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In Favor of Being Only Humean

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The twin conceptions of (1) natural law as causal structure and (2) explanation as passage from phenomenon to cause, are two sides of a certain philosophical coin, to which I shall offer an alternative – Humean – currency. The Humean alternative
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  M. THALOS IN FAVOR OF BEING ONLY HUMEAN (Received in revised form 12 May 1997)ABSTRACT. The twin conceptions of (1) natural law as causal structure and (2)explanation as passage from phenomenon to cause, are two sides of a certainphilosophicalcoin, to which I shall offeran alternative – Humean– currency.TheHumean alternative yokes together a version of the regularity conception of lawand a conception of explanation as passage from one regularity, to another whichhas it as an instance but of which it is not itself an instance. I will show that theregularity conception of law is the basis of a distinguished branch of physicalmechanics; thus the Humean conception of law, like its better-loved rival, enjoysthe support of a venerated tradition in mechanical theory – in fact, that strandwhich culminates in quantum theory. I shall also offer an account of explana-tory asymmetry, a natural companion to the Humean conception of explanationas passage from one regularity to another of greater scope, as an alternative tovan Fraassen’s unsatisfactory account. My account of asymmetry is just as freeof reliance on  context   as it is free of reliance on  cause . I shall thus proclaim thatexplanatoryasymmetry is at once a reality deserving of philosophical treatment –one not to be given over to the care of psychology or linguistics – and at the sametime susceptible of an account worthy of Hume.In speaking of cause and effect we arbitrarily give relief to those elements towhose connection we have to attend :::  in the respect in which it is importantto us. [But t]here is no cause nor effect in nature; nature has but an individualexistence; nature simply  is .– Ernst Mach 1 1. INTRODUCTION There are in circulation two well-known conceptions of natural law.I shall refer to the first of these as the  regularity conception  or – as itis an article of Hume’s estate – the  Humean conception . Accordingto it, laws of nature are nothing but regularities (in Hume’s terms,“constant conjunctions”) among observable natural quantities. 2 Iintend to defend this conception of natural law, and to do so in amanner that both refreshes and advances the debate Hume inaugu-rated. For Hume continues to inspire present-day empiricists in thedirection of a certain, very healthy, form of skepticism; but he gives Philosophical Studies  93:  265–298, 1999.c    1999  Kluwer Academic Publishers. Printed in the Netherlands.  266  M. THALOS his followers, as skeptics, no clear guidance for entering into thescientific enterprise without having to apologize for participation.I shall show that a highly respected, but philosophically neglectedtradition in mechanics – of all things – can provide some of themissing tutelage.The second conception of natural law is nowadays the morewidely embraced. For what it’s worth, it is also the more in keep-ing with common sense, as Hume himself pointed out, recogniz-ing all the while that ‘common sense’ is another name for certainaspects of the human condition which for one reason or anotherone cannot aspire to change. I shall refer to it as the  causal concep-tion .With theregularityconceptionit acknowledgesthatnatural lawinvolvesregularities,butproclaimsthatthereisinfact muchmoretonatural law than this. For, according to the causal conception, theremust be something more substantial standing behind regularities,which is such as to  explain  them. This more substantial somethingis  causal structure  or  causal order  ; and it lies in the world itself, notin constructions or construals of it. Causal order, as the conceptionhas it, concerns the manner in which physical influence is exertedby one event or state of affairs on another. The causal conception isthe legacy of Isaac Newton – the villain of this piece, as Hume isits hero. The causal conception designates certain events as havingbeen brought about, and others as the bringers-about, in a narrativewith a cast of characters and a plot that boasts  cradles  or  sources of influence,  beneficiaries  or  recipients  thereof, and  organs  or  vehi-cles  whereby the influence is carried from cradle to recipient. Thecausal conception of natural law is thus concerned with patterns of influence dispersal on the contours of space and time.These two conceptions of natural law differ, then, in that onlyone of them acknowledges the existence of certain systematicnonreciprocities, asymmetries or directionalities – an entire orderof agent-patient or donor-recipient relations among events. Moreplainly, given a list of episodes within a spatiotemporal region, thecausal conception marks certain of them as causes of certain otherswhich are designated as effects of the first, whereas the regularityconceptionacknowledgesnosuchsystematicallynonreciprocalrela-tions among events. And, to repeat, the two conceptions differ alsoin that only one of them – the causal conception – is comfort-  IN FAVOR OF BEING ONLY HUMEAN  267ably familiar. Mechanics textbooks prepared for undergraduates, forexample, are filled with narratives about physical influence and itstravels abroad. The regularity conception, on the other hand, hasenjoyed very little press in scientific treatises as a distinct concep-tionofnaturallaw–muchlessmadeitswayintointroductorycollegephysics textbooks.It is well known that Hume directed his epistemological remarksin particular towards Newton’s physics, writing with irony:“Astronomershadlongcontentedthemselveswithproving,fromthephenomena, the true motions, order, and magnitude of the heavenlybodies, till a philosopher at last arose who seems, from the happiestreasoning, to have determined the laws and forces by which therevolutions of the planets