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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These two conditions differ from (Pu1) <strong>and</strong> (Pu2) <strong>in</strong> a s<strong>in</strong>gle<br />
respect only: <strong>the</strong>y conta<strong>in</strong> <strong>the</strong> term ‘trope’ where<br />
(Pu1) <strong>and</strong> (Pu2) conta<strong>in</strong> <strong>the</strong> term ‘universal’. If (Pu1) <strong>and</strong><br />
(Pu2) lead to a regress, <strong>the</strong>n (Pt1) <strong>and</strong> (Pt2) equally lead to<br />
a regress. Instead of speak<strong>in</strong>g of universals or tropes, we<br />
can also formulate <strong>the</strong> matter <strong>in</strong> general terms, yield<strong>in</strong>g <strong>the</strong><br />
follow<strong>in</strong>g pair of conditions:<br />
(P1) Wherever an entity is <strong>in</strong>stantiated, <strong>the</strong>re is an<br />
<strong>in</strong>stantiation relation (not identical to one of <strong>the</strong> relata).<br />
(P2) The <strong>in</strong>stantiation relation is an entity.<br />
The regress argument poses a threat only to those who<br />
are committed to <strong>the</strong>se two conditions. The trope <strong>the</strong>orist<br />
may deny (P2) as little as <strong>the</strong> realist. He will underst<strong>and</strong><br />
‘entity’ as referr<strong>in</strong>g to tropes because he is committed to<br />
<strong>the</strong> view that all relations are particularised relations,<br />
hence tropes. A difference between trope <strong>the</strong>ory <strong>and</strong> realism<br />
concern<strong>in</strong>g <strong>the</strong>se conditions can thus at most be given<br />
by a difference <strong>in</strong> commitment to (P1). It will now be shown<br />
that <strong>the</strong>re is no such difference.<br />
To see this, we must locate <strong>the</strong> motivation for (P1),<br />
<strong>the</strong> condition that <strong>in</strong>stantiation dem<strong>and</strong>s an <strong>in</strong>stantiation<br />
relation. In my view, <strong>the</strong> motivation lies <strong>in</strong> <strong>the</strong> lack of a<br />
strict supervenience relation between <strong>the</strong> existence of <strong>the</strong><br />
relata of <strong>in</strong>stantiation <strong>and</strong> <strong>in</strong>stantiation itself: given a <strong>and</strong> F,<br />
it is not determ<strong>in</strong>ed that a <strong>in</strong>stantiates F. To illustrate this<br />
po<strong>in</strong>t, consider <strong>the</strong> situation <strong>in</strong> which <strong>the</strong>re are exactly four<br />
entities, particulars a <strong>and</strong> b <strong>and</strong> properties F <strong>and</strong> G. If we<br />
assume that both a <strong>and</strong> b <strong>in</strong>dividually <strong>and</strong> cont<strong>in</strong>gently<br />
<strong>in</strong>stantiate exactly one of <strong>the</strong> properties F <strong>and</strong> G, <strong>and</strong><br />
noth<strong>in</strong>g else, <strong>and</strong> if we assume that both F <strong>and</strong> G<br />
<strong>in</strong>dividually are (cont<strong>in</strong>gently) <strong>in</strong>stantiated by exactly one of<br />
<strong>the</strong> objects a <strong>and</strong> b, <strong>and</strong> by noth<strong>in</strong>g else, <strong>the</strong>n two<br />
situations are possible:<br />
W1: a <strong>in</strong>stantiates F; b <strong>in</strong>stantiates G.<br />
W2: a <strong>in</strong>stantiates G; b <strong>in</strong>stantiates F.<br />
Both situations comprise exactly <strong>the</strong> same particulars <strong>and</strong><br />
<strong>the</strong> same properties. Still, <strong>the</strong> situations differ; <strong>the</strong>y comprise<br />
different facts, different <strong>in</strong>stantiations. This means<br />
that <strong>the</strong> mere existence of particulars <strong>and</strong> properties does<br />
not necessitate a specific <strong>in</strong>stantiation. The mere existence<br />
of <strong>the</strong> car <strong>and</strong> blackness does not necessitate that <strong>the</strong> car<br />
is black. It may still be that <strong>the</strong> car is green, <strong>and</strong> what is<br />
