## 1. Historical treatments



The following historical trajectory motivates the characteristic
features and certain treatments of determinables and determinates;
those interested in cutting to the contemporary chase can skip to
SS2 with little loss of continuity.



The terminology of determinables and determinates stems from ancient
and scholastic treatment of the definition of a species, as analyzable
into two parts: a genus, or generic part of an essence--the
*pars determinabilis essentiae*, and the differentia, or
differentiating part of an essence--the *pars determinans
essentiae*. As we'll see, the terminology and its original
application eventually went separate ways, with the genus-species
relation standardly being treated in conjunctive terms (with a given
species being identified with the conjunction of a genus and one or
more differentia), and determination being treated as a distinctive
non-conjunctive specification
 relation.[1]


### 1.1 Aristotle's identification of a non-conjunctive specification relation



Some recent commentators have suggested that the notion of
determination has a precursor in ancient times. For example, Granger
(1984) has proposed that Aristotle's preferred treatment of the
relation between kinds and forms (a.k.a. genus and species) involves
key features of determination. Granger suggests that Aristotle's
conception of a form/species evolves from a conjunctive conception (as
in *Topics* VI.3. 140a27-29) to one on which differentia
entail their associated kind/genus rather than conjunctively
supplementing it. Granger motivates the non-conjunctive conception on
grounds that "Aristotle clearly maintains that [...] the genus
does not exist apart from its species, or exists merely as
matter" (1984: 15); in turn, he takes this conception to
indicate that



> 
> 
> genus and differentia are best viewed in terms of determinable and
> determinate. [...] A determinate [...] is not a conjunction
> of its determinable and something else logically distinct from its
> determinable. (1984: 19)
> 
> 
> 



Salmieri (2008) offers further support for this interpretation, citing
another important feature of determination--namely, that
determinates differ specifically in respect of their determinable. As
Salmieri puts it,



> 
> 
> Certain things are not merely other than one another--as
> *blue* is other to both *loud* and
> *inflation*--but are different from or "opponent
> to" one another, as *blue* is different from
> *red*. (2008: 78)
> 
> 
> 



And he sees this distinction as operative in Aristotle's
(*Metaphysics* I.3-4) remarks:



> 
> 
> But difference (diaphora)
> and otherness (eterotes) are
> distinct (allo). For, while the
> other and that which it is other than are not necessarily other in
> something (for everything that is some being is either other or the
> same), the different differs from something in something, so that
> it's necessary for there to be something the same in which they
> differ. This same thing is a kind or form; for every different thing
> differs either {i} in kind or {ii} in form [...]. (1054b22-31
> cf. 1018a9-15; translation quoted from Salmieri 2008, 79)
> 
> 
> 



The previous features--non-conjunctive entailment of the less by
the more specific, the specification's being somehow "in
respect of" the less specific, and the more specific
features' being opponent to one other--are indeed
characteristic features of determination, contrasting with other
specification relations (modulo deflationary strategies; we
won't always carry this qualification forward). As such, there
is at least a case here for Salmieri's claim that "we
ought to recognise Aristotle as the originator of this
distinction" (2008: 79).


### 1.2 Early modern motivations for determination



Throughout the scholastic and modern periods the genus-species and
genus-differentia relations are often treated in what Prior (1949)
calls "a confused blending" of the conjunct-conjunction
and determination relations. In the modern period motivations for
distinguishing the latter relations become increasingly salient.



One motivation stems from Leibniz's observation that a
conjunctive treatment of the genus-species relation does not fix a
direction of specification, since one can as easily take the
differentia to be the genus, as vice versa (see *Nouveaux
Essais*, III, iii, 10, Langley's translation, 313). Johnson
(1924) interprets Descartes and Spinoza as attempting to ensure
asymmetry by means of attributes and modes (see Descartes,
*Principles of Philosophy* I.53; Spinoza, *Ethics* 1p8s1
and Ep. 50), which Johnson suggests are "almost
equivalent" to the notions of determinable and determinate:



> 
> 
> What I call a determinable is almost equivalent to what they call an
> attribute, and my determinate almost equivalent to their mode of an
> attribute. (1924: III, v. 1)
> 
> 
> 



Prior (1949) similarly sees Spinoza as aiming to ensure asymmetry by
means of something like determination:



> 
> 
> If Leibniz brought consistency into the medieval view of the
> distinctness of genus and differentia by making the relation between
> them symmetrical, Spinoza brought consistency into the medieval view
> of the asymmetry of the relation between them by denying their
> distinctness. Spinoza's "modes" are not new
> qualities added to his "attributes", or qualities formed
> by the addition of something else to them, but determinations of them.
> (1949: 7)
> 
> 
> 



Prior also sees Locke as relying on the distinctive incompatibility of
same-level determinates as making sense of why "any subject may
have of each sort of primary qualities but one particular at
once", and similarly for "all sensible ideas peculiar to
each sense" (Locke, *Essay*, IV iii 5).



In the work of Locke and other empiricists, we also see precursors of
certain contemporary anti-realist or reductivist accounts on which
determinable attributions either indeterminately refer to determinate
properties (as Berkeley [1710] suggests, more generally, for
'abstract' terms), or on which determinable attributions
are (merely) ways of classifying determinates. Prior's
description of Locke's view might be seen as compatible with
either approach:



> 
> 
> Though we speak of an object as colored, what is there being referred
> to is not really a quality of the object but a quality of one of its
> qualities; what is meant is that one of its qualities belongs to the
> class "colors". (Prior 1949: 8-9)
> 
> 
> 


### 1.3 Johnson's systematic treatment of determination



The terminology of 'determinables' and
'determinates' as indicative of a distinctive relation is
first found in Volume I, Chapter XI--'The
Determinable'--of W. E. Johnson's *Logic*
(1921):



> 
> 
> I propose to call such terms as *color* and *shape*
> determinables in relation to such terms as *red* and
> *circular* which will be called determinates; and, in
> introducing this new terminology, to examine the distinction between
> the relation of *red* to *color* and the relation of
> Plato to *man* .... (1921: I, xi, 1)
> 
> 
> 



Johnson's discussion is also the first systematic attempt to
characterize the key features of determinables, determinates, and
their relation (see esp. 1921: 173-185), though as below, he is
not always clear about whether these features apply to properties or
rather to predicates. See Prior (1949) and Poli (2004) for detailed
discussion of Johnson's views and his influence on later
authors.



Some of these features are familiar, including that determination is a
specification relation:



> 
> 
> To predicate color or shape of an object obviously characterises it
> less determinately than to predicate of it red or circular; (Johnson
> 1921: I, xi, 1)
> 
> 
> 



that this specification is non-conjunctive:



> 
> 
> there is a genuine difference between that process of increased
> determination which conjunctivally introduces foreign adjectives, and
> that other process by which without increasing, so to speak, the
> number of adjectives, we define them more
>  determinately;[2]
>  (Johnson 1921: I, xi, 3)
> 
> 
> 



that same-level determinates are incompatible:



> 
> 
> if any determinate adjective characterises a given substantive, then
> it is impossible that any other determinate under the same
> determinable should characterise the same substantive; (Johnson 1921:
> I, xi, 4)
> 
> 
> 



and that same-level determinates are moreover
"opponent":



> 
> 
> the unique and peculiar kind of difference that subsists between the
> several determinates under the same determinable [...] does not
> subsist between any one of them and an adjective under some other
> determinable. (Johnson 1921: I, xi, 1)
> 
> 
> 



Johnson moreover develops these features, suggesting, for example,
that opponent differences often reflect that determinates are
comparable:



> 
> 
> many determinates under the same determinable [are such] that the
> differences between different pairs of determinates can be compared
> with one another [...]; e.g. the difference between red and
> yellow is greater than that between red and orange. (Johnson 1921: I,
> xi, 4)
> 
> 
> 



Attention to determinate comparability leads Johnson to suggest that
determinables may be determined along multiple
"dimensions":



> 
> 
> [A] color may vary according to its hue, brightness and saturation; so
> that the precise determination of a color requires us to define three
> variables which are more or less independent of one another in their
> capacity of co-variation; but in one important sense they are not
> independent of one another, since they could not be manifested in
> separation. The determinate color is therefore single, though complex
> .... (1921: I, xi, 4)
> 
> 
> 



That determinables may have multiple determination dimensions is an
important observation, which plays a foundational role in
Funkhouser's (2006) model of determination (see
 SS3.6.1).



Two other aspects of Johnson's discussion are worth noting.
First, he denies that determinables are in any sense shared by
determinates: "the ground for grouping determinates under one
and the same determinable is not any partial agreement between
them" but rather "the special kind of difference"
(1921: I, xi, 1) distinguishing opposing
 determinates.[3]
 As we'll see, this is a choice point for contemporary accounts.
Second, Johnson assumes that while limits in our perceptual or
instrumental capabilities require that we characterize objects in
determinable terms, it is nonetheless a



> 
> 
> universally adopted postulate that the characters of things which we
> can only characterise more or less indeterminately, are, in actual
> fact, absolutely determinate. (1921: I, xi, 5)
> 
> 
> 



The assumption that determinable characterization reflects (mere)
epistemic, perceptual, or representational limits remains common, and
pushes towards giving one or other deflationary account of
determinables. This is another choice point: on some contemporary
accounts determinables are both real and irreducible to
determinates.


### 1.4 Contemporary additions and refinements



In this sub-section, we discuss certain comparatively recent
contributions which influentially shaped the present understanding of
determination.



Prior's (1949) two-part discussion of determinables and
determinates is historically rich and philosophically subtle.
Interestingly, he suggests that the difference between determinates is
brute, admitting no explanation:



> 
> 
> we can say that the red and the blue agree in being colored, but of
> their difference we can only say either that their color is different,
> or that one is red and the other blue. (1949: 5-6)
> 
> 
> 



Some have seen this sort of statement as broadly contradictory, in
suggesting that what makes determinates similar (e.g., *color*)
is also that in virtue of which they are different ("of their
difference we can only say ... that their color is
different");
 see SS3.2.



Prior also considers and rejects Johnson's assumption that
determinates are similar only in respect to their unique form of
difference, rather suggesting (c.f. Salmieri's discussion of
Aristotle, above) that determinates are similar "in respect
of" that determinable:



> 
> 
> [I]t seems to me that determinates under the same determinable have a
> class unity [...]. Determinates under the same determinable have
> the common relational property [...] of characterising whatever
> they do characterise in a certain respect. Redness, blueness, etc.,
> all characterise objects, as we say, "in respect of their
> color"; triangularity, squareness, etc., "in respect of
> their shape". And this is surely quite fundamental to the notion
> of being a determinate under a determinable. (1949: 13)
> 
> 
> 



That determinates characterize objects in respect of their
determinables is indeed a key feature of determination, though there
remains disagreement about how best to metaphysically articulate this
feature (e.g., as involving shared determinables or not).



