Philosophy

Modal Logic and the Ontological Proof

The ontological proof for the existence of God (really “proofs” or perhaps “arguments,” as there are various versions) has popped up in the blogs a few times recently: e.g. Ophelia Benson, Josh Rosenau, Jerry Coyne. You’ve probably heard this one; it was most famously formulated by Saint Anselm, and most famously trashed by Immanuel “Existence is not a predicate” Kant. A cartoon version of it would be something like

  1. God is by definition a perfect being.
  2. It is more perfect to exist than to not exist.
  3. Therefore, God exists.

Now, this is a really cartoonish version of the argument — it’s not meant to be taken seriously. This kind of ontological proof is a favorite whipping-argument for atheists, just because it seems so prima facie silly. Just ask Jesus and Mo.

This kind of mockery is a little unfair (although only a little). What’s important to realize is that the ontological proof is perfectly logical — that is, the conclusions follow inevitably from the premises. It’s the premises that are a bit loopy.

It’s instructive and fun to see this in terms of formal logic, especially because the proof requires modal logic — an extension of standard logic that classifies propositions not only as “true” or “false,” but also as “necessarily true/false” and “possibly true/false.” That is, it’s a logic of hypotheticals.

So here is one formalization of the ontological argument, taken from a very nice exposition by Peter Suber. First we have to define some notation to deal with our modalities. We denote possibility and necessity via:

Just given these simple ideas, a few axioms, and a fondness for pushing around abstract symbols, we’re ready to go. Remember that “~” means “not,” a “v” means “or,” and the sideways U means “implies.” Take “p” to be the proposition “something perfect exists,” and we’re off: …

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Morality, Health, and Science

In our last discussion of morality and science, an interesting argument was raised in the comments (by rbd and then in more detail by Ben Finney), concerning an analogy between morality and health. Sam Harris has also brought it up. It’s worth responding to because it (1) sounds convincing at first glance, and (2) has exactly the same flaw that the morality-as-science argument has. That’s what a good analogy should do!

If I can paraphrase, the argument is something like this: “You say that morality isn’t part of science because you don’t know what a `unit of well-being’ is — it’s not something that could in principle be measured by doing an experiment. But one could just as easily say that you don’t know what a `unit of health’ is, and therefore medicine isn’t part of science. The lack of some simple measurable quantity is a simplistic attack against a sophisticated problem.”

This gets right to the point. Because, in fact, I don’t know what a “unit of health” is, which is why medicine is not — solely — part of science.

Let me explain what I mean. Obviously we use science all the time when it comes to medicine. Similarly, we should be very ready to use science when it comes to morality — it’s an indispensable part of the endeavor. But in both cases there is a crucial component that lies outside the realm of science.

Here’s how we do medicine, in a cartoonishly simplified version that is nevertheless good enough for our present purposes. First, we decide what we mean by “healthy.” Then, we use science to try to bring it about.

That first step is not science, no matter how much science might be involved in the definition. Various measurable quantities certainly belong to the realm of science — height, weight, pulse, blood pressure, lifespan, time in the 40-yard dash, etc. But what we decide to label “healthy” is irreducibly a human judgment, not an empirical measurable. Some people might think that extreme thinness is part of being healthy, while others might prefer a more robust physique. Some people might define health as the state that maximizes life expectancy, while others might put more emphasis on quality of life even at the expense of total years. It matters not a whit what people actually think, of course — even if everyone in the world agreed on what “healthy” meant, it would still be a judgment rather than an empirical measurement. If one contrarian person came up with a different definition, they wouldn’t be “right” or “wrong” in the conventional scientific sense. There is no experiment we could do to answer the question one way or another.

In the real world, we more or less agree on what constitutes health, so the non-empirical status of this choice isn’t treated as a crucially important philosophical problem. (At least, until you start reading the literature on disability studies, and you realize that what you thought was obvious maybe is not.) We agree on what health is, and we set out to achieve it, and that second part is very much science.

