Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
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Scerri’s says about <strong>the</strong> case of chromium: “It appears that<br />
both non-relativistic <strong>and</strong> relativistic calculations fail to predict<br />
<strong>the</strong> experimentally observed ground state which is <strong>the</strong><br />
4s 1 3d 5 configuration” (2004, 101), but he immediately<br />
goes on to admit “Of course I do not deny that if one goes<br />
far enough <strong>in</strong> a more elaborate calculation <strong>the</strong>n eventually<br />
<strong>the</strong> correct ground state will be recovered. But <strong>in</strong> do<strong>in</strong>g so<br />
one knows what one is driv<strong>in</strong>g at, namely <strong>the</strong> experimentally<br />
observed result. This is not <strong>the</strong> same as strictly predict<strong>in</strong>g<br />
<strong>the</strong> configuration <strong>in</strong> <strong>the</strong> absence of experimental<br />
<strong>in</strong>formation.” Right, it isn’t; but that failure has not revealed<br />
anyth<strong>in</strong>g new at work.<br />
As Galison says of a different case, “The reductionist<br />
physicists reply that it is true that you might not guess<br />
<strong>the</strong>se collective behaviors; but if you ask why very cold<br />
copper superconducts, <strong>the</strong> answer <strong>in</strong>cludes noth<strong>in</strong>g o<strong>the</strong>r<br />
than electrons <strong>and</strong> electrodynamics-<strong>the</strong>re's no magical<br />
supplementary th<strong>in</strong>g over <strong>and</strong> above <strong>the</strong>se” (2008, 121).<br />
We can see <strong>the</strong> po<strong>in</strong>t at issue <strong>in</strong> a case even Horst<br />
acknowledges is not decisive: <strong>the</strong> ma<strong>the</strong>matical <strong>in</strong>tractability<br />
of <strong>the</strong> three-body problem for Newtonian <strong>the</strong>ory is no<br />
reason to suppose that anyth<strong>in</strong>g new has entered a Newtonian<br />
system when a third mass is <strong>in</strong>troduced. The cases<br />
Horst th<strong>in</strong>ks are more significant than this do not seem to<br />
<strong>in</strong>volve anyth<strong>in</strong>g very different, however. I appeal to Azzouni’s<br />
authority <strong>in</strong> agree<strong>in</strong>g with Nagel that <strong>the</strong> idealis<strong>in</strong>g<br />
assumptions required <strong>in</strong> <strong>the</strong> <strong>the</strong>rmodynamics case are not<br />
a barrier to <strong>the</strong> worthwhile k<strong>in</strong>d of reduction she calls “scientific”.<br />
She says “Imag<strong>in</strong>e, contrary to fact, that a genu<strong>in</strong>e<br />
derivational reduction is available, but only if constra<strong>in</strong>ts<br />
are placed on gas states that are—given <strong>the</strong> physics of<br />
micro-particles—quite probabilistically low. In such a case<br />
… physicalism fails: emergent phenomena, <strong>in</strong>dicated by<br />
physically <strong>in</strong>explicable constra<strong>in</strong>ts on <strong>the</strong> probability space<br />
of micro-particles, show this” (2000, 45). She comments <strong>in</strong><br />
a footnote: “Garf<strong>in</strong>kel (1981:70-1) seems aware of this<br />
possibility, but seems also, falsely, to th<strong>in</strong>k that <strong>the</strong> actual<br />
derivation of <strong>the</strong> Boyle-Charles law from <strong>the</strong> statistical<br />
behavior of <strong>the</strong> ensemble of molecules illustrates it just<br />
because of <strong>the</strong> use of <strong>the</strong> conservation of energy (<strong>in</strong><br />
closed systems) <strong>and</strong> <strong>the</strong> assumption of a normal distribution<br />
of velocities.”<br />
There are, of course, contentious issues <strong>in</strong> what<br />
scientists consider successful or unsuccessful reductions<br />
(e.g. <strong>the</strong> temporal isotropy of statistical mechanics as<br />
aga<strong>in</strong>st <strong>the</strong> directedness of phenomenological <strong>the</strong>rmodynamics).<br />
But <strong>the</strong> types of idealis<strong>in</strong>g assumption that Horst<br />
is appeal<strong>in</strong>g to are not usually someth<strong>in</strong>g that should underm<strong>in</strong>e<br />
our confidence <strong>in</strong> a reduction.<br />
30<br />
Informal <strong>Reduction</strong> — E.P. Br<strong>and</strong>on<br />
While I have been happy to call upon Azzouni for<br />
support, <strong>and</strong> <strong>in</strong>deed f<strong>in</strong>d her account of scientific reduction<br />