Prior takes this feature to push against deflationary approaches on
which determinables exist, at best, merely to classify the having of
determinate properties. On the contrary, he maintains, if determinates
are unified by characterizing objects in a certain respect, then



> 
> 
> the "respects in which objects are to be characterised",
> to which determinable adjectives refer, are related to the objects not
> less but more intimately than the determinate qualities which
> "characterise" them. (1949: 13)
> 
> 
> 



Moving on, Searle (1959) usefully highlights that determination
appears to contrast not just with the conjunct-conjunction relation,
but also with the disjunction-disjunct relation:



> 
> 
> [C]learly not any two terms which stand in the relation of greater to
> less specific ipso stand in the relation of determinate to
> determinable: "yellow" is in some sense more specific than
> "yellow or angry" but it is not a determinate of
> "yellow or angry" in the sense in which it is a
> determinate of "color". (1959: 141-2)
> 
> 
> 



Searle also offers an explicit criterion of determination:



> 
> 
> For any two terms \(A\) and \(B\), \(A\) is a determinate of \(B\) if
> and only if \(A\) is a non-conjunctive specifier of \(B\), and \(A\)
> is logically related to all other non-conjunctive specifiers of \(B\)
> [where] any two terms are logically [i.e., conceptually] related if
> either entails the other or either entails the negation of the other.
> (1959: 148)
> 
> 
> 



Interestingly, this criterion doesn't rule out that \(B\) is a
disjunction of its determinates ('non-conjunctive
specifiers'), so long as the determinates stand in the requisite
conceptual entailment relations. Note also that Searle moves fluidly
between talk of determinable properties and talk of determinable
'terms'; until recently, this sort of slide was
common.



Searle notes, as well, that the structure of determinables and
determinates in the same family may give rise to "levels"
of determinates ordered by degree of specificity; as he says,
"we would like some way of showing that e.g., 'red'
and 'yellow' are on the same level as determinates of
'color' whereas 'scarlet' is on a different
and lower level" (1959: 145). Here too he offers a
criterion:



> 
> 
> Two terms \(A\) and \(B\) are same level determinates of \(C\) if and
> only if they are both determinates of \(C\) and neither is a specifier
> of the other. (1959: 149)
> 
> 
> 



(Here the notion of a 'specifier' is one according to
which *X* specifies *Y* iff *X* entails
*Y*, but *Y* does not entail *X*.) Seale's
criterion is flawed, however, since while it correctly deems
*red* and *yellow* same-level determinates, and
correctly deems *red* and *scarlet* different-level
determinates, it incorrectly deems *red* and *buttercup*
same-level determinates.



Next, Armstrong's investigations into the metaphysics of
properties (in, e.g., his 1978a,b, 1989, 1997, and 2010) are notable,
first, in treating determination as an explicitly metaphysical
relation, and second, in raising to salience the important question of
whether determinables are ontologically reducible to determinates,
asked against the commonly accepted background assumption that reality
itself is maximally determinate. As we'll see, Armstrong's
own position on this score swings from reductionism (1987) to
non-reductionism (1997), and back again (2010).



Finally, Yablo's (1992) is notable in offering a modal account
of (perhaps better: necessary condition on) determination as a
relation of asymmetric dependence, and in extending determination to
particulars (events) as well as properties. Since asymmetric
necessitation now serves as a common minimal characterization of
determination, it's worth seeing how Yablo motivates this
approach. He starts by observing a parallel between intuitive
characterizations of identity and of determination, as holding between
properties:




\(P\) is identical to \(Q\) iff: for a thing to be \(P\) is for it to
be \(Q\).



\(P\) determines \(Q\) iff: for a thing to be \(P\) is for it to be
\(Q\), not *simpliciter*, but in a specific way.




The parallel is useful in suggesting that determination is, like
identity, a particularly intimate relation, in that determinable and
determinate types and/or tokens may not be wholly distinct, and also
in suggesting a modal treatment of determination. Hence just as the
characterization of identity is illuminated by the following modal
condition (stemming from the principle of the indiscernibility of
identicals):


* (I) \(P\) is identical
to \(Q\) only if: necessarily, for all \(x\), \(x\) has \(P\) iff
\(x\) has \(Q\).



so too is the characterization of determination illuminated by the
following modal condition:


* (D)\(P\) determines
\(Q\) (\(P > Q\)) only if: (i) necessarily, for all \(x\), if \(x\)
has \(P\) then \(x\) has \(Q\); and (ii) possibly, for some \(x\),
\(x\) has \(Q\) but lacks \(P\).



The parallel also suggests that an account of determination
needn't impose conditions on conceptual entailment relations (as
Searle's did): just as Kripke's (1980) results undermine
the need for a conceptual entailment requirement on identity (e.g.,
water might be identical with H\(\_2\)O even if 'water' and
'H\(\_2\)O' don't conceptually entail each other),
"we should discount the traditional doctrine's conceptual
component and reconceive determination in wholly metaphysical
terms" (Yablo 1992: 253). That said, as Yablo admits, asymmetric
necessitation alone is insufficient to characterize determination
(since, e.g., allowing conjunctions to determine their conjuncts). We
will later consider various ways of filling in the modal condition,
including Yablo's own essence-based approach
 (SS3.5.1).



Yablo's discussion is also notable in highlighting an important
seeming feature of determinables and determinates, according to which
they do not causally compete:



> 
> 
> [No causal exclusion principle can] apply to determinates and their
> determinables--for we know that they are not causal rivals.
> [...] any credible reconstruction of the exclusion principle must
> respect the truism that determinates do not contend with their
> determinables for causal influence. (1992: 259)
> 
> 
> 



This feature is key to a recently popular strategy for solving the
problem of mental (and more generally, higher-level)
causation--an intriguing application which raised to salience the
potential usefulness of determination for metaphysical and other
philosophical purposes (see SS5.2).


## 2. Features and ontological categories


### 2.1 Features



We are now in position to list the features commonly taken to
characterize determinables, determinates, and their
 relation;[4]
 the presentation is in terms of properties, and may require
adjustment to apply to entities of other categories
 (see SS2.2).
 This is not a minimal or axiomatic set: some features follow from
others; moreover, there are cases to be made that some of these
features do not hold in full generality. In addition, how to
metaphysically understand these features varies, in ways we will
discuss down the line.


1. *Increased specificity*: If \(P\) is a determinate of
('determines') \(Q\), then to be \(P\) is to be \(Q\), in
a specific way.



Determination relates properties that are more or less specific,
relative to each other. For example, *red* is a determinate of
color; *scarlet* is a determinate of *red*.
2. *Irreflexivity*, *Asymmetry*, *Transitivity*: For
no \(P\) does \(P\) determine \(P\); if \(P\) determines \(Q\), then
\(Q\) does not determine \(P\); if \(R\) determines \(P\), and \(P\)
determines \(Q\), then \(R\) determines \(Q\).



These features, characteristic of strict partial orderings, follow
just from *Increased specificity*. For example,
*scarlet* does not determine itself, since no property can be
more specific than itself. If *scarlet* determines
*red*, then *red* does not determine *scarlet*,
since *red* cannot be both less and more specific than
*scarlet*. And if to be *scarlet* is to be red, in a
specific way, and to be *red* is to be colored, in a specific
way, then to be *scarlet* is to be a yet more specific way of
being colored, such that *scarlet* determines
*color*.
3. *Relative, leveled determination*: Except for minimally
specific determinables and maximally specific determinates, a
property's characterization as determinable or determinate is
relative. Relatedly, determinables can be determined at different
'levels' of specificity.



For example, *red* is a determinate of *color*, but a
determinable of *scarlet*; *red*, *blue*, and
*yellow* determine *color* at one level of
specification; *scarlet*, *navy*, and *buttercup*
determine *color* at another (more finely grained) level of
specification.
4. *Determination 'in respect of' determinables*: If
\(P\) determines \(Q\), \(P\) is more specific than \(Q\) in respect
of \(Q\).



The increase in specificity associated with determinates is, more
specifically, 'in respect of' the
 determinable.[5]
 For example, if *red* determines *color*, *red*
is more specific than *color* in respect of *color*.
Determination in respect of a determinable is sometimes further
explicated as involving specification along one or more
'determination dimensions' of the determinable--for
example, the determination dimensions of *color* are commonly
supposed to be *hue*, *saturation*, and
*brightness*.
5. *Determinate similarity/comparability*: If \(P\) and \(R\) are
different same-level determinates of a determinable \(Q\), then \(P\)
and \(R\) are similar, and moreover comparable, in respect of
\(Q\).



That determination is 'in respect of' determinables gives
rise to similarity and systematic comparability relations among
determinates. For example, determinates of
*color*--*red*, *blue*, *orange*,
etc.--are all similar in being colors, and any two colors are
comparable in this respect: *red* is more similar to
*orange* than to *blue* in respect of *color*,
and so on.
6. *Non-conjunctive specification*: if \(P\) determines \(Q\),
then \(P\) is not identical with any conjunctive property conjoining
\(Q\) with any property or properties independent of \(Q\).



The increase in specificity associated with determinates does not
involve conjoining or otherwise combining the determinable with
another property independent of the determinable. For example,
*red* is not appropriately understood as the conjunction of
*color* and another property independent of *color*.
7. *Non-disjunctive specification*: if \(P\) determines \(Q\),
then \(Q\) is not identical with any disjunctive property disjoining
\(P\) with any property or properties independent of \(P\).



The increase in specificity associated with determinates does not
involve disjunctive elimination. For example, *color* is not a
disjunction of *red* and some other property or properties
independent of *red*.
8. *Determinable inheritance*: For every determinable \(Q\) of a
determinate \(P\): if \(x\) has \(P\) at a time \(t\) then \(x\) must
have \(Q\) at \(t\).



Objects must have every determinable of any determinates they have.
For example, if something is scarlet, then it must also be both red
and colored.
9. *Requisite determination*: If \(x\) has a determinable \(Q\) at
a time \(t\), then for every level \(L\) of determination of \(Q\):
\(x\) must have some \(L\)-level determinate \(P\) of \(Q\) at
\(t\).



Objects must have a determinate of every determinable they have. For
example, if something is colored, then it must be some specific color
(e.g., red), and if something is red, then it must be some specific
shade of red (e.g., scarlet).
10. *Multiple determinates*: For every determinate \(P\) of a
determinable \(Q\), there is a determinate \(R\) of \(Q\) that is
distinct from, but at the same level of specificity as, \(P\).



With determinate specificity comes multiplicity or diversity. For
example, *color* has multiple determinates (*red*,
*blue*, *yellow*, and so on); *red* has multiple
determinates (*scarlet*, *crimson*, *burgundy*,
and so on).
11. *Determinate incompatibility*: If \(x\) has determinate \(P\)
of determinable \(Q\) at time \(t\), then \(x\) cannot have, at \(t\),
any other determinate \(R\) of \(Q\) at the same level of specificity
as \(P\).



