Science and crossword solving

from Lars Syll

Evidence and Inquiry: Towards Reconstruction in Epistemology by Susan Haack  - Hardcover - Reprint - 1994 - from Common Crow Books (SKU: B54435)The model is not . . . how one determines the soundness or otherwise of a mathematical proof; it is, rather, how one determines the reasonableness or otherwise of entries in a crossword puzzle. . . . The crossword model permits pervasive mutual support, rather than, like the model of a mathematical proof, encouraging an essentially one-directional conception. . . . How reasonable one’s confidence is that a certain entry in a crossword is correct depends on: how much support is given to this entry by the clue and any intersecting entries that have already been filled in; how reasonable, independently of the entry in question, one’s confidence is that those other already filled-in entries are correct; and how many of the intersecting entries have been filled in.

Yours truly — an avid crossword solver himself — can’t but agree.

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 analyzed 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.

What is Inference? | Ontotext Fundamentals SeriesThis, 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 crossword solvers and detectives — 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.

Sir. Austin Bradford Hill (1897-1991). | Download Scientific DiagramWhat I do not believe — and this has been suggested — is that we can usefully lay down some hard-and-fast rules of evidence that must be obeyed before we accept cause and effect. None of my viewpoints can bring indisputable evidence for or against the cause-and-effect hypothesis and none can be required as a sine qua non. What they can do, with greater or less strength, is to help us to make up our minds on the fundamental question — is there any other way of explaining the set of facts before us, is there any other answer equally, or more, likely than cause and effect?

Austin Bradford Hill

  1. Romar Correa
    August 24, 2022 at 4:00 am

    Beautifully put! I am reminded of the eloquence of Kenneth Binmore many years ago in his case for game theory contrasting it with the mathematics of Robert Aumann. Ongoing work on team reasoning, focal points, and so on, conducted by Andrew Colman and others, is rich and illuminates the world we live in. The agenda is to explain how players often arrive at the north-west corner of the box rather than get stuck in the south-east corner, how in the ordinary business of life without repeated interactions people approach superior outcomes rather than stay condemned to the Nash equilibrium. The insights are being used to work out cooperative social outcomes in noncooperative situations. The mathematical response would be to axiomatise the empirical assumptions to prove theorems of sufficient generality, often an intractable task.

  2. Point
    August 24, 2022 at 3:16 pm

    Are there ways to score a crossword puzzle that is filled in with incorrect answers that still seem to fit?
    Do puzzlers review their work routinely to see how their grid compares to the published answers?
    Somewhere an enterprising software app may be under development or perhaps even in circulation that includes that scoring feature for online crosswords.

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