Omniscience and Free Will

I’ve been teaching my Intro Philosophy students about supposed proofs of God’s existence, and the problem of evil, and it dawned on me (years later than it should have) that those wanting to reconcile free will with God’s existence have a rather intractable problem with one aspect of God that is generally taken to be inarguable: God is omniscient; that is, God knows everything (or, if you want to be a little more wishy-washy about things: God can know everything — he needn’t necessarily know something until he wants to know it).

If I’m right, theists have two options here: Give up the notion that God is omniscient; give up the notion that we have free will. Neither is a comfortable position for most theists.

What I’m Going to Eat for Lunch

Let’s assume that God, as per most religious beliefs, is omniscient — he knows everything. If this is true, then God knows what I’m about to eat for lunch. If he knows what I’m about to eat for lunch, then there’s a fact of the matter about what I’m going to eat for lunch — that is, if he knows what I’m going to eat for lunch, then he can’t be fooled about it. If God knows I’m going to eat a peanut butter and jelly sandwich for lunch, then I will eat a peanut butter and jelly sandwich for lunch — I can’t suddenly change my mind and eat a veggie burger, because God would’ve seen that one coming from a mile away. That is, if I were going to eat a veggie burger, God, being omniscient, must have known I was going to do so.

Do you see the problem here, for free will? I’d like to be able to say that I can change my mind about my lunch — i.e., that I have a genuine choice in the matter of what I will eat for lunch. I’d like, in other words, to say that I have free will about my lunch choice. (Indeed, the word “choice” presupposes that there is free will involved here.) But if I appear to change my mind, this can’t be a genuine choice in a universe with an omniscient God. No matter how many decisions I appear to make on the subject of my lunch, God knows the end result. And if God knows the end result, then there is no choice in the matter — my lunch has been predetermined somehow.

Even if we take the squishier position that God doesn’t necessarily know what I’m going to eat for lunch — his omniscience is of the variety where he could know about my lunch if he wanted to — we run into the same problem for free will. If God could know what I’m going to eat for lunch, it follows that there is still a fact of the matter about it. If he could know that I’m going to eat peanut butter and jelly, then it is the case that I will eat peanut butter and jelly, and thus I don’t possess genuine free will here.

Determinism: The Home Game

If you still think that an omniscient God would allow for free will, play along with me and see if you get my point…

Me: God is omniscient, right?
You: Yup, that’s what they tell me.
Me: So God knows what you’re going to have for lunch, right?
You: Yes, that follows.
Me: Can you change your mind about what you’re going to have for lunch?
You: It sure seems like I can. When it hits noon, I get unpredictable!
Me: So let’s say I’m tight with God, and I get him to write down your choice of lunch for me in a sealed envelope.
You: Okay.
Me: What were you just thinking you’d have for lunch?
You: I was thinking of a huge cheeseburger from Joe’s Diner.
Me: Oh, I heard that they just got cited for making their burgers out of rat parts and feces.
You: Gross! Okay, I’m changing my mind. I’m going to make myself a salad.
Me: [opening God’s envelope] Indeed, that’s just what God wrote down.
You: So it was predetermined the whole time!
Me: Yup. You didn’t really have a choice in the matter.

Vague Objects

Allow me to introduce my cat, Pinky.

Pinky the Cat

My cat, Pinky, has one semi-detached hair.

The metaphysical question at hand is this: Is the semi-detached hair a part of Pinky or not?

Any way you slice it, there’s some vagueness here. The more usual thought in philosophy is that the world is perfectly unvague — the world is utterly precise (the loose hair either does or does not belong to Pinky), everything just is whatever it is, and whatever vagueness humans encounter is simply a matter of human imprecision. Either our knowledge-generating faculties or our language faculties (or both, if there’s a difference), are imperfect, and incapable of discovering/representing the perfection of the world.

But there’s another possibility: The world itself is a vague place, and, even if we had perfect knowledge-generating faculties, we’d still struggle with issues of vagueness, because those issues are embedded in the fabric of nature.

So, let’s agree that there is indeed some vagueness at play, and ask: Is this vagueness actually in the world, or is it in our language/thoughts about an unvague world?

Unvague Cats; Vague Language/Thought

If the vagueness is just in our language, and not in the world, then there is a fact of the matter as to whether or not Pinky has that loose hair as a part of itself. If Pinky does indeed own that hair, then “Pinky” picks out the cat-like mass along with the loose hair.

Which cat is Pinky?

Which cat is Pinky? The one with the loose hair, or the one without?

As Michael Morreau sees it, this actually generates a metaphysical problem:

If vagueness is all a matter of representation, there is no vague cat. There are just the many precise cat candidates that differ around the edges by the odd whisker or hair. Since there is a cat,… and since orthodoxy leaves nothing else for her to be, one of these cat candidates must then be a cat. But if any is a cat, then also the next one must be a cat; so small are the differences between them. So all the cat candidates must be cats. The levelheaded idea that vagueness is a matter of representation seems to entail that wherever there is a cat, there are a thousand and one of them, all prowling about in lockstep or curled up together on the mat. That is absurd. Cats and other ordinary things sometimes come and go one at a time.

