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“garbage in, garbage out” (GIGO) and deduction
Some people sometimes mention that deduction conforms to the GIGO principle. I will here show that in a straightforward interpretation of that, it is false. “Garbage in, garbage out” is a metaphor or sorts. The mental image I form when I hear it is something like a huge machine that, when garbage is put into it, garbage comes out. Perhaps in smaller pieces. How can we apply this to deduction, that is, reasoning with deductively valid arguments? The most straightforward interpretation seems to be this: Deduction is some kind of machine, that when we put in bad data as premises, bad data conclusions comes out. What could bad data mean? The obvious candidate is false data, that is, false premises and false conclusions. What else could it mean? This interpretation thus means: All deductively valid arguments with false premises have false conclusions. This is simply false. Counter-examples are easy to come by and are given in most logic introduction textbooks, here is another:
1. All people that live in France have dark skin.
2. All people with dark skin live in Europe.
Thus, 3. All people that live in France live in Europe.
The premises are both false and the conclusion is true. The only thing guaranteed by a deductively valid argument is, if the premises are true, then the conclusion is also true. Deductively valid arguments are truth-preserving from the top to the bottom , which is just another way of saying that it is truth-preserving from premises to the conclusion. A deductively valid argument is not falsity preserving from the top to the bottom, however, it is falsity preserving from the bottom to the top, in other words, all deductively valid arguments with a false conclusion has at least one false premise. This is irrelevant to GIGO though.