Constructivism in Science
| Scientific Paper | |
|---|---|
| Title | Constructivism in Science |
| Read in full | Link to paper |
| Author(s) | Mogens True Wegener |
| Keywords | Poincaré, conventionalism, constructivism, Eddington, Milne, kinematic relativity, philosophy of science, group theory |
| Published | 1994 |
| No. of pages | 17 |
Read the full paper here
Abstract
Presented at the 1st Internat. Poincare Conf., 1994, International Academy for the Philosophy of Science.
Revised Version of Paper Published by ACERHP 1996, 'Philosophia Scientia', cahiers special.
The merits of Poincare as one of the greatest mathematicians of all times are globally acknowledged, but the value of his conventionalist theory of science is still greatly underestimated, and his contributions to physics and its philosophy have unjustly fallen into oblivion. The aim of the present paper is to stress the importance of Poincare to physical theory and the theory of physics by hailing him as the principal figure in the interplay between classical philosophy and modern cosmology.
Overview
The paper, with its full subtitle "The Views of Poincaré, Eddington, and Milne", was delivered at the first international Poincaré conference in 1994 and revised for the wiki archive in 2010. It is a work in the history and philosophy of science rather than a physical derivation: Mogens True Wegener sets out to rehabilitate Henri Poincaré's theory of science and to place him as the "central link" in a line running from Kant's Critique of Pure Reason to two non-standard cosmologies that are usually treated as incompatible — Eddington's fundamental theory and Milne's kinematic relativity.
The label the paper argues for is not the usual one. Poincaré's position is conventionally called conventionalism; Wegener, following Jerzy Giedymin, holds that constructivism covers it better. The point of the relabelling is that Poincaré is not a nominalist for whom theory choice is arbitrary. His position "assumes an empirical basis amounting to the existence of a kind of observational invariant beneath all theoretical conventions", knowable "up to the structural isomorphism of rival theories". What changes between successive theories is ontology and metaphor; what persists is formal structure. This, Wegener argues, is what makes real progress compatible with radical theory change — and it is also the modern, group-theoretic descendant of Plato's idea of harmony between mind and nature. The departure from the mainstream account is direct: Poincaré is credited with having had special relativity entire, and "before Einstein", the difference being one of emphasis; and the paper holds that Einstein's dissolution of distant simultaneity follows not from the topology of spacetime but from a particular conventional choice of metric.
The argument
From Kant to Plato
Kant's Copernican revolution divided reality-in-itself from reality-to-us, and grounded necessary knowledge of the latter in the collaboration of pure reason with pure intuition — the framework of time and space. Wegener notes that Kant's a priori argument for the inverse-square law of gravitation can be sustained if gravitational force is describable in flat vectorial 3-space, putting it "on a par with that leading to the so-called Olbers' paradox".
Poincaré broke with this. Because every attempted proof of the parallel axiom had failed, he denied that the structure of space can be demonstrated a priori. He allowed a pure intuition of space but held it "devoid of any formal structure, hence definable in negative terms only" — a position Wegener aligns with Plato's space as "the uterus of becoming", formless and causally neutral. Poincaré rejected the Cartesian aether-hypothesis for Leibniz's reason: abstract space is relational, not substantial. What survives of Kantianism, on this reading, is not geometry but "the active rôle of the intellect in the reconstruction of the world".
Poincaré: theories as constructions
Science on Poincaré's account is constructive and descriptive at once. It concerns not particular facts but classes of facts, "the order or structure of facts, not their essence or substance". Scientific facts are common-sense facts restated in the artificial language of mathematics. Wegener is careful to record the limit Poincaré set on his own doctrine: "it is a gross misunderstanding to believe that the scientist creates his own facts; all that is manufactured in a fact is the formal language in which it is enunciated, and it never depends on the scientist whether his prediction of a fact is fulfilled."
Geometry is treated as the formal study of groups, its premisses chosen for fruitfulness in describing physics; a continuum has no intrinsic metric, so metrical congruence is conventional. The conventionalism does not extend to arithmetic, which Poincaré grounded in a strict a priori intuition of whole numbers and mathematical induction — indeed he insisted the consistency of geometry be evaluated relative to arithmetic. Wegener records Poincaré's threefold classification of hypotheses: formal principles (always conventions, a priori in a relative sense); inductive generalisations (empirical laws, revisable, but promotable to the status of principle); and realistic interpretations (neutral if they leave the formal relations intact — "the same geometry may result, whether we begin with points, or lines, or planes"). "The physics of our own time is the physics of the principles," said Poincaré; any law can be split into an a priori principle and an a posteriori law. But the splitting cannot go all the way: "if a principle is wholly exempt from being contradicted by experience, it ceases to be informative".