are governed and directed.” (  Inquiry,Section I  ) Newton, as too is well known, was deservedly praisedfor bringing the same principles and instruments of analysis to treat-mentof  terrestrial motionastotreatmentof  celestial motion.Butitisless well known that within a century’s time of Hume’s publicationsa noncausal formulation of mechanics stood alongside Newton’s,rivaling the latter’s capacity to treat, in the same compass, the rangeof physical motions – terrestial and celestial – which Newton’sapproach treats. The ancestry of this noncausal branch of mechanicstoo has been very distinguished,and its continuing legacies in phys-ical theory profound: it is by no means a coincidence that quantumtheory traces its lineage to this noncausal formulation of mechanics.I shall begin my Humean account of explanation by giving brief characterizations of each formulation of mechanics – causal andnoncausal –, demonstrating thereby that the Humean conception of natural law enjoys the support of a mechanical tradition that rivalsits competitor’s considerable capacity to accommodate and predictthe results of observation.Then,byyokingtogethertheregularityconceptionofnaturallaw,soadmirablyexemplifiedbynoncausalmechanics,withaconceptionof explanation as passage from one regularity to a second which hasthe first as an instance, when the second is not itself an instanceof the first, I will furnish the Humean with significant resources forposingchallengestoherrival:amechanicaltheorythatmaybetakenliterally, rather than nominally,as an explanation of physical motion– to the satisfaction of Hume himself.  268  M. THALOS 2. MECHANICS AS THE TRANSMISSION OF INFLUENCE The causal conception of natural law finds perhaps its first quan-titative and comprehensive formulation in Newton’s physics; andit is carried to its highest expression in relativity theory. Motion –the explanandum in mechanics – is by its very nature a directedphenomenon. A natural description of motion introduces vectorialquantities, and vectorial variables to portray them. The Newtoniantreatment of motion takes vectorial analysis of motion one stepfurther, for with each alteration in motion it postulates an entity – a vehicle  or  organ , routinely interpreted as a  cause  – that brings aboutalteration by communicating an  influence  in the appropriate direc-tion. Like ordinary bodies, these vehicles through which influenceis communicated are both located and propagated along continuousspatio-temporalpaths. 3 DistinguishingmarksoftheNewtoniantreat-ment are as follows.1. First there is  influence , which is propagated from a source to abeneficiary, via a vehicle. For body, on the Newtonian concep-tion,doesnotactonbodydirectly,butthroughanintermediaryorvehicle. The vehicle is thought of as srcinating from the sourcebody, which is responsible,  ontologically  rather than causally,for the vehicle’s existence. The vehicle, known as a  force , isrepresented by a vectorial variable. One body acts on another,not directly, but by impressing a force. Forces, as the theorygoes, are entities that bring about alterations in both nonvec-torial quantities and certain other vectorial quantities.2. Then there are  recipients  of influence – quantities whose magni-tudes change according to the operations of force, taking ondifferent magnitude in succession as a result. Alterations inmagnitude for these quantities are thought of as being broughtabout in a continuous fashion over time, by the incrementaloperation of force, according to Newton’s Second Law.3. Not every alternative course of values for a particular quantityreceives attention or representation. In fact, there is only onecourse of values ever explicitly discussed for a system – theactual one.  IN FAVOR OF BEING ONLY HUMEAN  269 3. MECHANICS WITHOUT TRANSMISSIONS The second venerable branch of mechanics srcinated with ideasof Leibniz, Euler and Lagrange, and culminated in Hamilton andJacobi’s equations of transformation – which frequently are illegiti-mately treated as either reformulations or culminations of Newton’slaws (by those who view the field of classical mechanics as a seam-less enterprise, rather than one where philosophical lines are drawnin abundance). I will refer to this tradition as  analytical mechanics .This branch of mechanics treats transformations over time as a kindof wave phenomenon. But the wave disturbances are not distur-bances in a real medium (or substance) with a three-dimensionalspatial extension. The disturbances are, rather, disturbances in thephase space of quantities. There are no counterparts to the roles of source, vehicle and beneficiary in this formulation of mechanics.Simply, there are tides in the affairs of quantities, whereby quanti-ties conspire to undertake alterations together, and in keeping withvery general principles which make no mention of causes. The dis-tinguishing marks of analytical mechanics are as follows.1. There are no forces or influences of any kind to bring aboutalteration. Instead there are what are known as  variational principles . 4 Famous examples are Hamilton’s principle (that theintegral, over a system’s path, of the difference between kineticand potential energies is an extremum – typically a minimum)andHuygens’principleforoptics,whichleadstoFermat’s“prin-ciple of quickest arrival” (that the path of a light ray is distin-guished by the property that if light travels from one given pointM to another given point N, it does so in the smallest possibletime). 5 2. A variety of   alternative  courses of values for the quantitiesunder investigation are typically brought to attention. These arerevealed in one of two ways: (1) by specification of initial andfinalsystemconfigurations,or(2)byspecificationofaconstrainton motion. Both these means of specifying alternative coursesof values are denominated  boundary conditions . The variationalprinciples – which govern alterations in time – compare thesealternativecoursesofvalue,selectingoneasdistinguished(whena unique solution to the problem formulated is possible).
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