## The essence of scientific reasoning

26 Dec, 2018 at 16:54 | Posted in Theory of Science & Methodology | 5 Comments

In deductive reasoning all knowledge obtainable is already latent in the postulates. Rigour is needed to prevent the successive inferences growing less and less accurate as we proceed. The conclusions are never more accurate than the data. In inductive reasoning we are performing part of the process by which new knowledge is created. The conclusions normally grow more and more accurate as more data are included. It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based.

R. A. Fisher

In science we standardly use a logically non-valid inference — the fallacy of affirming the consequent — of the following form:

(1) p => q
(2) q
————-
p

or, in instantiated form

(1) ∀x (Gx => Px)

(2) Pa
————
Ga

Although logically invalid, it is nonetheless a kind of inference — abduction — that may be factually strongly warranted and truth-producing.

Following the general pattern ‘Evidence  =>  Explanation  =>  Inference’ we infer something based on what would be the best explanation given the law-like rule (premise 1) and an observation (premise 2). The truth of the conclusion (explanation) is nothing that is logically given, but something we have to justify, argue for, and test in different ways to possibly establish with any certainty or degree. And as always when we deal with explanations, what is considered best is relative to what we know of the world. In the real world, all evidence is relational (evidence only counts as evidence in relation to a specific hypothesis) and has an irreducible holistic aspect. We never conclude that evidence follows from a hypothesis simpliciter, but always given some more or less explicitly stated contextual background assumptions. All non-deductive inferences and explanations are necessarily context-dependent.

If we extend the abductive scheme to incorporate the demand that the explanation has to be the best among a set of plausible competing potential and satisfactory explanations, we have what is nowadays usually referred to as inference to the best explanation.

In inference to the best explanation we start with a body of (purported) data/facts/evidence and search for explanations that can account for these data/facts/evidence. Having the best explanation means that you, given the context-dependent background assumptions, have a satisfactory explanation that can explain the evidence better than any other competing explanation — and so it is reasonable to consider the hypothesis to be true. Even if we (inevitably) do not have deductive certainty, our reasoning gives us a license to consider our belief in the hypothesis as reasonable.

Accepting a hypothesis means that you believe it does explain the available evidence better than any other competing hypothesis. Knowing that we — after having earnestly considered and analysed the other available potential explanations — have been able to eliminate the competing potential explanations, warrants and enhances the confidence we have that our preferred explanation is the best explanation, i. e., the explanation that provides us (given it is true) with the greatest understanding.

This, of course, does not in any way mean that we cannot be wrong. Of course, we can. Inferences to the best explanation are fallible inferences — since the premises do not logically entail the conclusion — so from a logical point of view, inference to the best explanation is a weak mode of inference. But if the arguments put forward are strong enough, they can be warranted and give us justified true belief, and hence, knowledge, even though they are fallible inferences. As scientists we sometimes — much like Sherlock Holmes and other detectives that use inference to the best explanation reasoning — experience disillusion. We thought that we had reached a strong conclusion by ruling out the alternatives in the set of contrasting explanations. But — what we thought was true turned out to be false.

That does not necessarily mean that we had no good reasons for believing what we believed. If we cannot live with that contingency and uncertainty, well, then we are in the wrong business. If it is deductive certainty you are after, rather than the ampliative and defeasible reasoning in inference to the best explanation — well, then get into math or logic, not science.

1. “It is quite wrong to try founding a theory on observable magnitudes alone…It is the theory which decides what we can observe (quoted in Heisenberg, 1971, p. 31).”
— Albert Einstein

2. I think scientific thinking at its core is a search for mechanism. “Mechanism” is the dog that we set to the hunt for knowledge; explanation, per se, is merely that dog’s happily wagging tail.
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We look not for a simple fully observable event regularity, but for a system of relations among observables united and governed by a mechanism partially hidden.
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Working out the systemic logic of a proposed mechanism is as important to knowledge as the systematic observation and measurement of nature and nature’s patterns.
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At an advanced stage of knowledge building, what builds confidence that a proposed mechanism actually governs and unites the observables is the ability to probe and manipulate or, by imaginative proxy of manipulation, to extend interpretive explanation.
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In the circling between speculation about mechanism and methodical observation across the bridge of manipulation, logic and deductive reasoning make an appearance here and there. Nothing distinguished as “inference” usefully labels any but the whole process.

3. Science is about social consensus. The best explanation is the most politically correct. Wegener was so ridiculed for proposing continents drift, because consensus prevented scientists from even looking for evidence supporting his hypothesis, and obvious evidence like the shapes of the African and South American coastlines was dismissed using all sorts of logical and experimental reasons. Today’s consensus is just as arbitrary and social-context-dependent …

4. When R.A. Fisher prattles on about “accuracy” in deductive reasoning, I think it would be fair to suggest the great man was fatally confused.

• I suspect he means “valid” …

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