The Regularity Approach to Comparativismabout Dynamical �antities

Niels Martens

PoP-Grunch Oxford

Slides available athttp://users.ox.ac.uk/~corp2044

11 Feb 2016

Outline

1 The Regularity ApproachEmpiricism about laws of natureRegularity RelationalismRegularity Comparativism

2 ResponsesIt doesn’t workExplanatory CircularitySeparabilityEliminativism

Outline

1 The Regularity Approach

2 Responses

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Humean Supervenience

“ laws are parasitic on occurent factsEarman, 1984”

“ Humean supervenience is named in honor of the greater [sic] denier of nec-essary connections. It is the doctrine that all there is to the world is a vastmosaic of local ma�ers of fact, just one li�le thing and then another. ...We have geometry: a system of external relations of spatio-temporal dis-tances between points. Maybe points of spacetime itself, maybe pointsizedbits of ma�er or aether fields, maybe both. And at those points we havelocal qualities: perfectly natural instrinsic properties which require noth-ing bigger than a point at which to be instantiated. For short: we have anarrangement of qualities. And that is all. All else supervenes on that.

Lewis, 1986”Niels Martens Regularity Comparativism 4/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Unpacking Humean Supervenience I

1. Seperability

“The complete physical state of the world is determined by ... theintrinsic physical state of each spacetime point (or each point-likeobject) and the spatio-temporal relations between those points.”

(Maudlin, 2007)

Informal Gloss: “[A]ll fundamental properties are [intrinsic]properties and ... spatio-temporal relations are the onlyfundamental external physical relations.”

Niels Martens Regularity Comparativism 5/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Unpacking Humean Supervenience II

1.a. Strong Absolutism about all non-spatiotemporal quantities

1.a.1 AbsolutismIntrinsic quantities ground the ratios between those quantities.

1.a.2 �antity PrimitivismThese quantities are fundamental. (Dees, MS)

1.b. 4D-fundamentalismThe four-dimensional spacetime is fundamental. (Keming Chen, MS)

Niels Martens Regularity Comparativism 6/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Unpacking Humean Supervenience III

1. Seperability

“The complete physical state of the world is determined by ... theintrinsic physical state of each spacetime point (or each point-likeobject) and the spatio-temporal relations between those points.”

(Maudlin, 2007)

2. Supervenience

“All facts about a world, including modal and nomological facts,[supervene on] its [complete] physical state.”

(Maudlin, 2007)

Niels Martens Regularity Comparativism 7/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Best Systems AccountMill-Ramsey-Lewis

Popular way of cashing out the exact way in which the lawssupervene on the mosaic

Laws are theorems of the ‘best’ axiomatisations of the Humeanmosaic

best = ‘simplest’ + ‘strongest’

(Lewis, 1973; Earman, 1984)

Niels Martens Regularity Comparativism 8/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Regularity Relationalism

Response to i.a. Newton’s bucket (i.e. inertial e�ects)

Core Idea: It is merely the truth of Newton’s laws in certainframes that privileges those frames, not the structure ofabsolute space. (Van Fraassen, 1970)

Regularity Approach: Consider all possible reference framesthat are naturally adapted to the mosaic: only in some frameswill the best axiomatisations be Newton’s laws. Claim: thoseare the simplest laws overall.→ Inertial frames & laws supervene as a package deal.

(Hugge�, 2006)

Niels Martens Regularity Comparativism 9/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Regularity Relationalism in more detail

Leibnizian-Humean mosaic: Leibnizian spatial relations ofthe particles over time & their fundamental intrinsic propertiessuch as mass and charge.Ontological coordinate frames:

Adapted frame: adapted to a reference body if that body is atrest at the origin of the frameAdapted frames + all frames related to those adapted frames byarbitrary continuous spatially rigid transformations

Best System Coordinates: Subset of ontological coordinateframes which correspond to the axiomatisations that are bestoverall (i.e. Newton’s laws). That is, the inertial frames.

