Abstract
Reason in science has proven a more subtle and complex business than even its subtle masters supposed.
Friedman, M. (1992) ‘Kant on Causal Laws and the Foundations of Natural Science’ in Guyer, P. (1992) (ed.), The Cambridge Companion to Kant, Cambridge, Cambridge University Press.
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Notes
To some extent I here caricature my earlier self, since I spent the decade of the 1970s more preoccupied with trying to think through what a naturalist position was than with a detailed account of methodology. I have spent time in the ‘80s partially repairing this defect, e.g. through Hooker (1987), Chap. 8 and (1989b), and, from a different, complementary angle, Hooker (1989c), (1991a) and, from a still larger, complementary perspective in Hahlweg and Hooker (1989). All this while my original work on Bohr, Hooker (1972), lay unused, until its confrontation with these efforts in (1991b). This paper is a direct extension of those latter ideas, sparked by hearing Michael Friedman lecture on Kant (see Friedman 1992).
Here and in later acronyms I follow the labelling of Butts (1986), which is based on the original German title.
Reichenbach interprets this as equivalent to Einstein’s later principle of general covariance for physical laws and holds that it is certainly one which Kant would have held a priori since from ‘the Kantian point of view, according to which space and time are only forms of order and not part of nature such as matter and forces, this principle is actually obvious’ as it merely requires ‘that space have no physical properties, that the law be a function of the distribution and the nature of masses, and that the choice of the reference system have no influence upon the process’. (Reichenbach, 1965, 8) By comparison, the principle of inertial relativity ‘appears now as a special case’ because the actual dynamical magnitudes (forces, accelerations) are what it preserves invariant and which these are ‘only experience can teach’ (Idem).
The summary to follow is provided in Hooker (1991a), extracted from Friedman (1986), Harper (1986), (1989), (1990), Okruhlik (1989), Stein (1967), (1990a, and b) and Wilson (1970).
Consider objects C, S with C attracting S with a force G, thereby producing (L 2) an acceleration a s = G/m s . Then by L 3, S attracts C with a force -G producing an acceleration a c = m c a c + m s a S = 0 and so d/dt(m c v c + m s v s ) = 0, where v c , v s are the momentary velocities of C, S respectively. Thus, m c v c + m s v s is constant, that is d/dt(m c sc + m s s s ) is constant, so that the frame of reference whose centre is m c s c + m s s s has 0 acceleration. This is the centre of mass frame of reference.
For references see note 4 and below. I am particularly indebted to Stein and Harper for insight into Newton’s analysis in Principia Book 3.
Significantly, this requirement has its limits for all planets, and particular limits in the cases of Uranus, the moon and mercury; all these need explanations, the first two by inter-planetary perturbations — see M5 below, the third through the complexities of n-body dynamics and the fourth through relativistic theory.
One might introduce the radial form of the law and its inverse square variation as instances of two further parameters which may in principle have other values, but these values are shown to be cross-situationally invariant. A parameter that corresponds to a universal constant is no genuine parameter. So the proposed parameters here are ineffective or inoperative. Later on when a wider range of phenomena are studied these parameters again become of importance and their values are indeed shown to vary (the electromagnetic force is no longer radial, the nuclear force is not inverse square, etc.).
The classic example is the inverse square value of the radial variation of LUG which Newton shows to be measured by the degree of precession of orbits. But the geometrical form of the law is equally determined from the data on the closedness of the orbits, the mass of the sun is shown to be cross-situationally invariant among the motions and so on. (The only remaining parameters not mentioned are those of the positions and times themselves and these are directly determined as part of the original data.) Moreover, small variations in the values of any of these quantities gives rise to measurable variations in data. Even departures of a few percent from inverse square variation in LUG, e.g., is shown to give rise to measurable precession.
By an appropriate description of the phenomena is meant the fulfilment of two further conditions: (a) Well attested phenomena such as Kepler’s laws (KL) should still be shown to hold as an approximation, either an approximation which is within the ascertainable error range of the measurement procedures for the original data or an approximation which can be extracted from the finer data as a legitimate base case, i.e., where the data can be represented as the base case approximation together with small perturbations or variations on it. (b) There is convergence upon the two conditions (C1) and (C2) as successive approximations are removed from the system idealisation, and hence the fundamental values of theoretical parameters (inverse square, mass of sun, etc.) remain cross-situationally invariant across the de-idealisation process. In sum, there must exist a principled decomposition of mechanical systems, such that the proposed idealisation is the principled zero-order approximation and hence that there exists a principled calculation procedure for reversing the idealisation, i.e. for systematically introducing first and higher order corrections such that the proposed laws and their parameters remain appropriately invariant across the application of corrections. In the terminology of Hooker (1992), they are simplifying idealisations.
