



Friday, 13 December 2013

Modus Non Ponendo Ponens

I daresay actual Philosophers have a name for what I'm about to say in this blogpost, but I can't seem to find it on Wikipedia. I should probably stop relying on Wikipedia for my philosophical education. Here, though, on formal fallacy:
As modus ponens, the following argument contains no formal fallacies.

1.If P then Q
3.Therefore Q

A logical fallacy associated with this format of argument is referred to as affirming the consequent, which would look like this:

1.If P then Q
3.therefore P

This is a fallacy because it does not take into account other possibilities. To illustrate this more clearly, substitute the letters with premises.

1.If it rains, the street will be wet
2.The street is wet.
3.Therefore it rained.

Although it is possible that this conclusion is true, it does not necessarily mean it MUST be true. The street could be wet for a variety of other reasons that this argument does not take into account. However, if we look at the valid form of the argument, we can see that the conclusion must be true.

1.If it rains, the street will be wet.
2.It rained.
3.Therefore, the streets are wet.

This statement is both valid and sound.
No it's not, though. Maybe the Council have erected a giant awning over the street. Maybe it was a localised shower, and the wind blew the rain out of the way. Maybe it rained an hour ago and the street has subsequently dried. You take my point.

Do you, though? It is more than just to nitpick with that particular example. It is to say: there is no situation in the world which cannot be so nitcked. Thuswise nitpicken. 'Therefore it rained' does not follow in the third example, above, because, you know: maybe the streets are wet because a fire hydrant burst. But the same thing applies the other way around. Or more specifically, the attempt to rephrase the final example to exclude all the things that might falsify it -- as it might be, '(Assuming the council haven't erected a giant awning over the street, or that it was a localised shower, and the wind blew the rain out of the way, or that it rained so long ago that the street has subsequently dried etc ...) If it rains, the street will be wet' -- includes within it an 'etc' that potentially goes on forever. To quote the wiki again: 'This is a fallacy because it does not take into account other possibilities.' Ah, but there are always and inevitably other possibilities, no matter which way round you frame your argument.


  1. I'm sure you know all this already, but it's been bugging me all day, and I have to comment. Poor MPP! Along with its slightly less graceful brother, MTT, it's surely one of the greatest and most beautiful formulations in human history, and I feel a nerdy need to defend it a little.

    One obvious problem here is with that last "This statement is both valid and sound", which is ugly and awful. A statement or premise is only ever true or false. It's the arguments they form part of that are valid and/or sound. MPP as a form is always valid, because if premises 1) and 2) are true then 3) must be true as well. A particular instance of MPP will always be valid, but it will only be sound if both of the premises are true, because that means its conclusion must be true as well.

    The only way to refute an MPP argument as unsound is by attacking the truth of one of its premises. And what you seem to be doing here is arguing that an "If x then y" premise can never (or at least rarely) be true without all-but infinite caveats. But that implies the argument is intended as universally applicable, when of course, arguments rarely are. In the example above "the road" doesn't imply "all roads". It must be a specific road ("the road"), and whether the council has serviced that specific road with a roof would be a factor to take into account when deciding the truth-value of the first premise. There will be other factors, but they're all manageable. Otherwise we wouldn't make it through the day.

    Of course, most real-world arguments aren't decided by things like MPP, but basic rhetoric. And yet the principle stands. If we can't manage "If x then y" statements without infinite caveats, isn't that the end of science? On a less basic level, I’d like a glass of water right now. What will happen if I turn on a tap?

  2. I don't see that it would be 'the end of science'. Indeed, it seems to me 'science' already works on non MPP premises. By which I mean: you ask 'I'm thirsty, what happens if I turn on the tap?' The answer is, 'PROBABLY the water will come out, and your thirst satisfied.' That PROBABLY is no vagueness; quite a lot of contemporary science is concerned with calculating, often to extraordinary tolerances, how that 'probably' pans out. But my two related point in this post, in a nutshell: (a) probably is always the best we can actually do (in applied, not pure); and (b) MPP has no room for a probably. So, doesn't that imply ... goodbye MPP?

  3. "and your thirst satisfied..." >> "and your thirst will be satisfied..."

  4. But again, your argument is not with MPP, but with the idea that a statement of the form "if x then y" can ever be true. In a pure form, it obviously can be ("if I add 1 and 1 then I get 2"), but applied, yes, it does get more complicated. "If I turn on the tap then water will come out" is obviously not true if my water has been cut off - but this is where I think you're mixing up pure (or universal) and applied. An "if x then y" statement is rarely going to be universally true (or even intended to be) because the context, in the form of various suppressed and often obvious premises, will always be relevant.

    I don't think it's hyperbole to talk about it being the end of science. Surely science relies on "if x then y" statements? Experiments must be capable of being repeated, and scientific theories have to make predictions (if x then y). If I heat water to 100 degrees centigrade in my kitchen then it will boil. I can add caveats around water purity and atmospheric pressure, and so on, but they're just more complicated "if x then y" premises nested in to the initial x. Somewhere or later, an "if x then y" statement has to be accepted as true, or probably true to the exent that it's indistinguishable from truth, or else you can't do anything.