On reasoning

A simple way to see one aspect of the fragility of human reasoning is through joint probabilities.

P(1 .. n) = P(1) * P(2) * … P(n)

So, if I have an argument whose conclusion relies on 3 premises, and the argument is valid, then the chance that the argument is sound is:

probability (first premise being true) * probability (second premise being true) * probability (third premise being true)

(Assume independence of probabilities.)

Let’s say I’m ‘fairly sure’ about each premise, assigning each one a percentage of 80. That is, at each point along the argument, I’m fairly sure that it is right. At the end, I may then have the feeling that I should be fairly sure about the argument. Yet, this is not the case.

0.8 * 0.8 * 0.8 = 0.51, i.e., almost as likely to be unsound as sound.

Also see here.

One thought on “On reasoning

  1. bgc

    I think this is a real problem with complex and multi-step reasoning – and I think it is a problem which we feel intuitively. That any errors will multiply in long chains of logic, and at the end there will be more noise than signal.

    I think this is the problem of scholasticism, even Thomism (the best kind).

    It answers all the important questions, coherently, but has a tendency to over-extend into potentially misleading partial answers.

    My guess is that this is why Aquinas himself – after a spiritual revelation – pronounced his own system to be ‘straw’.

    It functions to show that all questions can be answered – and having been assured of this the safest thing is to drop it.

    Aquinas can answer all the questions (pretty much) but we seldom feel completely sure that all the premises are absolutely secure, and the more steps there are in the logic, the more we feel that the end-result (cantilevered out far beyond what is obvious to humans, and far beyond direct revelation) might be mistaken in some way.

    So the end result of complex reasoning itself needs to be checked by the same methods which give rise to it: reason and revelation.

    The Orthodox tradition, by contrast, seems to use much shorter chains of less complex and commonsense reasoning – it is therefore more secure and less likely to mislead profoundly – but this does mean than many/ most questions cannot be answered, and that there is more to be accepted on faith, somewhat blindly (security comes from the validation by people of exceptionally advanced holiness – Saints, Elders etc; but there must be an acceptance that there is much we cannot understand, and that the necessary may be inextricably mixed with the accidental in ways we cannot unravel).

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