Kolmogorov's account in his  of an absolute probability space presupposes given a Boolean algebra, and so does Rényi's account in his  and  of a relative probability space. Anxious to prove probability theory ‘autonomous’. Popper supplied in his  and  accounts of probability spaces of which Boolean algebras are not and  accounts of probability spaces of which fields are not prerequisites but byproducts instead.1 I review the accounts in question, showing how Popper's issue from and how (...) they differ from Kolmogorov's and Rényi's, and I examine on closing Popper's notion of ‘autonomous independence’. So as not to interrupt the exposition, I allow myself in the main text but a few proofs, relegating others to the Appendix and indicating as I go along where in the literature the rest can be found. (shrink)
Teddy Seidenfeld recently claimed that Kolmogorov's probability theory transgresses the Substitutivity Law. Underscoring the seriousness of Seidenfeld's charge, the author shows that (Popper's version of) the law, to wit: If (∀ D)(Pr(B,D)=Pr(C,D)), then Pr(A,B)=Pr(A,C), follows from just C1. 0≤ Pr(A,B)≤ 1 C2. Pr(A,A)=1 C3. Pr(A & B,C)=Pr(A,B & C)× Pr(B,C) C4. Pr(A & B,C)=Pr(B & A,C) C5. Pr(A,B & C)=Pr(A,C & B), five constraints on Pr of the most elementary and most basic sort.
In the French-language literature on education, the notion of the inheritor, popularized by Bourdieu and Passeron’s 1964 book, is still commonly used to evoke the ideal-typical student from the most socially advantaged backgrounds. But does it truly capture what is at stake today in the reproduction of social inequalities at school? Several societal and educational changes prompt us to take a new look at the theories and concepts used to explain and interpret the modes in which social inequalities reproduce themselves. (...) To condense and evoke what characterizes today’s privileged student, we have extended the metaphor of the ‘insider’, asking ourselves what are the adjustments this new language would suggest for the theory of social reproduction. The issue of access to elite institutions in France is an empirical illustration of the heuristic potential of such an approach. (shrink)
Consider a language SL having as its primitive signs one or more atomic statements, the two connectives ‘∼’ and ‘&,’ and the two parentheses ‘’; and presume the extra connectives ‘V’ and ‘≡’ defined in the customary manner. With the statements of SL substituting for sets, and the three connectives ‘∼,’ ‘&,’and ‘V’ substituting for the complementation, intersection, and union signs, the constraints that Kolmogorov places in  on probability functions come to read:K1. 0 ≤ P,K2. P) = 1,K3. If (...) ⊦ ∼, then P = P + P,K4. If ⊦ A ≡ B, then P = P.2. (shrink)
A lot of attention has been devoted to the study of discoveries in high energy physics, but less on measurements aiming at improving an existing theory like the standard model of particle physics, getting more precise values for the parameters of the theory or establishing relationships between them. This paper provides a detailed and critical study of how measurements are performed in recent HEP experiments, taking examples from differential cross section measurements with the ATLAS detector at the LHC. This study (...) will be used to provide an elucidation of the concept of event used in HEP, in order to determine what constitutes an observation and what does not. It will highlight the essential place taken by theory-ladenness in order to produce observational facts, and will show how uncertainty and sensitivity estimates constitute an operational approach to robustness, inside the practice of science, avoiding potential circularity problem traditionally implied by theory-ladenness. This is in contrast to robustness analyses typically considered in the literature. A careful analysis of systematic uncertainty estimates and of statistical tests used to set empirical conclusions from the observations will however demonstrate that quantitative statements obtained from these statistical tests cannot be more than simple guiding arguments for the production of knowledge, but do not determine it. This indicates that the frontier between theory and observation is blurry and that the dichotomy theory-experiment should be revised. (shrink)
DEALING INITIALLY WITH QC, THE STANDARD QUANTIFICATIONAL CALCULUS OF ORDER ONE, THE AUTHOR COMMENTS ON A SHORTCOMING, REPORTED IN 1956 BY MONTAGUE AND HENKIN, IN CHURCH'S ACCOUNT OF A PROOF FROM HYPOTHESES, AND SKETCHES THREE WAYS OF RIGHTING THINGS. THE THIRD, WHICH EXPLOITS A TRICK OF FITCH'S, IS THE SIMPLEST OF THE THREE. THE AUTHOR INVESTIGATES IT SOME, SUPPLYING FRESH PROOF OF UGT, THE UNIVERSAL GENERALIZATION THEOREM. THE PROOF HOLDS GOOD AS ONE PASSES FROM QC TO QC asterisk , THE (...) PRESUPPOSITION-FREE VARIANT OF QC. TURNING NEXT TO QC subscript = , THE STANDARD QUANTIFICATIONAL CALCULUS OF ORDER ONE WITH '=', AND TO THE PRESUPPOSITION-FREE VARIANT QC subscript = OF QC subscript = , THE AUTHOR NEXT ESTABLISHES THE LEMMAS NEEDED THERE TO PROVE UGT. THAT, GIVEN FITCH'S ACCOUNT OF A PROOF FROM HYPOTHESES, UGT HOLDS FOR QC subscript = WAS ARGUED IN LEBLANC'S "TRUTH-VALUE SEMANTICS", BUT THE PROOF WAS IN ERROR. (shrink)