Google Ngrams

Have you checked out Google Ngrams? You can search all of Google’s digitized books for keywords, and display the results in a graph.

Here’s what I got by searching for “dualism” versus “functionalism” (with a couple of other terms thrown in for comparison’s sake).

dualism v functionalism

Random Read: Roger Hancock, 1960

This is the first installment of the Random Read category — wherein I go to my local university library, pick an old journal up off the shelf, and read a random article therein. It serves the double duty of making me get out of my chair, as well as getting reacquainted with wonderful, beautiful printed matter. Remember books and journals? They are awesome.

Today I walked up to the University of Vermont, sauntered up to the second floor, and picked up the oldest volume of the Journal of Philosophy there: Volume 57, published in 1960. I thumbed through and picked an article to read, nearly at random. (The first article I picked wasn’t very interesting, so I gave myself the leeway to pick again.)

My thought is that, as a semi-regular exercise, this might be interesting for myself and (hopefully) for you. Philosophy is hyper-specialized, which means that sometimes reading a random article will leave one reeling with the righteous confusion of the non-specialist; but even in those cases, often something interesting will come of it. There’s always some good fodder for thought in any piece of philosophy.

Today’s random article: “The Refutation of Naturalism in Moore and Hare,” by Roger Hancock. Journal of Philosophy 57 (10), 1960.


The Players

I’m going to ignore R.M. Hare, here (sorry, R.M.), because he turned out not to be as contentious as Moore. G.E. Moore — the other subject of this essay — was a philosopher of tremendous note, whose Principia Ethica, published in 1903, made quite the splash in the philosophical community. In it, he argued (among other things) that the quality GOOD is indefinable.

My point is that ‘good’ is a simple notion, just as ‘yellow’ is a simple notion; that, just as you cannot, by any manner of means, explain to any one who does not already know it, what yellow is, so you cannot explain what good is.

This was a pretty radical idea, at the time, as philosophers were deep in the throes of a centuries-long process of trying to define goodness.

Consider yellow, for example. We may try to define it, by describing its physical equivalent; we may state what kind of light-vibrations must stimulate the normal eye, in order that we may perceive it. But a moment’s reflection is sufficient to shew that those light-vibrations are not themselves what we mean by yellow. They are not what we perceive. Indeed we should never have been able to discover their existence, unless we had first been struck by the patent difference of quality between the different colours. The most we can be entitled to say of those vibrations is that they are what corresponds in space to the yellow which we actually perceive.

Yellowness is not further reducible to physics, because we don’t perceive the physics — we perceive some sort of conscious experience that can’t be explained, because it has to be experienced. Yellow things do reflect light at a certain wavelength, but that isn’t what yellowness is. (He’s wrong about this, but let’s go on…)

Yet a mistake of this simple kind has commonly been made about ‘good.’ It may be true that all things which are good are also something else, just as it is true that all things which are yellow produce a certain kind of vibration in the light. And it is a fact, that Ethics aims at discovering what are those other properties belonging to all things which are good. But far too many philosophers have thought that when they named those other properties they were actually defining good; that these properties, in fact, were simply not ‘other’ but absolutely and entirely the same with goodness. This view I propose to call the ‘naturalistic fallacy’ and of it I shall now endeavour to dispose.

This formulation is rife with problems, and much ink has been spilled examining and critiquing it. Hancock’s 1960 article is one such critique in the rising pool of these.

Hancock’s main thrust is to examine what Moore means by “naturalistic,” “naturalism,” or “natural.” If we’re committing the “naturalistic fallacy” when we equate goodness with some natural property, then goodness itself must be non-natural, right? Hancock notes that:

‘Naturalism’… might be defined as the view that ethical words such as ‘good’ or ‘right’ are synonymous with expressions designating natural properties. But what is a natural property? It might be suggested that a natural property is one that can be observed. Yet Moore himself holds that ‘good’ designates a property which in some sense can be observed.

We can “see” goodness just like we can see yellowness, and if the sense of sight is generally taken to be something that operates solely in the natural world, then Moore has some sort of problem to deal with here.

