Truth, doubt & Popper #

We know what is false far better than what is true. So the honest posture is Popper’s: propose bold conjectures and try to refute them. These notes circle that idea — through language, through Gödel, and through the difference between agreeing and merely not disagreeing.

Agree, or disagree? #

If you talk with someone and want to express agreement, you can say either “it is not false” or “it is true.” But saying one or the other does not amount to the same thing.

Suppose someone says, “it is good to think before acting,” and you concede the point with “it is true”: you agree without any nuance. Yet if you are walking in nature and see a charging bull, it may be a very good idea to jump onto a nearby tree and think afterwards — not before. You run on survival instinct; there is no time to think, it is too slow, and it would cost you your life. So “it is good to think before acting” is not always true, when the difference between life and death is seconds.

Or, it is not false.

If instead you say “it is not false,” you mean that you detect no falsity in the statement — which does not mean none exists, only that you are not aware of it. You are conscious enough to know you might be wrong, and that ultimately leads to a better decision, since we cannot be sure of many things in life. A conversation in that spirit:

• John — It is good to think before acting.
• Mary — It is not false.
• John — It is always true.
• Mary — You cannot know how much you know, since you cannot possibly know how much you don’t know. You are essentially like an insect with antennae, sensing its environment a centimetre ahead — not even aware that I am observing it, since its compound eyes cannot make out motionless objects.
• John — That is a good point. It is not false.
• Mary — Exactly what I mean. If you agree to a theory that is “not false,” it means some part of it does not look false to you at this moment — but that itself may be false. You agree, while remaining aware of the conjectural nature of the statement.

Notes #

Studying to unlearn thinking #

I am studying to unlearn thinking.

We know the false better than the true #

We know better what is false than what is true — for example, what God is not, rather than what he is.

Conjecture and refute #

We know nothing from having merely seen it. The truth is hidden deep, inaccessible to humans — accessible only to God. All we can hope to do is conjecture and refute: propose bold theories and have them tested, or criticized, by others. That is the nature of learning — trying things out, for we know nothing and can know nothing, being human; we are too limited. Just look at a horse: is he aware that the Earth is round? Could you explain statistics to a horse? And does he need statistics to survive? What is the difference between a human and a horse? Both are animals; only, the human has this power of reasoning, which he uses to explain things after the fact. Is that all?

Popper’s truth-seeking #

If the world is chaos and we need a theory that works most of the time, then — I add personally — the assumption is this: the truth is something like an infinite tunnel between dimensions, which cannot be touched, but which we can approach by removing the false, by seeking what is not truth, so that there is less noise. Doing science, testing theories and finding them false, brings us closer to truth. But only theories that can be falsified — that can be tested and, in principle, found not to work. A theory that holds true whether A or B happens is no theory at all, because no test attached to it could make it false. So a theory needs test cases, as in programming, where one program tests another: the test runs the conditions under which the theory (the program) should fail, and expects that failure, proving that under certain conditions the theory breaks.

Ignorance breeds confidence #

Ignorance breeds more confidence than knowledge does. Why? If you know, then you know the whole world is random and unpredictable. When you don’t know — when you believe dogmatically in ideas and ideologies — that is ignorance. Such a person believes in a simple world with absolute rules, where the believers are the chosen ones. That is one way in which ignorance, with a dose of stupidity, can drive people to commit heinous crimes — as in a religious war, or any war.

The question over the answer #

The question is more important than the answer, because the question is definite, while answers are conjectures that can never be certain to be true.

Change is not progress #

Change in human society does not mean progress. Only in science is there change that is progress, because the theses are criticized — trial and error, in a way.

Husserl #

Opinion is ignorance that pretends to be knowledge.

