dramatic effect. There are a plethora of mind/body transfer stories told on film.

Here Comes Mr. JordanAnd early film taking full advantage of dualism was “Here Comes Mr. Jordan”, in 1941. The story has our hero, a boxer named Joe, die in a plane crash at the start of the film. Unfortunately, the death was a mistake, due to the slip-up of an absent-minded angel. Joe wasn’t really supposed to die for a good long time. (We can use this example to talk about determinism. Maybe someday…) Joe, obviously, isn’t happy about this, and so God allows Joe’s soul to be transferred into the freshly dead body of a corrupt millionaire, just murdered by his wife. Misadventures ensue, as the personhood — the identity — of Joe tries to navigate his way in a new body, in new circumstances.

The key for our discussion here is that Joe’s mind — his personhood; his soul — is completely separatable from any physical body. It is a different sort of stuff entirely, and can be housed in any host body by a sufficiently powerful supernatural being.

You might, at this point, be thinking the following very reasonable question: But how does this non-physical mind stuff actually interact with a physical body? Well, that’s a damn good question, and sits at the core of many criticisms of dualism. We usually think of causation as a purely physical process. Billiard balls smash into billiard balls and make them move; atoms collide into atoms, generating heat and occasionally atomic detonations; you push a door in order to open it; an avalanche crushes trees beneath its mass;… physical objects and physical movements cause other physical objects to move. How is a non-physical thing (a mind) supposed to cause anything physical to happen? If you’re a dualist, you’re in trouble here. The mind (a non-physical thing) thinks that you should raise your right hand; the physical hand moves. What is the causal chain here? Descartes postulated that the mind finds its way into the brain via the pineal gland; but this is really no answer — it just delays the answer. The new questions becomes: How does the mind interact with the pineal gland? And we are back at square one.

“Here Comes Mr. Jordan” was remade in 1978 as “Heaven Can Wait”, with Warren Beatty.

Heaven Can Wait

And ever since there has been no shortage of dualistic cinema to amuse us and make us question our philosophical takes on the philosophy and metaphysics of the mind.

Actually, there were several Disney flicks that got in on the dualistic action, before “Heaven Can Wait”.

1959’s “The Shaggy Dog”, starring Fred MacMurray as an unfortunate soul who gets transferred into a dog’s body:

The Shaggy Dog

In 1976, the franchise was continued with “The Shaggy D.A.”, starring (if you can call it that) Tim Conway as another unfortunate mind-transfer victim, into another dog’s body. (“The Shaggy Dog” was, naturally, remade in 2006 with Tim Allen, and a million dollars worth of computer graphics.)

“Freaky Friday” was another Disney movie that might have been the first actual mind-swap movie:

Freaky Friday

In this movie, a daughter and a mother actually swap minds — the mother’s mind takes up residence in the daughter’s body, and vice versa. A clearer illustration of dualism at work can’t be found. The mind “stuff” is completely separable from the body, and indeed can be transferred into a new body with the right sort of voodoo.

Dualism has, of course, also found its way into horror movies. Of course, every ghost movie, or life-after death movie, can be said to be dualistic in its nature. But one of the funniest expressions of dualism in a horror movie comes from the “Child’s Play” franchise, wherein the mind/soul of a murderous psychopath is severed from his own body and transferred into a talking children’s doll. The mind stuff doesn’t even need a brain, apparently! And it can control the doll’s movements to the extent of being able to wield knives and run relatively fast.

Child's Play

Other Philosophies of Mind

Dualism eventually gave birth to behaviorism, which begot physicalism, which begot functionalism. This isn’t the place to discuss all of these, but suffice it to say that functionalism is closely tied to the field of artificial intelligence, and thus is tied to a stack of other movies, from “2001” to “The Matrix”. But we’ll save that for another post.

Science and What Exists

To make the transition to Einstein’s universe, the whole conceptual web whose strands are space, time, matter, force, and so on, had to be shifted and laid down again on nature whole.