No Spoilers

I don’t intend to make a detailed analysis of Hancock’s article. I don’t know if it was well-received, or if it made any sort of impact on the philosophical landscape. My point in reading it was not to cement its place in history or start a new branch of investigation stemming from it. I simply wanted to immerse myself for a few minutes in a piece of philosophical history, and see if it made me think of anything interesting.

So what did I get out of this experience? Well, it got me thinking again about Platonism — the position that there are non-natural objects sitting in a non-natural “place”, to which humans have some sort of mysterious and privileged access.

Platonists have long been embroiled in a problematic epistemology, wherein they owe the rest of us an explanation of how humans can perceive non-natural things. (Our perceptual apparatus is fairly well understood, and is entirely explicable in physical terms.) They also owe us an explanation of why those non-natural things align so smoothly with natural things. If, as Moore seems to imply, yellowness is a Platonic object, then we can ask two questions of him: How is it that we see yellowness at all, since it is non-natural, and our visual apparatus is entirely physical? And, if we do see it, why does it so perfectly align with things that reflect light of a certain wavelength? (Moore said that it’s just coincidental that yellow things always reflect this sort of light. How does he explain this coincidence?)

Of course, the same analysis applies to goodness. If it is non-natural, how do we perceive it? And if it always lines up with some natural property, why is that?

God Created the Irrational Numbers

The eminent mathematician Leopold Kronecker was reported to have said: “natural numbers were created by God, everything else is the work of men”. Stephen Hawking entitled a recent book of his God Created the Integers, in honor of Kronecker’s slogan. (Let’s not split hairs over the difference between integers and natural numbers. I’ll stick with the integers from here on out.)

This statement, despite its theistic and metaphysical flavor, was meant to be taken foundationally, not metaphysically. Kronecker was speaking about the idea that if we assume the existence of integers axiomatically, definitions of and theorems about other sorts of numbers can be rigorously provided. For instance, if you assume that integers exist, then you can define a rational number as the quotient of two integers.

Speaking of rational numbers, it’s time to brush up on a bit of your old school math. Remember that some rational numbers are finite, when turned into decimal representations. For example, 1/8 is 0.125, a nice, neat, terminating decimal expansion. Some rational numbers will have infinitely many decimal places, but even these will still be well-behaved in one way or another. For example, 2/3 is 0.6666… where the sixes repeat forever. Another well-behaved rational number is 1/7, which is 0.142857142857…, where the ‘142857’ group of digits repeats forever.

The subject of this essay’s title — irrational numbers — are not so tidy. They are infinitely long, but don’t behave nicely like rational numbers do — i.e., they don’t terminate or cycle. Pi is a famous irrational number — it just goes on forever, never repeating, and no one can find any pattern within its endless chain of digits.

I would like here to posit that, contra the metaphysical interpretation of Kronecker and Hawking, irrational numbers — infinite and infinitely messy numbers — underlie (though, as you’ll see, I think even this is too strong a concept) the fabric of the universe, and that the integers are humanity’s unnaturally well-behaved grand creation. In fact, the universe does not contain anything genuinely integral or numerically tidy.

The Number 1

Let’s take the most basic of all integers: The number 1. When you speak about one apple or one table or one person, you are using the number 1 in its most starkly metaphysical role: you are using it to try to perfectly demarcate an object. This is the glory of integers: If we had to talk about 1.1258345257… apples, or pi tables, life would be difficult. And saying we have 1 apple in front of us not only lets us speak more easily about the world, it’s what allows us to talk about the world (and all its objects) at all. “An apple”, “the apple”, “one apple”,… all are ways to say that there is a thing called an apple, and that here’s an example of such a thing in front of us. This apple is perfectly demarcated — it sits completely formed and completely separated from everything else in the universe.

Integers, indeed, are epistemologically fundamental, and this is where they get their epistemological primacy from. Without them, we couldn’t understand much about the world.

But this doesn’t necessarily make them metaphysically fundamental (foundational, basic) the way Kronecker, et al imply they are.

In fact, perfectly demarcated objects simply don’t exist in the physical world. They, and the integers behind them, are human fictions.

The world is inherently vague — all of its objects are ill-defined and imperfectly demarcated. We’ve blogged about this in the past, but I’ll recap what I mean by this here.

