Proving things isn't the point of definitions

By Massimo Pigliucci

“Philosophy is a battle against the bewitchment of our intelligence by means of language,” said Ludwig Wittgenstein, one of the most influential philosophers of the 20th century. It seems that my colleague and friend Julia Galef has indeed been bewitched by language, so I’ll try some philosophy to rescue her.

Julia seems to be unaware of the fact that there is more than one type of definition out there. Particularly, in philosophy one makes the distinction between a linguistic and a conceptual definition. (For a nice introduction to this topic, see section 1.1 of A Short Course in Intellectual Self-Defense, by Normand Baillargeon, the text I use in my introductory course on critical reasoning).

Linguistic definitions are the sort of things for which dictionaries are very useful. If you wanted to know, say, what a quadruped is, you would simply look it up and find something along the lines of: “A quadruped is a four-footed animal,” and that would be that. No arguing required.

Now suppose you are interested in the meaning of justice. You can still look the word up in the dictionary, but in this case such a move would only be the beginning of the discussion, not the end. That’s because what you need is a conceptual definition, and that’s the territory of philosophy.

Let’s use one of Julia’s examples to make the difference more clear. Julia is quite right when she says that if one defines God as “the unknown” that such a definition is completely unhelpful. Not only do we already have a word for “unknown” (it’s, as Julia sardonically points out, “unknown”), but we have now created a pseudo-problem, namely how to investigate the properties of God — we can’t, because, by definition, it is unknowable.

But in fact few people actually define God as the unknown. For instance, the common concept of God in the Judeo-Christian-Muslim tradition is of a being who is simultaneously omnipotent, omniscient and omnibenevolent. Now that is something a philosopher can sink his teeth into, as John Mackie famously did in his essay on “Evil and Omnipotence,” still today a masterful and devastating criticism of the very concept of the J-C-M god.

The same goes for morality. Julia accuses me of sneaking in (“double-dipping”) a prescriptive stance into a descriptive definition. But the point is that definitions, again, come in two varieties, one of which (the linguistic) is indeed descriptive, the other (the conceptual) is prescriptive. There is no possible confusion as long as we keep this basic distinction in mind.

For instance, contra Julia, morality is not usually defined as the set of actions that augment human flourishing (that was my definition during our previous debate). A typical descriptive-linguistic definition of morality is this: “Principles concerning the distinction between right and wrong or good and bad behavior.” There is little disagreement possible here, since this is the way in which, according to dictionaries, people tend to use the term morality. Nowhere in there does anything about human flourishing appear.

So, when I said that I define a moral action as one that augments human flourishing, I was using a conceptual definition, which is open to both debate (one can reasonably reject that particular concept of morality) and needs to be unpacked (what exactly does one mean by “human flourishing”?). For instance, an Ayn Randian could argue that moral actions are those that increase one’s own welfare, and indeed for such a person my concept of morality would be im-moral! As for flourishing, that is why I referred readers to Aristotle’s virtue ethics, which is a way to unpack the concept by introducing and elaborating upon the ancient Greeks’ idea of “eudaimonia,” or happiness in the broad sense of a good and just life.

Of course Julia (or anybody else) can still disagree with my concept of morality, but that disagreement simply can’t be swept away by saying that it is all a matter of definitions (or “semantics,” a word that has gotten far too bad a reputation in common discourse, considering that it is defined — descriptively — as “relating to meaning in language and logic,” and is therefore crucial to understanding what we are talking about).

There is another way of looking at the issue of definitions and their multiple meanings. In the course of our debate on morality I brought up a parallel between ethics and mathematics. I hasten to say that this is a parallel, not an exact equivalence. I am not saying that ethics is precisely like mathematics. Indeed, the reason for my analogy was my criticism of Sam Harris’s claim that the only moral facts are scientific (i.e., empirical) facts. Part of my counter-argument was that we can derive non-arbitrary notions (which I still wouldn’t call “facts”) in wholly non-empirical ways, for instance in logic and mathematics, so that one cannot simply assume that if there are non-arbitrary notions in ethics they must be the same sort of facts with which science deals.

The reason that point is pertinent to this exchange with Julia is because of her contention that every claim needs support. Yet, mathematical theorems and logical proofs begin with generally unsupported claims — they are called axioms or assumptions. The theorem or proof is then developed by provisionally accepting that the axioms or assumptions are true and proceeding to examine what follows via deductive logic. Yes, one can always go back and examine the validity of axioms and assumptions, but that’s a different project that needs to be pursued separately. Moreover, 20th century attempts at meta-mathematics and meta-logic (i.e., at establishing self-consistent foundations for math and logic) have failed, and yet we do not reject either math or logic. (For a clear and entertaining take on that intellectual pursuit, check this out.)

Similarly, questions of meta-ethics (i.e., how do we justify ethical systems and reasoning to begin with) are distinct from discussions of the logical consequences of a small set of assumptions about ethics. Regardless of what the ultimate foundations of ethics may be, it makes a difference whether you look at an ethical problem from the point of view of a virtue ethicist, a deontologist, a consequentialist, or even a moral relativist.

Indeed, one could go a step further and turn the tables on Julia’s (and Harris’s) favored sacred cow: science itself. A quick look at an introductory text in philosophy of science will show that meta-science faces serious issues of its own, which cannot be resolved empirically (i.e., within science itself), just like math, logic and ethics (and dare I say, art?) cannot solve their own issues from within their own confines.

For instance, much of science is done by inductive (as opposed to deductive) reasoning. Yet Hume pointed out two and a half centuries ago that induction cannot be reasonably justified! Nobody so far has been able to give an account of induction that resolves Hume’s problem. You would think that scientists are spending many sleepless nights worrying about the fact that everything they have done cannot be rationally justified, but they don’t, and for a good reason: the problem of induction is an interesting philosophical issue (and there are plenty of really smart solutions that have been proposed — by philosophers), but does not really concern the everyday practice of science. As this xkcd cartoon aptly puts it, “Science works, bitches!” and from a pragmatic standpoint, that’s enough.

In the same way, we are not going to throw out math, logic, or ethics just because meta discussions of those topics seem to constantly get us into trouble. Hume would have approved retaining science, math, logic and ethics regardless of their respective foundational problems. But he would have simply smiled if someone rushed to him with a dictionary in hand to tell him that the problem of induction is all just a matter of definitions.