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Relation to truth· Truth, language and science

The calculus of probabilities

Axis: Scientific methodHow does science go about justifying its claims?

To know is to adjust degrees of belief. Each observation revises the probability of a hypothesis by Bayes' theorem: evidence does not prove, it makes more or less probable, starting from what one already believed.

Problems
  • Descriptive Thought experiment
    The black swan

    No number of white swans proves that all are white, but a single black swan is enough to belie it: how, then, does one establish a general law, by piling up cases, by hunting the counter-example, or by weighing the probabilities?

    a universal law
  • Descriptive
    What can evidence do?

    No accumulation of evidence proves a universal law; a single counter-example, on the other hand, seems enough to refute it: evidence would then count only by its power to belie, never to establish. But does it even truly refute? When a result contradicts a theory, it is never that theory alone that is at stake, but a whole bundle of auxiliary hypotheses, and one can always sacrifice one of them to save it. Prove, refute, or only make more or less probable: what, exactly, can evidence do?

    a piece of evidence, a test
  • Descriptive
    What confirms a hypothesis?

    "All ravens are black" is equivalent to "everything non-black is a non-raven", which a green apple would then confirm, without one's having seen a single raven. And the same past observations equally support incompatible predictions. What, exactly, does a piece of evidence confirm, and by how much?

    the link between evidence and hypothesis
  • Descriptive
    Is there a method at all?

    What if there were no universal rule of sound scientific reasoning? Feyerabend argues that the great discoveries often broke the canons of method, and that in science "anything goes": the logic reconstructed after the fact is not what actually advances knowledge.

    the methodological rule itself