Pinky and Blinky

Pinky and Blinky: Two different cats that share the same (mostly) space.

If the world is not vague, then both of these are perfectly unvague cat objects, and if one is a cat then there’s every reason to say that they both are. In fact there are thousands (billions? trillions?) of cats here, all walking around in one lump. So on the world-is-not-vague side, we have the repercussion of “Pinky” picking out one specific cat out of many taking up mostly the same space; Winky, Glinky, Zinky, Inky, Kinky, etc.

Vague Cats

So, let’s try the world-is-vague approach instead. On the world-is-vague side, there’s just one cat, but that cat is itself vague. There’s no metaphysical fact of the matter as to whether or not that loose hair counts as a part of Pinky. But that loose hair doesn’t suddenly create two unvague cats: Pinky and Blinky.

What would be problematic about a vague world like this?

Perhaps the biggest problem would be representational. If Pinky is a vague cat, then we have no chance of ever compiling the perfect representation of him. (The perfect representation would include a representation of that loose hair, if it’s a part of Pinky; and it would not include that hair if it’s not a part of Pinky. But if it’s vaguely attached to Pinky, our representations will fail in one direction or the other.) Those prone to thinking that representations should strive for perfection will be most unhappy with this state of affairs.

A related problem crops up in the philosophy of language. Language philosophers like to think that names (like “Pinky”) pick out unique, unvague objects (like Pinky). But if Pinky is himself vague, then the name “Pinky” can’t unambiguously refer to Pinky. This is particularly problematic for anyone harboring vestiges of a description theory — if that loose hair may or may not belong to Pinky, then we have a problem coming up with a complete description, wherein that hair plays a part (or not).

What would be the payoff for accepting vague cats into our ontologies? The non-proliferation of tightly bound brother cats to Pinky, for one thing. (There is no need, if Pinky is vague, to posit the existence of Blinky, Winky, Glinky, et al, existing in nearly the same space as Pinky.)

It also buys us a platform to talk intelligibly about such metaphysical conundrums as the Sorites paradox. If, similar to cats, heaps are vague, as opposed to just our knowledge of heaps being vague, we can escape some of the problems inherent with talking about heaps changing over time.

We’ll be talking about the Sorites paradox in a future post.

For now, take some comfort in the idea that your knowledge of the world isn’t inherently imperfect. The world itself is inherently imperfect.

Of course, knowing that might make you uncomfortable again. Sorry.


References

Morreau, Michael. “What Vague Objects Are Like,” Journal of Philosophy 99, 2002.

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.

Clones and You (no, the other You)

We have, over the past few weeks of (very) personal identity discussions, really come together as a family, I think. We know each others tics and tacs, smarts and spasms, love of chili con carne and even what that gross stuff is. But do I really know that it is the you that you are? Or are you some other you, a devious you made to make me think that you are you when in fact you are not you at all. And maybe even you are wrong to think that you are you, so well made have you been. If you are not you, the you that you think you are, then who are you? Surely you are not no one (well, maybe not surely, my medication is still being ‘balanced’, so you could easily be no one; but let’s try to remain optimistic, even if only medicatedly so), for everyone is someone (source: Seuss). Can you be wrong about who you are? Wrong according to who or what? This is why clones suck.

Before we go into more detail about any of the above, let’s get straight on what we mean (well, what I mean; c’mon, its not like you are writing this) when we talk about clones. The scientific ‘clone’ is only interesting in the scientific sense: it is genetic copy of another organism. Creatures with the same DNA need not act in the same ways though, and so only the most ardent materialist would claim that one’s identity is entirely due to one’s DNA. Such an ardent claim would be foolishly idiotic at best since such a concept of personal identity is not one that is of much use to almost all of us. Anyone out there know what your genetic code is? Mine starts with a ‘c’ – I often, to save time, just refer to my genetic code as “the c-word”. (For example, a lot of my inherent drive to be successful is due to the c-word.) Does anyone here ever wake up, wonder who you are, sequence your DNA, and then think,”oh, yeah – that’s me”? Right.

In personal identity, at least in this take on it, ‘clone’ is going to mean a ‘movie clone’, where the clone does not just have the same DNA, but also has the same scars, beliefs, desires, tattoos, etc., that the original has. While such a creature only exists in science fiction (what the hoi poloi call ‘sci-fi’), there is sound philosophical reasoning that such a creature could be, especially if you a materialist. Recall, if you will and can, our most previous discussion where you put the locus of identity into or about the brain. Since you go where the brain goes, it stands to reason that an exact duplicate of the brain would work just as the original does and so be you as well, right? All those neurons and chemicals and whatnot are the things of you, if you go where they are. A movie clone is just an exact copy of that brain (together with the rest of the body because, hey, we care about the customer), so why would it not think and behave just as the original brain does, so long as it has the same set of neurons in the same configuration firing in the same patterns at the same stimuli?

