Category Archives: Epistemology

Measures and Metrics

It was a day at the races for two young boys in Gimli, Manitoba. As crowds gathered to watch cars flick back and forth on the track, they took their bikes a few hundred metres away to re-enact the races on a derelict runway. Unbeknownst to them, a giant silently bore down upon them. Air Canada’s flight 143 had run out of fuel and was attempting to glide to a safe landing. We can’t imagine their terror. We can’t imagine what it was like to see their short lives flash before their eyes as they turned to see the jet nearly upon them. They stood still in shock for a moment then raced down the runway as fast as they could. They made it. Barely.

This crash was no tragedy. But it could have been. Hundreds of people could have been injured or killed. And for what? For a conversion error. The ground crew thought that they were adding fuel in kilograms but were actually adding pounds. Hence only about half the fuel was added than intended. That is, the Gimli Glider was a casualty of Canada’s metrication process. There were others, though much less severe. And yet, metrication is worth it. The metric system is the best measurement system we have available to us.

This is a weird claim. All measurement systems are arbitrary. Rulers and thermometers were not the gifts of Heaven like those law tables carved in stone. Humans have always used what was available to them to keep track of weights and measures. Humans have used stones and feet and thumbs and brines and cups and so on. The metric system is just one more in this long list of arbitrary measures.

But arbitrary things can also be more and less apt to accomplish what it was designed for. For metrics, there are at least three primary criteria we use to evaluate aptness: ease of use, ease of conversion, and its ability to represent real difference.

Most metrics throughout history were designed with ease of use in mind. Weights and measures needed to be compared to some standard, and that standard had to be readily available. The cubit is the gold standard in ease of use: what is more available to a carpenter than her own forearm? If she wishes to measure out a board, she need only count how many of her forearms it is long, and she has some measure. And since her forearm does not change in size, everything she measures with it will be bound to the same standard.

Now, the problem with a cubit is that it isn’t easily convertible into other measures. How many thumbs go into a cubit? How many feet? It isn’t obvious, and the carpenter must determine that for herself. If another carpenter were to use her measurements, he might find that his cubits are of a different size, and the ratios of his feet to his cubits might be different altogether. People solved this long ago by standardising their previously variable measures into formal units. The foot no longer corresponded to the carpenter’s own foot but to some arbitrary standard foot, say the king’s. And so too with thumbs and all the rest. And once this is established, the ratios between different measures remain static. There are twelve thumbs in a foot. There are sixteen ounces in a pound. There are two pints in a quart. And so on. This may slightly reduce the ease of use for these measures, but it vastly improves the overall utility of the measurement system.

Finally, the ultimate purpose of any measurement system is to record real differences in the world. We want to know whether two boards are the same size or different. We want to know whether our apple-only diet is helping us lose weight. We want to know whether it is warmer or cooler outside than it was yesterday. And this is the hardest part about any measurement system: some of those differences are more important to us than others, and our measurement system must recognise this.

So given all this, why metrication? There are of course practical questions. Metric is the international standard; US manufacturers lose millions of dollars every year because they have to convert quantities into metric for export, a phenomenon that does not plague manufacturers elsewhere. This also puts American students behind their peers from other countries. Metric is the official measurement system of science, and so students in American schools must not only learn the imperial system, but also the metric system. However, these pragmatic questions say nothing about metrication. The US could without too much difficulty exert its influence to motivate other countries to switch back to imperial. If we want to justify metrication, we need to do this internal to a theory of measurement alone.

So why is metric the gold standard? In no uncertain terms, it unambiguously meets the measurement criteria better than any other measurement system. Metric is no more difficult to use than any other measurement alternative. Both imperial and metric require standardised instruments, and both are equally available. But metric makes conversion easier than any other measurement system. Imperial maintains constant ratios between different units, but these ratios are not uniform. There are twelve inches in a foot, three feet in a yard, and 1280 yards in a mile. A person needs to remember each one of those ratios, or at least look them up in some rule book, before one can complete even the simplest conversions. Metric dispenses with this difficulty. The conversion ratios in metric are not only constant, but also uniform. Every unit is distinguished from the others as multiples of ten. And when in doubt, the conversion ratio is included in the name of the unit. A kilometre is a kilo-metre, or a thousand metres. Easy.