Heaps and Cats are Vague

There are objects that are obviously vague — that is, very few would argue that we can be utterly precise about them. Heaps are like this. Nobody thinks that when we say “a heap”, or “the heap”, or “one heap” we are speaking with much precision. A heap of sand, for instance, is still a heap if we take away (or add) a grain of sand from it. The heap is inherently vague and imperfectly demarcated.

Of course, you might be aware that this leads to an age-old paradox — the sorites paradox. Recapping our premise: A heap of sand is still a heap of sand if you remove one grain of sand from it. Well, if this is the case, then it’s still a heap if you remove another grain of sand from it. And another. And so on. But soon we will be in the position of saying that we still have a heap of sand even after all of the grains of sand have been removed. Paradox.

The problem is that there’s no absolute cutoff point where a heap becomes not a heap. E.g., it’s not like a collection of 500,000 grains of sand is a heap, but 499,999 grains is no longer a heap. If this were the case, then our initial premise would be wrong. In fact, there would be a clear case in which removing one grain of sand would turn it from a heap to a mere collection.

So there’s no genuine integral description of a heap. Perfectly demarcating a heap is impossible. But perhaps that’s because heaps are a vague sort of thing in the first place. What about things that generally aren’t considered vague? What about a cat?

Well, let’s take my cat, Herbie, who, as I type, is staring at me, wondering when I’ll feed him. What if (as is no doubt true) Herbie has a semi-detached hair on him, on the verge of falling to the floor? Is this hair a part of Herbie or not? If there’s a fact of the matter here, then Herbie is in fact a perfectly well-defined, non-vague object.

But could there really be a fact of the matter about this? If there is, and, say, that stray hair is a part of Herbie, then I’d better be damned sure that hair never falls off him, or else he’ll suddenly be a different cat. But this isn’t what cats are like. They’re vague objects, losing and gaining parts constantly. This vagueness is inherent. We need, epistemologically, to speak about “the cat” or “one cat”, because otherwise we wouldn’t operate very well in the world. (Imagine a caveman denying that there was exactly one saber-toothed tiger in front of him, much to his detriment.) But cats (and saber-toothed tigers) don’t have to be perfectly well demarcated in order to tear you to bits — it’s just a convenient short-hand to think this way. (Does it matter if you get smooshed by one boulder and a pebble, or two boulders, or two pebbles, or, as is more rightly the case, 1.03123124… boulders? You’re still getting smooshed. Same thing with 1.000041424553… saber-toothed tigers.)

Measuring Things

We all learned in geometry class that world is divided into objects that are 1-dimensional (straight lines and their ilk), 2-dimensional (flat shapes like triangles and circles), or 3-dimensional (things like spheres and cubes).

Actually, geometry lied to you, or at least your geometry teacher did. The “world” of geometry isn’t real — it’s a mathematical fiction meant to show us what a perfectly tidy realm would be like. But the real world contains none of these sorts of tidy objects. In fact, there is no such thing as an integral dimension at all, and genuine 1-, 2-, and 3-dimensional objects (things that “exist” in such integral dimensions) are a mathematical myth. A 1-dimensional line segment is a human fabrication — an abstraction. Any line segment you can physically create and/or interact with is bumpy, gappy, and wobbly, bringing it into the second dimension. It also has thickness — if, say, it’s drawn on paper, the ink on the page is raised slightly off of the second dimension, bringing it into the third dimension.

What does this mean for the realm of the physical? Well, if the dimensionality of a physical line segment is non-integral, that means its measure is irrational — that is, it is only measurable by irrational numbers, not by integers. (I know I’m making the leap from non-integral to irrational here, but anything truly measurable by a rational number would have to be some sort of incredible anomaly. The Sierpinski triangle, for example — one of the nicest, neatest fractal shapes there is — has an irrational dimension of 1.58496…. If a relatively well-behaved mathematical object has an irrational dimension, what hope is there for the messy real world to be any less messy?)

Reality is irrational-number based, not integer-based.

Perhaps this will be clearer with a brief discussion of the seemingly straightforward question: What if we try to measure the coastline of England? Well, it turns out there is no straightforward answer, thanks to the real world’s irrational messiness. Whatever answer we get, it turns out, depends on the length of whatever ruler we use.

