Well, I got your attention, right? Why on earth would one want to ban a word like ‘science’? I do not seriously mean to ban that word, although it sure would help people to think more clearly about science-related matters.

The trouble is the way people use ‘science’, to mean almost exclusively physics. Even other empirical subjects, like biology or chemistry, not to mention archaeology or sociology, are not usually in the mind of the person who utters that dreaded word, sometimes with something like an all too religious enthusiasm. But what about mathematics? Mathematics is much more scientific in a sense than biology or even physics — in the sense that it is much more precise, and its theories have the great track record, unmatched by physics, of never having been wrong.

Considering mathematics — and formal logic, oblivious to so many empirical scientists for purely historical reasons — helps one to see that many features people believe are responsible for the elevated status of science cannot be universally important: empirical verification. A mathematical theorem cannot usually be proved empirically (that may happen sometimes due to our own inability to come up with a proper mathematical proof, like the four colour map theorem). And mathematics is none the worse for it. It just so happens that the proper method in mathematics is mathematical proof and not empirical verification.

Ironically, there are many empirical sciences or studies that we would like to verify or test empirically, but alas we cannot: cosmology for the most part and also archaeology or even tectonics. In these cases we either rely on (sometimes far-fetched) empirical consequences of our theories or else on what meagre clues the past generously left us. Most of the time you cannot indeed empirically test a cosmological theory, and repeat the test, and repeat again just to make sure.

Most ironic though is the obvious fact that without trusting history there is no physics at all — for the simple reason that we have both to rely on reports of past observations and also on reports of past experiments and even past theories. Is physics built on sand, then? It is, if we ban history from the elevated status of what one could call religious science, just to make Dawkins a bit nervous.

We need to understand what is it that makes something scientific. And yet we cannot do that unless we recognize that we use the word ‘science’ to mean ‘physics and other like subjects’ — and even then, we fail to appreciate how much physics depends on history. What is it then that makes something scientific?

Empirical testing and verification does not fit the bill for the reasons above: mathematics is much more scientific in a sense, although it is not usually by empirical verification that we prove mathematical theorems. And even some empirical studies, like tectonics, large parts of cosmology and archaeology, not to mention history, are not amenable to empirical testing and verification. So, strike that.

What about being guided by natural law? Once a scientist told me that this is distinctive of science, being enough to separate it from pseudoscience. In that case, I replied, I am afraid you will have to consider mathematics a pseudoscience, for the obvious reason that it is not guided by natural law. Worse: any empirical pseudoscience, like alchemy or astrology, do talk about natural law — it is just that the world does not comply and the natural law they claim is nowhere to be found. Alas, most natural laws claimed by most scientists for most of history are nowhere to be found either — because those scientific theories (associated with phlogiston, ether, and many others) were wrong.

Strike that one too, then.

What about being provisional? Can that be a mark of science? Well, no: again, because almost all of mathematics has been right from the very beginning. The business of coming up with theories we later discover to be wrong is what biologists, physicists and astronomers do, not mathematicians. These later usually hit the jackpot each and every time they produce a proof. So unless you want to put mathematics out of the realm of science, forget about being provisional. Worse still: do you really want to throw contemporary physics into the dustbin of pseudoscience if it turns out (as it probably will) that contemporary physics is mostly right? Say that in the year 4587 of our Lord someone comes along and says: ‘Well, physics, as we know it, is pretty much the same since 1916, so it is not real science: strike it from the serious curricula!’

Is it that science is refutable? Can that be something distinctive about science? Well, it is closer to the real deal, but not quite. Again, there is a sense in which mathematics is not refutable: once you have a mathematical proof of a given theorem, that is it: there is nothing to be done to refute it. On the other hand, homeopathy, astrology, and alchemy are all quite refutable, empirically. It just so happens that its practitioners look daintily the other way when you present an empirical refutation of their claims, or else reinterpret in surprising and imaginative ways (conspiracy theories come to mind here) what we take as clear evidence against their most cherished theories . We all know how Karl Popper’s views about these moves are so attractive to scientists; unfortunately, they are quite indefensible.