Niels Martens Regularity Comparativism 10/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Regularity Comparativism I

Comparativism: Denial of absolutism: quantity ratios are notgrounded in intrinsic quantities

Case study: mass

Motivation: Ontological parsimony: throw away intrinsicmasses

Challenge: comparativism’s bucket

Niels Martens Regularity Comparativism 11/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Comparativism’s bucket

Fg = G mMr2 ve =

√2GM

r

v0 v0

F F

Double Mass

v0 v0

F F

(Baker, manuscripts; NM, manuscripts)

Niels Martens Regularity Comparativism 12/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Regularity Comparativism II

Absolutism-Relationalism debate concerns the relativefundamentality of intrinsic mass and mass ratios, but is o�enequivocated with the debate about the empiricalmeaningfulness of mass.

Wiggle room: accept that the comparativism’s bucketargument proves that intrinsic mass is empirically meaningful,but insist that that can be accounted for without groundingmass ratios in intrinsic masses.

Use the regularity approach

Niels Martens Regularity Comparativism 13/25

The Regularity ApproachResponses

Empiricism about laws of natureRegularity RelationalismRegularity Comparativism

Regularity Comparativism III

Core idea: Absolute mass scale is privileged because of thetruth of Newton’s laws (incl. Gravitational Law) for that choiceof scale, not because that scale is grounded in absolute masses.

Liberalisation: Replace the absolutist Humean mosaic by amosaic consisting of fundamental mass ratios.

Ontological ‘coordinates’: Consider all possible choices of anabsolute mass scale.

Regularity Approach: Claim: Only for one choice of theabsolute mass scale will the laws be the best axiomatisation,and those laws are Newton’s laws & the Gravitational Law.

Niels Martens Regularity Comparativism 14/25

Outline

1 The Regularity Approach

2 Responses

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

It doesn’t work

For any choice of mass scale, equally simple laws (i.e. the lawsof NG) can be found, simply by adjusting the value ofNewton’s Constant.

Mistake: equivocating mass magnitude/scale (= ontology) withmass quantity/parameter (= representation).

Niels Martens Regularity Comparativism 16/25

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

Explanatory Circularity

Should we be surprised that the regularity approach retrievesthe correct laws and mass scale? No!

Pu�ing the cart before the horse

Trajectories are explanandum, not explanans.

Generic problem of Humean Supervenience. (Maudlin, 2007b)

Niels Martens Regularity Comparativism 17/25

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

Separability

Comparativism violates Separability

Liberalise/Generalise Separability, or give it up altogether

Niels Martens Regularity Comparativism 18/25

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

Generalising Separability

Analogous quantum debate

Give up on 4D-fundamentalism

Generalised Separability (GS): quantify over points inconfiguration space instead (Albert, 1996)

Why care about GS? Or Separability?Albert, Lewis, Einstein: classical world is manifestly separable(Maudlin, 2007)

Inductive argumentWhy would this motivate GS?If GS, Separability is still violated.

Niels Martens Regularity Comparativism 19/25

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

Giving up on separability

Separability & Supervenience are logically independent, butcan Supervenience be motivated independently fromSeparability?

“ Humean supervenience is named in honor of the greater [sic]denier of necessary connections.

Lewis, 1986”

Humean Empiricism: dislike of necessary connections

-> motivates Humean Supervenience as a package deal

Ontological parsimony (Hugge�, 2006)

Not clear that separable mosaics are more parsimoniousNot clear that Humeanism is more parsimonious thanGoverning LawThis motivation leads to Eliminativism

Niels Martens Regularity Comparativism 20/25

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

Giving up on separability

Separability & Supervenience are logically independent, butcan Supervenience be motivated independently fromSeparability?

Humean Empiricism: dislike of necessary connections

“ Prima facie, the kind of world that violates Separability is onein which there are necessary connections between distinct ex-istents: that is, in which there are fundamental and irreduciblerelations between pointlike things.