For example, an object cannot be both *red* and *blue*
all over, at a
 time.[6]
 Determinate incompatibility is moreover 'opponent' in
that same-level determinates are exclusive
 alternatives.[7]
12. *Unique determination*: If \(x\) has a determinable \(Q\) at a
time, then \(x\) has a unique--one and only one--determinate
\(P\) at any given level of specification at that time.



*Unique determination* is entailed by *Requisite
determination* and *Determinate incompatibility*.
13. *Asymmetric modal dependence*: if \(P\) is a determinate of
\(Q\), then if \(x\) has \(P\) then \(x\) must have \(Q\), but for
some \(y\), \(y\) might have \(Q\) without having \(P\).



For example, anything that is scarlet must be red, but something might
be red without being scarlet (it might rather be, e.g., burgundy).
*Asymmetric modal dependence* is entailed by *Determinable
inheritance*, *Requisite determination*, and *Multiple
determinates*.
14. *Causal compatibility*: Determinables and determinates do not
causally compete.



For example, if a given patch is both *red* and
*scarlet*, there is no in-principle difficulty with both
*red* and *scarlet* being causally efficacious
*vis-a-vis* the pecking of a pigeon trained to peck at
any red patch.



Motivated as they are by a limited range of paradigm cases, not all of
these features may be characteristic of determination in the strong
sense of being required for the holding of that relation, as opposed
to being typically or generally true of some or most instances of the
relation (or its relata).



For example, counterexamples have been offered to *Determinate
incompatibility* (hence *Unique determination*). Johansson
(2004) notes that if *property* is a determinable, then
*Determinate incompatibility* will fail, noting that on this
score "Johnson [...] generalized too quickly" (2004:
117); what is rather true is that "for *some* ontological
determinables [...] two determinates cannot possibly exist in the
same space-time region" (2004: 118). Determinable odors, tastes,
and sounds also appear to have (some) compatible determinates; as
Armstrong (1978b) observes, "a sauce may be both sour and sweet.
A bell may have a tone which is composed of both a fundamental and a
number of higher overtones" (113; see also Fales 1990, Sanford
2014, and Massin 2013).



It may also be questioned whether all determinates of determinables
can be systematically compared, as per *Determinate
similarity/comparability*. It is unclear, for example, whether
being *pentagonal* is more or less similar in respect of
*shape* to being *square* or being *sextagonal*.
It is also unclear whether all determinates of *smell* admit of
systematic comparability (is the smell of pine more similar to the
smell of rose or of violet?), though recent empirical work identifying
the dimensions of "smell space" (see, e.g., Mamlouk &
Martinetz 2004) may reveal an underlying structure of the sort
(appealing to hue, saturation, and brightness) that serves as an
underlying basis for ordering determinate colors (which work might
also bear upon Armstrong's observations, above). The question of
whether all determinables may be systematically ordered with respect
to their determinables, either explicitly or implicitly, matters to
whether determinate/determinable relations can be modeled in spatial
terms along lines proposed by Funkhouser (2006)
 (see SS3.6.1).



*Unique determination* and *Requisite determination* may
also admit of exceptions. One might maintain (see Wilson 2013) that
even for paradigmatic determinables such as *color*, *Unique
determination* is not generally correct, since the case of an
iridescent feather admits of a reasonable interpretation according to
which the feather is (a) colored, (b) red from one perspective, and
(c) blue from another perspective, such that no one determinate shade
is non-arbitrarily identified as "the" unique determinate
determining the determinable *color* had by the feather; in
such a case, the determinates are had, at best, in relativized
 fashion.[8]
 Fales observes that *Requisite determination*



> 
> 
> appears to admit of exceptions in the case of certain objects of
> mental acts: for example, as regards the number of spots on an
> imagined or a hallucinated speckled hen. (1990: 167)
> 
> 
> 



Quantum mechanics and the associated natural treatment of observables
as determinables also offers apparent counterexamples to
*Unique* and *Requisite determination*, associated with
incompatible observables (so that if *position* is determinate,
*momentum* is not; see, e.g., Bokulich 2014: 463), and more
generally cases of value indeterminacy
 (see SS5.3).
 Relatedly, certain understandings of vagueness or indeterminacy
involve the rejection of *Unique* and *Requisite*
determination. Rosen and Smith (2004) suggest that vagueness may
involve an object's having a determinable without determinately
having any corresponding determinate, and Wilson (2013) offers a
determinable-based account of metaphysical indeterminacy as
characteristically involving an entity (object, system) having a
determinable but no unique determinate of the determinable, due either
to there being too many candidate determinates ('glutty'
indeterminacy) or too few ('gappy' indeterminacy); the
latter determinable-based account has been applied to value
indeterminacy in quantum mechanics
 (see SS5.3).
 The connection between the determinable *position* and
theories of location may also push against *Unique* and
*Requisite* determination, insofar as the latter principles
correspond to certain principles of location which are frequently
asserted to be subject to counterexamples involving, e.g., gunky
worlds, where an object may have a location but no exact location (see
Calosi 2019).



Finally, as we will see in
 SS3.4,
 a standard reductive approach to determinables takes these to be
disjunctive properties having associated determinates as disjuncts
(see, e.g., Clapp 2001, Rodriguez-Pereyra 2002, Dosanjh 2021);
disjunctive reductionists uniformly reject *Non-disjunctive
specification* as ever true of determination or its relata. Here
it is also worth noting that a common motivation for anti-realist or
reductionist approaches involves the supposition that, contra
*Causal compatibility*, determinables and determinates do
causally compete.


### 2.2 Ontological categories: bearers and relata



Though paradigm cases of determination (involving *color*,
*shape*, *mass*, and so on) appear to hold between
monadic property types, it is straightforward to extend the notion to
relations, as in suggestions (see Mellor 1998 and French 2014) that
laws of nature are or are constituted by determinable relations
 (see SS5.1).
 Hence Johansson says that while the restriction to monadic types is
'traditional',



> 
> 
> I do not think there are any good reasons for the restriction.
> [...] Relational concepts, just like property concepts, can be
> fitted into determinable-determinate trees. (2000: 117)
> 
> 
> 



Given that determinables are properties (including relations), the
question (what Meinertsen [2021] dubs "Mellor's
question", following discussion in Mellor [1995], Ch. 16) arises
of what determinables are properties of. It is commonly assumed that
determinables, like determinates, are properties of particulars (and
moreover, of the same particular--though certain applications of
determination may depart from this assumption;
 see SS5.3),
 such that, e.g., the table is shaped as well as rectangular. But it
has also been maintained that determinables are second-order
properties--that is, properties of associated determinates (see
Mellor 1995: 208; for a precursor see Prior 1949). See Meinertsen 2021
for a pro-particularist comparative assessment.



More controversially, determination has been taken to hold between
entities of ontological (including representational) categories going
beyond properties and relations.



To start, as above, historical discussion of determinables and
determinates (in, e.g., Johnson 1921) moves fairly freely between talk
of these as representational (linguistic/conceptual) and as
metaphysical. In some such cases, the target is plausibly a properly
metaphysical
 distinction.[9]
 In other cases--e.g., in empiricist treatments--the
characterization of determination in representational terms is clearly
intended to be metaphysically deflationary. We will later revisit
reasons for and against taking determinables or determination at
metaphysical face value
 (SS3.1,
 SS3.2).



Modulo deflationary concerns, there does not appear to be any
in-principle barrier to allowing that determination can hold between
entities of other
 categories.[10]
 Determination has been extended to actions or episodes (see, e.g.,
Mulligan 1992 and Cruse 1995: Ch. 6), events (Yablo 1992), fields (von
Wachter 2000), tropes (Funkhouser 2006), states (Fine 2011), and
substances (Massin 2013). That said, one might maintain (either on
grounds of systematicity or parsimony, or as reflecting independent
commitment to a view of determinables as properties, as above) that
determination as holding between entities of other categories is
ultimately a matter of these falling under or being partly constituted
by determinable and determinate properties. Whatever one's
position on which ontological categories the relata of determination
can fall under, there are (as per metaphysical usual) different
available understandings of the categories at
 issue.[11]



Another question pertaining to ontological categories concerns whether
some or all specification relations are themselves determinates of a
more general relation determinable (see Johansson 2000: sec. 8 for
endorsement of such a view).


## 3. Contemporary accounts of determinables and determinates



We turn now to canvassing contemporary accounts of determinables,
determinates, and their relation. The main varieties of contemporary
ontological accounts include anti-realist accounts, on which
determinables do not exist; reductive accounts, on which determinables
exist but are metaphysically reducible to (that is, identical with)
some or other construction of determinates; and non-reductive
accounts, on which determinables exist and are not metaphysically
reducible to any construction of determinates. Non-reductive accounts
furthermore split into versions on which determinables are (always)
less fundamental than associated determinates, and accounts on which
determinables can be as fundamental as, or even more fundamental than,
determinates; we reserve treatment of this further issue for
 SS4.
 A different sort of contemporary account is directed not so much at
the ontological question(s) as at elucidating certain structural or
broadly logical aspects of determination or associated relata.



As background for the ontological accounts to come, we start with a
number of considerations commonly offered as providing prima facie
support for taking determinables to exist, and to moreover be
ontologically irreducible to (again: not identical to any construction
of) determinates. We then consider some preliminary motivations for
deflationary (anti-realist or reductive) treatments of determinables.
One might wonder whether the motivations for taking determinables to
exist might be presented independently of the motivations for taking
determinables to be irreducible; this proves difficult, however, for
there typically isn't enough daylight between the initial
motivations for existence and for irreducibility to prise them apart.
The presentation thus reflects that the motivations for reducibility
(or for anti-realism) come later, as pushing against taking the prima
facie appearances of irreducible determinables at face value.


### 3.1 Preliminary motivations for the existence and irreducibility of determinables



There are perceptual, scientific, causal, semantic, and metaphysical
considerations weighing in prima facie favor of determinables'
existing and moreover being metaphysically irreducible to
determinates. Again, these motivations are preliminary; as we'll
see down the line, anti-realists and reductionists take there to be
good reasons to resist taking the seeming appearances of existence
and/or irreducibility at face value
 (see SS3.2).


#### 3.1.1 Determinables as perceived



Perception provides one source of prima facie support for there being
irreducible determinables. The best such motivations are indirect,
since bare claims that we can perceive determinables as distinct from
determinates are
 disputable.[12]
 One such indirect motivation appeals to Sorites phenomena as
indicating that we fail to perceive fully determinate instances of
many properties, including colors, tones, and textures. As Fales puts
it:



> 
> 
> [This] is a conclusion which seems forced upon us by the fact that
> each member of a series of colors, etc., may be perceptually
> indistinguishable from its immediate neighbors but easily
> distinguishable from more distant members of the series. (1990:
>  172)[13]
> 
> 
> 



Such a conclusion supports not just the existence but also the
irreducibility of determinables, since candidate reductions of
determinables (to, e.g., disjunctions of associated determinates)
appear to entail that any instance of a determinable is in fact an
instance of a (say, disjunct) determinate; but in that case
neighbouring patches in a Sorites series would be perceptually
distinguishable, which they aren't.



