Some Central Arguments about Torture Rendered into Precise Logical Form

0. It has occurred to me that it may be useful to look at some of the central arguments currently raging about waterboarding (and so too sleep deprivation, rectal hydration, etc.), torture, criminality, and punishment in the way in which logicians as engaged precisely in their role as logicians would look at them. Looking at these arguments as logicians as engaged precisely in their role as logicians do might well make it more clear just what the issues at hand are.

1. The arguments in question can be presented as a series of arguments. The first in the series, rendered in accordance with the formalities of classical logic, is the “categorical syllogism” that:

All acts of waterboarding are acts of torture.

All acts of waterboarding even on behalf of public safety are acts of waterboarding.

Therefore, all acts of waterboarding even on behalf of public safety are acts of torture.

This argument is clearly a valid argument, as logic would characterize it. That is, if the first two statements, the premises, are true, the conclusion, that “all acts of waterboarding even on behalf of public safety are acts of torture” must also be true. But an argument is a sound argument only if both it is valid and its premise is or its premises are in reality true.

Logicians as engaged precisely in their role as logicians cannot determine whether the premises of an argument or, for that matter, its conclusion, are true or not. It follows that it is not their role to determine whether or not an argument is sound; rather, their role is but that of determining whether or not an argument is valid.

In this specific case, of course, the second premise, that “acts of waterboarding even on behalf of public safety are acts of waterboarding,” is not likely to be challenged. But at least some people have thought it possible to find the first premise false.

Let me offer, to make the distinction a bit clearer, an example of an argument which is valid but which even the most resolute of defenders of waterboarding would see to be not sound:

All acts of charity are acts of torture.

All acts of waterboarding even on behalf of public safety are acts of charity.

Therefore, all acts of waterboarding even on behalf of public safety are acts of torture.

2. Let us look, a bit more quickly this time, at the second in the series of arguments relating waterboarding and criminality, one according to which:

All acts of torture are criminal acts.

All acts of waterboarding even on behalf of public safety are acts of torture.

Therefore, all acts of waterboarding even on behalf of public safety are criminal acts.

The second premise, of course, is the conclusion of the first argument in the series, above.

Now this argument too is clearly a valid argument, in that, if the two premises are true, the conclusion must also be true. Again, however, it is a sound argument only if, in addition to its being valid, its two premises are in reality true. And, of course, at least some people have thought it possible to find one or the other of them, or both, false.

3. Let’s move on to the next argument of the series, one taking on, not the form of a categorical syllogism, but rather that of the “horse’s head” argument, so-called from the earliest of its instances known. That instance can be formulated as follows:

All horses are animals.

Therefore, all heads of horses are heads of animals.

The argument’s validity is intuitively obvious, as is its soundness*. An equally valid but unsound argument would be:

All horses are butterflies.

Therefore, all heads of horses are heads of butterflies.

Putting then the argument now at hand into the same valid logical form, and taking as its premise the conclusion of our second argument, we find we have:

All acts of waterboarding even on behalf of public safety are criminal acts.

Therefore, all persons having engaged in acts of waterboarding even on behalf of public safety are persons having engaged in criminal acts.

The argument is perfectly valid, in that the conclusion follows from the premise. It is sound, however, only if both it is valid and the premise is true.

4. The final argument to be looked at here is another example of a categorical syllogism.

All persons having engaged in criminal acts are persons deserving of appropriate punishment.

All persons having engaged in acts of waterboarding are persons having engaged in criminal acts.

Therefore, all persons having engaged in acts of waterboarding are persons deserving of appropriate punishment.

Again, the argument is quite valid, but it is sound only if its premises are also true.

5. I will conclude with two suggestions. First, you may want to take note of what the results would be of substituting, first, sleep deprivation and, then, rectal hydration, etc., for waterboarding in the parallel series of arguments. Second, you may want to reflect on the definitions which would be necessary for us to have to go further in the direction of resolving the related disputes, beginning with that of just what an act of waterboarding is and ending with that of just what an appropriate punishment might be.

Until next time.

*The full justification of the validity of the argument, while readily available, would take us well outside the scope of the present post.

About Rchard E. Hennessey

See above, "About the Author/Editor."
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