Deduction: The dream and nightmare of absolute certainty
Last week I began comparing and contrasting computers and minds, examining both human intuitions and appetites regarding the prospect that our minds are governed by the same kind of direct one-to-one-correspondence kind of cause-and-effect we see in the physical world (Aristotle’s efficient cause). If minds are really like computers, just translating information from one form to another by determinate rules, then we would live in a deterministic universe. Just as Laplace thought, if you knew the determinate laws, you would be able to deduce all future states from past states. We’d be able to deduce all of tomorrow’s truths from things known today. On the one hand we’d miss out on the fun of surprises; on the other we would have gotten rid of uncertainty, the root of all anxiety. A word then about deducing and its connection to absolutely predictable computer-like causality. Deduction is the master recipe for “reasoning from the general to the particular.” If you start by knowing a certain kind of thing always has a certain property, then obviously any particular example of that thing will have that property. A deduction takes the form:
If A then B.
If [human] then [mortal].
If you then apply this to a certain thing X, the statement becomes:
If [X is A] then [X is B].
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If [Socrates is a man] then [Socrates is mortal].
Here’s the classic syllogism used by Aristotle to introduce the concept of deduction:
All men are mortal (which translates as If A then B–If man then mortal).
Socrates is a man (which translates as X is A).
Then Socrates is mortal (which translates as X is B).
Deduction is airtight logic–a one-to-one correspondence whereby inputting certain premises yields unambiguous answers–necessary conclusions with no room left for doubt. Deduction is the basis for all of what computers do. It’s what makes them so reliable through enormously complex algorithms. Deduction governs the production of all mathematical proofs, and it is the exclusive source of every powerful truth in math and geometry.
For over 2400 years, some people have been hoping to derive moral truths exclusively by deduction as well. Socrates himself appears to have believed it possible, and many religious leaders have thought so too. Start from the generalizations one can find in the bible, Koran, Tao, or any other great religious guidebook, and by deduction derive every other possible truth. You’ll have a complete recipe for living right.
Just think of all the hassle this would save. We would know the true laws and, so long as everyone followed them, things would be perfect or as close to perfect as possible. We wouldn’t have to wonder if we were doing the right thing. Everybody would have to surrender to the law, because debating the right answer to a moral deduction would be as ridiculous as debating the right answer to a long division problem.
By now most serious scholars have given up on the deductive approach to finding moral truths, partly perhaps because the idea of a predetermined world spoils life’s adventure of discovery, but primarily because fundamental problems interfere with attempts to deduce absolute moral truths. For one, since deduction always has to start with a generalization, you can’t really do deduction from the ground up. The ground is laid by truths not derived by deduction. For example, this is an airtight deduction:
All men are platypuses.
Socrates is a man.
Therefore Socrates is a platypus.
It’s airtight but wrong. Garbage in; garbage out. The first premise is false. So yes, while it seems likely that all men are mortal and Socrates is a man, or in math, that 1+1=2, or a line is two-dimensional, when it comes to deducing moral truths, the premises will always be more iffy. A weak foundation makes for a weak structure and so there’s no escaping the guesswork.
There are two more parts to this story. For one, it’s time to spell out what this guesswork entails, and that I’ll do next week. For the other, I’ll come back to computers and specify the parallels and contrasts to human thought-the practical payoff of which is some guidance about what processes we should and shouldn’t realistically want or expect to put on automatic.