A second indirect perceptual motivation for irreducible determinables
reflects that our perception of macro-objects typically fails to
register micro-determinate details. For example, *shape* is a
paradigmatic determinable, but we do not perceive the shapes of trees,
tables, and the like, in fully determinate microscopic detail (see
Hellie 2005, Stazicker 2016). In re this and the Sorites motivation,
it is worth noting that even if perceived objects are themselves
maximally determinate, perceptual experience may still motivate
irreducible determinables. As Wilson observes:



> 
> 
> Perhaps the (instances of) properties perceived are really maximally
> determinate, and only perceptual features or modes of presentation are
> determinable; but features of perceptual experience are also aspects
> of reality, so the larger point remains. (2012: 5)
> 
> 
> 



A third indirect perceptual motivation for irreducible determinables
is that these best explain our being able to perceive that different
determinates are similar in the relevant determinable respect. Hence
Fales suggests that since we are able "to notice or be aware
of" the similarity between different shades of red, "it
seems clear that red is observable every time we observe an instance
of a shade of red, even though it is not separable from that shade,
but is in the shade" (1990: 172).


#### 3.1.2 Determinables as scientific posits



Both fundamental physical and special-scientific posits and laws
appear to be characterized, at least in part, in determinable terms.
As Armstrong (1997) and French (2014) observe, it is natural to see
fundamental physical laws as relating determinables, such as mass and
charge, or to themselves be determinable
 relations.[14]
 Special science laws are also naturally seen as involving features
which are determinable in not being maximally precise; for example,
the features of aggregates relevant to thermodynamics and statistical
mechanics average over features of the lower-level entities composing
the aggregate, and morphological and physiological features of plants
and animals are characterized in determinable or functional terms,
again abstracting from micro-physical details. Relatedly, that special
science features abstract from micro-physical details enters into
various arguments for these being irreducible (see, e.g., Batterman
1998, Wilson 2010). More generally, the posit of existing and
irreducible determinables in both fundamental and special sciences is
in line with a principle of explanation pervasive in the sciences,
according to which good explanations do not cite unnecessary details
(see, e.g., Strevens
 2004).[15]


#### 3.1.3 Determinables as causally unspecific



Determinables appear to be causally unspecific, in having fewer
powers--in being able to contribute to causing fewer effects, in
the circumstances--than their associated determinates. For
example, *red* has the power to get Sophie the pigeon, who
pecks at any red thing, to peck; but *red* doesn't have
the power to get Sophie's picky cousin Alice, who pecks only at
scarlet patches, to peck; for a red patch might be not scarlet, but
some other shade of red--say, burgundy (see Yablo 1992, Wilson
1999, and Shoemaker 2001). Such a lack of causal specificity, combined
with a principle of individuation of scientific properties according
to which they are (perhaps only contingently) distinguished by
different sets of powers, has been taken to support not just the
existence but the irreducibility of determinable features. For
example, since instances of disjunctive properties are identical to
instances of their disjuncts, reducing determinables to disjunctions
of associated determinates would render determinable instances as
causally specific as determinate instances, and so fail to accommodate
the seeming causal unspecificity of determinables.


#### 3.1.4 Determinables as semantic referents



On a simple and in some sense default semantics, a sentence of the
form '\(a\) is \(F\)' is true just in case the entity
picked out by \(a\) has the property picked out by \(F\). Hence if
'This ruby is red' is true then on the default semantics
the predicate 'red' refers to the determinable
*red.* Irreducibility might moreover be motivated (see Rosen
2010:128) by noting that a speaker may be competent with a
determinable predicate without being familiar with all the associated
determinates (as reductions of determinables to logical constructions
of determinates might be thought to require).


#### 3.1.5 Determinables as a basis for similarity among determinates



As previously, one motivation for determinables is as providing a
metaphysical basis for perceived similarity among determinates
(Johansson 2000). More generally, determinables may be considered
'natural' in the 'joint-carving' sense of
Lewis (1983) in virtue of providing a non-gerrymandered basis for
objective similarity among determinates (Wilson 2012).



Again, each of the motivations in (3.1.1) - (3.1.5) is
preliminary. If the seeming appearance of there being irreducible
determinables can be defended against objections, however, the
philosophical work these can do in encoding distinctively unspecific
aspects of reality (as per the applications in
 SS5)
 would constitute additional positive support for their posit.


### 3.2 Preliminary motivations against the existence or irreducibility of determinables



The main preliminary motivations against determinables existing or
being metaphysically irreducible to determinates reflect concerns that
such determinables would be unparsimonious, give rise to causal
overdetermination, and/or violate the supposition that reality is
ultimately or fundamentally maximally determinate. These concerns and
associated support for anti-realist ('eliminativist') or
realist reductionist accounts are similar to those sometimes brought
to bear against irreducible higher-level (e.g., special scientific)
goings-on. Here again, the motivations are preliminary; as we'll
see down the line, realists offer various responses to these
concerns.



**3.2.1 Reality as maximally determinate**



One objection to irreducible determinables appeals to the supposition
that reality itself is maximally determinate, such that there are no
irreducible determinable properties; as Armstrong maintains,
"[a]ll universals must be determinate" (1978b: 117).
Relatedly, many suppose that there is no "vagueness" in
the world; as Lewis maintains, "[t]he only intelligible account
of vagueness locates it in our thought and language" (1986:
 212).[16]



**3.2.2 Determinables as failing to track exact
similarity**



Another objection to irreducible determinables is that they could not
do the work of explaining exact similarity (in a given respect)
between objects. Hence Armstrong takes "the powerful truism that
universals are strictly identical in their distinct
instantiations" to support the claim that "properties that
are lowest determinates [...] are good candidates for being
universals" (1997: 49). More weakly, one might maintain that the
best reason for positing properties, however understood, is as
explaining exact similarity (in a given respect) between objects.
Supposing so, one might moreover maintain that only determinates
exist, on grounds that particulars having determinable properties
might fail to exactly resemble in determinate respects (e.g., red
objects might be different shades of
 red).[17]



**3.2.3 Determinables as ontologically or causally
redundant**



Irreducible determinables have been taken to be ontologically and
causally redundant, since determinates which we have independent
reason to posit can explain or do anything that determinables
purportedly explain or do. Hence Massin (2013) maintains against
Johansson (2000) that perceived inexact resemblances between
determinates can explain the "seen unity of the determinate
colors", and Gillett and Rives maintain that determinables are
causally unnecessary:



> 
> 
> [P]ositing instances of determinate properties offers the best
> explanation for the causal relations we observe in the world
> [...] Should we also accept that there are instances of
> determinable properties corresponding to predicates such as 'is
> colored' or 'is charged'? [...] There is a
> clear concern that it is ontologically profligate to take two
> properties to be contributing causal powers, a determinable and its
> determinate, where one, the determinate, would apparently suffice.
> (2005: 487)
> 
> 
> 



Heil (2003) levels similar complaints.



**3.2.4 Determinables as inducing causal
overdetermination**



Related to the concern about causal redundancy is the concern that
irreducible broadly scientific determinables induce problematic causal
overdetermination (see again Heil 2003 and Gillett and Rives 2005). To
start, if such determinables exist, they need to earn their causal
 keep.[18]
 But following the concern about causal redundancy, determinables
simply reproduce the powers of their determinates, allowing instances
of distinct properties to give rise to the same effect on a given
occasion. And while such overdetermination sometimes occurs, as in
firing squad or double-rock-throw cases, this is not the right model
for determinables and
 determinates.[19]



**3.2.5 Determinables as incoherent**



Another objection to determinables is that they are in some sense
incoherent. Armstrong (1978a: 106-7, 117-18) maintains
this on grounds that determinables are supposed to constitute the
respect in which associated determinates are both similar and
dissimilar, so that, e.g., *red* and *yellow* are
supposed to be both similar and different in respect of
*colour* (see Elder 1996: 151 for
 discussion).[20]
 Fales (1990: 174) sees the objection as incorrectly presupposing that
determinables are second-order properties of or relations between
determinates. Massin (2013) takes the objection to depend on whether
the similarity at issue is exact or inexact; if inexact, there is no
problem ("[t]wo things that are imperfectly similar in their
colour can be imperfectly dissimilar in their colour") but if
exact--reflecting, e.g., determinables' being exactly
similar constituents of determinates--then incoherence follows,
since differences between determinates must be explained by what
"remains" once the shared determinable is removed, but we
cannot make sense of such removal.


### 3.3 Anti-realist accounts



While motivated by the previous concerns, anti-realists about
determinables also aim to explain or explain away (or
"debunk") at least some seeming motivations for
determinables. A common debunking strategy appeals to something like
Berkeley's (1710) claim that it is a mistake to suppose that
general terms denote abstract
 ideas.[21]
 For example, Heil (2003) echoes Berkeley's claim, taking
seeming semantic reasons for positing determinables to reflect an
uncritical tendency to suppose that "we can 'read
off' features of reality from our ways of speaking about
it" (207), such that even if, e.g., the predicate 'is
red' truly applies to some objects (tomatoes, apples, rubies) we
should not take this to be in virtue of their possessing the
"*very same* property".



At least five positive anti-realist accounts of determinable terms or
concepts and their function are available. First is an account on
which general terms/concepts indeterminately refer to determinate
features--here, generality is placed in language or mind, rather
than world (see Berkeley
 1710).[22]
 Second is a pragmatic account, on which the function of determinable
terms reflects that we happen to have perceptual systems suited for
tracking certain inexact similarities between objects having
(ultimately highly complex) determinate properties (see Heil 2003).
That the 'work' determinable terms do consists in tracking
inexact similarities between objects or determinates is also a theme
in the remaining anti-realist accounts. Third is an account on which
determinable terms are higher-order predicates of determinate
predicates (see Searle
 1959).[23]
 Fourth is an account on which determinable predicates are names of
classes of properties. Hence Mill maintains that determinable terms
are



> 
> 
> names not of one single and definite attribute, but of a class of
> attributes. Such is the word color, which is a name common to
> whiteness, redness, etc. (1843/1973: I.ii.5)
> 
> 
> 



Fifth is an account on which to have a determinable is just to have
one of the associated determinates. Hence Armstrong maintains that



> 
> 
> For a particular to "instantiate" a determinable is
> [...] for it to instantiate just one of a class of
> universals' [...] having the determinable property entails
> no more than having one of the determinate properties. (1997: 53; see
> also Armstrong 1978)
> 
> 
> 



One concern with anti-realist accounts has to do with the source of
classification of determinates under a determinable term or concept.
As above, this is usually taken to involve inexact resemblance, but if
inexact resemblance is primitive, then objections of the sort leveled
against resemblance nominalist treatments of inexact resemblance may
arise, *mutatis mutandis*--notably, that differentially
resembling pairs will themselves stand in second-order or higher
primitive resemblance relations, giving rise to regress (see Fales
1990: 117-20 for discussion, and Rodriguez-Pereyra 2002: Ch. 6
for a response). An alternative means of classification of
determinates appeals to "naturalness" (as per Lewis 1983)
as a primitive predicate or property binding determinates into
classes, but this approach, it might be complained, is not clearly
explanatory. Perhaps the most developed deflationary account of
determinate classification is Armstrong's, on which "the
resemblance of determinate universals is constituted by partial
identity, where the greater the resemblance the greater degree of
identity" (1997: 51), such that, for example, determinate
lengths resemble in virtue of sharing unit length
 universals.[24]
 Armstrong argues that his account makes sense of various features of
determination: *Determinate incompatibility* is accommodated
since, e.g., an object's length cannot be identical to different
sums of unit lengths; *Determinate similarity/comparability* is
accommodated since different determinate lengths share some but not
all unit lengths; *Asymmetric modal dependence* is accommodated
since specific sums of unit lengths entail the having of length, but
not *vice versa*. It has been complained, however, that such an
account cannot handle the full range of
 cases.[25]



A second concern is that the presupposition that all properties are
ultimately maximally determinate violates certain possible and
potentially actual conceptions of natural reality. For example, if
objects fill space, and space is both continuous and gunky (i.e., such
that every entity has proper parts), then the shapes and locations of
objects will be indefinitely subject to further determination (see
Salmieri 2008: 78,
 n47).[26]
 And certain interpretations of quantum mechanics
 (see SS5.3
 for further discussion) and certain field-theoretic understandings of
fundamental particles as having infinitely extensible boundaries
(reflecting these particles' being constituted by long-range
interactions) suggest that natural reality is to some extent
irreducibly determinable.