—Thomas Kuhn

One problem metaphysicians have been dealing with for, well, forever, is the unfortunately necessary intertwining of metaphysics and epistemology. Metaphysics is the philosophical study of what exists; epistemology is the philosophical study of knowledge. And it’s trivial to point out that the best we can do in detailing what there is that exists is to rely on our best epistemology: We can’t talk about what we know about, without talking about what (and how) we know. If we know about quarks, it’s not simply the case that quarks exist, but that we figured out that they exist. Our catalogue of items in the universe is inherently tied to our knowledge of those items.

Why is this problematic? Well, many metaphysicians are very conscious and conscientious about keeping existence separate from knowledge of existence. Much of the problem can be traced back to the venerable Bishop Berkeley, who posited that everything in the universe in actually mind-dependent for its very existence — it’s not, Berkeley thought, just that the computer screen in front of you is merely hidden from view when you close your eyes, but that this lack of observation actually means the computer screen is not really there when your eyes are closed. Problems with this theory forced Berkeley to say that God observes everything at all times, and so there’s no worry about things blinking in and out of existence with the blink of an eye. God never blinks. But regardless of the absurdity of this centuries-old bit of philosophy, the aftershocks have stayed with us. There’s something very compelling, apparently, about the idea that our minds have metaphysical power — that minds can create some of reality.

The great irony is that the best scientifically-minded philosophers of the 20th Century, while trying to shore up the mind-independence of the external world, actually gave proponents of mind-dependence a strong foothold in the metaphysical debate.

Naturalized epistemology — the brain child of W.V.O. Quine, though it was clearly anticipated hundreds of years earlier by David Hume — takes science to be the paragon of knowledge-farming; the discipline whose results we are most certain about. Naturalism, though, if we accept it, forces us also to acknowledge the following: We can’t make judgements about the world from some point of privileged access outside of science. That is, there is no way to step outside science and see what there is in the world; we don’t get a clearer picture of quarks without science — science itself tells us about quarks, and without science this piece of ontological furniture would not be accessible to us whatsoever. Our metaphysical house, chock full of interesting furniture, wouldn’t merely look somewhat different without science; it would be a bare, dirt-floored cabin with very little of interest in it.

This leads to a very tantalizing point. Science often changes its mind, and in such episodes of change what we take to be our ontology (our catalogue of things that exist) changes as well. For instance, once upon a time science told us that there was a substance called phlogiston that is released from things when they are burned. This substance — a consequence of a good scientific theory that explained several phenomena related to chemistry — was taken by scientists (and the informed public) as existing in the world. If science is our best arbiter of what exists, then, at the time during which science told us that phlogiston existed, there’s a strong sense in which it actually existed. Science, remember, tells us what there is, and there’s not privileged perspective outside of science to figure out our metaphysics. It turned out, however, that the phlogiston theory of chemistry ran into serious problems, and was more or less wholesale replaced by the oxygen theory of Lavoisier. In this new theory, there was no place for phlogiston. At this point, science told us that phlogiston does not exist.

There are (at least) two conclusions that can be drawn from this, each of which I will encapsulate using the Kuhnian metaphor at the top of this entry:

Standard Naturalism: The whole of science forms a conceptual web from which vantage point we purvey the world. There is no spot outside of the web from which to purvey the world. We can change science by changing some part of the web — this amounts to changing our ideas about an unchanging world. The world is independent of our ideas about it, even as we discover new ways to look at what exactly is in it. For instance, we were simply wrong about the existence of phlogiston. It never existed.

Kuhnian Mutant Naturalism: A scientific theory is a conceptual web that uniquely lays upon the world giving it its shape. When a new theory is developed, an entirely new web is made. There is still no place outside of the web from which to purvey the world, but we can shuck off the entire web in favor of a new one. The world is partly dependent for its existence on our ideas about it — whichever web we throw onto the world actually gives the world its shape. When we change our ideas, we change the world. For instance, phlogiston actually did exist while scientists were working with phlogiston theory. When Lavoisier came up with a new chemical theory, the world actually changed — phlogiston disappeared, and in its place oxygen and other items filled our metaphysical cupboards.

Many have noted from Kuhn’s version of naturalism that he is an anti-realist in the Kantian vein. We won’t get into the thickets of Kantian metaphysics here, but, in short, he believes that our ideas are not merely a pre-condition for theorizing about things, but that theorizing indeed is a pre-condition for the very existence of things. Contrary to this, standard naturalism usually goes hand in hand with common-sense and scientific realism, wherein, as Philip Kitcher notes: “Trivially, there are just the entities there are. When we succeed in talking about anything at all, these entities are the things we talk about, even though our ways of talking about them may be radically different.”

