Negatives and certainties


It is impossible to prove a negative, I hear.

This strikes me as a very stupid statement. (Then again, I don’t know anything about philosophy.)

In pure logic; in mathematics, say, proving a negative is the easiest thing in the world. “There is no even prime greater than two.” That’s a negative; it is proven in one line.

(“A Proof. An even number is divisible by two. Kapow!”)

(Well, okay. “And if that number is greater than two, it has two as a divisor and thus cannot be a prime, i.e. a number whose only divisors are one and itself. Any number you’d suggest, its demise I attest. KAPOW!”)

In real life (which I know considerably less about), you don’t ever prove anything, never, so not being able to prove a negative is a true statement, but not a particularly deep one.

Real life is a mess, you see: anything you claim you know about real life might be just a hallucination, a misunderstanding, a really convoluted mistake, or a lie. Real life has no “proof” that Copenhagen exists; just really good evidence, leading us to assume that why yes, that mermaid statue is there for real. There are people who say they’ve been to Copenhagen; there are satellite pictures, webcams, the like. It could all be a giant hoax, or a mistake (“Did I say Copenhagen? I meant Bielefeld!”) — but the most sensible interpretation of the observations is Copenhagen is there.

(Just for note: I don’t think I’m playing any postmodernist games here; I’m just a mathematician trying to express what I’ve heard scientists to say.)

And the negative in real life — well, you can be pretty sure there’s no unicorn behind you, watching you.

Don’t look; keep reading.

First, on a general level, the non-existence of unicorns is about as certain as the existence of Copenhagen: there’s no carcass, no photo of one; there’s no particular reason why a unicorn should exist; it is one in a bestiary of similarly no-show Medieval beasties; known “unicorn horns” are narwhal tusks; and so on. Unicorns could be invisible and immaterial; but there could be a hallucinogenic anomaly that makes people believe in Copenhagen, too. “Could” is not “is”, not even “likely is”.

If there is no good reason to think unicorns exist, there’s no good reason to think one is watching you.

I said don’t look. They don’t like it.

There’s no way to conclusively prove your non-watchedness; but reality is not a game that has a visible set of rules, like mathematics or Magic: the Gathering. In Magic, there’s no deep existential doubt about the number of cards in your hand; in mathematics, a set of four has four elements in it and no mistake. In real life the rule set is hidden, and we perceive it only through its effects, and the effects are dastardly complicated, and we can’t ever consult the rulebook. We just try new plays and try to figure out which rules are acting when the universe kicks us in the nuts. We could be missing “except”-clauses for a long time; we could be operating and testing in just an “except”-clause of a greater rule until we come up with something clever.

We’re assuming just that there are rules; the rest is conjecture.

When you’re playing that kind of an uncertain game, it’s silly to get stuck on not being able to prove negatives; in real life, you can’t prove anything. You just try to convince yourself and others, just try to sidle closer to truth. Every negative is a unicorn watching you; the negative proof is impossible in theory, and approximately doable in practice.

As regards actually being watched by a unicorn, the most stringent observers tend to be convinced that not being watched by one is the bet to make, the one to live your life by, the one to consider true when choosing windows and security alarms. And if one day you will be found in your chair ravaged by hooves and a horn, eh, we’ll be wiser the next day. (You, probably not; but you’ll get a footnote in a zoology manual. “First confirmed unicorn victim”, page 53.)

The reason why people talk about “proof” and “certainty” in real life is… eh, because people are dumb. That is, most people don’t realize how easy it is to be mistaken. I myself went through a phase when I thought anything in a book had to be true. Then I ran into a book by von Däniken.

The problem is, nothing has to be true just because it is written down.

Nothing has to be true just because it is in a published scientific paper, even.

Nothing has to be true because you feel like it, or because a teacher says it, or because everyone agrees about it.