It is the possibility of movie clones that make me think that the ‘cloning will lead to slavery’ debate is ridiculous. I do not want to get into ethics here, but much of the hullabaloo about cloning has to do with playing God or mistreating a living thing, but think about this: suppose you have a lot of work to do. Maybe you are a full-time student who also has a job and a kid to take care of (now do you see why condoms are important?), you are just the sort of person who needs a clone to take up some of the slack. So, you go to the cloning place (You2), have a clone made and bring it home.

“Right,” you say, “I am going to take a nap. “You,” you point at your clone, “can work on the research paper and make dinner.”

“Haha!” your clone says. “I am going to take a nap while you do that.”

See, your clone thinks and desires just as you do, and if you cannot convince your own lazy ass to get things done, how successful will you be at convincing an ass identical in every way to your own? So, slavery, as far as movie clones go, is unlikely at best and openly chaotic and murderous at worse. Mostly, clones will just confuse us. But, back to the topic at hand: is the movie clone you?

Yes, it is. If memories are what makes you who you are, then the clone is you as it has all the memories you do. It even remembers going to You2 and being cloned (and so it think thinks it is the original and you are the clone). Whatever memories you do not have any longer, it does not have either. It reacts in the same way in the same situations that you do.

If the body and brain are what makes you who you are, then the clone is you as it has the same body and brain. At least, there is no way for anyone at any level to tell the difference between the two of you: same DNA, same cellular structure, same neural configuration, and so on. Of course, what some of that means is pretty much what it does for the memory solution as our memories are stored or encoded in our neurons.

Hurray! We have a found a fire that both of our camps can gather about to tell ghost stories (even the materialist/body/brain camp cannot even begin to believe in something like non-material ghosts).

So, wow. Huh. (Movie) clones are you. Cool. This did not take too long at all. What’s that? Some of you disagree. But why? How could you? After all we’ve been through!? I don’t even know who you are anymore! (Yes, yes – I’ve been waiting weeks to work that one in.) Why might a clone of you, a movie clone even, not be you?

There are a couple of reasons, and I am just going to list them in as unbiased a fashion as I can manage (you inbred jackass!).

Both revolve around our (very basic) intuitions about what makes us who we are, and what we think that means. Think of the following example (and, dammit, remember this example as we are coming back to this in a few weeks when we talk about determinism and free will). We are going to make a movie clone of you, but the process requires that you be asleep. Both you and the clone wake up in identical rooms (same colors, furniture, feng shui, etc.). On the table next to your bed(s) are two glasses: one of apple juice and one of water. Whichever glass one of you reaches for is the same glass the other will reach for. Both will hold the glass in the same (though respective) hand, both will drink the same amount, both will place the glass back on the table in the same (though respective) place. What might seem like magic is, in fact, just the result of our above discussion about the brain and how it works. You like the food or drink you do because of your brain, so two brains that are exactly alike will like the same things exactly.

However, should one of you have a clock in the room, but the other be clockless, all bets are off. The neurons of the clocked individual will forever differ from those of the clockless (this is sometimes called the clock gap (no, actually; it isn’t)). Two questions spring forth from this example, both challenge the idea that the movie clone is the same person as you. (A) Did you, when both bodies drank, have two drinks or only one? If the clone is you, that implies that you live in two separate bodies simultaneously (shades of Parfitt!) and so you had two drinks at the same time. If the clone is not you, you only had one drink. But this leads to the second question: (B) Once the neurons change in the clocked you, which is the clone and which is you? Are those changes enough to make for a different person? Maybe not, but eventually, as both body’s experiences differ, there will come a division, but if there was initially no way to tell the difference between you and the clone, who is to say that you are the original and the other the clone now? Any decision seems mostly arbitrary and whatever identity comes down to, hopefully it is not arbitrary.

Now for the second big intuitive reason against the clone being you. Suppose that after the cloning procedure, we hold you (the original) up with paperwork but let the clone go home to your sweetie, and the two of them proceed to make ever-so-sweet woo. Has your sweetie cheated on you? Well, sweetie might not think so, but what do you think? Did you experience sweetie’s deliciously hot breath caress your neck, torso and nethers? Did you feel sweetie’s sweaty weight pulse and throb beneath and then above you? Was that you afterwards whose voice was hoarse due to multiple exclamations about heaven and all that is wonderful about it being there in the bed with you and sweetie? Or were you filling out paperwork back at You2?

This is really a question of anticipation. The relationship of anticipation is one that is special in the sense that you can only truly have it with a future you. You can look forward to a friend of yours winning a lot of money, but you do not look forward to that in the same way that you do about yourself winning a lot of money. Suppose I offer you a million dollars to be cloned, but the original body is destroyed and the clone is what gets the money. Do you think that is you who is getting the money? For many of you, that answer is ‘no’. For those of you who think the answer is ‘yes’, what happens if there is a mistake in the machine and the original is destroyed but the clone body is not made for one week: where are you during that week?

In conclusion: clones are and are not you. Maybe simultaneously. Also, sexy lightsabers.