One reason Kuhn is led to his odd metaphysics is because of his implicit description theory of reference. On a description theory, the only way to correctly refer to an entity is to have its unique description in mind; but if a scientific revolution changes the description associated with a key scientific term, then the old description no longer refers. This leads Kuhn to the idea that competing scientific paradigms are incommensurable. It also motivates his metaphysics. If a term once referred and now it does not, all on the basis of our changing descriptions, then by some inferential jump one could think that this correlation was causal; i.e., that our changing descriptive thoughts cause a change in the world.

We’ll examine description theories and the philosophy of language in an upcoming post. Stay tuned…

S#!+ Philosophers Say

Choosing a Kantian Maxim

Explaining anything about Immanuel Kant’s philosophy in a short blog post is a daunting and perhaps foolish task, but I am nothing if not undaunted and foolish.

I’d like here to address a particular problematic aspect of Kant’s ethical philosophy (and don’t let the terminology scare you off — it’s not as difficult as it’s about to sound): How one is supposed to go about applying Kant’s categorical imperative by way of universalizing a personal maxim?

Kant’s categorical imperative is the only pure (he had a thing about purity) moral law he could come up with, and it boils down to this: “Act only on that maxim by which you can at the same time will that it should become a universal law.” A maxim is a personal “ought” statement, like “I ought to save that puppy from that oncoming truck”. A universal law is generated from a maxim by applying it to the entire rational population. E.g., “Every rational person ought to save puppies from oncoming trucks.” And Kant’s categorical imperative asks us to use this process every time we wish to make an ethical choice: Come up with a personal maxim for the situation; universalize that maxim; and see if that universal law is something that should be followed by every rational person in every such situation.

Lying

Let’s go through an example of Kant’s process. Let’s say you’re faced with an instance where lying would be expedient. Here, then, is your personal maxim for the situation:

Maxim: I ought to lie in order to get out of a jam.

And then Kant asks you to universalize it:

Universal Law: Everyone ought to lie in order to get out of a jam.

According to Kant, this universalized version of your personal maxim shows us that your maxim is in fact immoral. Even though your maxim may seem harmless, and is certainly beneficial to you in the short term, by extending its reach to the whole of humanity, there arises something very bad. If we look at a world where everyone lies in every dicey situation, well, this is a world that is in trouble. And, thus, according to Kant, you should never lie. Period. No exceptions.

Lying to Nazis

This position leads to some obvious problems.

Say you’re in 1940 Germany, and you are harboring your Jewish neighbor in your attic, in order to protect her from the Nazis, who would like to find and kill her. Now imagine that the Nazis knock on your door and ask you: “Are you hiding any Jews in your attic? We’d like to kill them if you are.” The relevant moral question here, of course, is what do you do? Perhaps, as Kant thought, lying is a bad thing, but if you tell the truth in this situation, it will lead to your neighbor’s unwarranted death, which certainly seems worse, on the face of it.

Let’s look in a little detail at how Kant might have examined this situation. His logic went something like this:

  • If it’s okay for you to lie, then (according to the universalization of this maxim) it’s okay for everybody to lie.
  • But if everyone lies, then no one will ever believe anything anyone says.
  • And, thus, lies would become completely ineffectual.
  • Therefore, lying is a rationally inconsistent activity — it leads to its own conceptual destruction.

This rational inconsistency is at the heart of Kant’s claim that lying is immoral — he thinks that ethics has to be based on irrefutable, logical principles in order for it to be anything besides an argument over opinions. A concept that leads to its own self destruction certainly shows us that there is something inherently wrong with it. And so lying, in virtue of this, is immoral.

Choosing Your Maxim

But let’s look more closely at the procedure of picking your maxim in the lying example.

I should lie in order to help someone.

Is this a good candidate for a personal maxim? Well, no, not really. It’s certainly not generally applicable to moral situations. For instance, one could pretty easily argue that lying in order to help a mad bomber who is about to kill a thousand innocent people is probably not a very ethical thing to do.

