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Lecture18b - PHIL250 Lecture18 Supplement WM Kallfelz Page...

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1 PHIL250 Lecture18 Supplement Page 1 11/2/2007 WM Kallfelz Carl Hempel: “Inductive-Statistical Explanations” Recall (from “Two Basic Types of Scientific Explanation”): 1. The Deductive-Nomological Model (D-N) and the Inductive-Statistical 1 (I-S) models are two fundamentally different kinds of models of scientific explanation. 2. These models (which Hempel assumed were exhaustive , i.e. exhausted all the fundamental kinds of scientific explanation 2 ) are explications ; i.e. serve as 1 Hempel also discusses a special case of statistical explanations which are deductive (D-S). However, recall from today’s lecture that what distinguishes D-S from I-S models is the contingent issue concerning whether or not all the premises comprising the explanans happen to be true (for the realist) ( CC1998 , 716) or empirically adequate/instrumentally reliable, etc. (one might add, for the anti-realist.) The issue of truth being a contingent one primarily because theories of explanation for Hempel and others are primarily based on logical and epistemological issues (recall Lecture I ). While those like Hempel who argue from the logical empiricist tradition (which sharply divides contexts of discovery/justification as well viewing scientific theories and bodies of knowledge primarily in terms of sentences characterized by a particular logical syntax ) want to remain metaphysically agnostic concerning issues of truth. Stated another way, in terms of the structure of a scientific explanation, notions like “truth” and similar predicates (anti-realist analogues) are semantic , and hence contingent to the syntactic approach to scientific theories and knowledge. By semantics I am referring to the strictly logical sense in which predicates like ‘truth’ are characterized in terms of an interpretation , which is itself a mapping from the formal language Λ (conceived of as a ‘domain’) to something outside of Λ , i.e. the ‘range’. For example, in the ordinary binary interpretation of ‘truth’ such an interpretation is characterized as a mapping Π : Λ { , T } (or equivalently { 0 , 1} ) where the ‘range’ is a two-valued set denoting the ‘falsum,’ and ‘verum’ conceived as a binary “filter.” It’s important however to keep in mind that the syntactic view focuses just on the formal language Λ itself, whether regimented by FOPL or otherwise, since Λ is conceived of purely as a syntactic structure . In the case of FOPL its ‘sentences’ ϕ (or well-formed formulae ( wffs )) are generated by primitive constants ( a,b,c …), logical variables ( x,y,z,… ), quantifiers ( , ), logical connectives ( , , , ¬ , ) as well as by deductive consequence |- , where |- itself is syntactically characterized by rules of inference. Recall from Lecture II : footnote 13, p. 6: FOPL has 14 rules of inference: 6 introduction rules and 6 elimination rules (pertaining to , , , ¬ , , ) as well as EFSQ and DN where EFSQ means that any proposition can follow from a premise list containing a contradiction
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