Personal Identity and Brain Swapping

When last we left this perplexing topic, many of you were trying to get me arrested for a crime another I committed. (I say “many of you” even though only my mom and my lawyer were trying to do that, but my circle of friends has scant points about it, so ‘many’ it was.) When we are looking at memories as the signpost of identity-pointing, there are detours aplenty. Today, we are going to move on to the third of the potential candidates for identity fixing: the physical body.

Are You Your Body?

The pros and cons of the body as a candidate for personal identity here are pretty intuitive, and much of them we have seen earlier (with memories), if in slightly different form. The body is easily recognizable, and, in fact, is how we identify others. Slight changes, such as haircuts or tanning, seem to do little to distort or erase the recognizable features. However, which features matter the most? How many of them are necessary to maintain if one’s identity is to remain constant? Suppose you gain or lose three hundred pounds, you may well feel and be unrecognizable to both yourself and others. Are you a different person?Many soldiers are returning from Iraq and Afghanistan with missing limbs; are they different people? Both examples will result in the individual’s feeling different, but is that enough for identity to change as well? Think of the liquor store example from my previous post. How would that apply here?

Suppose that I rob the liquor store, but instead of getting hit by a car I instead cut off one of my arms.

Losing an arm

Is the the one-armed man the guilty person (I know Harrison Ford’s answer)?

What if I gain a lot of weight during the six weeks the police look for the robbing murderer?

Getting fat

I doubt there is much controversy to either of these scenarios, and almost every one of you is going to think that identity has remained constant, that the same person is still there or here or whatever, even if that same person is not exactly the same (what’s the difference?, you might wonder, and good for you, you wondering person; the topic of identity when not dealing with people is going to be dealt with soon).

Remember when we talked about the Ship of Theseus, and I suggested that there are some who suggest that every possible change results in new identity. Such an individual, if she is consistent, would have to say that I am not the person who robbed the liquor store because I cut my fingernails or because I removed some hair. Such a person, though, is not really a person in the traditional sense of the word ‘person’, but is more of a collection of experiences that are joined together. Such a person cannot recall her first date, as all her recollections belong to someone else, just as such a person cannot look forward to a happier time in her life, as it will not be she that is enjoying that time, only someone who looks and thinks much as she does.

Few of you think like that, though. But why? If you are not in the memory camp and the physical features have changed beyond recognition, why is a person still the same even after extensive physical changes? What’s that? Sorry, the sound on my computer is muted — what are you saying at your screen as though Skype were on and our conversation was being passively monitored by virtuous government agencies? Ah, I see. Thoughts! The thoughts have not changed. Good! It’s almost as though you knew where I wanted this post to go. Thanks!

Thoughts and Brains

Of course, by ‘thoughts’ what your philosophically ignorant train of thinking was suggesting was the brain. What most members of the physical camp believe to be the defining feature of identity anchoring is the brain. So long as you have the same brain, you are the same person.

Another way to get to the brain is by elimination. Which parts of the body matter? For the body, that is pretty simple: beards, arms, legs, livers, ears, moles, etc., are all pretty superfluous. The part that matters is the brain. How much of the body matters? Really, again, almost all of the body is superfluous except the brain. What if the brain is damaged and the thoughts no more work good? Well, that is not the same brain then, is it? As far as which parts matter and how much of those parts matter, what am I, a brain scientist? (Yes. Yes, I am. Not in the United States, of course; regulations and all that have proven quite the obstacle to my life goals).

The solution to those worries is normally dealt with by a kind of common sense functionalism. Most of us don’t know Broca’s area from the pubic bone, but if you cannot remember anything from last night back, your brain… it don’t work too good. So the parts and amounts that matter for personal identity are the ones, whichever they are (and brain scientists know which those are), that affect the functioning of the brain.

Simple enough then. You are your functioning brain, and wherever it goes, so go you. Right? Right. Right? Well, dammit.

Swapping Brains

Let’s swap brains, then, you and I, and see where we go. Who wakes up in a svelte killing machine of evolutionary perfection and who wakes up in body aimed at child predation? No, no. There are no trick questions on this site. You will wake up, most of you think, in a body not originally yours. If the swap is permanent, maybe your personality will change based on how people around you treat you (either with sexual fearsomeness or with fear of your sexual perversity), but you are still basically the same person. You are your brain.

Note that this is different from those mind swap movies that are made every other week or so. In those instances, it is, or seems to be, the memories that are swapped and not the brains. A brain-based identity theorist watches those movies and laughs (partly at their sheer delightful hilarity) because the only change is that the individuals involved wrongly believe themselves to be someone else. How could they be, though, since their brains are still where they have always been?

There is really no way to confound anyone’s intuitions about the brain as it relates to identity, is there? Hahahahahahahahahahahahaha! Sorry, sorry — whoo, man. You really had there for a minute. Alright, let’s get to the confounding.

Suppose a man, let’s call him Gary, was born with half a brain. This happens, you know. Gary can still function and get about, but he only has half a brain. Maybe he cannot recall as much stuff as you can, maybe his motor skills are shaky in places, but he is a person and his name is Gary. Everyone okay with this?