Morality is exactly the same way, although with somewhat less unanimity in the first step. We agree (or not) on what morality is, and once we do the process of achieving it is very much a scientific issue, in the broad-but-perfectly-valid definition of “science” as “an understanding of how the world works based on empirical data.” Once again, it doesn’t matter whether we agree or not, because that first step is a decision we human beings make, not something we measure out there in the world.

While both health and morality are human choices rather than empirically measurable quantities, they certainly aren’t random choices. Human beings aren’t blank slates; we have preferences. Most of us would prefer to live longer and be free of aches and pains; these preferences feed into how we choose to define “health.” Likewise for morality. But “we broadly agree on X” is not, and never will be, the same statement as “X is a scientific truth.” Understanding our preferences, turning vague impulses into precise statements, constructing logical frameworks based on them — that’s what the philosophy of medicine/morality is all about.

The case of morality is actually much more difficult than the case of health, because most interesting moral questions involve tradeoffs between the interests of different people, not only the state of one individual. So even if we could do experiments to establish a unique map between mental states and human well-being, we wouldn’t really be any closer to reducing morality to science. All very fun to think about, though.

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The Moral Landscape

Last year we talked a bit about Sam Harris’s attempts to ground morality on science:

See especially the third one there, where I try to be relatively careful about what I am saying. (Wouldn’t impress a philosopher by a long shot, but by scientist/blogger standards I was careful.) Upshot: concepts relevant to morality aren’t empirical ones, and can’t be tested by doing experiments. Morality depends on science (you can make moral mistakes if you don’t understand the real world), but it isn’t a subset of it. Science describes what happens, while morality passes judgments on what should and should not happen, which is simply different.

By now Harris’s book The Moral Landscape has appeared, so you can read for yourself his explanations in full. In a different world — one where I had access to a dozen or so clones of myself with fully updated mental states, willing to tackle all the projects my birth-body didn’t have time to fit in — I would read the book carefully and report back. This is not that world.

Happily, Russell Blackford has written a longish and very good review, in the Journal of Evolution and Technology. He also blogged about it, and Jerry Coyne blogged about Russell’s review. As far as I can tell, Russell and I basically agree on all the substantive points, and he’s more trained in philosophy than I am, so you’re actually doing a lot better than something one of my clones would have been able to provide. It’s an extremely generous review, always saying “I liked the book but…” where I would have said “Despite the flaws, there are some good aspects…” So you’ll find in the review plenty of lines like “Unfortunately, Harris sees it as necessary to defend a naïve metaethical position…”

Any lingering urge I may have had to jump into the debate again in a substantive way has been dissipated by Harris’s response to Blackford’s review, which appears in the form of a letter to Jerry Coyne reprinted on his blog. It seems that very little communication is taking place at this point. Coyne paraphrases Blackford as asking “How do we actually measure well being?; for that is what we must do to make moral judgments.” Seems reasonable enough to me, and echoes very closely my first point here. Harris’s response is:

This is simply not a problem for my thesis (recall my “answers in practice vs. answers in principle” argument). There is a difference between how we verify the truth of a proposition and what makes a proposition true. How many breaths did I take last Tuesday? I don’t know, and there is no way to find out. But there is a correct, numerical answer to this question (and you can bet the farm that it falls between 5 and 5 million).

This misses the point, to say the least. The problem of measuring well-being is not simply one of practice, it’s very much one of principle. I know what a breath is; I don’t know what a “unit of well-being is.” The point of these critiques is that there is no such thing as a unit of well-being that we can look inside the brain and measure. I’m pretty sure that’s a problem of principle. Of course, Russell and Jerry and I (and David Hume, and a large number of professional moral philosophers) may be wrong about this. The way to provide a counter-argument would be to say “Here is a precise and unambiguous definition of how to measure well-being, at least in principle.” That doesn’t seem to be forthcoming.

Latter Harris says this:

The case I make in the book is that morality entirely depends on the existence of conscious minds; minds are natural phenomena; and, therefore, moral truths exist (and can be determined by science in principle, if not always in practice).