Perhaps the most impressive benefit is the metric system’s ability to represent real difference. The metric system employs a greater diversity of units, in part due to its uniform conversion ratios, than any other measurement system. Objects as small as atoms and molecules or as large as stars and galaxies can be easily and coherently represented in metric units without ambiguity. And while the very small and very large do not affect ordinary people very often, the metric system does a better job with ordinary measures as well. The best example of this is temperature. The Fahrenheit scale is pinned to three different benchmarks: ice and salt brine, the freezing point of pure water, and human body temperature. These correspond to 0, 32, and 96 degrees respectively. These choices are arbitrary, of course. But they are also meaningless. There is no firm relationship between these standards that ties their temperatures nicely to a single scale. And moreover, they tell us nothing about what the temperature of a thing is like. The Celsius system is very different. It is pinned only to the phase changes of water. 00 is freezing. 1000 is boiling. This too is arbitrary, but it does tell us quite a lot about the world we live in. Water is fundamental to Earthly life, and its properties determine life’s conditions. It is plain that negative temperatures represent a different kind of weather than positive temperatures. Negative temperatures are associated with snow and ice. Positive with rain and warmth. Fahrenheit never gives us that clean divide. It could be snowing at 300 but raining at 350. Those five degrees are far more important than the scale lets on.

This is the reason the world has adopted the metric system. This is worth all the troubles metrication caused. The metric system is completely and unambiguously the superior measurement system. Now we need only for the most powerful country on Earth to catch up.



We live in an era of anti-skepticism. Skeptics are the enemy. They must be destroyed and overcome. This is what drove Descartes and Leibniz, Locke and Hobbes, and even Hume. They sought to naturalise the world, to conquer it, knowing its features with certainty. But this new tradition of anti-skepticism is very different. Philosophers today do not claim to certainly know. They in no way claim to refute the skeptic. The older eras held knowledge to be something lofty, fragile, godly. Knowledge was something not for man but for gods, for elites, for those deserving of special authority. In this new era, the anti-skeptics have lowered knowledge. It is not lofty: it is mundane. It is not godly: it is human. They have not refuted the skeptic: they have made her irrelevant. And the consequence is dire.

I begin by motivating contemporary anti-skepticism from its roots in Moore and Wittgenstein. Then I show how this tradition fails to overcome skepticism.

Moore begins with knowledge. Of course he knows that idealism is false. Of course he knows that he has hands and was once smaller than he currently is. What he doesn’t know is how to correctly analyse any sentence saying so. This looks dumb. Surely Moore cannot possibly know that he has hands: what if he is dreaming? What if he is hallucinating? What about Descartes’ evil demon or any of Hume’s or Kant’s skeptical challenges? But Moore is not troubled by these suggestions: these are only competing analyses of what it means to know. And these others are inferior. Why? As Moore suggests in “A Defense of Common Sense,” the skeptical analysis commits skeptics to far more than Moore’s analysis. Moore is committed to the truth of only a small set of basic claims—that there is a world, that he is an element of that world, that he was once younger and smaller than he currently is, and so on. The skeptic, on the other hand, is committed to these basic claims plus their skeptical claims. As Moore notes, the skeptic does not stop herself from going about in the world as a normal human being. She still wakes in the morning, commutes to work, constructs arguments for skepticism, and presents them to an audience of other philosophers. She demonstrates that she knows these things through her actions. Only she does not claim to know them: she both knows them and commits herself to not knowing them. This is extravagant. This is impossible. The consistent skeptic sits demure like Johannes Climacus, never stirring, never speaking, never thinking.

The idea is this: language is a practical thing. It has consequences. It does not matter whether we are dreaming, for we do not act like we are dreaming. If a debate is predicated on something so ethereal, something so benign, then it is not predicated on a correct understanding of language. Language is substantive and effective. We all know this: we all use language for some purpose. Our claims bear in some way on our lives. And what skeptics mean is just this: that when we say such and such, we could be wrong. This is trivially true, but the skeptic overstates her case. And for Moore, there is no sense in which we could ever be meaningfully wrong about whether there is a world or whether we were once smaller than we are now. There is a subset of propositions (Moorean propositions) that we cannot consistently and meaningfully deny.

