Approaching probabilistic laws.
In the general problem of verisimilitude, we try to define the distance of a statement from a target, which is an informative truth about some domain of investigation. For example, the target can be a state description, a structure description, or a constituent of a first-order language (Sect. 1). I...
| Published in: | Synthese Vol. 199; no. 3/4; pp. 10499 - 10520 |
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| Format: | Article |
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Springer Nature
Dec2021
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=154096904&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 154096904 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Dec2021 vid: 199 iid: 3/4 pid: 237 pub: Springer Nature artinfo: ui: 154096904 10.1007/s11229-021-03256-8 ppf: 10499 ppct: 21 formats: fmt: – @attributes: type: T – @attributes: type: P size: 1.5MB tig: atl: Approaching probabilistic laws. aug: au: Niiniluoto, Ilkka affil: Department of Philosophy, History, and Art Studies, University of Helsinki, P. O. BOX 24, Unioninkatu 40 A, 00014, Helsinki, Finland su: Probability measures Distribution (Probability theory) Operator functions Inheritance & succession Sects Kalman filtering sug: subj: Probability measures Distribution (Probability theory) Operator functions Inheritance & succession Sects Kalman filtering keyword: Divergence Legisimilitude Nomic constituent Probabilistic law Truthlikeness Verisimilitude ab: In the general problem of verisimilitude, we try to define the distance of a statement from a target, which is an informative truth about some domain of investigation. For example, the target can be a state description, a structure description, or a constituent of a first-order language (Sect. 1). In the problem of legisimilitude, the target is a deterministic or universal law, which can be expressed by a nomic constituent or a quantitative function involving the operators of physical necessity and possibility (Sect. 2). The special case of legisimilitude, where the target is a probabilistic law (Sect. 3), has been discussed by Roger Rosenkrantz (Synthese, 1980) and Ilkka Niiniluoto (Truthlikeness, 1987, Ch. 11.5). Their basic proposal is to measure the distance between two probabilistic laws by the Kullback–Leibler notion of divergence, which is a semimetric on the space of probability measures. This idea can be applied to probabilistic laws of coexistence and laws of succession, and the examples may involve discrete or continuous state spaces (Sect. 3). In this paper, these earlier studies are elaborated in four directions (Sect. 4). First, even though deterministic laws are limiting cases of probabilistic laws, the target-sensitivity of truthlikeness measures implies that the legisimilitude of probabilistic laws is not easily reducible to the deterministic case. Secondly, the Jensen-Shannon divergence is applied to mixed probabilistic laws which entail some universal laws. Thirdly, a new class of distance measures between probability distributions is proposed, so that their horizontal differences are taken into account in addition to vertical ones (Sect. 5). Fourthly, a solution is given for the epistemic problem of estimating degrees of probabilistic legisimilitude on the basis of empirical evidence (Sect. 6). pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2021. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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