Taken at face value, this implies that truths about the best TV shows or most delicious flavors of ice cream also exist. My opinion that The Wire is the best TV show of all time is a natural phenomenon — it reflects the state of certain neurons in my brain. That doesn’t imply, in any meaningful sense, that the state of my brain provides evidence that The Wire “really is” the best TV show of all time. Nor, more programmatically and importantly, does it provide unambiguous guidance concerning which new programs should be green-lit by studio executives. The real problem — how do you balance the interests of different people against each other? — is completely ignored.

At heart I think the problem is that Sam and some other atheists are really concerned about the idea that, without objective moral truths based on science, the field of morality becomes either the exclusive domain of religion, or simply collapses into nihilism. Happily for reality, that’s an extremely false dichotomy. Morality isn’t out there to be measured like some empirical property of the physical world, but that doesn’t mean it’s impossible to be moral or to speak about morality in a rational, thoughtful way. Pretending that morality is a subset of science is, in its own way, just as much an example of wishful thinking as pretending that morality is handed down by God. We have to face up to that temptation and accept the world as it is.

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Dysteleological Physicalism

As a special behind-the-scenes tidbit for loyal blog readers, I will reveal here that The Pointless Universe was actually my second entry in the Edge World Question Center. My first, making the same point but using different words, was entitled “Dysteleological Physicalism.” To me, that kind of title is totally box office, and I’m happy to take credit for coining the phrase. (Expect T-shirts and bumper stickers soon.) But apparently not everyone agrees, and it was gently suggested that I come up with something less forbidding. Here is my original version.

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DYSTELEOLOGICAL PHYSICALISM

The world consists of things, which obey rules. A simple idea, but not an obvious one, and it carries profound consequences.

Physicalism holds that all that really exists are physical things. Our notion of what constitutes a “physical thing” can change as our understanding of physics improves; these days our best conception of what really exists is a set of interacting quantum fields described by a wave function. What doesn’t exist, in this doctrine, is anything strictly outside the physical realm — no spirits, deities, or souls independent of bodies. It is often convenient to describe the world in other than purely physical terms, but that is a matter of practical usefulness rather than fundamental necessity.

Most modern scientists and philosophers are physicalists, but the idea is far from obvious, and it is not as widely accepted in the larger community as it could be. When someone dies, it seems apparent that something is *gone* — a spirit or soul that previously animated the body. The idea that a person is a complex chemical reaction, and that their consciousness emerges directly from the chemical interplay of the atoms of which they are made, can be a difficult one to accept. But it is the inescapable conclusion from everything science has learned about the world.

If the world is made of things, why do they act the way they do? A plausible answer to this question, elaborated by Aristotle and part of many people’s intuitive picture of how things work, is that these things want to be a certain way. they have a goal, or at least a natural state of being. Water wants to run downhill; fire wants to rise to the sky. Humans exist to be rational, or caring, or to glorify God; marriages are meant to be between a man and a woman.

This teleological, goal-driven, view of the world is reasonable on its face, but unsupported by science. When Avicenna and Galileo and others suggested that motion does not require a continuous impulse — that objects left to themselves simply keep moving without any outside help — they began the arduous process of undermining the teleological worldview. At a basic level, all any object ever does is obey rules — the laws of physics. These rules take a definite form: given the state of the object and its environment now, we can predict its state in the future. (Quantum mechanics introduces a stochastic component to the prediction, but the underlying idea remains the same.) The “reason” something happens is because it was the inevitable outcome of the state of the universe at an earlier time.

Ernst Haeckel coined the term “dysteleology” to describe the idea that the universe has no ultimate goal or purpose. His primary concern was with biological evolution, but the conception goes deeper. Google returns no hits for the phrase “dysteleological physicalism” (until now, I suppose). But it is arguably the most fundamental insight that science has given us about the ultimate nature of reality. The world consists of things, which obey rules. Everything else derives from that.

None of which is to say that life is devoid of purpose and meaning. Only that these are things we create, not things we discover out there in the fundamental architecture of the world. The world keeps happening, in accordance with its rules; it’s up to us to make sense of it.

