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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Informal <strong>Reduction</strong><br />
E.P. Br<strong>and</strong>on, Cave Hill, Barbados<br />
This paper was provoked by Horst’s recent book (Beyond<br />
<strong>Reduction</strong>: <strong>Philosophy</strong> of M<strong>in</strong>d <strong>and</strong> Post-<strong>Reduction</strong>ist<br />
<strong>Philosophy</strong> of Science) that argues for a metaphysical<br />
pluralism largely on <strong>the</strong> basis of claims about <strong>the</strong> status of<br />
what one might call <strong>the</strong> reductionist programme <strong>in</strong><br />
philosophy of science.<br />
Horst’s position is that <strong>the</strong> idea that <strong>the</strong> mature<br />
physical sciences display extensive, metaphysically significant<br />
reductions is an illusion that philosophers of science<br />
have exposed but which too many of us <strong>in</strong> o<strong>the</strong>r areas of<br />
philosophy mistakenly cl<strong>in</strong>g to. Whatever <strong>the</strong> formal obstacles<br />
that Horst po<strong>in</strong>ts to, I am not conv<strong>in</strong>ced that <strong>the</strong>y constitute<br />
a refutation of a metaphysically important reductionism,<br />
so my aim is to try to clarify, <strong>in</strong>formally, what that k<strong>in</strong>d<br />
of reductionism is concerned with, <strong>and</strong> to suggest that our<br />
best bet <strong>in</strong> identify<strong>in</strong>g successful, <strong>and</strong> unsuccessful, reductions<br />
of that type rema<strong>in</strong>s with <strong>the</strong> scientists <strong>the</strong>mselves,<br />
ra<strong>the</strong>r than with <strong>the</strong> models we have created of what ideal<br />
reduction should <strong>in</strong>volve.<br />
Ernest Nagel provides, for many, <strong>the</strong> st<strong>and</strong>ard account<br />
of what <strong>the</strong> reductionist programme aspired to. My<br />
strategy is to briefly review what Nagel actually claimed for<br />
reduction, <strong>and</strong> <strong>the</strong>n to consider <strong>the</strong> type of issue that more<br />
recent specialists have urged aga<strong>in</strong>st it.<br />
Very roughly, <strong>the</strong> formal ideal Nagel set out <strong>in</strong>volves<br />
<strong>the</strong> laws <strong>and</strong> predicates of two <strong>the</strong>ories. Theory one is<br />
reduced to <strong>the</strong>ory two just <strong>in</strong> case <strong>the</strong>re are bridg<strong>in</strong>g pr<strong>in</strong>ciples<br />
l<strong>in</strong>k<strong>in</strong>g <strong>the</strong> predicates of <strong>the</strong>ory one with those of<br />
<strong>the</strong>ory two, <strong>and</strong> <strong>the</strong> laws of <strong>the</strong>ory one can be deduced<br />
from those of <strong>the</strong>ory two with <strong>the</strong> help of such bridg<strong>in</strong>g<br />
pr<strong>in</strong>ciples. While writ<strong>in</strong>g of deduction here, Nagel is clear<br />
that <strong>the</strong>se deductions should embody explanations of <strong>the</strong>ory<br />
one <strong>in</strong> terms of <strong>the</strong>ory two, so <strong>the</strong> relationship is deduction<br />
plus whatever o<strong>the</strong>r constra<strong>in</strong>ts explanation requires.<br />
Ra<strong>the</strong>r than focuss<strong>in</strong>g on Nagel’s formal account itself,<br />
I want to stress that methodologically he was a naturalised<br />
epistemologist avant la lettre: his discussion derives<br />
from <strong>the</strong> positions of practis<strong>in</strong>g scientists on whe<strong>the</strong>r<br />
reduction has been successful; he takes reduction as a<br />
fact accepted by most scientists <strong>in</strong> <strong>the</strong> relevant fields <strong>and</strong><br />