A third and related concern is that it is unclear how the
eliminativist can accommodate (or debunk) all the motivations for
determinables. It remains unclear, for example, how to explain Sorites
phenomena if all properties--including perceptual modes of
presentation--are maximally determinate.


### 3.4 Reductionist accounts



Reductionists take determinables to exist but to be reducible to
determinates--that is, to be identical to classes or broadly
logical constructions of (ultimately maximal) determinates.


#### 3.4.1 Disjunctive reductionism



The most common reductionist strategy takes determinables to be
identical to disjunctions of (ultimately maximal) determinates (see,
e.g., Clapp 2001; Rodriguez-Pereyra 2002; Antony
 2003;[27]
 Massin 2013, and Dosanjh 2021). On this view, for example,
*color* is identical to a disjunctive property having every
maximally specific color shade as a disjunct.



Disjunctivism explains several features of determination:
*Requisite determination* is accommodated since the instancing
of a disjunction requires the instancing of a disjunct;
*Determinable inheritance* is accommodated since the instancing
of a disjunct entails the instancing of any associated disjunctions
(see Rodriguez-Pereyra 2002, Massin 2013); *Causal
compatibility* is accommodated via the identity of determinable
(disjunctive) and determinate (disjunct) instances (see Clapp 2001).
And while disjunctivism violates *Non-disjunctive
specification*, disjunctivists preserve some contrast by
stipulating that determinables are a special sub-class of the class of
disjunctive properties--ones having resembling determinates as
disjuncts (see Clapp 2001; Dosanjh 2021) or which are projectible in
Goodman's (1983) sense (see Antony 2002). Other stipulations may
be required to accommodate *Determinate incompatibility*,
*Determination 'in respect of' determinables*, and
*Unique determination*.



Three concerns face disjunctivist accounts, besides concerns that the
required stipulations are unexplanatory, and that reality may not be
(ultimately, entirely) maximally determinate. The first reflects
reasons for rejecting disjunctive properties. One such
reason--namely, Armstrong's concern that "disjunctive
properties offend against the principle that a genuine property is
identical in its different particulars" (1978a: 20)--may be
put aside if the disjuncts at issue are genuinely resembling, as
proponents of disjunctivism suppose. This response will not, however,
satisfy those taking disjunctions to be mere logical constructions,
with no metaphysical import.



The second concern is that taking the disjuncts identified with
determinates to be genuinely resembling, as is needed in order to
answer Armstrong's concern and to provide an alternative basis
for the contrast flagged in *Non-disjunctive specification*,
will open the door to looking for a source of the supposed
commonality, which source might well end up being an irreducible
determinable. Here again the question of how best to treat the inexact
resemblance between determinates is pressing.



The third concern is that a disjunctive account cannot accommodate
certain prima facie motivations for determinables as present in
perception and thought. To start, if determinables are disjunctions of
maximal determinates, then every instance of a determinable is an
instance of a maximal determinate; but Sorites phenomena and our
failure to perceive micro-determinate shapes of macro-objects seem
precisely to indicate that some instances of determinables in
perception are not maximally determinate. Relatedly (as above), Rosen
suggests that a disjunctivist approach imposes implausibly strong
conditions on competence with determinable terms or concepts, contra a
case in which someone familiar with many shades of blue has no
conception of *cerulean* (indeed, is perhaps even incapable of
thinking of this shade), but where this deficit "would not
prevent him from being competent with the word 'blue', or
from knowing a great deal about the color blue" (2010: 128).


#### 3.4.2 Relational accounts



On a relational account of the sort advocated by Bigelow and Pargetter
(1990), what it is for determinates to fall under a common
determinable is for the determinates to instantiate second-degree
relations of difference from one another, and for pairs of these
differences to in turn instantiate third-degree proportions
(58-62). Bigelow and Pargetter motivate a relational account as
explaining both why determinates are similar and why they differ.
Irreducible determinables are insufficient unto this task, they
maintain, on grounds, first, that taking determinables to be
irreducibly distinct from but necessarily accompanied by determinates
introduces unexplained necessary connections (1990: 118), and second,
that determinables alone don't explain differences between
determinates (1990: 54, 58; see also Armstrong 1978b: 113).



Besides the usual concerns with reductive accounts, two concerns
attach to a relational account. The first is that attention to the way
in which determinates differ doesn't in itself serve to
characterize the way in which determinates resemble. As Elder puts
it,



> 
> 
> although properties such as being blue or rich or stabbingly painful
> do come in different degrees or intensities, there is more that is
> common to the various precise "values" of these properties
> than just that they differ from one another in graduated ways. (1996:
> 155)
> 
> 
> 



The second is that, as Elder also observes, from the metaphysical
irreducibility of determinables to determinates, it doesn't
follow that their necessary connection is mysterious: if



> 
> 
> the various determinates [...] each embodies the same property as
> the others [...] it is hard to see any great mystery in the fact
> that possession of any one of these determinate shades necessarily
> goes with possession of the relevant determinable. (1996: 157)
> 
> 
> 



Also worth noting is that concerns about necessary connections
typically arise from acceptance of Hume's Dictum, according to
which there are no metaphysically necessary connections between
distinct existences; but post-empiricist motivations for believing
this principle are unclear (see MacBride 2005 and Wilson 2010).


### 3.5 Non-reductive accounts



We turn now to accounts on which determinables are taken to
irreducibly exist. These accounts are typically implemented under the
assumption that determinables are less fundamental than--are
metaphysically posterior to--determinates. In
 SS4
 we'll consider whether determinables may be as fundamental as
determinates, and whether certain of the non-reductive accounts to
follow are compatible with fundamental as well as non-fundamental
determinables.


#### 3.5.1 Essence-based accounts



Asymmetric necessitation (i.e., *Asymmetric modal dependence*)
has been taken to be a neutral modal basis for theorizing about
determination. As Yablo initially suggests:



> 
> 
> \(P\) determines \(Q\) just in case the traditional relation's
> first, metaphysical component is in place, where this consists
> primarily in the fact that \(P\) necessitates \(Q\) asymmetrically.
> (1992: 253, note 23)
> 
> 
> 



Since reductionists also accept *Asymmetric modal dependence*,
a modal account requires supplementation if it is to be
non-reductive.



Yablo goes beyond asymmetric necessitation in considering how (token,
particular) events--the assumed relata of the causal
relation--might stand in the determination relation; his approach
appeals to the notion of essence of an event, and to the idea that the
essence of one such event might be included in or subsumed by the
essence of another:



> 
> 
> Determination involves the idea that the requirements associated with
> one thing include the requirements associated with another; and
> although properties are requiremental on their face, particulars are
> not. Hence the need for a notion of individual essence, where
> essential properties of a thing are those it cannot exist without.
> [T]he essence of a thing is supposed to be a measure of what is
> required in order to be that thing. Thus if more is required to be
> \(y\) than to be \(x\), this should be reflected in an inclusion
> relation between their essences:
> 
> 
> 
> 
> When \(q\)'s essence is a subset of \(p\)'s essence, \(p\)
> is said to subsume \(q\) (\(p \geq q\)); and \(p\) determines \(q\)
> (\(p > q\)) when the inclusion is strict. (1992: 261)
> 
> 
> 
> 



Granting that essences exist and bracketing continuing controversy
about their nature (see, e.g., Robertson Ishii and Atkins 2020),
Yablo's approach characterizes determinable events (e.g., a
patch's being coloured at a time) in properly non-reductive
terms at both the type and token levels, and might be extended to a
more general non-reductive account of determinables, capable of
accommodating the range of motivations for irreducible determinables.
Taking determinable events to have essences contained within
associated determinate events would also clearly explain various
features of determination, including (besides *Asymmetric modal
dependence*, which is presumably still in force), *Determinable
inheritance* (constitutive objects of determinate events are also
constitutive objects of determinable events) and *Determination
'in respect of' determinables* (the essences
of/requirements on determinates include but go beyond the essences
of/requirements on their determinables). More needs to be said,
however, if an appeal to essences is to explain other features of
determination, including *Non-conjunctive specification*,
*Requisite determination*, *Determinate
incompatibility*, and--importantly for Yablo's intended
application of determination to the problem of mental causation;
 see SS5.2--*Causal
 compatibility.* The latter feature might be gained if the
essences at issue are constituted by powers (see below), in which case
an essence-based account might shade into a powers-based account, to
be next discussed.


#### 3.5.2 Causal and powers-based accounts



Causal and powers-based accounts of determination are typically
motivated by the problem of mental/higher-level causation, expressed
by the question: How can higher-level properties bring about effects,
as they seem to do, given that the physical properties upon which
these higher-level properties depend are sufficient to cause these
effects? As we'll see in
 SS5.2,
 different causal accounts provide different answers to this question.
An important choice point, which will be tracked here, concerns
whether determinable and determinate instances are taken to be
token-identical.



Though MacDonald and MacDonald (1986) don't officially offer an
account of determination, they were the first to see determination as
useful for addressing the threat of causal overdetermination.
Effectively, they suggest that the relation between mental and
physical properties is analogous to determination: in both cases the
properties at issue are, they maintain, type-distinct but
token-identical, thus avoiding problematic overdetermination while
preserving type-level causal relevance. It is unclear, however,
whether taking determinables and determinates to be token-identical
can accommodate certain of the (e.g., perceptual) motivations for
irreducible determinables; token-identity accounts are also subject to
an extension of Horgan's (1989) 'problem of mental
quausation' and the associated concern with reductive accounts
of mental states, according to which, given that the causal relata are
ultimately located particulars (events, objects, property instances),
the efficacy of determinables *qua* determinable--that is,
*qua* distinctively unspecific--requires that determinable
and determinate tokens as well as types be distinct.