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Translational Invariance and Newton’s God

Tim Maudlin is writing a two-volume introduction to the philosophy of physics, and I was fortunate enough to get a peek at a draft of Volume One, about space and time. There is one anecdote in there about Leibniz’s objections to Newtonian physics that is worth passing along. This came up in the course of the Leibniz-Clarke correspondence.

Leibniz was quite fond of proclaiming overarching a priori principles. Perhaps the most famous/infamous is the Principle of Sufficient Reason, which states that everything that happens does so for some good reason. But there was also the Principle of Identity of Indiscernibles, which states that if two things have all the same properties, they are really the same thing. Sounds reasonable enough (although one might worry what qualifies as a “property”), but it can get you in trouble if you take it too far.

Remember that Newton believed in absolute space — a rigid three-dimensional set of points that forms the arena in which physics takes place. Leibniz, on the other hand, claimed that space should be thought of purely in terms of relations between different points, without any metaphysical baggage of “absoluteness.” (From a modern perspective, Leibniz was closer to correct, given Galilean relativity; but once we allow for spacetime curvature in general relativity, the relational view becomes less useful.)

So far, so good. The weird part, to modern ears, comes in when we consider Newtonian cosmology. In order to explain matter in the universe, Newton departed from the strict consequences of his Laws of Motion. Instead, he imagined that empty space existed for an infinite period of time, before eventually God decided to create matter in it.

That’s the part Leibniz couldn’t go along with. He didn’t believe God would work that way, for reasons that amount to what we would now call the translational invariance of space. If God is going to create all this matter in empty space, Leibniz reasons, He has to put it somewhere. But where? Every point is equally good! Therefore there can’t be any “sufficient reason” to create it in one place rather than in some other place. Therefore there must be a deep metaphysical flaw at the heart of Newton’s theory. Interestingly, he didn’t go for “matter has been around forever,” but instead came down on the side of “there is no such thing as absolute space.”

Maybe he was worried about Boltzmann Brains?

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Against Space

The Philosophy of Science Association meeting in Montreal was great fun. For one thing it was in Montreal; for another I got to hang out with Doctor Free-Ride; and as a bonus there were some interesting and provocative talks about the nature of time. I chatted with Tim Maudlin, Huw Price, Craig Callender, Nick Huggett, Chris Wuttrich, David Wallace, John Norton, and other people I always learn from when I talk to. Philosophers always force you to think hard about things.

Here are the slides from my own talk, which was supposed to be about time but ended up being more about space. Not much in the way of original research, just some ruminations on what is and is not “fundamental” about spacetime (with the caveat that this might not be a sensible question to ask). I made two basic points, which happily blended into each other: first, that the distinction between “position” (space) and “momentum” is not a fundamental aspect of classical mechanics or quantum mechanics, but instead reflects the particular Hamiltonian of our world; and second that holography implies that space is emergent, but in a very subtle and non-local way. This latter point is one reason why many of us are skeptical of approaches like loop quantum gravity, causal set theory, or dynamical triangulations; these all start by assuming that there are independent degrees of freedom at each spacetime point, and quantum gravity doesn’t seem to work that way.

Sadly the slides aren’t likely to be very comprehensible. There’s a lot of math, and the equations don’t come out completely clearly — my first time using Slideshare, so perhaps they would look better if I uploaded a pdf file rather than PowerPoint. (Hint: the slides are much more clear if you switch to full-screen mode by clicking on the bottom right.) Also I didn’t make any attempt to have the slides stand by themselves without the accompanying words. But at least this will serve as documentation that I really did give a talk at the conference, no just hang out in restaurants in Montreal.

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Physicalist Anti-Reductionism

In a philosophical mood at the moment, because I’m about to head to Montreal for the Philosophy of Science Association biennial meeting. Say hi if you’re in the neighborhood! I’m on a panel Thursday morning with Nick Huggett, Chris Wüthrich, and Tim Maudlin, talking about the emergence of spacetime in quantum gravity. My angle: space is obviously not fundamental, though time might be.