aims to characterise it. It is important for him also to stress<br />
<strong>the</strong> many failures of reduction, perhaps most notably <strong>the</strong><br />
impossibility of a mechanical reduction of electromagnetism,<br />
as well. His is not <strong>the</strong> style of argument that shows<br />
that a putative reduction fails to fit a formal model <strong>and</strong> so is<br />
shown not to be a case of genu<strong>in</strong>e reduction. While formal,<br />
his model is recognised to be a model, an ideal case, <strong>and</strong><br />
so <strong>in</strong>herits <strong>the</strong> mess<strong>in</strong>ess of models throughout <strong>the</strong> sciences.<br />
So, for <strong>in</strong>stance, Nagel supposes that <strong>the</strong> Boyle-<br />
Charles’ law were <strong>the</strong> only th<strong>in</strong>g derivable from <strong>the</strong> k<strong>in</strong>etic<br />
<strong>the</strong>ory of gases <strong>and</strong> says “it is unlikely that this result<br />
would be counted by most physicists as weighty evidence<br />
for <strong>the</strong> <strong>the</strong>ory … For prior to its deduction, so <strong>the</strong>y might<br />
ma<strong>in</strong>ta<strong>in</strong>, this law was known to be <strong>in</strong> good agreement with<br />
<strong>the</strong> behavior of only “ideal” gases, … Moreover, physicists<br />
would doubtless call attention to <strong>the</strong> tell<strong>in</strong>g po<strong>in</strong>t that even<br />
<strong>the</strong> deduction of this law can be effected only with <strong>the</strong> help<br />
of a special postulate connect<strong>in</strong>g temperature with <strong>the</strong><br />
energy of <strong>the</strong> gas molecules—a postulate that, under <strong>the</strong><br />
circumstances envisaged, has <strong>the</strong> status of an ad hoc<br />
assumption, … In actual fact, however, <strong>the</strong> reduction of<br />
<strong>the</strong>rmodynamics to <strong>the</strong> k<strong>in</strong>etic <strong>the</strong>ory of gases achieves<br />
much more than <strong>the</strong> deduction of <strong>the</strong> Boyle-Charles’ law.<br />
There is available o<strong>the</strong>r evidence that counts heavily with<br />
most physicists as support for <strong>the</strong> <strong>the</strong>ory <strong>and</strong> that removes<br />
from <strong>the</strong> special postulate connect<strong>in</strong>g temperature <strong>and</strong><br />
molecular energy even <strong>the</strong> appearance of arbitrar<strong>in</strong>ess”<br />
(Nagel 1961, 359-60). He notes that <strong>the</strong> special assumptions<br />
can be replaced by o<strong>the</strong>rs known to be closer to reality,<br />
<strong>and</strong> that <strong>the</strong> reduc<strong>in</strong>g <strong>the</strong>ory can “augment or correct”<br />
<strong>the</strong> currently accepted body of laws of <strong>the</strong> reduced <strong>the</strong>ory.<br />
The same methodological po<strong>in</strong>t can be derived from<br />
an article quoted by Horst (from Silberste<strong>in</strong>), though nei<strong>the</strong>r<br />
author goes on to elaborate on it, that most scientists<br />
would th<strong>in</strong>k that <strong>the</strong> errors of philosophers show <strong>the</strong>y have<br />
a bad model of reduction ra<strong>the</strong>r than that <strong>the</strong>re are no<br />
reductions. “Focus on actual scientific practice suggests<br />
that ei<strong>the</strong>r <strong>the</strong>re really are not many cases of successful<br />
epistemological (<strong>in</strong>ter<strong>the</strong>oretic) reduction or that most philosophical<br />
accounts of reduction bear little relevance to <strong>the</strong><br />
way reduction <strong>in</strong> science actually works. Most work<strong>in</strong>g<br />
scientists would probably opt for <strong>the</strong> latter claim” (Silberste<strong>in</strong><br />
2002, 94).<br />