On special relativity, Wegener follows Keswani. Poincaré credited Lorentz's local time with saving relativity, and Hendrik Lorentz in turn praised Poincaré for stating the transformations in their most convenient form ahead of Einstein and Minkowski. Poincaré took Lorentz's invariance requirement and produced a Lorentz-invariant action-at-a-distance theory of gravitation; North's judgement is quoted that had sympathy not so decisively favoured a field theory, "Poincaré's memoirs might well have become a turning point in the history of the subject". Stump's objection is stated fairly: a consistent conventionalism must give a relational account of both gravitation and inertia, and Einstein's spacetime theory of gravitation looks like an effective disproof of pure relationalism. Roxburgh and Tavakol are cited for a family of consistent gravitational theories that cannot be geometrised in a Riemannian manifold but only in a Finsler framework.
Eddington: pure numbers from epistemology
Eddington's principle, in Whittaker's formulation, is that the pure numbers relating the constants of nature can be calculated by a priori mathematical deduction from epistemological principles — knowledge prior to measurement, though not prior to exact specification of the measuring procedure. Wegener presents the epistemology behind it: physics rests on pointer-readings, primary (intensities), secondary (location in time and space) and tertiary (experimental context); lengths and durations are therefore "not properties which inhere in the external world: they are the relations of things in the external world to a particular observer". Since all observable variety comes from relations, the intrinsic natures of the relata reduce to sameness — whence Eddington's implication that there is only one kind of fundamental particle, the observed variety being "a manifestation in disguise of this one". The recognition that all physical knowledge is structural was claimed by Eddington to dissolve the dualism of consciousness and matter. His E-number calculus, a generalisation of Hamilton's quaternions, is presented by analogy with Hamilton's own Kantian reading of quaternion algebra as "the science of pure time": Eddington's algebra is "the science of space-time". Yolton's demurral is recorded — that Eddington made no real a priori deduction. The Alternative Natural Philosophy Association, with Bastin, Kilmister, Parker-Rhodes and McGoveran, is noted as the continuing tradition.
Milne: deduction from a signalling observer
Milne built a model universe of uniformly dispersed fundamental particles satisfying a cosmological principle of isotropy, and showed that superposing arbitrarily moving accidental particles on that substratum produces spontaneous accelerations — "in this way he fulfilled the relationalist programme of Poincaré". His method starts from a single observer's awareness of a temporal sequence and coordinates defined by radar signals and clocks. He claimed to deduce the inverse-square law of gravitation and its sign from premisses that reduce gravitation to inertia. The justification offered is historical: geometry passed from an "Egyptian inductive phase", in which the Pythagorean relation was a brute fact discovered by measurement, to a "Greek deductive phase" in which axioms are definitions and theorems need no verification. Milne's wager is that dynamics can make the same passage, and "the extent to which the process can be carried out is simultaneously our measure of the degree to which we can regard the universe as rational". Wegener notes the descendants of the radar method in Whitrow, Walker, Törnebohm, Schutz and Bondi's k-calculus, and that Robertson's and Walker's derivations of the RW metric rest on Milne-inspired assumptions. He closes with the observation that Milne's "output appears to exceed his input", and with Milne's own view that cosmology presupposes a rationality of the universe for which it can give no reason except a rational creator.
Assessment
The paper's strength is its central historical thesis, which is genuinely illuminating and rarely made: that Poincaré's constructivism, Eddington's a priori derivation of the constants, and Milne's kinematic relativity are three moments of one programme, and that the connecting thread is the doctrine that physical knowledge is knowledge of structure up to isomorphism. The distinction Wegener draws between conventionalism and constructivism is well earned and defended with the right quotation — Poincaré's insistence that the scientist does not manufacture facts, only the language in which they are stated, is exactly what separates his position from the radical conventionalism he himself denounced. The treatment is also scrupulous about counter-evidence: Stump's objection about relativising acceleration and Yolton's verdict that Eddington performed no genuine a priori deduction are both allowed to stand rather than being argued away.
The difficulties are those of the essay form the author chose — he says at the outset he will draw "with coloured brush and sweeping gesture", and the sweep sometimes outruns the argument. Three points bear noting. First, the priority claim about special relativity is asserted through Keswani rather than argued from Poincaré's 1905–6 papers, and it passes over the substantive difference: Poincaré retained a preferred frame and treated local time as a calculational device, whereas the kinematic reinterpretation of simultaneity for all frames is precisely what he did not commit to. To say the difference is "one of emphasis" understates it. Second, the suggestion that Einstein's dissolution of distant simultaneity "depends on his particular (conventional) choice of space-time metric" is left as a belief about what Poincaré would have welcomed; the paper offers no construction of the alternative metric, and any such construction must still reproduce the null-cone structure that the Michelson–Morley and Kennedy–Thorndike results, and modern one-way-speed constraints, fix to high precision. Third, the Eddington section reports the programme without confronting its record: the numerical values Eddington deduced for the fine-structure constant and the number of particles in the universe do not agree with the measured fine structure constant, and a philosophical defence of a priori derivation is weakened, not strengthened, by leaving that unmentioned. Wegener's own framework — that theories are answerable to an observational invariant — is what supplies the standard he does not apply here.
None of this touches the paper's main service, which is to keep a serious philosophical tradition in view. Wegener writes as a historian of ideas making a case for a road not taken, and the case is worth hearing: the question whether the metric of spacetime is discovered or stipulated has never been settled by experiment alone, and the paper states it more clearly than most.