Here’s a Philosophy TV dialogue between John Dupré (left) and Alex Rosenberg (right). They are both physicalists — the believe that the world is described by material things (or fermions and bosons, if you want to be more specific) and nothing else. But Dupré is an anti-reductionist, which is apparently the majority view among philosophers these days. Rosenberg holds out for reductionism, and seems to me to do a pretty good job at it.

John and Alex from Philosophy TV on Vimeo.

To be honest, even though this was an interesting conversation and I can’t help but be drawn into very similar discussions, I always come away thinking this is the most boring argument in all of philosophy of science. Try as I may, I can’t come up with a non-straw-man version of what it is the anti-reductionists are actually objecting to. You could object to the claim that “the best way to understand complex systems is to analyze their component parts, ignoring higher-level structures” but only if you can find someone who actually makes that claim. You can learn something about a biological organism by studying its genome, but nobody sensible thinks that’s the only way to study it, and nobody thinks that the right approach is to break a giraffe down to quarks and leptons and start cranking out the Feynman diagrams. (If such people can be identified, I’d happily join in the condemnations.)

A sensible reductionist perspective would be something like “objects are completely defined by the states of their components.” The dialogue uses elephants as examples of complex objects, so Rosenberg imagines that we know the state (position and momentum etc.) of every single particle in an elephant. Now we consider another collection of particles, far away, in exactly the same state as the ones in the elephant. Is there any sense in which that new collection is not precisely the same kind of elephant as the original?

Dupré doesn’t give a very convincing answer, except to suggest that you would also need to know the conditions of the environment in which the elephant found itself, to know how it would react. That’s fine, just give the states of all the particles making up the environment. I’m not sure why this is really an objection.

This is purely a philosophical stance, of course; it means next to nothing for practical questions. Nor does the word “fundamental” act in this context as a synonym for
“important” or “interesting.” If I want to describe an elephant, the last thing I would imagine doing is listing the positions and momenta of all its atoms. But it’s worth getting the philosophy right. I could imagine hypothetical worlds in which reductionism failed — worlds where different substances were simply different, rather than being different combinations of the same underlying particles. It’s just not our world.

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Is Dark Matter Supernatural?

No, it’s not. Don’t be alarmed: nobody is claiming that dark matter is supernatural. That’s just the provocative title of a blog post by Chris Schoen, asking whether science can address “supernatural” phenomena. I think it can, all terms properly defined.

This is an old question, which has come up again in a discussion that includes Russell Blackford, Jerry Coyne, John Pieret, and Massimo Pigliucci. (There is some actual discussion in between the name-calling.) Part of the impetus for the discussion is this new paper by Maarten Boudry, Stefaan Blancke, Johan Braeckman for Foundations of Science.

There are two issues standing in the way of a utopian ideal of universal agreement: what we mean by “supernatural,” and how science works. (Are you surprised?)

There is no one perfect definition of “supernatural,” but it’s at least worth trying to define it before passing judgment. Here’s Chris Schoen, commenting on Boudry et. al:

Nowhere do the authors of the paper define just what supernaturalism is supposed to mean. The word is commonly used to indicate that which is not subject to “natural” law, that which is intrinsically concealed from our view, which is not orderly and regular, or otherwise not amenable to observation and quantification.

Very sympathetic to the first sentence. But the second one makes matters worse rather than better. It’s a list of four things: a) not subject to natural law, b) intrinsically concealed from our view, c) not orderly and regular, and d) not amenable to observation and quantification. These are very different things, and it’s far from clear that the best starting point is to group them together. In particular, b) and d) point to the difficulty in observing the supernatural, while a) and c) point to its lawless character. These properties seem quite independent to me.

Rather that declare once and for all what the best definition of “supernatural” is, we can try to distinguish between at least three possibilities:

  1. The silent: things that have absolutely no effect on anything that happens in the world.
  2. The hidden: things that affect the world only indirectly, without being immediately observable themselves.
  3. The lawless: things that affect the world in ways that are observable (directly or otherwise), but not subject to the regularities of natural law.

