Approaching probabilistic and deterministic nomic truths in an inductive probabilistic way

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.

Probabilistic truthlikeness, content elements, and meta-inductive probability optimization

The paper starts with the distinction between conjunction-of-parts accounts and disjunction-of-possibilities accounts to truthlikeness (Sects. 1, 2). In Sect. 3, three distinctions between kinds of truthlikeness measures (t-measures) are introduced: (i) comparative versus numeric t-measures, (ii) t-measures for qualitative versus quantitative theories, and (iii) t-measures for deterministic versus probabilistic truth. These three kinds of truthlikeness are explicated and developed within a version of conjunctive part accounts based on content elements (Sects. 4, 5). The focus lies on measures of probabilistic truthlikeness, that are divided into t-measures for statistical probabilities and single case probabilities (Sect. 4). The logical notion of probabilistic truthlikeness (evaluated relative to true probabilistic laws) can be treated as a subcase of deterministic truthlikeness for quantitative theories (Sects. 4–6). In contrast, the epistemic notion of probabilistic truthlikeness (evaluated relative to given empirical evidence) creates genuinely new problems, especially for hypotheses about single case probabilities that are evaluated not by comparison to observed frequencies (as statistical probabilities), but by comparison to the truth values of single event statements (Sect. 6). By the method of meta-induction, competing theories about single case probabilities can be aggregated into a combined theory with optimal predictive success and epistemic truthlikeness (Sect. 7).

Dummetova koncepcija kao teorija značenja za Hintikkin tip semantike teorije igre (III)

With the analysis of the key terms such as truth/use, proof - verification, falsification, inductive probability/semantic probability, winning/losing, winning strategy, it is shown that Dummett’s general theory of meaning does not include Hintikka’s game theory, that it, the conception of the winning strategy. The difference between them arises from the different understanding of Wittgenstein's idea about language games and from their attitudes toward theoretical proof theory. Hintikka’s semantic games about exploration of the world do not reject the bivalence principle but he gives it a different characteristic - one of the two players always has a winning strategy. Looking at Dummett’s philosophical theory of meaning and the most recent Hintikka’s suggestion about general information - seeking through questioning and answering, the author establishes that Dummett’s falsificational and dialogical games as well as Hintikka’s semantic games are subparts of Hintikka’s general information - seeking game Thus Dummett’s statement that Hintikka’s semantic games can be subsumed under Dummett’s conception is rejected and thus the answer is partly given to Saarinen’s suggestion that new affinity should be established. Apart from the comparison of these views with the outline of possible Wittgenstein’s general theory of meaning as rule - testing, together with his treatment (although not always adequate) of verification/falsification, inductive probability and čonfirmation/corroboration, the advantage of Wittgenstein’s view is affirmed.

Feature Selection for Supervised Learning via Dependency Analysis

A new feature selection method based on Inductive probability is proposed in this paper. The main idea is to find the dependent attributes and remove the redundant ones among them. The technology to obtain the dependency needed is based on Inductive probability approach. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected feature subsets. The dependence between two attributes is determined based on the probabilities of their joint values that contribute to positive and negative classification decisions. If there is an opposing set of attribute values that do not lead to opposing classification decisions (zero probability), the two attributes are considered independent, otherwise dependent. One of them can be removed and thus the number of attributes is reduced. A new attribute selection algorithm with Inductive probability is implemented and evaluated through extensive experiments, comparing with related attribute selection algorithms over eight datasets such as Molecular Biology, Connect4, Soybean, Zoo, Ballon, Mushroom, Lenses and Fictional from UCI Machine Learning Repository databases.