Notes on strawson on induction

Synopsis

  1. What reason do we have to rely on induction?
  2. Proving induction inductively is absurd, as it is proving deduction deductively
  3. Nevertheless, induction has absolutely no deductive value
  4. If asking for the two above is absurd, we might as well affirm that induction is not justifiable
  5. We could make inductive propositions deductive by generalizing them; how does this happen?
  6. Supposing we have a general valid proposition
    1. Such proposition entails all of the possible single generalizations
    2. How many observations of an event would be necessary to safely generalize the proposition to a deductive proposition? This number would be arbitrary
    3. It can’t be too vague nor too strict
    4. It’s impossible to frame such a proposition
  7. The example of a sample and a population


We have to remember, too, the great complexity of the ways in which background beliefs may be related to foreground problems; […] When we bear in the mind these things, it will not seem surprising either thatno precise rules of general application can be formulated for the assessment of evidenceor that no precise vocabulary is available for the description of its degrees.

Strawson,Introduction to Logical Theory, §9, p. 248.


The use of the wordjudgmentis revealing: he has a lot of experience, but he is no specialist

Our use of words for grading evidence will in part reflect the degree of caution demanded by the action proposed. Evidence which the general public finds conclusive may not satisfy the judge.

The above and the previous quotes are related to[[Francis Bacon#Idols|Bacon’s idols]].

The main questions

  • What reason have we to place reliance on inductive procedures?
  • It is our habit to form expectations in this way, but can the habit be rationally justified?

This doubt must be thoroughly analyzed.

As deductive reasoning can’t be logically questioned without involving a deductive procedure in the process, the same happens with inductive reasoning:

to call a particular belief reasonable or unreasonable is to apply inductive standards, just as to call a particular argument valid or invalid is to apply deductive standards.

Following a deductive reasoning, inductive standards are invalid (Hume). If every argument we produce is invalid to prove induction in general (and not a peculiar principle), we have no good reason for any of our inductive conclusions.

Suppose we take a supremely general valid proposition, such that the generalization of every instance is implied by it. Any justification would be found, for the simple reason that as long as the former holds, all the entailed statements are valid. How many inductive observations are necessary to get to a deductive generalization of the instance? Such number would be arbitrary.

To avoid this, we should make the general proposition vague, but it would follow that the entailments to the peculiar statements are too weak.

We therefore conclude that finding such a proposition is as impossible as it is to identify precise rules for the assessment of evidence.

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