I should lie in order to keep someone safe.

No, this has the same problem… what if you’re lying in order to keep the mad bomber from being arrested? This is arguably not a moral thing to do.

I should lie in order to save a life.

We’re getting better, but we still have the same problem lurking. If your lie is to save the life of an evil person, it’s at least arguable that the lie is not the morally right thing to do.

So let’s include something in our maxim to account for the idea that you are lying to protect someone innocent:

I should lie in order to save an innocent person from death at the hands of an evil person.

What happens if we universalize this maxim?

Everyone should always lie in order to save an innocent person from death at the hands of an evil person.

This is not bad, actually, but there’s still the Kantian objection of conceptual self-destruction lurking: If we always lie to evil people who want to kill innocent people, the evil people will start to catch on, and thus the lies will become self-defeating.

In fact, the example of lying is one of the best for Kant’s system — when he applies his system to other sorts of moral cases, it all starts to go to hell. But with lying, he has found a case where there is something internally irrational about the endeavor, when applied universally. But I’d like for a moment to talk about a general problem with Kant’s procedure. How, exactly, do you go about choosing your maxim?

The Problem of Specificity

One major problem here is that of specificity of the maxim you choose.

You could make your maxim very general:

I should lie to strangers.

This is just about the most general maxim you could use here; and certainly this isn’t universalizable. Not only would you not want to universalize it (everyone should lie to every stranger would be an odd moral rule!), but it harbors the same problem of lies being self-defeating.

What about if you go to the other extreme, and choose a very specific maxim?

I should lie in order to save the life of the Jewish person hiding in my attic in 1940 Germany from the Nazis who will kill her.

This is about as specific as you can get with your maxim. And actually this is pretty well universalizable, because by universalizing it you don’t lose much specificity — your universalized law is still quite specific and actually probably a good moral rule:

Everyone should lie in order to save the life of the Jewish person hiding in Alec’s attic in 1940 Germany from the Nazis who will kill her.

(You might generalize the universal law here a bit more: Everyone should lie in order to save the life of the Jewish person hiding in his or her own attic in 1940 Germany from the Nazis who will kill that Jewish person. Still, this is arguably easy to accept as a good universal law.)

The issue here is that very specific maxims will be easy to universalize, while very general ones won’t. And this is a problem because very specific maxims will usually be very uninteresting as the basis of moral tenets. Very general ones will usually be interesting.

Imagine instead of a moral law like “Murder is wrong”, we had a law that said “Murdering Joe Smith on August 24, 1968, because he applied the wrong postage to a letter, is wrong”. Other ethicists would mercilessly laugh us out of the business. Our law may be true, but is not very interesting.

So the only way to use Kant’s procedure to generate a sound moral rule is by picking a maxim that is so specific that it is morally mundane.

Other Problems With Kant

There are a million and one problems for Kantian ethics (although there are a million and two Kantian ethicists in the philosophical community today). But perhaps the most obvious concern with Kant’s ethics is that it doesn’t (in fact, explicitly so) account for the ends of one’s actions. Most of us are disposed to say that killing a mad bomber in order to save a thousand innocent lives is a moral action, regardless of the fact that it involves killing someone. Kant disagrees, saying we can’t rely on a good outcome (saving a thousand lives) as the basis of our ethics.

He’s got a point. What if you decide to kill the mad bomber, but by a fluke of luck you actually wind up wounding him instead, and he escapes, only to kill ten thousand people the next day? That fluke of luck turns you from a hero into a villain. This idea of moral luck is a fascinating topic on its own, but for our purposes here, it does cast Kant’s hardcore position in a somewhat better light. If good outcomes are dependent on luck, then perhaps a genuinely moral decision shouldn’t depend on its outcome — perhaps a good act is good no matter what the outcome.

Famously, a school of moral philosophy called utilitarianism (or more generally consequentialism) sprang up in direct opposition to this perspective. We’ll talk about some of its pluses and minuses in a future post.

Do Numbers Exist?

According to your disposition, you might have an immediate gut reaction to this question. My initial reaction (oh so long ago) was: “Of course numbers don’t exist. You can’t pick up the number 3 and throw it through a window.” That is, my intuition was that the only things that exist are the kinds of things that can be physically manipulated, and numbers, by almost every account, just aren’t this kind of thing.

