On Philosophy

October 6, 2007

Deduction And Knowledge

Filed under: Epistemology — Peter @ 12:00 am

Logical deduction is sometimes held up as the best kind of reasoning, that which can’t go wrong if conducted properly, which can produce certain truths. But I would claim the exact opposite, that logical deduction is the poorest kind of reasoning. In any situation where we are reasoning logically we are dealing with two things: the subject matter itself and the formalism with which we are reasoning about it. We want to know things about the subject matter, but logical deduction is unable to tell us anything about it, all it can do is inform us about the formalism through which we are reasoning about it. This is not useless information, the formalism is a necessary tool, and so it is often worth spending energy improving it. But what we are really concerned about is the subject matter, and to know about it we can’t rely on logical deduction but must instead employ empirical reasoning, in the form of generalization, application, and extension.

To argue for my claim about logical deduction I must divide the claims that we might see it as motivating into two categories: the negative, which are arrived at through revealing contradictions, and the positive, which involve deducing new claims on the basis of existing ones. Let us first consider the negative claims. The negative claims can further be divided into two groups, those that result from deductions with a basis in two or more theories and those that stem from a single theory. A contradiction arising from two theories indicates, for obvious reasons, simply that the formalizations involved in both theories are different, and that a straight translation of the terms of one into the terms of the other is impossible. For example, if one theory states that a type of event P occurs 90% of the time and the other says that P type events occur 30% of the time we can derive a “contradiction” because it is clear that P type events cannot occur with two different frequencies. But this shows only that the two theories must be designating different kinds of events with the same label. Which is why I say that the contradiction reveals an inconsistency not in the theories themselves, but in the associated formalism that treats the label as meaning the same thing in both. Literally it is impossible for two different theories to contradict each other. Consider the most famous example of such an apparent contradiction, between quantum physics and general relativity. Both theories are true, in the sense that they are apparently correct generalizations over the observed phenomenon. But, on the other hand, when put together they contradict. This is not a real contradiction though, what it means is that the formalism, in this case mathematical, is in error, that it is not suited for describing the cases where they contradict; they are true descriptions of the phenomena that justify them, but the formalism of one or both must be in error in the way it extends the theory beyond the observed cases.

With that out of the way we can turn our attention to negative claims that stem from a single theory, where the theory itself implies a contradiction. Again, I would argue that this simply shows that our formalism is in error, in this case that it can’t possibly be a true description of the subject matter. Suppose, for example, that 40% of all the plants being studied have property A and that the other 60% have B. And we hypothesize that X is the cause of A while the absence of X, ~X, is responsible for B. Furthermore this X is not a new invention, but has already been postulated as the only cause of property C. However, our sample has some plants that have both B and C properties. Thus we have a contradiction, some plants are supposed to have X and ~X present. Obviously this shows nothing about the plants themselves, but instead demonstrates that the way we have formally described things must be in error. Either ~X is not responsible for B (or X for C) or X can be replaced by ~X, or vice versa, in such a way that both B and C show up. And, as it should be obvious, to know anything about X and its relationship to B and C requires more that simply hypothesizing about it, but requires a way to determining whether X is present, and then generalizing on the basis of that data.

But maybe no one expects negative claims to tell us much of anything in the first case, after all to say that something is not the case is certainly not to say what is the case, unless your options are very limited in number. Logical deduction can, produce positive claims as well. For example, if we took the claims “all Ps are S” and “all Ss are Q” we could logically deduce that “all Ps are Q”. And this statement does seem to be the kind that is saying something new about the world and so is providing us with new knowledge. But I claim that any valid deduction either tells us nothing that was not already evident from the samples or is not a proper generalization. For example, in the case given previously it should be clear from our observation of Ps that they are all Qs, without any need to deduce that fact from the two others. In fact it is probably better not to, because the two facts given as premises may be later rejected while the claim that “all Ps are Q” may remain a true description. Let me put things in another way: either a conclusion from logical deduction is already justified by a generalization from the evidence we already have, in which case it isn’t telling us anything new. Or it isn’t justified by those facts, it yields a claim about which we have no evidence either confirming or denying. But such claims can’t be considered knowledge, we must investigate them to see if they really hold, and what such investigations may reveal is that it is not actually the case, and that what we have here is a negative claim, as discussed above, which reveals that our formalism was a poor one.

What logical deduction illuminates then are not facts about the subject matter, but facts about the formalism with which we are attempting to capture it. If logical deduction yields a conclusion it does not indicate that this is in fact the case but that our formalism is such that this fact is a consequence, an artifact of how we constructed that formalism. Now it might not be unreasonable to investigate those implications, both in order to test the correctness of the formalism and possibly to discover something new, but it is important to keep in mind that what the deduction of this claim indicates is not that the claim is the case, but that the way we initially formalized the subject matter implies that it is the case. And so, on the basis of such thinking I conclude that logical deduction cannot be the basis of knowledge, but is rather a tool for improving our formalisms, and that it is the process by which we construct these formalisms in the first place that yields knowledge.

But if we aren’t relying on logical deduction for knowledge then what should we use instead? Hopefully you don’t expect me to provide a complete theory here (I am only a finite being), but I can provide a sketch of some of the key principles. First we have generalization, a principle that justifies general claims on the basis of a finite same of cases, with varying degrees of certainty depending on the situation. And, the reverse of generalization, we have application where we use our general principles to draw conclusions about specific cases. But these conclusions are not the same kind of knowledge as that which her have concerning the samples we generalize from or the general principles themselves: these conclusions be used as the basis for generalizations, and if the claims turn out to be false they in turn falsify the general principle from which they were derived. And, finally, we have extension. Extension is the process by which we extend general claims to situations that we do not have samples with which to confirm or deny the principle. For example, we extend the general physical principles we discover here on Earth to apply everywhere, not just near the surface of the planet. While extension is better justified more than a wild guess the certainty of the generalizations resulting from it is less than those from which they were extended.

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