Approaching probabilistic and deterministic nomic truths in an inductive probabilistic way

Theodorus Kuipers*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

Theories of truth approximation in terms of truthlikeness (or verisimilitude) almost always deal with (non-probabilistically) approaching deterministic truths, either actual or nomic. This paper deals first with approaching a probabilistic nomic truth, viz. a true probability distribution. It assumes a multinomial probabilistic context, hence with a lawlike true, but usually unknown, probability distribution. We will first show that this true multinomial distribution can be approached by Carnapian inductive probabilities. Next we will deal with the corresponding deterministic nomic truth, that is, the set of conceptually possible outcomes with a positive true probability. We will introduce Hintikkian inductive probabilities, based on a prior distribution over the relevant deterministic nomic theories and on conditional Carnapian inductive probabilities, and first show that they enable again probabilistic approximation of the true distribution. Finally, we will show, in terms of a kind of success theorem, based on Niiniluoto’s estimated distance from the truth, in what sense Hintikkian inductive probabilities enable the probabilistic approximation of the relevant deterministic nomic truth. In sum, the (realist) truth approximation perspective on Carnapian and Hintikkian inductive probabilities leads to the unification of the inductive probability field and the field of truth approximation.
Original languageEnglish
Pages (from-to)8001–8028
Number of pages28
JournalSynthese
Volume199
Issue number3-4
DOIs
Publication statusPublished - 14-Dec-2021

Keywords

  • probabilistic truth
  • the true probability distribution
  • deterministic truth
  • nomic truth
  • truth approximation
  • truthlikeness
  • verisimilitude
  • inductive probability
  • inductive logic
  • estimated distance from the truth

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