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Carnap provides a general understanding of symbolic induction, given as c(h, e)=r.

  1. c = degree of confirmation
  2. h = hypothesis
  3. e = evidence
  4. r = outcome

What exactly is meant by Carnap's 'degree of confirmation'? Is it an expectation given h and e, as a method of belief? If so, did he think of developing a ranking criteria towards his inductive method? Does this work for c?

Also, he mentions the 'm' function. However, I cannot seem to wrap around how this relates to the 'c' function.

Furthermore, are there modern advancements on Carnap’s inductive probability, still used in statistics, or programming?

Mark Andrews
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Meilton
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  • See [Carnap: Inductive Logic](https://plato.stanford.edu/entries/carnap/index.html#InduLogi) with [Supplement](https://plato.stanford.edu/entries/carnap/inductive-logic.html) – Mauro ALLEGRANZA Jan 26 '21 at 10:30
  • Having read both; Not much is mentioned on the m-function and its relation to the c-function. – Meilton Jan 26 '21 at 16:24
  • Although, this article clarifies both functions [Carnap's System](https://www.jstor.org/stable/pdf/20114867.pdf?casa_token=6Y7n_Vd0QscAAAAA:M1CGu-Z8meHDDQICz2gCPO5uWm0ELCRjkS0l6wj4Nn-ZWiGCf-b48C1zwvYexumtuiZKLqLUUghhtL0p8NIVOOFiCy9NXEIJUdevQuU848Mkrebxgu0) – Meilton Jan 27 '21 at 00:25
  • If you're looking for a method to objectively find the best explanation for some phenomenon given some available (and possibly noisy) data, see [this approach](https://math.stackexchange.com/a/1736327/21820). All other approaches that I have seen so far fail to achieve the same guarantees. – user21820 Feb 06 '22 at 18:14

1 Answers1

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The function 'm' Carnaps details as a 'measure functions', in a finite system L_N; This is any distribution of positive real numbers, whose sum is 1, among the state-description. Then we define m(j) for a sentence j as the sum of the m(state-descriptions) for those state-descriptions in which j holds.

By degree of confirmations, this ultimately is dependent on the tautology of the statement. Given that it follows probability axioms, like conditional expectation therefore:

c(h.e)/c(e)

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