There may be some difficulty involved in figuring out which category something fits, but once we’ve done so it shouldn’t be so hard to agree on how to deal with it. If something is in the first category, having absolutely no effect on anything that happens in the world, I would suggest that the right strategy is simply to ignore it. Concepts like that are not scientifically meaningful. But they’re not really meaningful on any other level, either. To say that something has absolutely no effect on how the world works is an extremely strong characterization, one that removes the concept from the realm of interestingness. But there aren’t many such concepts. Say you believe in an omnipotent and perfect God, one whose perfection involves being timeless and not intervening in the world. Do you also think that there could be a universe exactly like ours, except that this God does not exist? If so, I can’t see any way in which the idea is meaningful. But if not, then your idea of God does affect the world — it allows it to exist. In that case, it’s really in the next category.

That would be things that affect the world, but only indirectly. This is where the dark matter comparison comes in, which I don’t think is especially helpful. Here’s Schoen again:

We presume that dark matter –if it exists–is lawful and not in the least bit capricious. In other words, it is–if it exists–a “natural” phenomena. But we can presently make absolutely no statements about it whatsoever, except through the effect it (putatively) has on ordinary matter. Whatever it is made of, and however it interacts with the rest of the material world is purely speculative, an untestable hypothesis (given our present knowledge). Our failure to confirm it with science is not unnerving.

I would have thought that this line of reasoning supports the contention that unobservable things do fall unproblematically within the purview of science, but Chris seems to be concluding the opposite, unless I’m misunderstanding. There’s no question that dark matter is part of science. It’s a hypothetical substance that obeys rules, from which we can make predictions that can be tested, and so on. Something doesn’t have to be directly observable to be part of science — it only has to have definite and testable implications for things that are observable. (Quarks are just the most obvious example.) Dark matter is unambiguously amenable to scientific investigation, and if some purportedly supernatural concept has similar implications for observations we do make, it would be subject to science just as well.

It’s the final category, things that don’t obey natural laws, where we really have to think carefully about how science works. Let’s imagine that there really were some sort of miraculous component to existence, some influence that directly affected the world we observe without being subject to rigid laws of behavior. How would science deal with that? …

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The Arrow of Time and the Multiverse on Philosophy TV

Craig Callender is a philosopher of science at UC San Diego, who has written a lot about the nature of time, including a fun illustrated book. He’s more than a bit skeptical of the multiverse idea, and somewhat contrarian about the low-entropy nature of the early universe: he thinks it’s just a fact we should observe and accept (“nomological”), rather than a feature that cries out for a better explanation.

Here we’re having a chat on the recently launched Philosophy TV, sort of Bloggingheads for philosophers. Craig’s head obviously looms much larger than mine, so I had to use my wiles to bob and weave, intellectually speaking.

Callender and Carroll from Philosophy TV on Vimeo.

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Stephen Hawking Settles the God Question Once and For All

Stephen Hawking has a new book coming out (The Grand Design, with Leonard Mlodinow). Among other things, he points out that modern physics has progressed to the point where we don’t need to invoke God to explain the existence of the universe. This is not exactly a hot flash — I remember writing an essay making the same point for a philosophy class my sophomore year in college — but it makes news because it’s Hawking who says it. And that’s absolutely fine — Hawking has a track record of making substantial intellectual contributions, there’s every reason to listen to him more than random undergraduates waxing profound.

This issue is, of course, totally up my alley, and I should certainly blog about it. But I can’t, because I’m on hiatus! (Right?) So, as an experiment, I made a video of myself talking rather than simply typing my words into the computer. Radical! Not sure the amount of information conveyed is anywhere near as large in this format, and obviously I didn’t sweat the production values. I fear that some subtleties of the argument may be lost. But if we’re lucky, other people elsewhere on the internet will also talk about these questions, and we’ll get it all sorted out.

Let me know if the Grand Video Experiment is worth repeating and improving, or whether it’s just a waste of time.

Something that I should have said, but didn’t: there doesn’t need to be some sophisticated modern-physics answer to the question “Why is there something rather than nothing?” The universe can simply exist, end of story. But it’s still fun to think carefully about all the possibilities, existence and non-existence both included.

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