Two paradigms of evidence

Many people take valid deductive arguments to be the guiding ideal or “paradigm” of evidence. There are two obvious reasons for this. The first is that in mathematics, the proof of a theorem is essentially a deductive argument, and mathematical proof is perhaps the closest thing we can have to certainty. The second is that when people try to persuade one another of something, they appeal to shared beliefs, which each hopes will imply something the other has no choice but to accept. This gives the shared beliefs the function of premises — and persuasion becomes the derivation of a conclusion from those premises.

Buoyed by the thought that proof and persuasion are achieved by arguments, we cast about in search of their equivalent in “empirical enquiry” — and inevitably arrive at induction. (By ‘induction’ I always mean enumerative induction: for example, the sighting of several white swans leads to the general claim that all swans are white.) An inductive “argument” with true “premises” doesn’t guarantee the truth of its “conclusion” as a valid deductive argument does, but it does lead to it with mechanical inevitability. It leaves no room for choice as to what its conclusion will be. No “guesswork” is involved — the “data” determine the resulting “theory”. The latter is “based on” the former in much the same way as the conclusion of a deductive argument is “based on” its premises.

The ubiquity of the thought that “evidence consists of arguments” is underlined by the widespread use of words like ‘basis’, ’grounds’, ‘foundations’, ‘support’, etc. — as if these words were synonymous with ‘evidence’.

There’s a remarkable fact about arguments, which can be loosely expressed as follows: “the conclusion doesn’t tell us anything genuinely new — it just rearranges information already contained the premises”. That’s a loose way of putting it, because obviously theorems in mathematics can be surprising. But they’re mostly surprising because we don’t expect them to be able to say what they do say, given that they were derived from such meagre “input” as is contained in the axioms.

Theorems never “reach out” beyond what can be derived from the axioms. And the conclusion of an inductive argument only reaches out beyond what is contained in its premises inasmuch as it merely generalises from them. It can’t come up with new concepts. If we were limited to deduction and induction, we might be able to do logic and mathematics, and to generalise about what we can observe directly. But we wouldn’t be able to talk about the sort of things science talks about. In that sense, both deduction and induction are “closed” with respect to their “raw material”. Everything mentioned in their conclusions is internal to the system of axioms or beliefs expressed by their premises.

If we assume that evidence consists of arguments, it amounts to “being implied by what you know already”. It’s analogous to what can be got from a library that contains nothing but books you have already read. It’s an internal guarantee or assurance, the sort of thing that invites adjectives like “strong”, or possibly “overwhelming”.

But that sort of evidence doesn’t play a big role in science. Science isn’t trying to give us an internal sense of assurance, but to give us an understanding of external reality. In other words, it’s not aimed at justification but at truth. Unlike the best that can be achieved by deduction and induction, science “reaches out” beyond any system of axioms or beliefs working as premises. To achieve that, science simply cannot avoid guesswork. In embracing guesswork, scientific theory is not fully constrained by observation. In other words, theory is underdetermined by “data”. Typically, several possible theories are consistent with any given set of “data”.

A scientific theory is a representation of its subject matter. It can represent it by literally being true of it, or by modelling it. Hypotheses are true or false — they consist of symbols, some of which stand for real things. Models mimic the behaviour of some aspect of reality in some relevant respect. Either way, evidence in science consists of mere indications, often sporadic and peripheral, that the representations in question do in fact represent their subject matter faithfully or accurately. A theory is related to its subject matter in somewhat the same way as a map is related to its terrain. The image of map and terrain is appropriate — and the old image of conclusion and premises of an argument is inappropriate. The main purpose of observation in science is not to gather “data” to work as premises in an argument, but to check here and there to see whether the “map” and the “terrain” do in fact seem to fit.

Understood in this way, evidence is no longer a matter of proof or persuasion — of leaving no alternative to accepting a “conclusion” — but of seeking new indications that a representation is accurate. The most obvious such indications are passing tests and providing explanations. A theory passes a test when it predicts something that can be observed, and new observation confirms the prediction. A theory explains successfully when it newly encompasses something formerly baffling. Both involve seeking new facts rather than mechanically deriving something from old facts.

Science is more a process of discovery rather than of justification, and scientific evidence is more like what an explorer can bring to light through travel than what a scholar can demonstrate in his study.