Now let’s suppose that another person, Harry, has a regular, whole brain. But, egads! Harry is hit by a crazed Canadian driver and the resulting life-saving operation leaves him with half a brain. Now, this is not how it would work, but let’s suppose he still has around half his memories and the like. Is anyone here, aside from the identity-extremists, going to suggest that Harry is no longer Harry? Harry is still Harry even if only half of his brain is there since Harry can still function, to some degree, to some recognizable degree, as Harry used to.

Alright, and if we were to swap Harry’s half brain and Gary’s half brain, I suspect that you are going to think they, the people, go whither their brains do. Fine, fine. And if there was a third person, Terry, who lost his brain altogether, where is Terry? Gone. Right.

Brain swaps

What about this, though (and this is due to philosopher Derek Parfit): let’s take Gary’s half and Harry’s half and put them together into Terry’s head. Who is that? It has half of each person’s brain (well, I guess, it has all of their available brain, so whatever) and, so, we are suggesting here, it has half of each person’s memories, is it both Gary and Harry? If not, why not?

If Harry with a brain in his head was still Harry and not dead, then Harry’s half with Gary’s half should make them both be (please try not to laugh) who they once were. Can the one body be two persons? What if both Harry and Gary had had whole brains that we split, combining one half from each in two separate bodies? Can two bodies then be four persons? Oh, philosophy, what have you done to our so carefully coddled beliefs about all that is personally identical in the world?

Next Time…

Next time: clones! And light sabers! And sex!!! But mostly, and only, just clones.

Personal Identity and Lifetime Movies

My last post dealt with the Ship of Theseus. It was a kind of primer about personal identity. What you think about the ship, whether it was the same ship or not at the end of the journey, might reflect what you think about identity when it comes to individuals. If you thought the ship was different at the end of the journey, perhaps what matters to you are the physical parts of the body. If you thought that the ship was the same at the end of the journey, perhaps identity lies in something a bit more ephemeral. But what? Well, let’s see. And then let’s see why you’re wrong. (Alec is all about showing you what different people think; I am all about trying to get you to see what you think and why you are wrong for thinking so. That is why Alec gets more fan mail and I get more slashed tires.)

Personal identity has to do with what makes you who you are over time. There are three big common-sense solutions to the question of personal identity:

  1. The soul
  2. Memories/experiences
  3. The physical body

Let’s get rid of the soul right away. Whatever the hell you use to figure out who you are, it is a pretty safe bet that it is not the soul. That is not to say there is no such thing as a soul; maybe there is, and maybe there is not. You do not sense your soul in any sort of direct fashion, and so it is probably not what you use to determine your identity. Most of you who believe in a soul do so because of faith, not because of direct evidence. Is who you are based on faith as well? What if your soul left your body and another soul came in? Would you notice? How? I suspect that most of what believe the soul to be responsible for can be explained by the issues with the other two solutions, and since neither of them really work either, you shouldn’t sweat this one too much.

How about memories/experiences (that slash is going to be important in a later post, so don’t forget it)? If memories are what makes you who you are, what happens when you lose those memories? Suppose you get amnesia. Are you the same person you were before? Let’s just go right to a Lifetime Movie example to test intuitions (your intuitions, of course; mine are forged in the surly steel of philosophic uncertainty).

A woman is driving through, uh, let’s say northern Canada…

Driving through Canada

…and she loses control of her car, crashing into the Canadian forest.

Car Crash

In a dazed state, with a broken arm and minor head trauma, she wanders a bit until she comes upon a small town. She is quickly noticed and taken to the local medical clinic where they see to her wounds. Upon asking her who she is, where she is from, and if there is anyone they can call, the staff realize the woman has amnesia. Furthermore, she has no ID on her. Despite looking for many days, the townspeople have no luck finding out who she is or where she came from. Still, these are very nice, Canadian people, and so they ‘adopt’ her. She picks a new name, gets a job at the very hospital that helped patch her up, and then gets an apartment. She works there for a year or two, meets and then dates and then marries (awwwww…) a doctor. She is happy. This is Lifetime, though, so the good times only last about forty minutes or so into the tale.

She has been married, as the story goes, for five years, when one day she hears a knock on her door. Opening it, as she is now a trusting Canadian, she sees a man she does not recognize, and yet he seems to recognize her. “I’ve found you,” he says. “I’ve finally found you?”

“Who are you?” our plucky heroine asks.

“I’m your husband,” he says. And he has pictures to back this up: pictures of their wedding, her parents, her childhood, and so forth. She, of course, has no memory of him, her parents, or her childhood.

Now: philosophy!

Not to imply that marriage implies or entails (or anything else like those two) ownership, but this is just the easiest way to ask this question: Whose wife is she? The first guy or the second (current amnesiac state) guy? Keep in mind that we are not writing some sort of Lifetime Slash fiction here. She is probably not going to want to be with both. In fact, if asked, she expresses a clear preference for the second guy (since, you should recall, unless you are being ironic, she has no memory of the first guy).

