The Laws of Thought

21 May

Over at Facing the Intelligence Explosion there is a page with the title of “the laws of thought”. This is a page that goes into a bit more detail about what it means to be skeptical. Many atheists know about these ideas, but they are inconsistently applied because they don’t know many of our cognitive biases, which are generally based on intuition, that make us use those vague tools selectively. What’s worse, one cognitive bias is called the sophistication effect, where the most knowledgeable people, because they possess greater ammunition with which shoot down facts and arguments incongruent with their own position, are actually more prone to succumb to one of these biases! Luke writes in one of his earlier writings:



As you might have guessed, I’ve written about many of those subjects before from the viewpoint of Bayes Theorem and other probability theory. For example, extraordinary claims require extraordinary evidence, claims should be specific and falsifiable, and Occam’s razor. Basically, if you want to be more efficient at being skeptical, you should know some probability theory. If you don’t know the basics then all you’re doing is professing and cheering, signalling that you are part of the Skepticism Tribe. *pom-pom pump* Gooooo Skepticism! *backflip*

He expands on this further in his “laws of thought” page. There are three general laws of thought: Logic, Probability Theory, and Decision Theory. Decision theory follows (almost) necessarily from Probability Theory, which (almost) necessarily follows from logic.

Luckily, not many people disagree about logic. As with math, we might make mistakes out of ignorance, but once someone shows us the proof for the Pythagorean theorem or for the invalidity of affirming the consequent, we agree. Math and logic are deductive systems, where the conclusion of a successful argument follows necessarily from its premises, given the axioms of the system you’re using: number theory, geometry, predicate logic, etc… Why should we let the laws of logic dictate our thinking? There needn’t be anything spooky about this. The laws of logic are baked into how we’ve agreed to talk to each other.

Logic follows from some basic axioms, like the law of identity (A = A) and the law of non-contradiction (A can’t be both A and ~A). If we disregard the laws of logic, then no one would be able to understand each other. Certain logical fallacies are predicated on violating the identity part of logic. My favorite example of this is the fallacy of equivocation. The relevant version of this fallacy is when people conflate “faith” in the general sense with “faith” in a probabilistic sense and then conclude with some variant of the fallacy of gray.

Say you’ve got two revolvers on a table, and you’re forced to play Russian Roulette. One revolver has 1 bullet chambered out of 6 and the other has 5 bullets chambered out of 6. A proponent of this fallacy of equivocation/fallacy of gray combo claims that everyone has faith and therefore no faith is better than any other. Yet if that were the case, then if we want to survive in the Russian Roulette game above, their logic dictates that it makes no difference which revolver they choose. Whereas a rational person would obviously choose the revolver with less ammunition chambered.

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…

What is probability? It’s 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).

Several authors have shown that the axioms of probability theory can be derived from these assumptions plus logic.1,2 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.

I really wish I could write a simpler guide on why probability theory — correct probability theory — follows from logic. Unfortunately the references that Luke provides at what I’ve indented at 1 and 2 are the simplest I’ve come across. Anything simpler and something essential will get left out. It suffices it to say that if we were to build an artificial intelligence, it would have to know probability theory in order to make sense of and function in the world. And when we think of computers and AI, we automatically think of “logic”, so the association (hopefully) makes intuitive sense.

Next he talks about Decision Theory which I’ve poked a little bit. This is the most subjective part of it, but even so, there are objective ways to assess your own subjective decision theory / utility function.

So there you have it. If you want to stop just sitting in the stands waving your Skepticism Banner to let everyone know which team you support and start actually practicing good skepticism, you should start learning these three areas.

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Posted by on May 21, 2013 in Bayes, skepticism


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