Pythagoras proved that the world of sound is governed by exact numbers, and he went on to prove that the same thing is true of the world of vision.
We do not understand why the world of mathematical truth is accessible to us.
The Reification of Physical Laws
The epistemological status of the so-called laws of physics can be usefully clarified in terms of the interpersonal system of modality, in which modalisation (probability, usuality) is distinguished from modulation (obligation, inclination). Congruently, the laws of physics are best understood as propositions — descriptions held with high interpersonal certainty — in which the experiential content is construed with very high degrees of modalisation: high probabilities or high usualities.
However, when such descriptions are taken as laws in the sense that the universe obeys them, the construal becomes metaphorical — specifically, interpersonally metaphorical — and this metaphor needs to be unpacked to avoid epistemological confusion. In this reinterpretation, modalisation is misread as modulation, i.e., as obligation.[1] A description of what usually or probably happens is re-presented as a command that must be followed.[2] The clause type has not changed — it remains a proposition — but its interpersonal meaning has: the indicative statement has been metaphorised as if it were an imperative.
Mistaking this metaphor for a congruent rendering leads to ideational inconsistencies about the epistemological status of the laws of physics. Two such inconsistencies are especially prominent.
The first equates the laws of physics with the phenomena they describe. Here, the model and the modelled are treated as one and the same — with one copy “out there” in the observable world and another copy “in the heads of physicists.” This leads to an apparently profound, but ultimately misplaced, sense of wonder: that humans are somehow able to understand the universe.[3] But understanding is not a miracle. It is a function of recognition — the brain’s capacity to build consistent models of experience.
The second inconsistent stance takes the metaphor at face value: that the physical laws govern the universe. This assigns to the laws a governing role that transcends the phenomena they describe. Abstract relations, which are part of the modelling system, are projected into a transcendent realm beyond the material universe — effectively a Platonic heaven of pure form.[4] Since these laws are imagined as both outside the universe and in control of it, they inherit the role of deity — occupying the same explanatory niche that gods once filled.[5]
Notes
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Obligatory modulation (e.g. x must y) is congruent with the experiential clause type of passive causation (e.g. x is required to y). See Halliday & Matthiessen (2004: 523).
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This metaphor also pervades mathematics, physics’s primary modelling tool. Descriptions such as “consistently describable by numbers” are reinterpreted as “governed by numbers.” For example, Bronowski writes:
Pythagoras proved that the world of sound is governed by exact numbers, and he went on to prove that the same thing is true of the world of vision.
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This confusion extends to mathematics. As Ruelle (1993: 161) puts it:
We do not understand why the world of mathematical truth is accessible to us.
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Before General Relativity, time and space were similarly construed as transcendent — with the universe seen as being “in” space and time, rather than space-time being the dimensions of the universe itself.
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For example, Einstein’s famous metaphor: God (the laws of physics) does not play dice — a personification of the laws as a rational agent rejecting randomness.