Dewar, MS”

-> motivates Humean Supervenience as a package deal

Ontological parsimony (Hugge�, 2006)

Not clear that separable mosaics are more parsimoniousNot clear that Humeanism is more parsimonious thanGoverning LawThis motivation leads to Eliminativism

Niels Martens Regularity Comparativism 20/25

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

Giving up on separability

Separability & Supervenience are logically independent, butcan Supervenience be motivated independently fromSeparability?Humean Empiricism: dislike of necessary connections

-> motivates Humean Supervenience as a package deal

Ontological parsimony (Hugge�, 2006)

Not clear that separable mosaics are more parsimoniousNot clear that Humeanism is more parsimonious thanGoverning LawThis motivation leads to Eliminativism

Niels Martens Regularity Comparativism 20/25

The Regularity ApproachResponses

It doesn’t workExplanatory CircularitySeparabilityEliminativism

Non-ad-hoc criterion & Eliminativism

Why stop at reducing intrinsic masses? Why not eliminatemass altogether (i.e. give up �antity Primitivism)?Regularity Eliminativism (Hall, manuscript)

Ontologically parsimoniousNo motivation for �antity Primitivism anywayRemoves problems with mass & charge swapping (Esfeld)

Non-ad-hoc criterion needed to block further reduction (Pooley,

2013)

Not a problem for regularity relationalism (pace Pooley)

Problem for comparativism: throwing away the massive babywith the bath water“Transcendental” argument

Narlikar, 1939

Niels Martens Regularity Comparativism 21/25

Conclusion

1 RC uses the Mill-Ramsey-Lewis Best Systems Account to havethe absolute mass scale supervene on a comparativist mosaictogether with the laws of Newtonian Gravity as a package deal.

2 I have made plausible that the approach does do what it claimsto do.

3 The regularity approach is explanatorily circular, since it isbased on Humean Supervenience.

4 RC is manifestly non-seperable. Humean Empiricists cannotgive up Seperability without losing Supervenience as well.Ontological parsimony might provide an independentmotivation for Supervenience.

5 The regularity approach favours regularity eliminativism overregularity comparativism, which is fatal for comparativism.

References

D.Z. Albert (1996), ‘Elementary �antum Metaphysics’, inJ.T. Cushing et al. (eds.) Bohmian Mechanics and �antumTheory: An Apraisal, 277-284, Kluwer Academic Publishers

D.J. Baker, ‘Some Consequences of Physics for the ComparativeMetaphysics of �antity’, Manuscript

N. Dewar (2015), ‘What the Humean cannot say aboutentanglement’, manuscript

J. Earman (1984), ‘Laws of Nature: The Empiricist Challenge’, inD.M. Armstrong, R. Bogdan (ed.), Profiles, Vol.4, Dordrecht:D. Reidel Publishing Company.

N. Hall, ‘Humean Reductionism About Laws of Nature’,Manuscript

References - continued

N. Hugge� (2006), ‘The Regularity Account of RelationalSpacetime’, Mind 115:457

D. Lewis (1973), Counterfactuals, Cambridge, MA: HarvardUniversity Press

D. Lewis (1986), Philosophical Papers, Vol. ii, Oxford: OUP

N.C.M. Martens, Transfer & Confirmation of StatusDissertations, Oxford University, Manuscripts

T. Maudlin (2007), ‘Why Be Humean?’, in The MetaphysicsWithin Physics, Clarendon Press (UK)

References - continued

T. Maudlin (2007b), ‘The Whole Ball of Wax’, in The MetaphysicsWithin Physics, Clarendon Press (UK)

V.V. Narlikar (1939), ‘The Concept and Determination of Massin Newtonian Mechanics’, The London, Edinburgh, and DublinPhilosophical Magazine and Journal of Science: Series 7,27(180):33-6

C.G. Pendse (1937), ‘A Note on the Definition andDetermination of Mass in Newtonian Mechanics’, PhilosophicalMagazine, 24:1012-1022

O. Pooley (2013), ‘Substantivalist and Relationalist Approachesto Spacetime’, in R. Ba�erman (ed.) The Oxford Handbook ofPhilosophy of Physics, Oxford: OUP

B.C. Van Fraassen (1970), An Introduction to the Philosophy ofTime and Space, New York: Columbia University Press