The coastline of Great Britain, measured with different rulers. (Graphic from Wikipedia)

If our coast-measuring ruler is a mile long, when we lay it along the coast, it will cut through parts of England’s interior, wherever the coast is convex, and it will also cut through parts of the ocean, wherever the coast is concave. If we do this around the entire coast, we will get a very rough, rational measurement, that will be wrong (though perhaps useful). Well, we could decrease the size of our ruler in order to get a more precise measurement. Our calculation will be very different for a one inch ruler than for a one mile ruler. Well, it turns out that it’s more correct to think of things like coastlines having what’s called in mathematics a “fractal” dimension — a dimension that’s not an integer. And, yes, that means they are irrational.

It turns out that coastlines’ dimensions are somewhere between 2 and 3, depending on the intricacy of the coast in question. We are taught to think of these things abstractly — coastlines are, mathematically, just smooth 2-D curves. But reality isn’t so tidy.

Abstract is Too Nice

Actually, I don’t think that even infinitely messy irrational numbers genuinely underlie the fabric of reality. The idea that anything mathematical is somehow more ontologically foundational than the actual world is simply giving humanity too much credit (and the world too little). Mathematics is, despite what some philosophers believe, a human endeavor, subject to human foibles and error. It is without a doubt incredible, the usefulness of mathematics applied to problems in the real world. We can travel to the moon without (too much) fear of exploding in space; we can pinpoint small objects from great distances; we can create artificial cherry flavorings that (hopefully) won’t kill us. But, in the end, to think that mathematics underlies the natural world is an example of human hubris. It’d be better to say that mathematics describes things about the natural world, but even this could grant mathematics too much. Is it genuinely descriptive to say that the coast of England is of dimension 2.18747636658698…? Or is it just pointing out that our knowledge of this fact is limited, because we can’t plumb the depths of this ugly, non-repeating, infinitely long number?

So, really, the title of this post should’ve been “God (or the Big Bang) Created the World; Humanity Tries to Describe it With Irrational Numbers”. But that’s sort of unpoetic.

The Doctrine of Double Effect

Sometimes doing the right thing involves a morally bad consequence. For instance, if someone is about to murder your family, and the only thing you can do to stop him is to yourself kill that person, it certainly seems that the right thing to do is to kill the murderer. And yet there is the morally bad consequence of killing someone at play here.

It’d be great for moral philosophers if we could adopt simple moral rules that apply in every situation, like “thou shalt not kill”. But situations like the above make it clear that the world is seldom so kind to those of us who would plumb the depths of ethical reality. So, if you’re looking to create a coherent moral system, you’d better be able to explain why it is that you are justified in killing a murderer who is intent on killing you and your family. Under what circumstances is killing okay?

Perhaps if we view the killing in this situation as a regrettable consequence of doing the right thing… That is, perhaps the moral action of saving your family — even if it results in the killing of someone — is the real action that you are undertaking. And perhaps the killing of the murderer is a tangential, unavoidable, bad moral consequence. In this analysis, we might be able to work things out to the effect that you are not a killer — you are a family-saver whose actions led (regrettably) to an unintended killing.


Aquinas, back in the 13th century, was thinking of a similar situation, and came up with four conditions that he thought must be met for acting morally with a tangential bad moral consequence:

  1. The Nature-of-the-Act Condition. The action itself cannot be morally wrong.
  2. The Means-End Condition. The bad effect must not lead directly to the good effect.
  3. The Right-Intention Condition. The intention must be the achieving of only the good effect with the bad effect being only an unintended side effect. The bad effect may be foreseen, but not desired.
  4. The Proportionality Condition. The good effect must be at least as morally good as the bad effect is morally bad.

If Aquinas’ analysis is on the money, then you can save your family with a clear moral conscience, despite the fact that you wound up killing someone in order to do it.

Unfortunately, in the case of killing the murderer, we hit a pretty significant problem right off the bat with condition one. The action itself here seems to be one of killing. Isn’t this almost definitionally morally wrong? To get himself out of this fix, Aquinas argues that the actual action undertaken here is saving one’s family, and that the killing is the bad but unintended side effect: “Accordingly, the act of self-defense may have two effects: one, the saving of one’s life; the other, the slaying of the aggressor.” I’m not sure I buy that, but let’s step through the other conditions…

Actually, condition two seems problematic as well. Indeed, the saving of your family’s lives seems to be a direct consequence of you killing the murderer. But Aquinas would argue that actually the bad effect of killing the murderer somehow comes later in the chain of cause-effect than the good effect of saving your family. Honestly, this seems like complete bullshit to me, but let’s keep riding this train to the station and see where we end up.