To be clear about our terms, you can pick up numerals — that is, you can pick up concrete instances of numbers, like the plastic number signs at the gas station telling you how much gas costs, or the printed numerals in a book, denoting page numbers. But you don’t, by virtue of tearing out page three of a book and tossing it out a window, throw the number 3 out the window, any more than you throw me out of a window by drawing a picture of me and throwing that out the window.

Numbers, if they exist, are generally what philosophers call abstract objects, and those who maintain that such things exist claim that they exist outside of space and time. If you’re like me, you shake your head at such talk. “Outside of space and time? What does that even mean? Gibberish!” If you are similarly disposed, you might be a nominalist (in case you’re accumulating self-descriptive philosophical terms), and you are part of a long, proud philosophical tradition that thinks that existence is the exclusive domain of the physical.

However, your nominalism begins to run into problems pretty quickly. Never mind numbers. What about things like, say, novels? What exactly is the novel The Catcher in the Rye? It’s not any of the particular instantiations of it — it’s not the copy on your bookshelf; it’s not the copy on mine. All of the print copies on the planet could be eradicated and still the novel could be able to be said to exist. Is the novel the original manuscript sitting in a safe somewhere? But that could be burned and you could still argue that the novel exists. But if the novel itself is not identified with any of its particular instantiations, then the nominalist is in a bit of a quandary. On this perspective, the copies of the novel are instantiations of the novel itself, and the novel itself is seeming to be something abstract — something non-physical.

So the idea of something somehow existing outside space and time is suddenly not as absurd as it may have seemed. What about numbers, then? Of course there are disanalogies between numbers and novels. Novels are invented by humans, while, on most views of the subject, numbers exist whether or not humans ever happened to discover them. But, putting such differences aside for the moment, perhaps the existence of novels as abstract objects gives us some traction to say that numbers exist as abstract objects.

Abstract objects

What other sorts of things could be included in the category of abstract objects? The funny thing is that in many seminal texts on the subject, one has to plumb deep to find mention of what would count as an abstract object. Mathematical objects generally top the list (numbers, points, lines, triangles, etc.), followed by things like chess moves, games in general, pieces of music, and propositions. How are these things abstract? We generally think of a chess move, for instance, as something that exists by virtue of a concrete chess player actually moving a concrete chess piece in accordance with the rules of the game (which could themselves be considered abstract, but never mind this for the moment). But that seemingly concrete move can be instantiated in so many concrete ways — you could be replicating someone else’s game on your own chess board, you could make the move on a hundred different boards all at (nearly) the same time, you could make the move in your head before you make it on the board,… and all of these concrete possibilities point to the metaphysical problem here: If you believe there is only one move, and it’s concrete, then which move is the one move? And then what are the other moves? Copies of the move? Or instantiations of the same move? If you believe in abstract objects, you have, on some takes, an easier time of it. The move itself is an abstract object, and every physical version of that move is a concrete instantiation of that move. That is, none of the concrete, physical moves are actually the move — there is only one move and it is abstract, and any physical move is a copy, like a sculpture of a real person. (You can have a thousand sculptures of a person, but there’s only one person. The sculptures are imitations or instantiations of the person.)

This perspective is (loosely) called platonism, named after Plato’s idea that there are ideal “forms” — perfect archetypes of which objects in the real world are imperfect copies.

Why would these ideal forms not exist in space-time? I.e., why would they have to be abstract? Well, objects in space-time (the real world) are all imperfect copies of something. So if an ideal form existed in, say, your living room, then it would be non-ideal by virtue of existing in your living room. To put it perhaps less question-beggingly, if, say a chess move were instantiated in a thousand ways, how would you pick out the ideal version from which all others were copied? All of the instantiations would have similar properties, and so no one instantiation would stand out as different enough to count as the move, the platonic form of that move. Therefore, it makes sense to posit an abstract version of the move — something perfect, and outside of space-time, from which all the worldly versions are copied.