I’ll have Alec set up some sort of poll for this question, but I am going to go ahead and forecast/predict that the majority of people are going to choose the second guy as the winner. But why, you might wonder, even those of you who agree but who have come to philosophy as a means to better elucidate your thoughts and opinions. Here is why: you believe that memories are what makes a person who she is. You are you because you remember doing the stuff you did. You do not remember all of it, but you think, and perhaps rightly, that you don’t need to. You do remember starting this article (it’s not that long yet, is it?); you remember eating dinner last night; you remember graduating from high school or junior high school or grade school (you preciously precocious bastard); and so on. What you do not remember doing, you common sensically believe you didn’t do. Maybe you are not always right (hey — that is a good topic for a later post! Thanks for that suggestion), but you still have that intuition. Our lovely Canadian is in the same memory leak of a boat. She recalls her current husband, but no other. Hence, she is only the woman she remembers being.

What happened, then, to the first husband’s wife? I suspect many of you are not comfortable with stating that she is dead, but then, where is she if she is not married to the second guy? Gone? Away? Buried deep in the mind of this new woman? Some of you are sure and some of you are not. Note that the answer here becomes murkier when we talk about her parents: did they lose their daughter as their son-in-law lost his wife? Physically no, but mentally yes? Are you comfortable with that? Would alcohol help?

Let’s change the example a bit, and then end this entry, giving you something to think on a bit or two. Suppose instead of a woman driving a car through the Canadian forest, it is me and I am at a liquor store. And instead of a car crash, I am buying a bottle of Maddog 20/20 (they all taste like gas, so let’s get the blue one because it is the prettiest). And instead of being found by benevolent Canadian townsfolk, I am shooting to death the liquor store operator, writing my name and social security number on the wall in his blood, leaving my driver’s license and hair and nail clippings in bag labeled “DNA” on the counter, and then walking outside yelling, “Hey, everyone! I just killed the liquor store operator of my own, sane volition!”

Liquor Store Robbery

And then, instead of being given a job at a Canadian hospital, and falling in love with a lovely Canadian man, I am hit by a car (maybe driven by a Canadian), given severe head trauma, and awake in a hospital with permanent amnesia, having been arrested by the police who, given all the evidence I left behind, tracked me down in about five weeks.

With those slight and subtle changes in place, we can ask basically the same question we asked above: Is the person in the hospital bed the same as the the person who killed the liquor store operator? If you thought the woman was not the same as the one who had married the first guy in the first story, you should also think that the person in the bed is not the same guy as the one who killed the liquor store operator. And yet… And yet… You do. Why? Do you hate me? Are you sexist? Do you think that justice is more important than metaphysics (it isn’t)? Let’s end here and we will take this up and more in the next installment of: Do you know who I am? Who the hell are you?

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.

Identity and the Ship of Theseus

The Ship of Theseus is a great example of identity, though it does not work for everyone when it comes to personal identity, or the identity of people. Here is the basic idea. A guy named Theseus has a phenomenal ship that everyone wants, but he is not selling for any amount. However, one day, a merchant from a distant land offers Theseus an enormous sum to build an identical ship. The merchant wants the exact same sort of timbers from the same forest, the same nails from, uh, wherever the hell nails come from, the same sail material from the same cotton plants, and so on. If there is a plank of wood that has a knothole in it, the merchant wants an identical knothole in the same place on the duplicate ship. Sounds crazy, right? Well, most rich people are crazy. Theseus agrees and loads his ship with everything he needs to build a duplicate ship and then sets sail. He is only out of port for a couple of hours when one of the planks on his ship warps slightly and allows water into the ship. Theseus could return home and patch it, but he would just as soon get to the merchant, build the duplicate ship and then roll around on his big pile of money. With that in mind, he takes the corresponding piece, its identical counterpart, from the supplies and swaps the two planks out. (If you like, he makes a note of this switch, but his honesty does not matter for how the example works). As the journey continues, he needs to swap out more pieces: sail is torn, carpet is frayed, he needs a new wi-fi router, and so on. For ease of talking points, let’s make the following supposition: Once Theseus is 1/4 through his journey, he has 75% original parts and 25% new parts; at the 1/2 part, he has 50% original parts and 50% new parts; at the 3/4 mark, he has 25% original parts and 75% new parts; and finally, at the end of the journey, he has 0% original parts and 100% new parts.

Here’s the question: is the ship at the end of the voyage the same as the ship at the beginning of the journey? There are only two answers: yes, and no. A bunch of you are going to, somehow, try to wriggle more than that out of the situation, and your insane hearts are in the right place, but that will not make the insanity any less prevalent. Most of you are going to think the ship is not the same, so let’s talk about that first.

If the ship is different (and why wouldn’t be, you are collectively screaming), then when did it become different? At one point on the journey can we point at and say, “There! Did you see that? A different ship!” Here the answers are not so clear, but are not too difficult to lump together. Most people are in one of three categories: a) the very first change; b) right at or after the 50% mark; and c) the final change or replacement of parts. My question to all three groups is basically the same: why there? Why did you pick the percentage mark or the piece that you did?