I suggest that <strong>the</strong> ma<strong>in</strong> po<strong>in</strong>t 1 of <strong>the</strong> reductionist<br />
programme is to claim that some particular area of <strong>in</strong>terest<br />
can be comprehended, expla<strong>in</strong>ed, by certa<strong>in</strong> entities, features,<br />
ways of work<strong>in</strong>g, <strong>and</strong> no o<strong>the</strong>rs are needed. The<br />
area of <strong>in</strong>terest is <strong>the</strong>n noth<strong>in</strong>g but <strong>the</strong> entities, features<br />
<strong>and</strong> <strong>the</strong>ir ways of work<strong>in</strong>g used <strong>in</strong> <strong>the</strong>se explanations.<br />
These claims are rough, <strong>the</strong>y constitute a scientist’s <strong>in</strong>formal<br />
patter, ra<strong>the</strong>r than <strong>the</strong> technical, strict derivations she<br />
might offer with<strong>in</strong> a <strong>the</strong>ory. They <strong>in</strong>dicate <strong>the</strong> wider significance<br />
of <strong>the</strong> <strong>the</strong>ory, <strong>and</strong> of course <strong>the</strong>y may prove to be as<br />
fallible as anyth<strong>in</strong>g else, but <strong>the</strong>y are not groundless. If this<br />
idea is on <strong>the</strong> right l<strong>in</strong>es, it casts considerable doubt on <strong>the</strong><br />
salience of <strong>the</strong> po<strong>in</strong>ts that have been made aga<strong>in</strong>st Nagel,<br />
<strong>and</strong> relied upon by Horst <strong>in</strong> his application to <strong>the</strong> philosophy<br />
of m<strong>in</strong>d.<br />
This account can be defended by look<strong>in</strong>g at Scerri’s<br />
discussion of <strong>the</strong> relation between chemistry <strong>and</strong> quantum<br />
mechanics, <strong>in</strong> particular <strong>the</strong> role of <strong>the</strong> latter <strong>in</strong> account<strong>in</strong>g<br />
for <strong>the</strong> periodic table. Scerri <strong>in</strong>sists that we cannot rely on<br />
<strong>the</strong> quantum mechanical <strong>the</strong>ory <strong>and</strong> <strong>the</strong> approximations it<br />
allows ab <strong>in</strong>itio but ra<strong>the</strong>r we accept <strong>the</strong>m when <strong>the</strong>y yield<br />
what are known empirically to be <strong>the</strong> right results <strong>and</strong><br />
complicate <strong>the</strong>m when we have empirical evidence that <strong>the</strong><br />
first approximation is mistaken. I am <strong>in</strong> no position to deny<br />
that this is what happens, nor I th<strong>in</strong>k is his commentator,<br />
Friedrich, but our po<strong>in</strong>t is that <strong>the</strong>re is absolutely no suggestion<br />
that <strong>the</strong>se cases where <strong>the</strong> <strong>the</strong>oretically derived<br />
structure is known to be mistaken <strong>in</strong>volve <strong>in</strong>explicable<br />
emergent properties or new <strong>the</strong>oretical notions. They simply<br />
show that our approximations have left out someth<strong>in</strong>g<br />
important which we already knew about. So, for <strong>in</strong>stance,<br />
1 As with virtually every philosophical position, <strong>the</strong>re are a number of variants.<br />
The historically <strong>in</strong>formed account of emergent properties (Timothy O'Connor<br />
<strong>and</strong> Hong Yu Wong 2006, http://plato.stanford.edu/entries/propertiesemergent/)<br />
<strong>in</strong> <strong>the</strong> Stanford Encyclopedia of <strong>Philosophy</strong>, for example, dist<strong>in</strong>guish<br />
between ontological/metaphysical <strong>and</strong> epistemological construals of <strong>the</strong><br />
same issue, <strong>and</strong> <strong>the</strong>n fur<strong>the</strong>r subdivides those approaches.<br />
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