black is <strong>the</strong> bike. The existence of particulars <strong>and</strong> properties<br />
may determ<strong>in</strong>e that facts <strong>and</strong> <strong>in</strong>stantiations obta<strong>in</strong>, as<br />
some authors (<strong>in</strong> particular Wittgenste<strong>in</strong> 1922 4 <strong>and</strong> Armstrong<br />
1997) ma<strong>in</strong>ta<strong>in</strong>. But it does not determ<strong>in</strong>e which<br />
facts, which <strong>in</strong>stantiations obta<strong>in</strong>. As a recent author sums<br />
up this po<strong>in</strong>t:<br />
100<br />
Even if a <strong>and</strong> F-ness cannot exist except <strong>in</strong> some<br />
state of affairs or o<strong>the</strong>r, <strong>the</strong>re is noth<strong>in</strong>g <strong>in</strong> <strong>the</strong> nature<br />
of a <strong>and</strong> noth<strong>in</strong>g <strong>in</strong> <strong>the</strong> nature of F-ness to require<br />
that <strong>the</strong>y comb<strong>in</strong>e with each o<strong>the</strong>r to form a’s be<strong>in</strong>g F.<br />
(Valicella 2000, p. 238)<br />
Instantiation between two entities does not strictly supervene<br />
on <strong>the</strong> existence of <strong>the</strong> entities alone, if <strong>the</strong>se entities<br />
are considered to be cont<strong>in</strong>gently related. We need more<br />
than <strong>the</strong> relata of <strong>in</strong>stantiation. This need is expressed by<br />
condition (P1). (P1) is <strong>the</strong> reaction to cont<strong>in</strong>gent <strong>in</strong>stantia-<br />
4 Wittgenste<strong>in</strong> makes this claim with <strong>the</strong> help of <strong>the</strong> notion of <strong>in</strong>completeness,<br />
which he borrows from Frege (1994/1892) but which he applies to all ‘objects’,<br />
properties <strong>and</strong> particulars alike. Toge<strong>the</strong>r with <strong>the</strong> idea that <strong>in</strong>complete objects<br />
cannot exist on <strong>the</strong>ir own, Wittgenste<strong>in</strong> arrives at his famous view that “[t]he<br />
world is <strong>the</strong> totality of facts, not of objects” (Wittgenste<strong>in</strong> 1922, 1.1).<br />
Does Bradley’s Regress Support Nom<strong>in</strong>alism? — Wolfgang Freitag<br />
tion. The properties F <strong>and</strong> G <strong>in</strong> my example can be understood<br />
both as tropes <strong>and</strong> as universals. 5 It follows that,<br />
given cont<strong>in</strong>gent <strong>in</strong>stantiation, <strong>the</strong> trope <strong>the</strong>orist is as much<br />
committed to (P1) as <strong>the</strong> realist is. David Armstrong has<br />
seen this very clearly:<br />
Suppose that <strong>the</strong> l<strong>in</strong>k between a particular <strong>and</strong> its<br />
tropes is not necessary. Then it is cont<strong>in</strong>gent. But if<br />
it’s cont<strong>in</strong>gent, <strong>the</strong>n it seems that we have a clear<br />
case of a relation between a particular <strong>and</strong> its trope,<br />
<strong>and</strong> an external relation at that. But <strong>the</strong>n a Bradleian<br />
regress ensues […]. (Armstrong 2006, p. 242)<br />
This concludes <strong>the</strong> argument for my first claim: realism is<br />
no more committed to Bradley’s regress than at least one<br />
form of nom<strong>in</strong>alism, namely trope <strong>the</strong>ory. I now proceed to<br />
<strong>the</strong> argument for my second claim: nei<strong>the</strong>r position is<br />
committed to <strong>the</strong> regress.<br />
2. How to avoid Bradley’s regress<br />
2.1 Avoid<strong>in</strong>g commitment to (P1)<br />
Cont<strong>in</strong>gent <strong>in</strong>stantiation leads to (P1) <strong>and</strong> starts <strong>the</strong> regress.<br />
In order to avoid (P1), avoid cont<strong>in</strong>gent <strong>in</strong>stantiation.<br />
Make <strong>in</strong>stantiation necessary. There is a variety of<br />
different positions, both nom<strong>in</strong>alist <strong>and</strong> realist, which conceive<br />
of <strong>in</strong>stantiation as be<strong>in</strong>g necessary <strong>and</strong> hence avoid<br />