See Hooker (1987) Chap. 8, refined in Hooker (1989b). These treatments contain a critique of an earlier attempt by Friedman at a characterisation of the relation between unification and explanation and my own attempt to establish a broader context for the issue.
As both Butts and Friedman emphasise, this certainly precludes any simple reading of Table 1 as a straight deduction.
In the terminology of Appendix 1, we can be sure that nature [n] falls under the concepts of Nature [N] and instantiates its laws.
Those concerned with pursuing this task will want to start with the neo-Kantian Cassirer (1953). I leave that project to others.
He allows technical concepts of classical physics to be added to the commonsense ones, e.g., and there are clear difficulties for a Bohrian account of interacting but unobserved macroscopic objects; see the discussion in Hooker (1972).
One of the deeper appreciations of Bohr from this point of view is that of Petersen (1968). Recalling that for Bohr language was concerned with unambiguous description, i.e., with the use of unambiguous concepts, in Hooker (1972), note 104, I wrote as follows: “Petersen characterises the traditional mode of philosophising as the ‘ontological mode of philosophising’ and contrasts it to Bohr’s position ... Moreover, in the light of the preceding remarks concerning Bohr’s Kantianism, Petersen’s recollections of such Bohrian remarks as, ‘We are hanging in language. We are suspended in language in such a way that we cannot say what is up and what is down’ (Petersen 1968, p. 188) take on a less obscure meaning and assume their full Kantian significance”. However, we can also note that subject/object separation is achieved in Newtonian mechanics not, as Petersen and many others suggest, because interactions with measuring instruments can be made small (often they cannot be), but because the theory permits the construction of unique counter-factual conditional claims concerning what the observed system state would have been in the absence of interaction. The ‘indivisible quantum of interaction’ renders such constructions impossible, as Bohr saw.
The quotes from Bohr to which I have limited myself tend to treat the first of these more thoroughly, but the second is also present and further references could be given. And today we have a formal proof that no strengthening of quantum descriptions, i.e., of the quantum state, can be made consistently with the quantum formalism; see e.g. the papers in Hooker (1975/79). As I wrote in (1972), it is essentially this Kantian philosophical methodology, with its emphasis on the conditions for unambiguously communicable description of empirical experience and the construction of knowledge on its basis with its ‘anti-metaphysical’ orientation (see Butts 1986c), that give Bohr the superficial appearance of being operationalist (Hooker, 1972, 171).
Considering that fundamental progress in physics has been deeply related to generalisation in this sense, see Hooker (1991b), it is remarkable how little attention is devoted to it. Honner (1987), the most Kantian of recent Bohr commentaries, has almost nothing explicit to say about it, while e.g. Folse (1985) and Murdoch (1987) give some elementary technical account of it but don’t explore its wider significance.
But note that if the ‘quantum logic’ view prevailed quantum theory would be reached by expanding the category of logic in a similar way to that of geometry — interestingly, Reichenbach early on tried just such a generalisation, 3-valued logic, but it can be shown not to be adequate. (See e.g. Hooker, 1975/79, Holdsworth/Hooker, 1983, and references). There he also introduces a term, ‘inter-phenomena’, to stand for what in reality connects the truth-making conditions of true propositions; this is close to Kant’s ‘Ding-an-sich’ (thing-in-itself) and something Bohr rigorously excluded from well-defined communication. (But see also Butts, 1986c, on Kant on metaphysics).
Material in the remaining sections has been adapted and abbreviated from Hooker (1991 b).
On these objections see Hooker (1972), section 14. The structure of quantum mechanical conditional probabilities has e.g. this striking(ly non-classical) feature: From a determinate value for a single observable the transition probabilities for all other determinant values for all other observables uniquely follows. Such features tend to be ignored in philosophical commentaries. In Hooker (1989a) I provide a list of nine such features (see also Hooker, 1991 b, note 18).
The new breed of Bohr books — see note 18 references plus Faye (1991) — have relatively little to say about any of these problems, yet they are philosophically more astute than the earlier discussions of physicists; the acquisition of conceptual sophistication is evidently matched by a lowering of intuitive feeling for the physics. Cf. also note 21.
An argument for this negative decision in the case of Bell’s theorem is given in Hooker (1989a). See also the review of recent writing on quantum field theory in Hooker (1990).
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Hooker, C.A. (1994). Bohr and the Crisis of Empirical Intelligibility: An Essay on the Depth of Bohr’s Thought and Our Philosophical Ignorance. In: Faye, J., Folse, H.J. (eds) Niels Bohr and Contemporary Philosophy. Boston Studies in the Philosophy of Science, vol 153. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8106-6_8
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