{"id":79,"date":"2011-11-30T17:56:40","date_gmt":"2011-12-01T01:56:40","guid":{"rendered":"http:\/\/facingthesing.wpengine.com\/?p=79"},"modified":"2014-12-01T13:02:02","modified_gmt":"2014-12-01T21:02:02","slug":"the-laws-of-thought","status":"publish","type":"post","link":"https:\/\/intelligenceexplosion.com\/sv\/2011\/the-laws-of-thought\/","title":{"rendered":"Tankelagarna"},"content":{"rendered":"

Tyv\u00e4rr \u00e4r denna artikel enbart tillg\u00e4nglig p\u00e5 English<\/a>, Fran\u00e7ais<\/a>, \u0440\u0443\u0441\u0441\u043a\u0438\u0439<\/a>, Sloven\u010dina<\/a>, \u4e2d\u6587<\/a> och Italiano<\/a>.<\/p>

I<\/span>f someone doesn\u2019t agree with me on the laws of logic, probability theory, and decision theory, then I won\u2019t get very far with them in discussing the intelligence explosion because they\u2019ll end up arguing that human intelligence runs on magic, or that a machine will only become more benevolent as it becomes more intelligent, or that it\u2019s simple to specify what humans want, or some other bit of foolishness. So, let\u2019s make sure we agree on the basics before we try to agree about more complex matters.<\/p>\n

Logic<\/h3>\n

Luckily, not many people disagree about logic. As with math, we might make mistakes out of ignorance, but once someone shows us the proof<\/em><\/a> for the Pythagorean theorem or for the invalidity of affirming the consequent<\/a>, we agree. Math and logic are deductive<\/em> systems, where the conclusion of a successful argument follows necessarily<\/em> from its premises, given the axioms of the system you\u2019re using: number theory, geometry, predicate logic, etc. (Of course, one cannot fully escape uncertainty: Andrew Wiles\u2019 famous proof<\/a> of Fermat\u2019s Last Theorem is over one hundred pages long, so even if I worked through the whole thing myself I wouldn\u2019t be certain I hadn\u2019t made a mistake somewhere.)<\/p>\n

Why should we let the laws of logic dictate our thinking? There needn\u2019t be anything spooky about this. The laws of logic are baked into how we\u2019ve agreed to talk to each other. If you tell me the car in front of you is 100% red and at the same time and in the same way 100% blue, then the problem isn\u2019t so much that you\u2019re \u201coperating under different laws of logic,\u201d but rather that we\u2019re speaking different languages. Part of what I mean<\/em> when I say that the car in front of me is \u201c100% red\u201d is that it isn\u2019t also 100% blue in the same way at the same time. If you disagree, then we\u2019re not speaking the same language. You\u2019re speaking a language that uses many of the same sounds and spellings as mine but doesn\u2019t mean the same things.<\/p>\n

But logic is a system of certainty, and our world is one of uncertainty. In our world, we need to talk not about certainties but about probabilities<\/em>.<\/p>\n

Probability Theory<\/h3>\n

Give a child religion first, and she may find it hard to shake even when she encounters science. Give a child science first, and when she discovers religion it will look silly.<\/p>\n

For this reason, I will explain the correct theory of probability first, and only later mention the incorrect theory.<\/p>\n

What is probability? It\u2019s a measure of how likely a proposition is to be true, given what else you believe. And whatever our theory of probability is, it should be consistent with common sense (for example, consistent with logic), and it should be consistent with itself (if you can calculate a probability with two methods, both methods should give the same answer).<\/p>\n

Several authors have shown that the axioms of probability theory can be derived from these assumptions plus logic.1<\/sup><\/a>,<\/sup>2<\/sup><\/a> In other words, probability theory is just an extension of logic. If you accept logic, and you accept the above (very minimal) assumptions about what probability is, then whether you know it or not you have accepted probability theory.<\/p>\n

Another reason to accept probability theory is this (roughly speaking): If you don\u2019t, and you are willing to take bets on your beliefs being true, then someone who is<\/em> using probability theory can take all your money. (For the proof, look into Dutch Book arguments.3<\/sup><\/a>)<\/p>\n

Perhaps the most useful rule to be derived from the axioms of probability theory is Bayes\u2019 Theorem, which tells you exactly how your probability for a statement should change as you encounter new information. (In the cognitive science of rationality<\/a>, many cognitive biases are defined<\/em> in terms of how they violate either basic logic or Bayes\u2019 Theorem.) If you\u2019re not using Bayes\u2019 Theorem to update your beliefs, then you\u2019re violating probability theory, which is an extension of logic.<\/p>\n

Of course, the human brain is too slow to make explicit Bayesian calculations all day. But you can<\/em> develop mental heuristics that do a better job of approximating Bayesian calculations than many of our default evolved heuristics do.<\/p>\n

This is not the place for a full tutorial on logic<\/a> or probability theory<\/a> or rationality training<\/a>. I just want to introduce the core tools we\u2019ll be using so I can later explain why I came to one conclusion instead of another concerning the intelligence explosion. Still, you might want to at least<\/em> read this short tutorial<\/a> on Bayes\u2019 Theorem before continuing.<\/p>\n

Finally, I owe you a quick explanation of why frequentism, the theory of probability you probably learned in school like I did, is wrong. Whereas the Bayesian view sees probability as a measure of uncertainty about the world, frequentism sees probability as \u201cthe proportion of times the event would occur in a long run of repeated experiments.\u201d I\u2019ll mention just two problems with this, out of at least fifteen:4<\/sup><\/a><\/p>\n