Moore did not succeed in this argument. But, says Wittgenstein, he is not wrong. He has rather failed to carry his insight to its logical conclusion. Moore remains vulnerable to skeptical attack by those who do not understand what it means to be certain, to know, and to doubt. Wittgenstein does. He will finish what Moore began.

For Wittgenstein, knowledge is located within a discourse: one knows such and such only if competent others recognise her as knowing such and such. This means that the claim must be recognised as true, but also that the reasons she gives for her claim are recognised as appropriate. This is not to reduce knowledge or even truth to something communal or legislative. A community cannot agree to collectively upend their knowledge system by changing what they believe and accept as valid reasoning. We are bound to a language in which we have no say. Our language gives us the concepts and thoughts to which our perception of the world conforms. In Kantian terms, language is the source of the categories of experience. Some of these are grounded in our form of life. In this Wittgenstein agrees with Moore. Others are grounded in particular grammars. But in neither case is the result a kind of relativism. It is rather a kind of contextualism: language merely shapes the world; it does not construct it.

The skeptic here has no room to move. Doubt can only occur concurrently with certainty. That is, where one aspect of a discourse is brought into question, it is questioned on account of other aspects of that discourse. When Copernicus doubted that the Sun revolved around the Earth, he did so on grounds acceptable to him, namely the simplicity of the heliocentric model and God’s preference for simplicity. Without these certainties, it is incoherent to doubt geocentrism. Doubt itself must be justified.  The skeptic does not do this. She holds an apple in her hand and asks “Is this apple an apple, or is it something else?” The question is senseless. Of course the apple is an apple. If it were not, it would not be an apple. The skeptic’s only reply undermines her claim: “You miss my point, Wittgenstein. I mean to say that we all know what an apple is, but cannot with certainty suppose that this object I hold in my hand is an instance of the general concept. And so also with any instance of any general concept.” This may be a legitimate and sensible question. Surely someone once pointed to a whale and asked whether that fish is a fish only to be answered in the negative. Surely it is never obvious when any object is an instance of a concept. But skepticism this isn’t. The relevant doubt is localised and predicated on a kind of certainty: that one knows what an apple is. And in general, if one is comfortable identifying the object of doubt with a name that is under dispute, the doubt is easily assuaged. Of course the apple is an apple: we call it an apple.

Whether a doubt is sensible and appropriate always depends on the context it is present. Some contexts place a greater demand on one’s knowledge of a claim than others. And some others will open up the possibility of doubt from some claims and not others. This is the skeptic’s greatest error. They always wish to doubt that which is never open to doubt. They wish to doubt those claims that are predicated on our form of life. They wish to doubt Moorean propositions. It’s curious that the skeptic claims to doubt the external world, yet stands upon the stage to address an audience. It really makes one think.

But in truth, the skeptic is well within her rights to do this. The most pressing questions in philosophy are not about apples or astronomy. They are about who we are and how we ought to live. There is nothing more fundamental to our form of life than not knowing who we are or how to live. And answering those questions requires inquiring into our history and our constitution. Not everyone who so inquires is a skeptic. The skeptic is only one who has so inquired and found herself at a loss. She is one who feels uneasy about who she is and how she ought to live. This is not absurd. This is not incoherent. It strikes me that this is the most natural, the most human feeling possible. For who among us truly knows how to live?

Contemporary anti-skeptics don’t satisfy these questions. They rule them out from the outset, and they themselves know this. Both Moore and Wittgenstein famously stood in an odd relationship to philosophy’s most pressing questions. For Moore, “the good is good, and that is the end of the matter.” (PE, §6) Wittgenstein agrees. Value is indefinable. It is something nonsensical: though it is everywhere present to us, it cannot reside in the world of facts. Both Moore and Wittgenstein surrender to a kind of bland mysticism. And what good is mysticism in answering our deepest questions? What good is anti-skepticism if it cannot actually overcome our skepticism? Moore and Wittgenstein offer no authority. They offer no guidance. Anti-skepticism is useless.