The Sound of Logic …

As the regulars on FTB are taking Dawkins to task over his discussions of logic and emotion, there’s a lot of talk about logic on those sites. P.Z. Myers is the latest to get into the fray, claiming that pure logic can or does lead to things like the firing of flechette bombs at Palestinian children:

We can stand aloof from the events and carry out thought exercises, and we can carefully weigh the pros and cons of war—this side did this horrible thing, that side did that horrible thing, this side has this worthy cause, that side has that worthy cause—and we can attempt to calculate who is slightly better and who is slightly worse, although even there it’s striking how often different people seem to come up with completely different sums, as if maybe, somehow human lives resist being reduced to simple numbers. Let us reason together, you say; if only we could get everyone to look at the situation logically, if only everyone would be a dispassionate observer like me, if only everyone would sit back and coldly analyze all possible actions to arrive at an optimal conclusion that maximizes idealized outcomes…

…and then we arrive at this moment where all the brilliant science and technology of our civilization culminates in this beautifully intricate weapon, designed, machined and assembled by highly educated teams of engineers and executives and politicians, aimed at a small child. One human being, persuaded by the moral calculus of their side that this action is a logical necessity, pushes a button and turns another innocent human being into shredded meat.

We don’t need any more logic. What we need now is more appreciation for the value of life.

As you read through the comments, the justification for claiming that pure logic leads to this is one that I find disturbingly common: comments that they can make a logically valid argument that has whatever horrible or insane proposition as its conclusion and claim that therefore “pure logic” validates thinking that the conclusion is true. And while pure logic classes do spend a lot of time pointing out the importance of logical validity and how logical validity does not depend on the truth of the premises or even the conclusion, if you actually learn what logic is you’ll understand that that isn’t where logic stops.

So, then, what does it mean to say that a logical argument is valid? Simply this: if the premises are all true, then the conclusion cannot be false (ie must be true). Now, what we want from a logical argument are to know what propositions are true and what propositions are false. So, given a logically valid argument, can I say anything about the actual truth of the conclusion, just by knowing that the argument is logically valid? No. All I know is that the conclusion is true if the premises are true (it’s not even an if and only if, because it is possible in a valid argument for at least one of the premises to be false and the conclusion to still be true, based on another argument), but without knowing if the premises are all true I can’t say if the conclusion is itself true or false.

Thus, the criteria of a logical argument that everyone keeps forgetting when they talk about “pure logic”: the soundness of the argument. An argument is sound, roughly, if the argument is valid and the premises are all true. If you have an argument that is valid and sound — the conclusion is true if the premises are all true and the premises are all true — then you know that the conclusion is true. If it isn’t, then you don’t, at least not from that argument.

If I had a pure and fully logical argument that said that the moral thing to do was to use flechette bombs, meaning that the argument’s conclusion was “The moral thing to do was to use flechette bombs” and the argument followed from premises such that if all of the premises were true the conclusion had to be true and the premises were indeed known to be true, and if I was the sort of person who would indeed choose to act morally, I dearly hope that no pictures of dead children would sway me from using the “pure logic” argument and in fact using them. I can’t think of a valid and sound argument for that, because I don’t think there is one, once you include the unstated moral premises into the debate. And thank God for that. But contrary to Myers’ assertions, we don’t need less logic, but more logic. We need to remind people that simply making a valid argument logically doesn’t mean that you are reasonable in thinking the conclusion true, which is one of the first things formal logic classes teach you about logical validity. And we need to remind people that they have to include all of their hidden premises, especially when dealing with morality. It’s the failure of people to use pure logic that causes problems like Myers talks about, not the fact that people use it too much instead of their own emotional reactions.

If you can make a valid and sound argument for a conclusion, then no amount of emotion, concern, or care ought to convince anyone that that conclusion is actually false. If that happens, you are being irrational, and dangerously slow. But you cannot forget that soundness part; validity is not enough.

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One Response to “The Sound of Logic …”

  1. So Happy Together? | The Verbose Stoic Says:

    […] decisions, and particularly towards moral decisions. Unfortunately, most of the posts from her and from others don’t really seem to have a central thesis to them; they seem to be based on a strawman view […]

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