– <strong>in</strong>tentionally or not – commitment to (P1):<br />
(1) One position that makes <strong>in</strong>stantiation necessary<br />
is class nom<strong>in</strong>alism. This position, proposed <strong>in</strong>ter alia by<br />
Anthony Qu<strong>in</strong>ton (1957), underst<strong>and</strong>s hav<strong>in</strong>g a property as<br />
be<strong>in</strong>g a member of a certa<strong>in</strong> class of particulars. The<br />
object a <strong>in</strong>stantiates F iff a is a member of <strong>the</strong> F-class.<br />
Because classes are identified by <strong>the</strong>ir members <strong>and</strong><br />
class-membership is a necessary relation, <strong>in</strong>stantiation<br />
between a <strong>and</strong> F strictly supervenes on <strong>the</strong> existence of<br />
<strong>the</strong> F-class alone. In this way, class nom<strong>in</strong>alism can<br />
avoid (P1) <strong>and</strong> <strong>the</strong>reby <strong>the</strong> regress. Class nom<strong>in</strong>alism<br />
naturally escapes (P1).<br />
(2) Trope <strong>the</strong>ory also has its means of<br />
avoid<strong>in</strong>g (P1). In fact, a trope <strong>the</strong>orist has two options:<br />
(2a) Trope <strong>the</strong>ory <strong>in</strong> comb<strong>in</strong>ation with a bundle <strong>the</strong>ory of<br />
particulars, as defended by, e.g., John Locke <strong>and</strong>, <strong>in</strong> more<br />
modern times, by D. C. Williams (1953), holds that<br />
particulars are sets or bundles of tropes. Consequently,<br />
a <strong>in</strong>stantiates F iff <strong>the</strong> F-trope is <strong>in</strong> <strong>the</strong> a-bundle. S<strong>in</strong>ce <strong>the</strong><br />
identity of <strong>the</strong> a-bundle is, I take it, def<strong>in</strong>ed by <strong>the</strong><br />
constitut<strong>in</strong>g tropes, a’s <strong>in</strong>stantiat<strong>in</strong>g F strictly supervenes<br />
on <strong>the</strong> existence of <strong>the</strong> a-bundle. (2b) The second type of<br />
trope <strong>the</strong>ory comb<strong>in</strong>es a subject–attribute view with <strong>the</strong><br />
doctr<strong>in</strong>e of nontransferable tropes. A recent proponent of<br />
this view is John Heil (2003, chs. 12 <strong>and</strong> 13), although he<br />
prefers <strong>the</strong> term ‘mode’ to <strong>the</strong> term ‘trope’. Accord<strong>in</strong>g to<br />
this position, a trope is <strong>in</strong>stantiated by <strong>the</strong> very same<br />
object <strong>in</strong> all possible worlds. Given <strong>the</strong> nontransferable<br />
trope F <strong>and</strong> <strong>the</strong> particular a, <strong>the</strong> <strong>in</strong>stantiation between<br />
a <strong>and</strong> F follows by necessity. 6 Aga<strong>in</strong> (P1) can be avoided.<br />
5 That F <strong>and</strong> G, understood as universals, are, <strong>in</strong> <strong>the</strong> case discussed, <strong>in</strong>stantiated<br />
only by a s<strong>in</strong>gle entity, is not of relevance here. To see this, simply<br />
change <strong>the</strong> example accord<strong>in</strong>gly.<br />
6 This is simplified. There are at least three conceptions of <strong>the</strong> nontransferability<br />
of tropes: (i) F is <strong>in</strong>stantiated <strong>in</strong> all possible worlds, <strong>and</strong> it is<br />
<strong>in</strong>stantiated <strong>in</strong> all possible worlds by a. This presumably implies that a must<br />
exist <strong>in</strong> all possible worlds. (ii) F is not <strong>in</strong>stantiated <strong>in</strong> all possible worlds, but<br />
where it is, it is <strong>in</strong>stantiated by a. Option (ii) comes <strong>in</strong> two varieties: (a) <strong>in</strong> those<br />
worlds <strong>in</strong> which F is not <strong>in</strong>stantiated, a does not exist; (b) <strong>in</strong> some worlds <strong>in</strong><br />
which F is not <strong>in</strong>stantiated, a does exist. The supervenience claim <strong>in</strong> <strong>the</strong> ma<strong>in</strong><br />
text holds only for (i) <strong>and</strong> (ii.a).