Condition three seems really to get at the heart of the matter. You don’t first and foremost intend to kill the murderer; you intend to save your family. Perhaps this is really the keystone of moral goodness. If you don’t intend to kill the murderer, then you’re not committing murder yourself. But if killing the murderer is something that has to happen in order for you to save your family, then so be it.

Condition four is also conceivably well-met by our case. Saving your family, ceteris paribus, is arguably at least as morally important in the positive as killing the murderer is in the negative.

Abortion and Euthanasia

The Catholic Church has used Aquinas’ thoughts on double effect to weigh in on two weighty moral issues of our time: abortion and euthanasia.

Many have argued that even if abortion is immoral, it is morally permissible to perform an abortion to save the life of the mother. The Church, contrary to this, has argued that saving the life of the mother in this sort of case would fail to meet both criteria one and two above.

But you can apply this same reasoning to the case of self-defense above. I’ll leave it to the reader to cogitate on this further. (Hint: If saving-your-family is the true and moral act in the first case, then why isn’t saving-the-mother the true and moral act in this case? In both cases, then, the killing would be consequent to the saving.)

The Church meant to draw a distinction between plain abortion and, for instance, performing a hysterectomy on a pregnant woman with uterine cancer. In the case of our cancerous woman (so goes the Church’s logic), the result of the hysterectomy would be an abortion, but the actual intention of the doctors is to save the woman from cancer, not to kill her fetus. This is a nifty bit of face-saving, but, again, isn’t the real intention of the doctors in the abortion case to save the woman’s life? And thus the abortion is secondary to the life-saving, and should be morally acceptable.

There’s a similar Church line taken on euthanasia. A doctor killing a patient with an overdose of morphine is (argues the Church) unacceptable, because it fails conditions one and two again. That is, even if the desired end-result is that of mercy, getting to that end via a morally bad act (killing) is wrong.

However, the Church allowed for doctors overdosing patients on morphine under the circumstance where the intention is to prevent pain. That is, if the act in question is the morally good one of pain prevention, then the unintended consequence of death is morally okay.

We’ll leave it to another day to discuss the absurdity of the presumed immorality of euthanasia, but note again that these two situations are really not that different. No doctor (or no doctor I’ve ever met, anyway) outright intends to kill her patients. They intend to ease suffering, and they know that death is often the ultimate and only suffering-ender that will work in some unfortunate circumstances.

Trolley Cases and Double Effect

Are you up to speed on philosophical trolley problems? If not, take a quick look at our primer on the subject. In fact, it was the publishing of two recent books on trolley problems in philosophy that got me thinking about double effect for this post. (Both are excellent little books, by the way, and well worth a read: Would You Kill the Fat Man, by David Edmonds, and The Trolley Problem, or Would You Throw the Fat Guy Off the Bridge? by Thomas Cathcart.)

Some will use the doctrine of double effect to justify their intuitions about trolley cases. For instance, in the standard case, a driver of a train with no brakes can either continue down his track and kill five unsuspecting workers, or divert the train down a spur and kill one unsuspecting worker. It turns out that most people believe that killing the one worker is the right thing to do in this situation. And often people will cite utilitarian reasoning here: ‘Well, one life isn’t as valuable as five, so it’s the right thing to kill one if you can save five.’

But if we change the circumstances of our thought experiment, the utilitarian justification loses some weight. Say the only way to save the five workers is to push a heavy object in front of the train. But the only object heavy enough is a fat man who happens to be above the tracks on a bridge. Would it be the right moral thing for you to push the fat main off the bridge and let the train run over him, saving the five lives further down the tracks? Well, it turns out that the general moral intuition here is that it’s actually not the right thing to do. And, if this intuition is correct, utilitarianism fails here. But the doctrine of double effect could be used to explain things! In the first trolley case, you don’t intend to kill the one worker on the spur. And your action isn’t really killing that worker — the action is saving the five workers by steering the train down a different track. The killing of the one worker that results from your action is regrettable, but is not the intended effect of the whole affair. But in the case of the fat man, you have to take direct action against the one person in order to save the five. Your action is directly killing the fat man.