Thinking about geometric objects is perhaps the clearest way to think about abstract objects. A line segment (a true, geometric line segment) is a perfectly straight, one-dimensional object with a determinate length. There are no such objects in space-time. Every object you could possibly interact with is three-dimensional — no matter how thin a piece of, say, plastic you create, it always has a height and a thickness, giving it three dimensions. Nothing, therefore, in the concrete world, is a real geometric line segment. We have things that approximate line segments — very straight, very thin objects. But none of those things will ever be perfectly straight and with zero thickness. So if there does, somehow, exist a true line segment, it certainly isn’t in the concrete world, and therefore it must be in some sort of abstract realm.

Knowledge of abstract objects

One of the most damning aspects of platonism is its failure to come to terms with how we learn things about abstract objects. The general picture of how we acquire knowledge goes something like this: We perceive an object in the physical world, via physical means (e.g., light bounces off the physical object and hits our eyes), and eventually we process such perceptions in our brains and work with mental representations — i.e., brain states — of the object in question. But an abstract object can’t be processed like this. It is non-physical, and so, e.g., light can’t reflect off of it. So our usual causal theory of knowledge acquisition fails for things like numbers.

Well, then, how is it that we come across any knowledge of abstract objects, if they indeed exist? Some mathematical platonists, like the venerable logician Kurt Gödel, resorted to the idea that we just know truths about mathematical abstracta. As he wrote:

But, despite their remoteness from sense experience, we do have a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don’t see why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception…

But this is clearly an unacceptable answer to the problem of knowledge of abstract objects. How exactly do the axioms of set theory force themselves upon us? Waving your hands and saying “they just do” isn’t an account of the process, and leaves us in the dark as to how they just do, which is precisely what we need before we can take the platonist seriously as an epistemologist. (One need merely look at the history of geometry to see one serious problem with seeing the “obvious” truth of axioms. Until Lobachevsky and Riemann came along with consistent non-Euclidean geometries, nearly everyone though that Euclid’s fifth postulate “forced itself upon us”.) How does some feature of a non-spatiotemporal object force itself upon our spatiotemporal brains? The only way would be somewhat magical, and you could look to Descartes to see the folly of such a plan. Descartes posited that minds are distinct substances from brains, and indeed were non-spatiotemporally located. Of course, this leaves the problem of how the mind somehow slips into the brain and affects it. Descartes’ answer was that it crept in through the pineal gland. But this is no answer; it merely delays the answer for a moment. How does the non-spatiotemporal mind creep in through the pineal gland, and then into the brain? Descartes had no answer for this, of course, because the whole thing would be terribly mysterious, explaining how the non-physical interacts with the physical.

Worries like this keep nominalists well-motivated to stay on their side of the debate.

The argument from indispensability

Even if you’re dead-set against granting the existence of numbers, you think platonism is absurd, you have challenged platonism’s picture of knowledge, and you somehow have all of your nominalist ducks in a row, there is still one very influential argument to contend with as regards numbers’ existence: The argument from indispensability. Hardcore nominalists are often quite scientifically-minded, scientifically-motivated philosophers. And it is this love of science that gets them into trouble with denying the existence of numbers. The argument runs, in broad strokes, like this:

  1. Science is the best arbiter of what exists.
  2. Therefore, if science says something exists, we should accept it.
  3. Science relies (heavily and intractably) on mathematics.
  4. Therefore, science says that numbers exist.
  5. Therefore, numbers exist.

If you’re a good nominalist, you’re more than likely feeling obliged to accept this argument as sound. But if you accept its conclusion, then you’re right back to the issue of explaining what numbers are. They can’t be physical objects, therefore they must be abstract. But, as a nominalist you claim that there are no abstract objects! And you are caught in an intractable dilemma.

Many nominalists give up at this point. Hilary Putnam wrote resignedly:

Quantification over mathematical entities is indispensable for science…; but this commits us to accepting the existence of the mathematical entities in question. This type of argument stems, of course, from Quine, who has for years stressed both the indispensability of quantification over mathematical entities and the intellectual dishonesty of denying the existence of what one daily presupposes.

The talk of “quantification” is a bit of logic talk, but we can paraphrase it into regular English: “If science uses numbers, then science is committed to the existence of numbers.” You might see a glimmer of nominalist hope here. Science also uses frictionless planes, for example, and yet no scientist feels committed to the existence of those. Perhaps there is a way out of our commitment to numbers in the same way. Or perhaps, one might argue, frictionless planes actually do exist as platonic, abstract objects.

