“Is there an answer?” Searching for the meaning of life in The Hitchhiker’s Guide to the Galaxy.

(posted at 3 Quarks Daily)

The Austrian philosopher Ludwig Wittgenstein gets credit for pointing out that many classic philosophical conundrums are unsolvable not because they are so profound, but because they are incoherent. Instead of trying to solve such questions, he argued, we should try to dissolvethem, by demonstrating how they misuse words and investigating the confusion that motivated the question in the first place.

But with all due respect to Wittgenstein, my favorite example of the “dissolving questions” strategy comes from Douglas Adams’ The Hitchhiker’s Guide to the Galaxy, which contains a cheeky and unforgettable dissolution of which I’m sure Wittgenstein himself would have been proud:  A race of hyper-intelligent, pan-dimensional beings builds a supercomputer named Deep Thought, so that they can ask it the question that has preoccupied philosophers for millions of years: “What is the answer to life, the universe, and everything?”

After seven and a half million years of computation, Deep Thought finally announces the answer: Forty-two. In response to the programmers’ howls of disappointment and confusion, Deep Thought rather patiently points out that the reason his answer doesn’t make any sense is because their original question didn’t make any sense either. As I’ve written before, questions like this one, or the very similar “What is the meaning of life?” question, seem to be committing a basic category error: life isn’t the kind of thing to which the word “meaning” or “answer” applies.

But in this article I want to take my analysis a little further than that.

Read the rest, at 3 Quarks Daily.

What is 0^0? And is math true, or just useful?

When you hear mathematicians talk about “searching” for a proof or having “discovered” a new theorem, the implication is that math is something that exists out there in the world, like nature, and that we gradually learn more about it. In other words, mathematical questions are objectively true or false, independent of us, and it’s up to us to discover the answer. That’s a very popular way to think about math, and a very intuitive one.

The alternate view, however, is that math is something we invent, and that math has the form it does because we decided that form would be useful to us, not because we discovered it to be true. Skeptical? Consider imaginary numbers: The square root of X is the number which, when you square it, yields X. And there’s no real number which, when you square it, yields -1. But mathematicians realized centuries ago that it would be useful to be able to use square roots of negative numbers in their formulas, so they decided to define an imaginary number, “i,” to mean “the square root of -1.” So this seems like a clear example in which a mathematical concept was invented, rather than discovered, and in which our system of math has a certain form simply because we decided it would be useful to define it that way, not because that’s how things “really are.”

This is too large of a debate to resolve in one blog post, but I do want to bring up one interesting case study I came across that points in favor of the “math is invented” side of the debate. My friends over at the popular blog Ask a Mathematician, Ask a Physicist did a great post a while ago addressing one of their readers’ questions: What is 0^0?

The reason this question is a head-scratcher is that our rules about how exponents work seem to yield two contradictory answers. On the one hand, we have a rule that zero raised to any power equals zero. But on the other hand, we have a rule that anything raised to the power of zero equals one. So which is it? Does 0^0 = 0 or does 0^0 = 1?

Well, I asked Google and according to their super-official calculator, the answer is unambiguous:

Indeed, the Mathematician at AAMAAP confirms, mathematicians in practice act as if 0^0 = 1. But why? Because it’s more convenient, basically. If we let 0^0=0, there are certain important theorems, like the Binomial Theorem, that would need to be rewritten in more complicated and clunky ways. Note that it’s not even the case that letting 0^0=0 would contradict our theorems (if so, we could perhaps view that as a disproof of the statement 0^0=0). It’s just that it would make our theorems less elegant. Says the mathematician:

“There are some further reasons why using 0^0 = 1 is preferable, but they boil down to that choice being more useful than the alternative choices, leading to simpler theorems, or feeling more “natural” to mathematicians. The choice is not “right”, it is merely nice.”

Philosophy Referee Signals

Ok, I love it when I can combine my passion for discussing philosophy with my interest in sports. Check out these philosophy referee signals:

I think I’ll enjoy this most during public debates – I can just see my friends and me gesturing wildly from the back of the auditorium.

Can you think of other signals that would be useful?

What’s my ethical system? A disambiguation.

Jeremy Bentham, founder of utilitarianism

A friend of mine recently asked me what system of ethics I subscribe to. For all that I’ve thought, read, and talked about ethics over the years, I still have trouble answering that question clearly and coherently. This time, at least, I had the useful realization that my difficulty discussing this in the past is partly due to the fact that there are several ways of interpreting the question, each of which leads to a different answer from me.

I’m sure I’ll write a lot more about each of these topics in the future, but for now, I want to share a brief disambiguation. Even if your answers to these questions are different from mine, it still might be helpful for you to break down your own answer along these or similar lines.

“What’s my ethical system,” then, could be interpreted any of the following ways:

1. What ethical system am I most comfortable with intellectually? Act utilitarianism. This system holds that in any given situation, you should do whatever will maximize expected utility over all sentient beings. There are some tricky questions involved (for example, are you maximizing the sum of total utility, or the average? How do you take into account the utility of future beings?). Nevertheless, utility is the only good which I think it makes sense to care about — if you told me “We should try to pursue/avoid result X, even though it won’t affect anyone’s utility,” that wouldn’t make any sense to me intellectually.