As with the above analyses, I think there’s something actually amiss here. If you put an intermediate step in between your action and the fat man dying, that wouldn’t make it any more or less acceptable. There has got to be another analysis that we can apply.

And, in the spirit of cliffhanger serial short movies from the golden age of Hollywood, I’ll leave you with the promise that we’ll explore this different analysis in a future post…

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.


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

Dogs Are People, Too

A very interesting article in the New York Times, on mapping brain activity in dogs. (And a very nice use of neuroscience to break free of the bonds of behaviorism.)

Although we are just beginning to answer basic questions about the canine brain, we cannot ignore the striking similarity between dogs and humans in both the structure and function of a key brain region: the caudate nucleus.

[M]any of the same things that activate the human caudate, which are associated with positive emotions, also activate the dog caudate. Neuroscientists call this a functional homology, and it may be an indication of canine emotions.

The ability to experience positive emotions, like love and attachment, would mean that dogs have a level of sentience comparable to that of a human child. And this ability suggests a rethinking of how we treat dogs.

We’ll talk about animal rights in a future post. Even without this scientific exploration into animal sentience, there are serious ethical issues with the way we think about the treatment of animals.

Frege Was From Venus

If you spend any time mucking around in the philosophy of language, you’re going to run headlong into Gottlob Frege at some point. Frege, round about the turn of the 20th century, was a key figure in the emerging fields of logic and the philosophy of mathematics, but he may well be best remembered for his contributions to the theory of meaning.

What is Meaning?

The basic question that any philosophy of language must address is this: What can we say about the meaning of a word (and — what perhaps amounts to the same thing — the meaning of a sentence)?

A first stab at analyzing this is to say that the meaning of a word is just what it points to — what it designates or refers to. For instance, the word (or name, in this case) “Herbie” refers to my cat, Herbie. (Make sure to get your head around the difference between a word and an object referred to by that word. We’ll have a post about this “use/mention” distinction soon. For now, just stay alert to the use of quotation marks to distinguish a word from its associated object.) The word “Herbie” points to the creature that is at the time of this writing tapping my leg with his paw, trying to get me to play with him. (I’ll be right back…)

Reference - Herbie

We can apply the same analysis to numbers. The ink-on-paper numeral “7” that you might write down in your checkbook or on a math test, refers to the actual number 7, which for the sake of argument we’ll take to be some object out there in the universe somewhere. Similarly, and perhaps easier to comprehend, the words “seven”, “siete”, “sept”, and “sieben” all refer to the number 7 as well (in English, Spanish, French, and German, respectively).

Reference 7

If this is the right picture, it would give us a convenient way to explain how “seven” and “siete” both mean the same thing: It’s because both words refer to the same thing.

Reference Ain’t Enough

If this were all there is to meaning, then “12” and “7 + 5” would mean the same thing, because they both refer to the number 12.

But as Kant famously pointed out (in his analytic/synthetic, a priori/a posteriori distinctions), these two words/phrases might well mean different things.

To see why, let’s look at the following statement: “12 = 12”.

Compare that with this statement: “7 + 5 = 12”.

The first statement doesn’t say much except that a thing is always identical with itself. The second says something significantly new about 12 (that it’s the sum of 7 and 5).

If this is true, then “12” and “7 + 5” do not have the same meaning; and if this is the case, then there has to be more to meaning than the idea of reference. You can see this difference more clearly if you look at these in a different context.

“I know that 12 = 12.” One can know this without knowing anything about addition.

“I know that 7 + 5 = 12.” To know this, one has to know something about addition.

This becomes even clearer with a more complex mathematical fact.

“I know that 812,285,952 = 812,285,952.”

“I know that 24,789 x 32,768 = 812,285,952.”

Anyone can utter the first sentence without any more knowledge than ‘everything is equal to itself’. But to say the second sentence with any sort of certainty, you’d have to have done some complex calculations (or had a calculator do them for you). There’s something about the second statement that is differently meaningful than the first.