The ship becomes a different ship at the very first change. This makes sense, I think, until you think about it and whether it makes sense. Suppose the very first change is a nail and not a piece of wood, does that matter? It shouldn’t. The percentage difference between a nail and a plank when the ship is taken as a whole is virtually negligible. What if a bird crapped on the ship? That is a change, but does it make for a different ship?

Of course, not. Bird crap is an extraneous feature of the ship, but is not integral to the identity of the ship itself “Integral”? Very impressive term! So if the ship loses a nail (one pops free), and that nail is not replaced, does that make for a different ship, Mr. Integral? Perhaps the nail was not an integral part, but then what is? If the sail is replaced, does that matter? What if only the hull is replaced? See, the problem is trying to figure out which parts are integral.

We often think of integral parts as though which cannot be taken away and the object still be whatever the hell it is. That can be due to reasons of either identity or function. If we take away the sail of the ship, it still floats and can haul freight (though it takes much longer), and I suspect none of us would have any issue with calling it the same ship. Is the same true if we took away only the hull? Not only would it look the same, but it is not going to float or hold any freight. So far, all of that is fairly intuitive. Let’s take away just the nails. The ship would probably fall apart very quickly, but until it does, is it the same ship? It looks that way and, at least for the moment, it functions in the same way.

Function As Identity
An issue with identity as function is this: Suppose we identify one another by function. First, how the hell do we ever figure out what our function is? If we are using it to fix identity, it cannot be something general like ‘reproduction’ or ‘making money’, because then how would we differentiate between individuals who are doing both or either? Let’s say that we resolve that issue, though, and fix your identity as ‘runner’ because that is what you do when you get any free time, or you are a competing runner or whatever. Dammit, just accept this as your function. Now, suppose you are hurt and can no longer use your legs, and so can no longer run. You can no longer perform the running function — what does that do to your identity? Is it gone? Is it changed?

More than half of the ship must change for the ship to be different: If one little change, even an little integral one, does not make for a different object, then what about a change of 51%? Again, the same questions can be asked: does it matter at all what that extra 1% change is?

Every single piece must change for the ship to be different: I won’t be petty and go rehash the above paragraph again (though I could, because it works). Let’s instead agree that the identity does not change until the last piece is swapped out. Does that make the last piece integral then? What if it is a nail instead of a plank? What if it is a stitch in the sail instead of a nail? Suppose we take that last piece out but do not replace it? 99% of the ship has been changed and the last one percent is just taken away, what does that mean for its identity? Yeah. I know.

Fine, then — the ship does not change. It is the same at the beginning as it is at the end. I can see, now, why you might think that. And everyone who originally thought it are now crowing to the moon about their daringly correct choice. Let’s suppose we now take all of the original parts and put them back together. It would be a fairly crappy ship, but why would that not be the original ship? Yeah. I know.

What you think about the Ship of Theseus might indicate what you think about identity for people. We will see as we continue on this topic in later (though soon upcoming) posts.

What is True Depends on What is the Truth

This is a follow-up to Alec’s nicely written post on realism and its varieties. I put forth in the comments section the idea that what one believes to be the case with regards to realism v. anti-realism is going to color what one takes to be true in the world. Or, at the very least, what one considers to be a candidate of truth in the world. Here is why that is (and note that this is not merely my opinion, but is an established line of argument and belief among metaphysicians).

Realism, as Alec eloquently stated, is the view that the world is a particular way in a mind-independent fashion. Anti-realism is the view that the world is mind-dependent, and so derives many, perhaps all, of its features because of how it is perceived. Those are very quick takes on the two views and should not be satisfactory in and of themselves to anyone. Again, I refer you to Alec’s post.

Depending on which of the views you hold, your idea of what is true (or at least what you believe to be true) need not change, but what makes something true (its truth conditions) does change. Why might this be? First, let’s talk about the common sense view of truth.

Suppose a person makes the following utterance, “snow is white.” That utterance has a truth value. It is true if snow is white, and it is false if snow is any color other than white. How do we go about determining if it is true? Well, we go and look at snow. “Look”, you might say, if you live somewhere other than NYC or Chicago, “there is some snow, and it is white.” Hurray! We have verified its truth status. Or, dum dum dum, have we?

If you are a realist, you think that there are properties in the world that we can discover. This does not just mean that we can encounter snow, but that when we encounter snow, we can learn something about it, such as it being cold, malleable, crunchy, and white. If those are characteristics that we cannot discover or encounter, there is no way we can determine the truth value of any statements that make reference to such characteristics. The utterance, “snow is white”, is true only if snow is actually white. We laugh at a child who says, “snow is brown” because we know that snow is not brown (even in NYC, snow is white until it hits the dirty, dirty ground there). This is called the correspondence theory of truth. An utterance is true if it corresponds with what is actually the case in reality. “My keys are in the bowl by the door” is only true if my keys are in the bowl that is by the door. If they are in a dish, if they are in the kitchen, if I have no keys at all, the utterance is false because it does not correspond with how things actually are in reality. Hopefully you can see why a realist is drawn to the correspondence theory (though the two are not necessarily conjoined).