very close to what I have been urg<strong>in</strong>g myself, 2 I will close<br />
with one quibble. If we can legitimately see scientific reduction<br />
as not requir<strong>in</strong>g formal derivations but simply “all<br />
that is desired is an extension of <strong>the</strong> scope of an underly<strong>in</strong>g<br />
science <strong>in</strong> a way illum<strong>in</strong>at<strong>in</strong>g both to that science <strong>and</strong><br />
<strong>the</strong> special science above it” (2000, 40), I would like to<br />
suggest that we can extend <strong>the</strong> same sympathy to Nagel’s<br />
own derivational model of reduction. As I <strong>in</strong>dicated at <strong>the</strong><br />
start, Nagel saw <strong>the</strong> relation as explanatory. Work<strong>in</strong>g with<br />
<strong>the</strong> tools available to him he took that to <strong>in</strong>volve formal<br />
derivation, though actual cases, of explanation <strong>and</strong> of reduction,<br />
might well only exhibit <strong>the</strong> elements that Hempel<br />
called an “explanation sketch” (Hempel 1965 [1942], 238,).<br />
Allow<strong>in</strong>g for Nagel’s clear recognition that his account is<br />
<strong>in</strong>deed an idealisation of <strong>the</strong> reductions we actually f<strong>in</strong>d,<br />
we may resist agree<strong>in</strong>g with Azzouni that <strong>the</strong> concern for<br />
derivation has been altoge<strong>the</strong>r a mistaken “obsession with<br />
words”. It provides a picture that we can adjust to get<br />
closer to <strong>the</strong> realities we are <strong>in</strong>terested <strong>in</strong>, as <strong>in</strong>deed her<br />
own explorations reveal.<br />
Literature<br />
Azzouni, Jodi 2000 Knowledge <strong>and</strong> Reference <strong>in</strong> Empirical Science,<br />
London: Routledge.<br />
Friedrich, Bretislav 2004 “…Hasn’t it?”, Foundations of Chemistry<br />
6, 117–132.<br />
Galison, Peter 2008 “Ten Problems <strong>in</strong> History <strong>and</strong> <strong>Philosophy</strong> of<br />
Science”, Isis 99, 111–124.<br />
Hempel, Carl G. 1965 [1942] “The Function of General Laws <strong>in</strong><br />
History”, <strong>in</strong>: Aspects of Scientific Explanation, New York: The<br />
Free Press.<br />
Horst, Steven 2007 Beyond <strong>Reduction</strong>: <strong>Philosophy</strong> of M<strong>in</strong>d <strong>and</strong><br />
Post-<strong>Reduction</strong>ist <strong>Philosophy</strong> of Science, Oxford: Oxford University<br />
Press.<br />
Nagel, Ernest 1961 The Structure of Science, London: Routledge<br />
<strong>and</strong> Kegan Paul.<br />
O'Connor, Timothy, <strong>and</strong> Hong Yu Wong 2006 “Emergent Properties”,<br />
<strong>in</strong> Stanford Encyclopedia of <strong>Philosophy</strong><br />
(http://plato.stanford.edu/entries/properties-emergent/).<br />
Scerri, Eric 2004 “Just How Ab Initio is Ab Initio Quantum Chemistry?”<br />
Foundations of Chemistry 6, 93-116.<br />
Silberste<strong>in</strong>, M., 2002. <strong>Reduction</strong>, Emergence <strong>and</strong> Explanation. In<br />
The Blackwell Guide to <strong>the</strong> <strong>Philosophy</strong> of Science, edited by P.<br />
Machamer <strong>and</strong> M. Silberste<strong>in</strong>. Oxford: Blackwell.<br />
2 She says, for <strong>in</strong>stance, “talk of <strong>the</strong>re be<strong>in</strong>g a scientific reduction <strong>in</strong> this sort of<br />
situation is still legitimate because we really do take As, <strong>and</strong> what is go<strong>in</strong>g on<br />
with <strong>the</strong>m, to be noth<strong>in</strong>g more than Bs, <strong>and</strong> what is go<strong>in</strong>g on with <strong>the</strong>m; we<br />
recognize <strong>and</strong> expect that if, <strong>in</strong> certa<strong>in</strong> cases, we overcome (particular) tractability<br />
problems (as we sometimes do) <strong>in</strong> treat<strong>in</strong>g As as Bs, we will not discover<br />
recalcitrant emergent phenomena. Scientific reduction is a project with methodological<br />
depth: <strong>the</strong> idealized model is one where deviations from what is<br />
actually go<strong>in</strong>g on are deviations we can study directly, extract <strong>in</strong>formation<br />
from, <strong>and</strong>, when we're lucky, m<strong>in</strong>imize. This is <strong>the</strong> full content of <strong>the</strong> claim that<br />
As, <strong>and</strong> what is go<strong>in</strong>g on with <strong>the</strong>m, are really just Bs, <strong>and</strong> what is go<strong>in</strong>g on<br />
with <strong>the</strong>m” (43-44).