Abstract
With this chapter we begin the development of a view about those scientific laws each of which has associated with it, a background that consists either of some theory, or a loosely knit collection of statements that involves various physical magnitudes that are involved in the expression of the law. We shall refer to the latter kind of background as the theoretical scenario for the law.
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Notes
- 1.
In our discussion of the difference between laws and accidental generalizations Chap. 7), it was assumed that there was some explanation of the instances of laws (and in our discussion of Braithwaite’s account (Chap. 8) it was assumed by him that laws were always embedded in some deductive system. Here we assume something weaker: a theory or a theoretical scenario for each law, that provides a background of physical magnitudes, but we do not assume that it provides enough information to guarantee an explanation or even a deduction of the law.
- 2.
We will present a more exact discussion below.
- 3.
E.J. Dijksterhuis, The Mechanizaton of the World Picture, Tr. by C. Dikshoorn, Oxford University Press, 1961.
- 4.
It is a false generalization, which deductively yields Kepler’s second law about equal areas being swept out in equal times. It says that if a planet moves on a circle with center C, and r is the radius from the planet to a point E off the center C (the center of an eccentric circle), then the velocity of the planet is proportional to the inverse of r. Kepler seems to have thought that this law holds even when planets move on ellipses.
- 5.
Dijksterhuis, 310.
- 6.
Roughly, that the distance traversed by a falling body is proportional to the square of time elapsed.
- 7.
Dijksterhuis (339).
- 8.
Cf. the incisive discussion by J.C. Maxwell “On Ohm’s Law”. Reprinted from the British Association Report, 1876, reprinted in The Scientific Papers of James Clerk Maxwell, ed. W.D. Niven, MA., FRS. Two volumes bound as one volume. Volume 2, pp. 533–537.
- 9.
The Nature of Thermodynamics, Harvard U. Press 1941, Harper Torchbooks 1961, p.17.
- 10.
Philosophical Concepts in Physics, Cambridge University Press, 1998, p.290.
- 11.
The Elements of Classical Thermodynamics, Cambridge University Press, 1957, p. 29.
- 12.
Mathematical Foundations of Thermodynamics, 1964 Macmillan, p.17.
- 13.
Giles, 1964, p.22.
- 14.
Giles, 1964, p.24. p.112).
- 15.
Cf. Foundations of Measurement, volume I, Additive and Polynomial Representations, D. H. Krantz, R. Duncan Luce, Patrick Suppes, and Amos Tversky (1971, Academic Press), 2007, Dover Press. vol 1, p. 112.
- 16.
“The mathematics of physical quantities. Part I: Mathematical models for measurement. Part II: Quantity structures and dimensional analysis”. American Mathematical Monthly, 1968, 75, 115–138, 226–256.
- 17.
Foundations of Measurement, volume I, Additive and Polynomial Representations, D. H. Krantz, R. Duncan Luce, Patrick Suppes, and Amos Tversky. (1971, Academic Press), 2007, Dover Press, p.459.
- 18.
The functionals on the elements of a vector space V are members of the dual vector space V^. There is an important connection between functionals on a magnitude space and laws which we shall explain in a later chapter.
- 19.
Aristotle’s Posterior Analytics, Oxford University Press, 1975, Tr. J. Barnes, PA, A13. 78a23-78b15., and quoted in David-Hillel Ruben, Explaining Explanation, Routledge, London, p. 105.
- 20.
David-Hillel Ruben, Explaining Explanation, Routledge, 1992, p. 106.
- 21.
Aristotle, Posterior Analytics, in Prior Analytics and Posterior Analytics, tr. by A.J. Jenkinson and G.R.G. MurePart, Digireads.com Publishing, 2006, §, slightly modified.
- 22.
We shall give a precise definition of the relation of subsumtion in Chap. 12.
- 23.
The Cartesian product of two sets A and B is the set of all the ordered pairs <x, y> with x and y being members of A and B respectively.
- 24.
That is, we think that the very states themselves that are modal possibilities, (analogoous to the idea that it is the elements of a probability sample space that indicate the possibilities). Each of these states is a modal possibility in a structure. There are examples of what we call modal entities, rather than modal operators. We also will show the connection of these possibilities to an associated modal operator.
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Koslow, A. (2019). Theories, Theoretical Scenarios, Their Magnitude Vector Spaces and the Modal Physical Possibilities they Provide. In: Laws and Explanations; Theories and Modal Possibilities. Synthese Library, vol 410. Springer, Cham. https://doi.org/10.1007/978-3-030-18846-7_10
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