An explicitly causal account of determination is Fale's (1990)
account of 'determinable or generic' and
'specific' universals, on which the former have a proper
subset of the 'causal relations' of the latter:



> 
> 
> If \(S\) and \(S'\) are specific universals and \(G\) is a
> determinable or generic universal under which they both fall, then the
> causal relations between \(G\) and other universals are a subset of
> the causal relations between \(S\) and other universals; and also a
> subset of the causal relations between \(S'\) and other universals.
> For \(S\) and \(S'\) to be species of a common genus is for them to
> share some subset of causal relations, which subset can itself
> constitute the causal essence of a universal, such as \(G\). For \(S\)
> and \(S'\) to be distinct species is for this subset to be a proper
> subset of the causal relations which characterize \(S\), and also of
> the causal relations which characterize \(S'\): there must be some
> causal relation which \(S\) has, but not \(S'\), and some causal
> relation which \(S'\) has, but not \(S\). (1990: 175)
> 
> 
> 



A subset-of-causal-relations account of generic/determinable
universals promisingly accommodates many features of determination,
for reasons similar to those attaching to powers-based accounts,
below. It also ensures the metaphysical irreducibility of a
generic/determinable type to any specific/determinate type, by the
principle of the indiscernibility of identicals (if \(G\) has only a
proper subset of causal relations of \(S\), \(G\) cannot be identified
with \(S\)); and if this proper subset relation is preserved at the
level of tokens, it will also block token-identity. More needs to be
said, however, if this account is to ensure accommodation of
*Non-disjunctive specification* (and more generally, if it is
to block the metaphysical reducibility of determinable types to
certain constructions of determinate types), since one might suggest
(as a variation on the theme of Antony 2003) that disjunctive types,
like Fales's generic types, have (only) the causal relations in
the intersections of their disjunctions. Fales's account also
fails to provide a clear basis for accommodating *Non-conjunctive
specification*, since as stated it is compatible with a given
determinate/species' being conjunctively analyzable into (for
example) a genus and differentia, each associated with a proper subset
of the powers of the species. Even so, Fales' account of
determination is a clear precursor both of Yablo's (1992)
essence-based
 account[28]
 and the powers-based account, to be next discussed.



A powers-based account of determination may be seen as an application
of a powers-based approach to the metaphysical dependence (a.k.a.
'realization') at issue in physicalism (see Wilson 1999).
As Wilson observes, powers serve as a properly metaphysical basis for
characterizing realization (improving on supervenience-based and
epistemic approaches to this notion, in particular); moreover, she
argues, a variety of seemingly diverse non-reductive physicalist
accounts, including Yablo's determination-based account, are
similar in aiming to ensure that the powers of a realized property are
a proper subset of those of its realizing property (properties). Hence
she maintains:



> 
> 
> One way to make [Yablo's] conjecture more plausible is to put
> the point in terms of the causal powers of the properties involved.
> [...] the reason why "determinables and their determinates
> are not causal rivals" is because it is plausible, in the case
> of determinables and determinates, that each causal power of the
> determinable is identical to a causal power of its determinate.
> [Moreover, and for example,] the property of being scarlet, which is a
> determinate of the property of being red, evidently has more causal
> powers than the property of being red. (1999: 47)
> 
> 
> 



These considerations suggest the following first-pass powers-based
account of determination:




*Powers-based determination* (first pass): Property \(P\)
determines property \(Q\) iff \(Q\) is associated with a [non-empty]
proper subset of the powers associated with \(P\).




On this approach, a determinate is more specific than its determinable
(as per *Increased specificity*) in being associated with a
more specific set of powers. Clarke (1999), Shoemaker (2001, 2007),
and Clapp (2001) also take determination to be a case-in-point of a
non-reductive realization relation satisfying the proper subset
condition on powers, where the powers associated with a given
determinable property are those in the intersection of the sets of
powers associated with its determinates.



A powers-based account of determination provides a basis for
distinguishing determinable and determinate instances, contra
MacDonald and MacDonald (1986) and Ehring (1996); for on a
token-identity approach, determinable instances would be associated
with more powers than are associated with their type--but that
would be reason for denying that the instance was of the determinable
type (see Wilson 2011). Hence the proper subset relation between
powers plausibly holds for determinable and determinate tokens as well
as types. This consideration also pushes against taking determinable
types to be metaphysically reducible to (identified with) disjunctive
or other constructions from determinates, since such reductive
strategies entail that instances of determinables and determinates
(and hence the respective sets of token powers) are token-identical.
As such, and in particular, a powers-based approach accommodates
*Non-disjunctive specification*.



Proponents of powers-based accounts accommodate *Non-conjunctive
specification* in different ways. On Shoemaker's version of
a powers-based account of realization/determination,
*Non-conjunctive determination* is stipulated:



> 
> 
> Property \(X\) realizes property \(Y\) just in case the conditional
> powers bestowed by \(Y\) are a subset of the conditional powers
> bestowed by \(X\) (and \(X\) is not a conjunctive property having
> \(Y\) as a conjunct). (2001: 78).
> 
> 
> 



Wilson (2009) rather accommodates *Non-conjunctive
specification* by requiring that the powers in the complement of
the sets associated with a determinate and any of its determinates,
respectively, do not themselves constitute a set associated with any
property, as per her second-pass formulation:




*Powers-based determination (second pass)*: Property \(P\)
determines property \(Q\) iff \(Q\) is associated with a [non-empty]
proper subset of the powers associated with \(P\), and the set of
powers had by \(P\) but not by \(Q\) is not [in itself] associated
with any property.




A powers-based account accommodates most other standard features of
determination. *Causal compatibility* is accommodated, since
every power of a determinable instance is token-identical with a power
of an associated determinate. *Asymmetry*,
*Irreflexivity*, and *Transitivity* are inherited as
features of the proper subset relation between powers.
*Determinable inheritance* is accommodated in that in having a
determinate property with an associated set of powers, an object will
thereby have the determinables associated with proper subsets of the
determinate's powers (assuming that properties are at least
contingently individuated by associated powers; see below for further
discussion). *Determination 'in respect of'
determinables* and *Determinate similarity/comparability*
are accommodated by determinates' sharing the powers of their
associated determinable but having further powers, where the powers of
the determinable constitute the respect in which determinables are
similar, and powers had by determinates but not the determinable serve
as a basis for ordering the determinates by degree of similarity
(effectively: determinates sharing more powers will be more similar).
Accommodation of *Determinable similarity/orderability* also
provides a basis for responding to concerns that we cannot make sense
of irreducible determinables since we cannot 'get a grip'
on the difference-makers of determinates
 (see SS3.2):
 on a powers-based view, the difference-makers are, comprehensibly,
the powers in the complement of determinate and determinable sets.
That said, more could be said about how the sharing of determinable
powers makes sense of how these additional powers count as being
'in respect of' the determinable and its powers, and as
providing a basis for ordering by
 similarity.[29]
 It is also worth noting that a powers-based account does not itself
ensure the accommodation of either *Requisite determination* or
*Unique
 determination*,[30]
 though these omissions may ultimately be a virtue
 (see SS5.3).



A powers-based approach to determination faces two main concerns. One
is that the view requires endorsement of a controversial "causal
theory" of properties, on which properties are (following, e.g.,
Shoemaker 1980) essentially and exhaustively constituted by their
powers; for if properties have non-causal quiddities (primitive
identities, which float modally free of powers), satisfaction of the
proper subset condition on powers won't guarantee that
determinables are completely metaphysically dependent on
('nothing over and above'; 'grounded in')
determinates (see, e.g., Melnyk 2006: 141-43 and McLaughlin
2007), since the status of the determinable's
'quiddity' is left untreated; nor will it explain
*Determinable inheritance*, since satisfaction of the condition
on powers is compatible with the absence of the determinable
quiddities. Here it is worth noting that while certain proponents of a
powers-based approach to determination (e.g., Clarke, Shoemaker,
Clapp) presuppose a causal theory of properties, such a commitment may
be dispensable: since non-causal quiddities are scientifically
inaccessible and besides the point of solving the problem of
higher-level causation
 (see SS5.2),
 their presence or absence is irrelevant to the status of
determination (and more generally, realization) as a relation between
broadly scientific properties (see Wilson 2011, 2021).



A second concern with a powers-based approach is that, in applying
only to broadly scientific goings-on, it doesn't make sense of
determination as holding between abstracta or other entities lacking
powers. In response, a proponent of a powers-based account might try
to extend the approach beyond specifically causal powers to one
involving non-causal functional roles associated with, e.g., being a
number (determinable), and being a prime number (determinate). This
extension remains speculative, however; at present the account is not
fully general.


#### 3.5.3 Constitutional accounts



It is natural to think of irreducible determinables as in some sense
shared parts or constituents of determinates. Such a view would
provide a natural way of accommodating *Determinate
similarity*, *Determinable inheritance*, and other
features. A powers-based account might be seen as taking determinables
or associated powers to be constituent parts of determinates; here we
consider non-powers-based constitutional accounts.



Johansson (2000, 2004) endorses a constitutive account of
determinables--more precisely, of 'maximal'
determinables (such as color, shape, and smell) located at the top of
a determination hierarchy--taking *Determinate similarity*
and *Determinate gradability* as its starting point. According
to Johansson, it is characteristic of determinables and determinates
that "two different determinates of the same determinable can
always be continuously connected" (2000: 108), in a way
providing the basis for the gradeable resemblance of the determinates.
Conversely, he maintains, determinates under wholly different
determinables are not connected in this fashion: "No
color-determinate resembles more closely a shape-determinate or
volume-determinate than any other" (2000: 108). This
'gap' between determinables acts as a criterion, whereby a
determinable is posited if and only if there is such a gap--hence
it is that only maximal determinates exist, by lights of
Johansson's criterion. In cases where a determinable is
appropriately posited, the determinable is shared by its determinates
and explains their similarity; for example, all color-determinates
have the determinable property *color* in common (Johansson
2000: sec. 3). Johansson's view is a mixed
eliminativist/non-reductionist view, since he assumes that any
non-maximal determinables do not exist, but are merely "man-made
constructions" (2000: 113). Such a view might be challenged,
however, since even in the absence of a 'comparability
gap' between same-level determinates (e.g., *yellow* and
*red*), one might still suppose that the difference between
*yellow* and *red* is not a matter of convention.
Another concern with Johansson's account reflects that the mere
posit of a shared determinable does not (as Bigelow and Pargetter
[1990] and Massin [2013] have observed) in itself make sense of
determinable differences, though the appeal to the 'continuous
connection' between determinates may be able to do work
here.



