Abstract
The aim of this work is to show that for some theoretical terms, i.e. terms which are not definable by using only empirical terms, the possibility exists of formulating definitions which can be considered empirical in a weaker sense. This will be shown on the example of the definition of the term ‘genotype’ in Mendelian genetics.
A shortened version of an article first published in Studia Logica 15 (1964). Translated by S. Wojnicki.
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References
J. H. Woodger, Biology and Language, Univ. Press, Cambridge 1952
M. Przełęcki, ‘On the Concept of Genotype’, in: Form and Strategy in Science, (edited by John R. Gregg and F. T. C. Harris), D. Reidel, Dordrecht 1964.
The example has been taken from S. Skowron’s handbook Zarys nauki o dzie-dziczności (Outline of the Science of Heredity), Wiedza — Zawód — Kultura, Krakow 1947, p. 20.
The example is taken from the same source, p. 104.
J. Neyman, First Course in Probability and Statistics, H. Holt and Co., New York 1950. In the 3rd chapter of this book, entitled Probabilistic Problems of Genetics (pp. 96–163), Neyman presents the axioms and soms theorems of simplified Men-delian genetics, as an example of the application of probabilistic calculus to a concrete science. The theorems presented in this paper, and denoted as T2, 3,4, 5, 6, correspond to the theorems in Neyman’s book. On the other hand, the axiomatics adopted here differs considerably from that formulated by Neyman. Some of Neyman’s axioms have been left out here because of the restriction to problems of inheriting genotypes for only one sort of properties. The modification of Neyman’s Axioms 1, 4 and 5 consists in that Neyman’s axioms concern some regularities in the division and joining of pairs of alleles in connection with the division of cells into gametes and their joinign into zygotes; therefore the probabilities of inheriting definite genotypes with respect to the genotypes of the pair of parents are calculated in the sets of gametes of the parents organisms; further, considering questions of heredity in populations of organisms Neyman utilizes probabilities calculated in these populations, i.e. in classes of organisms. In the theory presented here all probabilities are calculated in classes of organisms. Moreover we take here as axioms some assumptions tacitly adopted by Neyman in the course of deriving the theorems, as well as those adopted by him only for some situations (panmixia and the independence of genotypes from sex). Finally, we adopt here an axiom establishing certain relations between genotypes and observable properties of organisms which is indispensable for deriving empirical definitions of genotypes.
J. Neyman, Mathematical Statistics and Probability, Washington 1952.
Karl R. Popper, ‘The Propensity Interpretation of Probability’, British Journal for the Philosophy of Science X (1959).
J. Mehlberg, ‘Positivisme et science’, Studia Philosophica III (1948).
H. Mehlberg, The Reach of Science, Toronto Press, 1958.
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© 1977 PWN - Polish Scientific Publishers - Warszawa
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Mortimer, H. (1977). Probabilistic Definition on the Example of the Definition of Genotype. In: Przełęcki, M., Wójcicki, R. (eds) Twenty-Five Years of Logical Methodology in Poland. Synthese Library, vol 87. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1126-6_21
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DOI: https://doi.org/10.1007/978-94-010-1126-6_21
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