The Morning Star and The Evening Star

The more usual example philosophers of language use is (happily for most of you) not mathematical.

The ancient Greeks, looking at the dark sky above them, noticed two very bright stars. One came up shortly after the sun went down in the evening, and was brighter than any other star around it; the other star came up shortly before the sun came up in the morning and was similarly bright. They named these two stars: “The Morning Star” and “The Evening Star”.

Well, maybe you saw this coming, but it turns out that these two stars were actually the same object: Venus. (Of course, not even a star after all, but a brightly reflective planet.) So here’s the referential picture the ancient Greeks had:

Morning Star / Evening Star Greeks

A few centuries later, astronomers gave us this picture instead:

Reference Venus

Now, if reference is all there is to meaning, then these two sentences would have the same meaning:

“The Morning Star is the Morning Star.”

“The Morning Star is the Evening Star.”

Because by just considering reference those two sentences translate to this one sentence:

“Venus is Venus.”

Reference Sentences

But clearly these sentences have very different meanings — the first sentence is obvious to anyone, even those without any knowledge of astronomy; the second sentence is something that one would only know by virtue of synthesizing some significant piece of astronomical knowledge, namely that “The Morning Star” and “The Evening Star” both refer to the same heavenly body: Venus.

Frege’s Solution

So hopefully you’ll agree that reference can’t be all there is to meaning.

Frege’s idea was that while reference is important to meaning, there is another important dimension to meaning as well, which he called sense. He called the sense of a term the “mode of presentation” of the referent. So while “the Morning Star” and “the Evening Star” both refer to the same thing, they have different senses: the sense of “the Morning Star” is something like “the bright star that rises in the early morning”, while the sense of “the Evening Star” is something like “the bright star that rises in the early evening”. Same reference; different sense.

On this scheme, when we say “the Morning Star is the Evening Star”, we’re comparing senses, not references, and this is why it’s a statement of new knowledge (synthetic, a la Kant) and not just an obvious truth (analytic, a la Kant). “The Morning Star is the Morning Star” is comparing two things that not only have the same references, but the same senses. And this is semantically not interesting.

Sense Without Reference

One interesting consequence of Frege’s philosophy of language is that it turns out that not everything with a sense has a reference.

“The novel written by Richard Nixon” has a sense — it presents an idea to us in a clearly understandable way — but has no reference — Nixon never (as far as I know) actually wrote a novel. So in fact the meaning of a sentence might not have to rely at all on reference. “The novel written by Richard Nixon is long and boring” has a meaning even though the subject of the sentence doesn’t exist. We’ll take up this interesting idea in a future post.


I haven’t used Zotero in a couple of years, but I thought I’d revisit it. It’s a great tool for philosophy essay writers.

It’s a free browser plugin (originally for Firefox, but now available for Chrome as well) that helps researchers wrangle bibliographic info in a central location. Once you’ve gathered your references, you can easily include them in Word or OpenOffice with the Zotero word processing plugins.

Check out the official intro video for a nice overview:

Or if you’re old-school, you can actually read about it here.

The Philosopher of the Pool

I ran across this old stereoscopic picture in a random walk through the interwebs just now. Titled “The Philosopher of the Pool”, it got my mind running down lots of interesting tracks as to what could have dubbed this man with so grand a title.

Philosopher of the Pool

The truth is often not as grand as the fictions of the mind. But there are aspects of the truth here that certainly are fascinating. While information regarding this man is scant, I did find this (I’ve bolded what I think is the most interesting paragraph, but the whole story is worth a read):

In the annals of the little town of Pardeeville, picturesquely situated on the Fox River and two lakes, John Merrill, a settler from New Hampshire, who was related to S.S. Merrill, an early resident of Milwaukee, and to Henry Merrill, sutler at Old Fort Winnebago, occupies a conspicuous niche.