Worley (1997) sketches a different sort of a constitution-based
account, as a way of supplementing Yablo's (1992) asymmetric
necessitation account. She illustrates with triangularity, analyzed as
involving the constituent features associated with being a closed,
three sided plane figure, which features can vary in ways associated
with equilateral, isosceles, and scalene triangles, among others.
Worley sees this as motivating an account of determination on which
"the constituents of each determinable are proper subsets of the
constituents of each of their determinates", such that, e.g.,
the determinable *triangular* and the determinate
*equilateral triangular* would share features such as
*three-sided* and *closed plane figure*, but the latter
would be additionally constituted by *equilateral*. As Worley
observes, this account accommodates various features of determination,
including *Determinable inheritance*:



> 
> 
> There can be no metaphysically possible world in which an instance of
> a determinate can fail to be an instance of its determinable, since
> anything which is an instance of a determinate will be so in virtue of
> having certain features, which features will also be sufficient to
> make that object an instance of the determinable. (1997: 290)
> 
> 
> 



The shared constituent features also provide a basis for
*Determination 'in respect of' determinates* and
*Determinate similarity/comparability*, and perhaps the
additional features of the determinates can provide a basis for
*Determinate incompatibility*. The main concern with
Worley's account is that it doesn't accommodate
*Non-conjunctive determination*, and in fact seems to require
its denial.


#### 3.5.4 Grounding-based accounts



'Grounding' (here capitalized to distinguish use of this
term from traditional schematic uses of 'grounding' as
neutrally ranging over specific metaphysical dependence relations) is
a recently-introduced primitive relation or notion of metaphysical
dependence, taken to be operative in any context where such dependence
is at issue (either as holding between facts or propositions
pertaining to some goings-on, or between worldly goings-on
themselves). Proponents of Grounding typically take determination to
be a paradigm case of such dependence, with determinables being
Grounded in determinates. For example, Correia suggests that
"the determinate features of a thing" are the Grounds of
"the determinable features of a thing" (2005:
49-50); Schaffer (2016b) takes a case of determination as the
primary exemplar of his 'structural equations' approach to
Grounding; and Rosen (2010) endorses the following principle:




*Determinable-Determinate Link*: If \(G\) is a determinate of
the determinable \(F\) and \(a\) is \(G\), then \([Fa] \leftarrow
[Ga]\)




Here, \([Fa] \leftarrow [Ga]\) stands for 'the fact that \(Fa\)
is Grounded in the fact that \(Ga\)'.



Though Grounding is primitive, proponents stipulate that it has
various features--most commonly, those of a strict partial order,
in which case a Grounding-based account of determination will satisfy
*Asymmetry*, *Irreflexivity*, and
 *Transitivity*.[31]
 The also-common assumption that Grounding entities metaphysically
necessitate Grounded entities accommodates *Determinable
inheritance*. How to accommodate other features (including
*Non-conjunctive specification*, *Non-disjunctive
specification*, *Determination 'in respect of'
determinables*, and so on) is less clear, since Grounding
doesn't itself distinguish determination from other dependence
relations.



Correspondingly, the main concern with a Grounding-based account is
that primitive Grounding alone fails to shed any substantive light on
determination, instead simply registering the common supposition that
determinables metaphysically depend on determinates in a way
conforming to certain stipulated formal features. This concern is a
case-in-point of the more general concern raised in Wilson (2014),
according to which Grounding is too abstract to shed any useful
metaphysical light on its own. Some proponents of Grounding attempt to
provide more substance to a Grounding-based account of determination
by deriving or modeling the claim that determinables are Grounded in
determinates, but whether these attempts succeed is unclear; see,
e.g., Schaffer's (2016a,b) suggestion that determination can be
modeled using the apparatus of structural equations (*a
la* Pearl 2000 and Spirtes and Scheines 1993), and reasons to
resist that suggestion offered by Koslicki (2016) and Wilson
(2016).


### 3.6 Accounts of the structure or logic of determination



We now discuss three accounts or models which are best seen as
elucidating certain structural or broadly logical features of
determination or determinates.


#### 3.6.1 Property-space accounts



A property-space model of the sort advanced in Funkhouser 2006 (see
Funkhouser 2014 for further exposition) starts by filling in what it
is to have a determinable "in a specific way"
(*Increased specificity*) by attention to 'determination
dimensions'--features along which a determinable may be
determined, such as, e.g., *hue*, *saturation*, and
*brightness* in the case of *color*. The suggested
methodology for identifying determination dimensions of a given
determinable is broadly empirical, and involves inquiring after
"the ways in which determinates under the determinable \(X\) can
differ from one another with regard to their \(X\)-ness" (2006:
551), which suggestion picks up on both *Determination 'in
respect of' determinables* and *Determinate
incompatibility*.



Funkhouser then offers a model on which determination dimensions,
assumed to have discrete or continuous ranges of values, serve as
coordinate axes of a 'property space' for a given
determinable. The space as a whole corresponds to the determinable;
points in the space correspond to maximal determinates, associated
with specific assignments of values to each determination dimension;
subspaces of the space correspond to less than maximal determinates
(which themselves may be determinables relative to contained subspaces
or points). For example, *color* has determination dimensions
*hue*, *saturation*, and *brightness*, such that,
e.g., *red* determines *color* if and only if the
property space of *red* is a proper subspace of the property
space of *color*. More generally:




Property \(B\) determines property \(A\) iff


1. \(A\) and \(B\) share the same determination dimensions
2. \(B\) has the non-determinable necessities of \(A\) and
3. The property space of \(B\) is a proper subset of the property
space of \(A\).




'Non-determinable necessities' are those features of a
determinable not allowing for variation (e.g., being three-sided, in
the case of triangularity); condition (2) registers that sharing of
non-determinable necessities is also required for determination, in
addition to the increase in specificity associated with conditions (1)
and (3), registering that determinates differ with respect to the
values of one or more determination dimensions associated with the
determinable.



Modeling determinates as subspaces of a determinable space
accommodates many features of determination, including, to start,
*Increased specificity*, *Determination in-respect-of
determinables*, *Asymmetry*, *Irreflexivity*, and
*Transitivity*. *Determinate incompatibility* follows
from subspaces' being disjoint; *Determinate
similarity/comparability* may be elucidated by reference to
metrics on the spaces, whereby subspaces of a determinable space may
be nearer or further apart. Funkhouser also aims to accommodate
*Causal compatibility* by taking determinable and determinate
instances (tropes) to be identical.



With this latter claim, Funkhouser's account moves into
ontological territory, and might be plausibly seen as a sophisticated
variation on a disjunctivist or other reductionist theme--say,
one elucidating the internal dimensional structure of determinate
disjuncts *vis-a-vis* associated
 determinables.[32]
 As with reductive accounts, Funkhouser's assumptions that
reality is ultimately maximally determinate and that determinable and
determinate instances are token-identical might be challenged as
either empirically inadequate or such as to not properly accommodate
the perceptual and other motivations for determinables. That said, it
seems likely that the structural aspects of Funkhouser's
approach could be preserved even if these assumptions are relaxed,
such that, e.g., 'points' in a property space aren't
taken to correspond to maximal determinates (see note 46).


#### 3.6.2 Metric-space accounts



The metric-space account of
"determinables-together-with-their-determinates" advanced
by Denby (2001) "identifies abundant determinables and
determinates with impure sets and the having relation with a
set-theoretical relation" (2001: 316). Determinables are defined
as follows:




\(F\) is a determinable iff \(F\) is a pair \(\langle S, f\rangle\)
where:


1. \(S\) is a metric space; and
2. \(f\) is a function from concrete particulars into the points of
this metric space.




Here a determinable is thought of as a "classification" of
particulars. The metric space \(S\) is a collection of points together
with a "distance" relation on these points; it defines the
possible classificatory locations and how they are related. Each point
corresponds to a determinate of that determinable, and the distance
relation provides a measure of the similarities among them. The
function \(f\) maps each concrete particular in its domain to a unique
point in the metric space.



Determinates are defined as follows:




\(F\) is a determinate iff \(F\) is a pair \(\langle D, E\_i\rangle\)
where


1. \(D\) is a determinable; and
2. \(E\_i\) is the extension of point \(i\) in the metric space
encoded by \(D\).




In set-theoretic terms, a determinate is thought of as a
"centered" classification of particulars, defined by a
determinable and by the determinate's extension. Denby moreover
sees determinables as ultimately categorizing the possession of
maximal or "sparse"
 determinates;[33]
 as such, he interprets his model along anti-realist or reductionist
lines.



This approach to determinables and determinates is attractive, Denby
argues, in that sets are ontologically unproblematic and their
identity-conditions and relations are well-understood (and similarly
for functions and metric spaces), and in that the account accommodates
"the pre-theoretic intuitions about the logical relations among
properties" (2001: 310), including *Unique
 determination*,[34]
*Determinate
 similarity/comparability*,[35]
 and *Determinate incompatibility*. The primary concerns here
are again those associated with anti-realist or reductive views of
determinables, though as with Funkhouser's account it might be
that the broad structure of Darby's metric conception of
determinables is compatible with a non-reductivist reading.


#### 3.6.3 Co-determination accounts



Fine's aim in his 2011 is to characterize "what it is for
the world to possess the kind of structure that it has when the
determinate/determinable distinction is in play" (2011: 162),
taking as inspiration Wittgenstein's post-Tractarian view, on
which



> 
> 
> the atomic propositions might exhibit the kind of dependence that is
> characteristic of the way in which different determinants of a given
> determinable are exclusive of one another. (2011: 161)
> 
> 
> 



Fine's project reflects the usefulness of *Determinate
incompatibility* for his truthmaker semantics (Fine
2012a,b)--most notably, in providing a non-similarity-based
account of the worlds entering into counterfactual deliberation, with
the general idea being that a counterfactual world will be just like
the actual world but for the replacement of some actual state \(s\)
with a state \(s'\) that is a determinate under the same determinable
as \(s\). As such, Fine's ultimate aim is to provide a
definition of the 'co-determinable' relation between
states--a task which "avoids the tricky question of saying
what exactly a determinable is" (2011: 184), though certain
structural characterizations of determinables fall out of his account.
Since Fine's approach to characterizing determinable-determinate
structure is rather intricate, we direct the interested reader to the
attached
 footnote.[36]


## 4. Are determinates metaphysically prior to determinables?



It is commonly assumed that determinables, if they exist, are less
fundamental than determinates. Of course, this assumption is true on
reductionist
 accounts;[37]
 but even those taking determinables to be irreducible to determinates
often suppose that the latter are prior to the former. In this section
we canvass reasons for and against taking determinates to be
metaphysically prior to determinables.