2. What ethical system am I most comfortable with emotionally? Some mishmash of act utilitarianism + rights theory. Even though my emotional intuitions usually accord with act utilitarianism, there are some cases in which I simply don’t like the action that act utilitarianism prescribes. For example, I tend to feel that people have a “right” to autonomy even if you knew that they would end up happier if you forced them to make a certain choice. I also tend to feel that people have a “right” to know the truth about certain things, even if you knew that it would make them less happy overall.

But I don’t have any justification for my feelings about those situations, nor do I think any such justification exists — I don’t think the concept of a “right” makes any sense except as a convention we all choose to respect. So I’m still trying to figure out how to reconcile my strong overall preference for act utilitarianism with my strong emotional inclination to discard it in cases like these.

3. What ethical system do I think is “correct?” None. I’m pretty much an error theorist when it comes to ethics, which means that I think ethical claims (e.g., “Causing gratuitous suffering is wrong”) can’t be said to be true or false the way empirical claims (e.g., “Poisoning the well will cause gratuitous suffering”) can. That doesn’t imply that ethical claims are entirely meaningless. Clearly ethical claims can express emotions like disgust and outrage, and a kind of prescriptivism, i.e., “Don’t do X”.

But in my experience, people making ethical claims tend to also believe they are making a factual claim about a property (“wrongness”) that some act has, and that’s where the “error” in “error theory” comes in — I don’t think that properties of rightness and wrongness exist, objectively, in the world.  The explanation that most closely matches my views on this is J. L. Mackie’s, laid out in Ethics: Inventing Right and Wrong.  So the preferences I laid out in #1 and #2 are just that — preferences.

4. What ethical system do I actually follow on a day-to-day basis? Some mishmash of #2 + weakness of will + selective apathy + social pressures and habits. I’m not perfect, even by the standards of the system of ethics I myself have chosen. There are plenty of relatively easy things I could be doing to reduce suffering in the world which I am not doing, mainly out of inertia and the knowledge that society won’t judge me harshly for not doing them. I can and intend to remedy this gap, to some extent, but there’s no clear answer to the question of how high a standard to hold oneself to.

Map and Territory: Navigating Language

Three philosophy grad students were stranded on an abandoned island. They started wandering around exploring, making a map of the territory. To make it easier to talk about, they labeled the northern part of the island “Section A” and the southern part “Section B”, writing it in big letters on the top and bottom of the map.

After exploring a bit, Chris called out excitedly. “I found a radio in Section A! Check it out, we’re saved!” His friends came running.

“This is in Section B, not Section A,” said Bruce. “It’s south of the tree line, which is the obvious division between north and south.”
“Of course it’s Section A,” replied Alice. “This is north of the river, which is the way to divide the island.”

Chris shrugged. “I guess we never decided exactly what the border was; I just assumed we were using the river. It’s not like the radio moves based on what section we call this. We agree that it’s north of the river and south of the trees. It’s Section A if we use the river, Section B if we use the forest. Let’s just decide to use one or the other. Neither way is ‘right’ or ‘wrong’; we’re making them up.”

Alice and Bruce weren’t buying it.

“What do you mean, we’re just making it up? The forest is real and the river is real. One of them makes the real boundary between Section A and Section B!”

Chris sat down to use the radio to call for help, leaving his two friends to their bickering.


Alice and Bruce were experiencing the “map and territory” confusion. A map is a mind-made categorization of real things in the territory. It doesn’t make sense to say that the decision to divide the territory in one way or another is “right” or “wrong”, only more or less useful in different contexts.

This comes up all too often in language. Like sections on a map, words are societal tools we use to categorize and communicate the real things we experience. Our society has some well-defined words like ‘hydrogen’ – we have a good shared understanding of exactly which conditions must be met to determine whether or not we should call something ‘hydrogen’.

But the boundaries around other words are hazier. People argue over whether to call something ‘love’, whether to call it ‘art’, and (one of the most contentious) whether to call it ‘moral’. By some definitions, a urinal on a pedestal qualifies as art, by other definitions it doesn’t. Society hasn’t agreed upon clear-cut boundaries for which feelings, objects, or actions fit into those categories. But the arguments are not about reality itself – they’re over the labels, the language map.

Read more of this post

A philosopher of religion calls it quits

My latest article, for Religion Dispatches, examines the controversy generated last fall when philosopher of religion Keith Parsons quit the field and declared the theistic arguments to be hopelessly fallacious. The article also delves into the different approaches to philosophy of religion — are we trying to answer questions of the form “Is X true?” or of the form “If X were true, what would follow from that?”

Keith Parsons himself now has a blog post up about my piece, and responds to some comments readers left at RD. There’s also a comment thread about the article going at Jerry Coyne’s blog, Why Evolution is True.

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