In John Merrill’s life were many unique incidents. He had a fair education, was widely read of an ingenious turn of mind, with a bent for natural science. While living in New Hampshire he wrote a book entitled “Cosmogony or Thoughts on Philosophy” which contained a refutation of Isaac Newton’s theory of gravitation. Mr. Merrill contended that the center of the earth consists only of space and that our globe consists is composed of various layers, earth, air, and water in regular order. He held that at each pole there is a large hole, and that into the one at the North Pole the ships of missing Artic explorers sank. He described the agricultural activities of the inhabitants of the interior of our planet and the way in which the sun’s rays reached the region…

Mr. Merrill’s manuscript was polished and copied with pen and ink by a woman resident of Pardeeville and printed in pamphlet form in New Hampshire. Many copies were sold in those early days especially in his native state, where he owned a celebrated nook in the White Mountains called the Pool. It was situated at Franconia Notch, at the foot of Mount Lafayette, in a canyon on the Pemigewasset River. Each summer after settling in Pardeeville he made a trip to his pool, where from tourists he gathered a harvest of dollars for the use of his boats.

Naturally John Merrill did a flourishing business in his books, as well as his boats. He gave lectures on his theory before many famous persons, including a number from abroad, and he wrote a letter to Queen Victoria and sent her a copy of his scientific work.

One eventful day he received what purported to be a reply from the ruler of the British Empire. A copy was made by a printer in New Hampshire and is in the possession of Charles W Merrill of Pardeeville, John Merrill’s grandson. It is yellowed by age. The original is supposed to have been lost or inadvertently destroyed after the death of John Merrill at the home of his daughter in Pardeeville.

The printed copy read as follows:

Royal Despatch of her Majesty to Ho. John Merrill, Flume House NH – Her Seal & N
By Lord Napier British Minister Aerial Mansior
High Picacoddy Royal Ramparts, Thames Tunnel July 4th Anno Domini 1857,Albertus Princeps

To his August Highness Hon John Merrill director of the pool, artic philosopher, practical philanthropist etc, etc

Monsieur: I am commissioned by her most gracious majesty’s royal high butler to communicate to your obsequious highness the most transatlantic compliments of Alid el Kader; and to acknowledge the receipt of your most learned, antiloquent and circumambient state document dated Aug 28, 1854; which has been under profound consideration of the grand lama ever since. The grand lama fully concurs in your new views of the hole in the earth; and believes it was caused by a derangement of the north pole — affected by the scintillations of the hyperborean aurora borealis, which have ” shaken the bark of Sir John Franklin from outside into the inside of the pole,” as you say.

The grand lama takes this opportunity to express to your obsequious highness the great satisfaction which the most grand butler of her majesty feels after the perusal of so learned a document and begs to salute you as a man of transcendental prognostications.

By royal command and my own royal pleasure. Signed in the grand culinary department with a royal goose quill.

By Albert

What could be thought of a document like that? Among the early Pardeevillians it aroused considerable amazement; on the part of some, hilarity. It is left to the reader to guess its source. Although a few unsuspecting individual marveled at the peculiarity of the royal phraseology, it was generally y considered as being the composition of jokesters, who in some way had learned of the sending of the book and letter to Queen Victoria. As to whether the original document showed evidence of having been sent from England, Charles W Merrill is unable to say. He remembers, however, that it bore impressive looking seals and other fancy touches. The supposed reply may have been the production of American college students who heard of the letter to Queen Victoria and who took great pains to make the document resemble an official one from a European monarchy.

In 1888 an eastern newspaper und the caption “The Philosopher of the Pool” printed a complimentary mention of John Merrill with the following letter from him:

Mr. Editor: Please say to my friends that I have retired from The Pool, after being there 34 years, and concluded to spend the rest of my days on the homestead in Pardeeville, Wis. Where I can sit and see the 100 acres of crops almost ready for harvest. Crops never looked better. Give my best and respects to all, till we meet in heaven. I am almost home. This is my eighty-seventh year. Am well, only old age says stay with my children. Yours in love, JOHN MERRILL

The editor adds: Thus after having paddles his skiff so many years, the old philosopher drops his oars with this plaintive strain, and thus too, a rugged landmark, second only in importance to his more aged rival, the “Old Man of the Mountains,” disappears from view.

The author philosopher died in 1892 at the age of 90 years and was buried in the Pardeeville cemetery. On his monument is inscribed a map of our globe, on which he spent so much time and thought. He is remembered as one of the picturesque figures in Wisconsin history.

The Milwaukee Journal Sunday September 23, 1928