Today's post, The Nature of Logic was originally published on 15 November 2008. A summary (taken from the LW wiki):


What logic actually does is preserve truth in a model. It says that if all of the premises are true, then this conclusion is indeed true. But that's not all that minds do. There's an awful lot else that you need, before you start actually getting anything like intelligence.

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What is logic good for? The article gives the example of checking the design of the circuits inside a computer. There is something unsatisfactory about this example.

I'm not up to date on modern computer design, but the basic principle at issue has changed. When you design a logic gate you build in margins. For example, what is logic low? For TTL outputs it is specified to be below 0.4 V, but for TTL inputs it is specified to be below 0.8 V. Computer engineers refer to the difference, 0.4 V as the noise margin. Provided that the various defects and practical problems in the construction of the computer do not consume the entire noise margin, it will function as intended. Logic applies to computers because they have been designed to ensure that logic applies to them.

We asked the general question: what is logic good for. We get a narrow answer: its good for systems specially designed so that logic will be good for analyzing them. That makes logic see narrow and contrived.

Perhaps that is right. The attraction of logic is that it is tractable. Instead of doing probability on 2^n basic conjunctions, you do logic on n booleans. You pay a price in terms of being just plain wrong, when a Bayesian approach could give a more nuanced answer, and you hope to win overall by taking more decisions before their deadlines.

What is logic good for?

Also discovering Bayes' theorem. Also extrapolating the consequence of physical laws.