But I suspect you can also see why the anti-realist is not going to favor a correspondence theory of truth. For the anti-realist, most of what we believe to be the case about the world is due to how our minds project or create certain features or characteristics of what we perceive. For the anti-realist, the utterance of “snow is white” is expressing an opinion since there is no objective characteristic of ‘white’ in the world; there is only the experience that I refer to as ‘being white’. Whiteness, then, is a mind-dependent characteristic. It exists only because our minds create it. What does that do to the truth value of the utterance then? Well, as there is no objective reality to compare the utterance to, we cannot rely on the correspondence theory. Even if there were an actual characteristic of being white in the world, how could we ever know what that characteristic was like when our perceptions are so unreliable? And yet, the anti-realist does not want to say that there is no such thing as truth. Instead, what determines truth is something different from correspondence. It is called the coherence theory of truth. For the anti-realist (for many of them, at least), our mind-dependent experiences build up a large collection of beliefs about what we think the world is like. Since we cannot say what the world is actually like, we judge truth based on how well an utterance coheres (fits in) with our collection of beliefs. We want our collection of beliefs to be as coherent as possible. Note that coherence here does not merely mean understandable or rational, it means something larger: that our collection of beliefs not contain contradictions. We do not want to believe that we are both standing in the rain and we are not standing in the rain. We do not want to believe that snow is white together with snow is not white. (Of course, we can believe variations of those, but the contradictions are smoothed away by adding unspoken caveats to the utterance. For example, “snow is white” need not contradict “snow is not white” if we have the unspoken belief that the second utterance is about NYC snow which is changed or altered snow. “I am standing the rain” need not contradict “I am not standing in the rain” so long as we have the unspoken belief that I am standing beneath an umbrella which means that I am in the rain without being rained upon.)

Truth and Language
This can quickly become an issue of semantics or philosophy of language and so worth another, different post. Briefly, though, we know what we mean when we say what we do. When I point at snow and say, “snow is brown”, I do not literally mean that I believe snow is brown. Instead, I mean that snow, in such and such a state or condition (whatever condition is present, perhaps), is brown. If someone, maybe Alec, who knows, were to ask me, “do you mean to say that you think snow is brown?” I can honestly and reasonably say, “That is not what I meant when I said, ‘snow is brown.’ I meant that the snow here is brown, by which I meant to say, this is some really dirty snow.’” There is the demonstratrive sense of the utterance, by which I point and so indicate a particular batch of snow. Think of the old example about eskimos having eighteen different words for snow. That is a ridiculous example, I think, meant to suggest that eskimos like snow so much they talk about it a lot. But guess what? We non-eskimos have lots of different words for snow too: snow, wet snow, dry snow, soft snow, heavy snow, light snow, sleet, hail, etc. Wait a minute, you might exclaim, those are just the word ‘snow’ with an adjective in front of it. Yep — many of our words are like that. In fact, many words are like that: compound concepts captured in one word. What does ‘slush’ mean, if not icy rain? What is ‘beautiful’ aside from ‘pretty’ preceded by some number of ‘very’s?

Back to the topics at hand though, for an utterance to be true for the anti-realist, then, just means that the utterance fits in with my already accepted beliefs. “Snow is white” is true if what I call ‘snow’ is associated with the characteristic that I call ‘white’, and it means nothing beyond that. So, which theory of truth is correct? The realist theory is not correct, as there is no way to verify if what we have said actually corresponds with what is actually the case in the world. There is the experience I have whenever I come across a sensation that I label ‘white’, but why think that particular experience matches up with the way the world truly is? Perhaps I am color blind. Perhaps I am hallucinating. But you are not, the realist might contend. But how do you know that I am not? Can you prove that you are sensing the world as it actually is? If you could, there would be no anti-realist camp.

The anti-realist theory is not true either though, at least not obviously so. Coherence is an important attribute for any system of beliefs. For any system of beliefs, we want there to be as few outright contradictions as possible. Yet, why think that coherence alone is enough to establish truth? Someone who is schizophrenic or just simply insane might have a very coherent view of their experiences, but it only seems coherent to them because they are crazy. The schizophrenic person believes he hears voices separate from his own; he may even believe he sees people talking to him. We consider him sick though, because he is experiencing what no one else is or can. We say that the schizophrenic is wrong, not because his beliefs are not coherent, since many of them are (perhaps even as many of his beliefs cohere as do our own), but because he has beliefs that do not correspond to reality, to what we think is actually true. A claim, by the way, the schizophrenic will agree with once he is on successful medication.

What is the upshot of all this? Well, the realist maintains that our intuitive conception of truth is based on correspondence, not coherence, and the anti-realist maintains that we can never know whether our beliefs correspond with anything external to the mind, but that we can determine if our beliefs cohere with one another. Which you favor seemingly depends on what you think is real (though, to be fair, some suggest that what you think is real depends on what you think makes something true). However, it more often depends on what you think you justify as being true. That, however, has to do with straight up epistemology, and so must wait for another post.