Still, this idea is in the right direction; it is just that it is not quite like that. Before I elaborate, let me say a few words about a latecomer in these debates: the idea of peer review and universal acceptance. The thought here is that what makes science scientific is the fact that its conclusions are arrived at by the process of peer review and that they gather universal acceptance. For once, this idea has the distinctive advantage of being able not to exclude mathematics.

It is also wrong however, on two counts. First, most scientific theories did not pass the peer review process (this is a relatively new thing in the academic world). Einstein’s two versions of his theory did pass that test; however, Darwin’s did not, and neither did Galileo’s or Newton’s. Secondly, and more importantly, any group of experts in say the spirituality of dreaming of Jesus can make their own learned society, publish their peer-reviewed Annals and they may be none the closer to being truly scientific.

The thought of universal acceptance as a criterion for science does not fare any better. First, because most people who believe in scientific theories do so not because they actually understand even the fundamentals, but rather because they rely on the authority of scientists and teachers — that is, they believe in science in exactly the same way Thomas Aquinas claimed most people in his time had to believe in God: by relying on the authority of the learned, since they do not have the time nor the energy to devote themselves to those studies. Secondly, because we have only an appearance of universal acceptance because the political and educational structures are such that people with strongly anti-scientific views are just excluded and we pretend they do not exist. You have but to look closely at ordinary people to see how much they believe in the most unscientific ideas, most of which can be plainly proven wrong. And yet they persist. One should never underestimate people’s resistance to rationality.

My own take on this is the Aristotelian concept of intellectual virtue: a given study is scientific (meaning: cognitively serious) if and only if it is conducted under the strictest intellectual virtue. So the whole thing hangs on what exactly is intellectual virtue. I am sorry to break it to you this late in the text, but all I manage to do is to point to some very obvious intellectual virtues:

1. Searching for the best methods we can come up to test our theories. If we can prove something logically or mathematically, that is what we should do. If not, we have to think of other methods: can we test it in the laboratory repeatedly? Can we make repeated accurate observations? Can we derive logically or mathematically empirical consequences from our otherwise untestable theories in such a way that those consequences may prove the theory false? (This is Popper’s point, and it is just part of the story — a very small part indeed). Can we but develop hypotheses as carefully as possible (philosophy, I am looking at you)?
2. Always having in mind that we make mistakes all the time: observational mistakes, but also mistakes in reasoning. We must check and double check and produce theories and ideas that allow others to triple check. This is what John Stuart Mill had in mind in this passage of his On Liberty: ‘The beliefs which we have most warrant for, have no safeguard to rest on, but a standing invitation to the whole world to prove them unfounded.’ And he had in mind, here, Newtonian physics (‘philosophy’, as he called it, because those modern words, ‘physics’ and ‘science’, were not yet common in his day.)
3. Promoting epistemic pluralism. Precisely because of 2 above, we must allow people with the strangest beliefs to manifest themselves, free from persecution, public ridicule and other ways of promoting epistemic monism. Of course that most of those people are either fools or have very foolish ideas; we cannot however trust our gut to tell apart really foolish ideas from radically innovative ideas but not foolish at all. Let everyone speak his or her mind. (There are difficulties here, having to do with the cacophony and consequent silencing of good ideas just because they are not sexy, or are not presented in a sexy way, or because its detractors are politically motivated. We must strike a balance, but however we do strike that balance it must not allow for the expulsion from the public debate and life of those with which we most strongly disagree: I am looking at you, new atheists).

Perhaps I am wrong, but to my mind it seems pretty naïve to believe that in order to be as scientific as physics any field must be like physics in being testable or observable or evidence-driven. As a matter of fact, it seems to me that in order to be as scientific as physics, any field must be as like itself as physics is like physics: that is, we must find the best methods to theorise and review those theories and detect their mistakes and correct them. Just like physics.

Alas, I may be wrong.