The machine that names things #

Popper imagines a machine fitted with a lens and a voice, which names any medium-sized object placed before it — “cat,” “dog” — or, in some cases, says “I don’t know.” It can be made more human still: made to answer only when asked, “Can you tell me what this is?”, or to reply now and then, “I am getting tired, leave me alone for a while.” If such a machine behaved much like a person, we might mistakenly believe it describes and argues — just as someone ignorant of how a radio works might think the receiver describes and argues. Yet an analysis of its mechanism shows nothing of the kind happens: the radio does not argue, though it expresses its physical states and signals. (After Popper, Conjectures and Refutations.)

Language has bugs, like code #

If you take human language and look for paradoxes — “all Cretans are liars,” and other circular or unclassified quirks, or bugs, to use the term from software — you find something worth noticing.

A computer language is a special kind of program, an interface between the human and the chip (a gross simplification, for the sake of the argument). It can contain errors, mistakes and miscalculations that surface over time and are corrected by programmers. Now, if we think of human language in the same terms, it too can have built-in errors, miscalculations and irrationalities — the Cretan paradox, for instance, or arithmetic irrationalities, or even irrational numbers. (Mathematics is just another specialist language, like Latin or COBOL; it is invented by humans. It does not lie ready-made in nature. Humans developed it, starting perhaps from those who still use only “one,” “two” and “many.”)

So you might think the world is irrational — that things sometimes make no sense: an idiot gets voted into office, numbers turn out irrational, and so on. But all these irrationalities exist only in our imagination, or stem from our imagination and knowledge. Nature knows no mathematics, no theories, and needs no humans; it is humans who need nature. So all those irrationalities are failures, in the Popperian sense, of conjectures — either not yet refuted, or refuted and still in use because nothing better is at hand and the rule works well enough. Take an atomic clock, proven by experiment: fly it in a jumbo jet for a few hours, and it slows marginally — you were, in miniature, in a time machine. So even when a theory seems not to hold and something happens anyway, it only means the theory correlated with the facts this time. Since the conjecture was never refuted before, there is no certainty it will keep working one day — and, reversed, near-certainty that one day it will fail. These are failures not of nature but of the theories, for theories — like maps or maquettes — are only approximations and distortions of reality: it will never be possible to compress the same detail into a smaller scale without shedding and distorting something. Human languages are so much talk, sometimes corresponding to reality, sometimes for a long time, sometimes not. As with nations and species, nature eliminates one variant and experiments with another. Men keep making their theories, but it is nature that has the last word.

Gödel, and the drop of poison #

Here is my small understanding, after watching a few videos, so forgive me, dear reader, if it is off. If any part of an interconnected theory is false — where one element links to the others, directly or through any number of nodes — then the whole theory is false. It is like putting poison in a tank of water: even one drop of cyanide spoils the entire tank. The same with the falsity of a theory.

Now, Gödel: given that mathematics is an imperfect language, to fix this illogicality (or perhaps falsity) he proposes to reduce it into smaller elements that make it less obvious. It is like throwing an intricate carpet over a puddle of soft mud: the mud and the moisture will eventually seep through the carpet. A theory B derived from something false — and proven false, like irrational numbers — cannot be true, since false plus true equals false, as with the tank and the poison. So, for me, his theory is refuted on the ground that it is built by logical derivation from a false base B. Given that theory A is false (“mathematics is a perfect language”), one cannot add any true logical object — such as Gödel’s theory of smaller parts, made up in part of false elements — and rebuild a new theory with any probability of soundness, using those false elements from the previous false story. Nor is there any certain way to judge whether whoever chose which elements are true and which are false got it right. So this theory cannot be true, given a base B we know to be false (conjecture: mathematics is a perfect human language; refutation: no — there are paradoxes, even in logic, like the Cretan liar). Building any theory on a previous theory as its base is a perilous endeavour.

To read, on doubt #

• Sextus Empiricus, Pierre Bayle, Nicolas d’Autrecourt.
• The Name of the Rose (book and film); Charles Sanders Peirce and Victor Brochard (1878), close to Popper; and Hempel’s paradox.