Topics Logic

Question Are there any philosophers that deny that a logically derived conclusion from a series of true propositions is also true?

Accepted:
August 6, 2011

Comments

So far as I know, there is no one who holds quite this view. The reason is very simple. We say that an inference is logically valid just in case, whenever the premises are true, so must the conclusion be true. So if one starts with some true premises and "logically derives" some conclusion, then the conclusion has to be true, simply by definition. This assumes, of course, that our logical derivation is correct: that we haven't made mistakes, that the inferences on which we're depending really are logically valid, and so forth.

Now, all of that said, philosophers can and do disagree about what inferences really are logically valid. So you might have thought that the inference from "If I go to the movie, then, if I go to the movie, then I'll have a good time" to "If I go to the movie, then I'll have a good time" is logically valid. But there are philosophers who deny that it is. In this particular case, they think, there are additional hidden premises that can be used to make it valid. But all by itself, no. Why do they think this? Well, it has to do with the so-called Liar Paradox. If you deny that this sort of inference is valid, then you can evade the contradiction the Liar delivers. It's a high cost, it seems to me---too high---but it gives you a sense for the possibilities.

On a quite different line, you might have asked your question this way: Are there any philosophers who think that a logically derived conclusion from a series of true propositions may be false? You might think that is just the same question: I've already said that everyone thinks such a conclusion must be true. But there are philosophers who would agree with that, but who think the conclusion might also be false! Here again, such philosophers are largely driven by paradoxes like the Liar.

Finally, there have been philosophers who worried about the effect of "chaining" inferences. So we normally assume that, if A logically implies B, and if B logically implies C, then A logically implies C. You might reason as follows: Suppose A is true; since A logically implies B, B must also be true; but since B logically implies C, then C must be true; so A logically implies C. But, if you look carefully at this argument, you'll see that it is assuming something very close to what it means to be proving. So, it turns out, it is possible coherently to deny that this kind of "chaining" always works. So, on this view, you could have a bunch of true premises, and then engage in some logical reasoning, where each individual step was logically valid, but the overall chain of reasoning was not logically valid, and so the conclusion is not true. That would be something quite close to what was suggested in the original question.

This last view tends to be motivated by concerns about a different paradox: The Paradox of the Heap. But again, in my view, this is a pretty desperate response.

Question Are there any philosophers that deny that a logically derived conclusion from a series of true propositions is also true? Accepted:August 6, 2011

Question Are there any philosophers that deny that a logically derived conclusion from a series of true propositions is also true?

Accepted:
August 6, 2011