But there are two more “obvious” ways to be a nominalist about mathematics.

First, you could argue that numbers exist, and are actually physical objects. Penelope Maddy argues something close to this in her early work, Realism in Mathematics. She actually is here arguing for a version of naturalized platonism — the idea being that what is usually thought of as abstract objects are actually somehow existent in the physical world. But, platonist labels aside, the gain for nominalism on this take would be obvious: numbers, if they are physical objects, would be just another part of the down-to-earth nominalist physical world, like cats, trees, and quarks. This brave strategy, however, ultimately fails. It would take us into some metaphysical thickets to explain why, so I have relegated this to a paragraph at the very end of this post.

Second, you could argue that numbers aren’t actually indispensable to science. Hartry Field famously tried this strategy, claiming that science in fact only seems to rely on mathematics. On Field’s view, this seeming reliance is really just a fiction. In order to prove this Field attempted to nominalize a chunk of physics, by removing all reference to numbers within it. This complicated, counterintuitive project has met with equal parts awe and criticism. The consensus is that his project is untenable in the long term.

So do numbers exist or not?

Well, if you’re a platonist, you would answer “yes, numbers exist”. And further you would claim that they possess a sort of existence that is abstract — different from the sort of existence that stones, trees, and quarks enjoy. Of course, this means you are in the unenviable position of explaining the coherence of this sort of existence, along with the herculean task of explaining how we know about anything in this abstract, non-physical realm.

If you’re a nominalist, you’d probably answer “no, numbers do not exist”. However, now you have the unenviable job of explaining why mathematics seems so indispensable to science, while science is perhaps our best tool for saying which things exist. The two best nominalist answers to this conundrum seem untenable.

Probably, as is usually the case in philosophy, dogmatically sticking to one side of a two-sided debate will be inadequate. Maddy’s attempt at naturalizing platonism was a brave bridge across the nominalist-platonist divide, but clearly isn’t the right bridge. We’ll examine some other options in a future post.


References and Further Reading

Balaguer, Mark. (1998) Platonism and Anti-platonism in Mathematics. Oxford: Oxford University Press.

Benacerraf, Paul. (1973) “Mathematical Truth”, Journal of Philosophy 70.

Colyvan, Mark. (2001) The Indispensability of Mathematics. Oxford: Oxford University Press.

Irvine, A.D. (1990) Editor. Physicalism in Mathematics. Dordrecht: Kluwer.

Lowe, E. & Zalta, E. (1995) “Naturalized Platonism Versus Platonized Naturalism,” Journal of Philosophy 92.

Maddy, Penelope. (1992) Realism in Mathematics. Oxford: Clarendon Press. Revised paperback edition.


A note on Maddy’s naturalized platonism

Maddy actually thinks that we perceive sets. Number theory, as many logicians are proud to point out, can be reduced to set theory — i.e., numbers can be reduced to sets, which are, of course, generally seen as just another sort of abstract object. Maddy’s move is to bring those sets into the natural world. So that when we see an egg, we are perceiving that egg, but are also perceiving the set containing that egg. (A set containing an object is different from the object itself, you may recall from your math studies.) And that set containing the egg is a natural object, different from the egg itself. But now we run into trouble. Certainly there must be something different between an egg and a set containing that egg; otherwise ‘set containing that egg’ is just a proper name denoting the egg in question, and nothing metaphysical hangs on the distinction. (If you call me “Alec” or “author of this post”, you are not positing the existence of two people — these are just two different names for the same person.) Well, the usual distinguishing feature of abstracta is that they are not spatiotemporally located; but on Maddy’s scheme sets are spatial objects. The problem: Our egg and the set containing it necessarily co-exist in the same exact region of space-time, and yet they are supposed to be different things. In what does this difference consist? Well, certainly nothing physical, otherwise they wouldn’t co-exist in the exact same region of space-time. But then the difference must be something non-physical — i.e., something about the set must be abstract. And if this is the case, then we’re right back to all of the problems inherent in platonism, particularly the problem of how we can have any knowledge of such abstracta.

The Mostly German Philosophers Love Song