The universe doesn’t give us answer sheets; there’s no ringing bell when we’re right about something. The universe gives us more than enough rope to hang ourselves by our mistakes. Because this is fucking scary, and also non-obvious, and because we have a limited lung capacity, we say “certain” and mean “as certain as I can imagine it being”; we say “proof” when we mean “all the evidence is for it”; and we say “truth” when we mean “truth, as far as we’ve found ways of testing it”. (Not “a truth”, but “an approximation of the truth”.)

That way, proving a negative is doable; and most times, that is enough for life.

* * *


The preceding is, as I understand it, what the middle part of this Matt Cartmill quote is about.

“As an adolescent I aspired to lasting fame, I craved factual certainty, and I thirsted for a meaningful vision of human life — so I became a scientist. This is like becoming an archbishop so you can meet girls.”

* * *


Tangentially related: this is what skepticism is about. I’m certain-with-footnote that there is no Bigfoot; that homeopathy has nothing in it; that there is no God, too. I’m not baldly, boldly CERTAIN because that’s more than I can honestly say; that’s for persons that have no subtlety.

But, and this is the important point, while not capital-C certain, I’m not an agnostic either. The question of Bigfoot is unsolvable in the deep philosophical sense either way; it could be really good in hiding, or any presented carcass could be a hoax (“This living Bigfoot is just manufactured to be like a Bigfoot!”); but the question is solvable in the practical sense, in the same sense that Copenhagen’s existence is solvable, and solves: in the sense of, “good enough, consistent enough, elegant and observation-fitting enough, for now”.

If you ask me — people usually don’t — skepticism in the practical sense doesn’t mean agnosticism, that is unwillingness to decide, or willingness to surrender to uncertainty. Skepticism means going for the best explanation, with all the evidence, with all the wits you got, while admitting there might come a better explanation come tomorrow. But until then, the findings of today will do. With enough days of that attitude, the next different day will be farther and farther away. It’s possible to be Right without being Certain of it.

* * *


And, well, if you had a Cosmic Answer Sheet, or some Fundamental Oracle, how would you even know it was correct?

Maybe the first ten answers correspond to independent observations, to some extent. Maybe the first ten thousand. But maybe the thing is the work of some more advanced but still fallible scientist. Maybe it contains non-obvious untruths. A trivial mathematical example would be the fallacy of crossing out the sixes. It is true that

26/65 = 2/5


16/64 = 1/4,

but it would be a very bad idea to suppose those two examples serve to establish a general rule. Similarly, in real life, there were two centuries between Newton and Einstein that were full of people certain that time was fixed, and no funny business happened even if you moved really fast. Because getting to a fraction of c with a horsecart is difficult, the untruth (well, the incompleteness) was non-obvious; Newton seemed to be an Oracle.

Conversely, maybe the Absolute Tome is right, but you disregard it because your independent test is faulty, being based on an insufficient understanding of the nature of reality: the Tome is Wegener, and you’re unable to see how true its theory of plate tectonics is, because you reason from unsafe assumptions.

Well, the Sheet might try to convince you by saying it is infallible, but saying so doesn’t make it so.

The only way such a Cosmic Answer Sheet could work was if it gave the answers along with the route of arriving at them; but even then, those steps would need to be checked. (Come to think of it, that could be a Holy Book I would be willing to believe in: one that contained novel true statements whose truth could be independently checked and/or derived using given instructions. The usual offerings are not persuasive: “This unclear, many-valued, poetic past statement was about this concrete later past event or discovery!”; most “prophecies” are on the level of Assassinations foretold in Moby Dick.)

Even in math, if you had a collection of statements and one of them was “All of these statements are true”, it would not help you. That one statement could be either true or false with no contradiction, with no problem with the rules of the game. And I fear if you tried to improve that statement you’d end up in the wonderful nightmare land of set theory, which could just as well be named for Set, the Egyptian demon god of deserts and chaos.

* * *


To sum this all up: There is no certainty anywhere, but there are pretty good odds.

One Response to “Negatives and certainties”

  1. heather clem Says:

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