### 4.1 Asymmetric necessitation/supervenience



One criterion of priority takes it to be sufficient for some goings-on
to be less fundamental than some others that the former are
asymmetrically necessitated by (or "metaphysically supervene
on") the latter. As per *Asymmetric modal dependence*, it
is characteristic of determinates that they asymmetrically necessitate
their associated determinables, thanks to the distinctively unspecific
nature of determinables. Hence Armstrong says:



> 
> 
> A point to be taken very seriously is that because determinates entail
> the corresponding determinable, the determinable supervenes on the
> determinates, and so, apparently, is not something more than the
> determinates. (1997: 50)
> 
> 
> 



Asymmetric necessitation appears to be insufficient for
non-fundamentality, however, as is reflected in standard concerns that
(even asymmetric) supervenience is too weak to guarantee complete
metaphysical dependence (see, e.g., Horgan 1993, Wilson 2005, and
McLaughlin and Bennett
 2005).[38]
 Nor is asymmetric necessitation necessary for the holding of a
priority relation, as Fine's (1994) case of Socrates and the
singleton set of Socrates shows. As such, one can reasonably deny that
the asymmetric necessitation of determinables by determinates
establishes that determinables are less fundamental than
determinates.



Even accepting the criterion, one can question whether it shows that
determinates are metaphysically prior to determinables. As French
(2014) observes, while determinable instances do not entail any
particular determinate instances, there is nevertheless
'two-way' entailment: every determinate instance entails
determinable instances, and every determinable instance entails some
determinate instance. One might respond that the word
'some' expresses residual asymmetry in priority as opposed
to simply reflecting that determinables are less specific than
determinates, but as French notes, "those who exclude
determinables from the fundamental base need to show what specificity
has to do with fundamentality" (2014: 284).


### 4.2 Naturalness



Another criterion takes more fundamental properties to be more
'natural', in the terminologically
 inapropos[39]
 meaning of Lewis (1983), in making for greater objective resemblance
between their possessing particulars than do less fundamental
properties. This conception appears to deem determinables less
fundamental than determinates: since determinables are less specific
than their associated determinates, particulars sharing a given
determinate property (e.g., *scarlet*) will be more objectively
similar in the relevant respect than will be particulars sharing an
associated determinable property (e.g., *red*). However,
objective resemblance can hold between properties as well as
particulars; hence even granting that determinates make for more
objective resemblance between particulars, one can reasonably maintain
that among the perfectly natural joints are those associated with
determinables, understood as making for objective resemblance between
associated determinates (see Wilson
 2012).[40]
 Such a consideration would support McDaniel's (2010)
supposition that the increase in specificity at issue in determination
differs from that at issue in the disjunction-disjunct relation, in
that determinables, unlike disjunctions, are as natural as their
specifications.


### 4.3 The argument from fixing



Another criterion of fundamentality, associated with intuitive
"all God had to do" scenarios, is one according to which
fundamental entities fix all the rest. This criterion again seems to
support taking determinates to be prior to determinables, for once the
specific, or determinate, facts are fixed, then, it seems, more
general/determinable facts are thereby fixed, with the latter being at
best ontologically real abstractions from the former. By way of
contrast, fixing the determinable facts does not fix the determinate
facts (as is reflected in *Asymmetric modal dependence*).



That determinable facts are fixed by determinate facts can be
challenged, however, by attention to the constitutive modal fact about
any given determinable instance--say, a given instance of
*red*--that it is of a type that might have been
differently determined--say, by *scarlet* rather than
*maroon (*see Wilson 2012). Here the suggestion is that no
determinate fact or complex combination of such facts can provide a
non-gerrymandered basis for such a constitutive modal
 fact.[41]



One response is to maintain that a fundamental base need only ground
the contingent non-modal facts at a world, as Schaffer (2004: 90)
suggests; if so, then the failure of determinate instances to ground
certain modal facts about determinable instances won't impugn
the priority of determinates. One might maintain, however, that a
supposed "ground" for some entity which failed to provide
a metaphysical basis for modal facts constitutive of the entity would
be incomplete, at best. As French puts it,



> 
> 
> fixing the non-modal facts and leaving modal flexibility out of the
> picture would yield an incomplete inventory. And the most obvious way
> of fixing the modal facts would be to include the determinables
> themselves in the fundamental base. (2014: 284)
> 
> 
> 



There is a worry that this line of thought will overgenerate, in that
many higher-level features and objects (e.g., tables) are to some
extent constitutively modally flexible. A possible response is that
whether the line of thought applies to a given case will depend on
whether the basis for the modal flexibility is itself derivable from
or otherwise clearly generated by lower-level goings-on. For example,
multiply realizable higher-level features (say, temperature in
thermodynamic systems) whose modal flexibility results from the
imposition of lower-level physical constraints would not be
appropriately deemed fundamental (or as fundamental as their physical
realizers).


### 4.4 Questions and implications



The previous considerations suggest that some determinable features of
reality might be fundamental, or as fundamental as determinate
features. This result raises several questions, answers to which have
implications for our understanding of determinables and determinates,
and of the fundamental.



One question pertains to whether the determinates associated with
fundamental determinables are also part of the fundamental base. It
might seem so; for even granting that (fundamental) determinates
cannot completely ground determinables, determinates seem also to be
needed to be existential witnesses for more specific goings-on. In
that case, a further question arises concerning how determinables and
determinates jointly participate in a fundamental base. Wilson (2012)
suggests that a model for understanding such joint founding may be
found in the sciences, and more specifically in how general scientific
laws combine with initial or boundary conditions (15-16), an
analogy developed by French, who maintains that "scientific
determinables and determinates jointly enter into the fundamental base
for everything else" (2014: 285). That said, there are arguably
metaphysical views on which only determinables are fundamental; for
example, Hubner and Matyasi (2020: 634) observe that Spinoza rejects
the view that determinates are among the fundamenta (insofar as the
one fundamental entity has only determinable features): "his
substance is both the least specific (indeterminate) and the most
fundamental entity" (e.g. Ep36; IV/185/29).



A further question concerns whether existing non-reductionist accounts
of determinables can make sense of these being fundamental. On the
face of it, there is no special difficulty with accommodating
fundamental determinables on either powers-based or constitution-base
accounts of determination, or with such accounts' making sense
of joint determinable/determinate founding. On Johansson's
(2000) account, for example, it might be that determinates depend on
determinables in that the latter are constitutive parts of the former
(*nota bene*: not obeying weak supplementation), and
determinables depend on determinates in that, modulo certain outside
case (e.g., gappy quantum indeterminacy;
 see SS5.3),
 determinable instances must be parts of some determinate whole.



That determinables and determinates may be jointly fundamental has
implications for our understandings of fundamentality and metaphysical
dependence. Fundamental entities are commonly assumed to be
independent, in being wholly distinct, and (relatedly, as per
'Hume's Dictum') in being such that each can either
exist together or exist apart. But if (some) determinables and
determinates can be equally fundamental, this understanding is
incorrect; for given the intimate relationship between determinables
and determinates, to say that these are equally fundamental is
evidently not to say either that they are wholly distinct or (even
granting Hume's Dictum) modally independent. Moreover, if
determinables and determinates can mutually found each other, other
commonly stipulated suppositions are called into question--e.g.,
that the fundamental entities are those that do not depend on any
other entities, and that metaphysical dependence is asymmetric.



The possibility of fundamental determinables also bears on various
first-order metaphysical topics. For example, Paul (2002, 2012)
endorses a one-category ontology ('mereological bundle
theory'), on which properties and relations are fundamental, and
property composition is "the fundamental glue" (2012:
242). Paul allows that determinables might be among the fundamental
properties and relations (note 22), and moreover suggests that such
posits may be required to accommodate theories couched in terms of
properties and relations which are "extremely abstractly
specified" (2012: 245).


## 5. Applications



We now canvass three topics in metaphysics where attention to
determinables and determinates has played a significant
 role.[42]


### 5.1 Laws of nature and nomological modality



As mentioned previously, determinables and determinates have been seen
as relevant to our understanding of laws of nature in both physics and
the special sciences. Armstrong (1997) argues that irreducible
determinables are needed to make sense of functionally specified laws
in physics. Consider Newton's law of gravitation:



\[F = K (M\_1 M\_2)/D\]


As Armstrong notes (see also Fales 1990: 61, Mellor 1998: 190, 208,
and French 2014), substitution of the determinable quantities \(F\),
\(M\), and \(D\) with determinate values gives rise to "a law
which stands as determinate to the original, determinable, law"
(1997: 63). One might try to provide an anti-realist or reductionist
treatment of these seemingly determinable laws. Armstrong (1997)
argues, however, that such deflationary treatments cannot make sense
of the role of functional laws in sustaining counterfactuals, at least
if properties are Aristotelian universals, whose existence depends
upon their being instantiated; for then there will typically (and
perhaps necessarily, for the case of continuous quantities) be gaps in
the actual instantiations of functional laws. As such, the unity of
determinates in these cases involves not just partial identities (as
discussed in
 SS3.3)
 but "strictly identical second-order properties", which
are the "real [...] determinables" (1997: 247).
Mellor similarly maintains that in Newton's law, "the
determinables ... are second order universals" which exist along
with associated first-order determinate universals (1998: 209).
Functional laws of nature are then taken to be relations between these
determinable universals.



French offers a structuralist account of laws of nature as expressing
determinable relations (a position Mellor also considers; 1998: 209).
As regards Newton's law, French says:



> 
> 
> If we insert specific values [...], we obtain a determinate
> instance of the law, expressing the relation that holds between
> determinate properties. So, the law as a whole can be regarded as
> expressing a determinable relation, which can be made determinate in
> specific situations. (2014: 300)
> 
> 
> 



Again, French allows that determinable laws/relations may be
fundamental. Reflecting that one reason for taking (some)
determinables to be fundamental is that these are partly constituted
by modal facts pertaining to their possible determinations (see Wilson
2012), French moreover suggests that the determinable nature of laws
provides a basis for physical modality:



> 
> 
> these determinate instances correspond to solutions that can be
> represented by (more) specific models of the theory, and it is the
> shared structure between these models that yields the relevant
> physical modality. The relationship between the more generic and more
> specific models can be captured by that between determinables and
> determinates. (2014: 300)
> 
> 
> 



Another application of determination to the metaphysics of laws
concerns whether these are contingent, in having at best a restricted
physical or nomological modality, or rather are metaphysically
necessary. Kistler (2005) argues that such laws are metaphysically
necessary, first arguing that the quantities in 'laws of
association' such as the ideal gas law are reasonably seen as
different determinables of the same determinate states, such that such
laws are necessary; then generalizing on the base of systematicity
considerations to other kinds of
 laws.[43]


### 5.2 The problem of mental/higher-level causation



How can mental goings-on bring about physical effects, as they seem to
do, given that the physical realizers of mental goings-on are already
sufficient to cause these effects? This question gives rise to the
problem of mental (more generally, higher-level) causation, encoding
two threats: first, that mental properties, if efficacious,
problematically overdetermine their effects; second, that avoiding
overdetermination requires that mental properties be causally excluded
by their realizers. Overdetermination and exclusion are avoided if
mental and physical goings-on are identical, but in that case it seems
that mental goings-on are not efficacious *qua* mental (see
Horgan 1989); as Yablo puts it: "Mental events are effective,
maybe, but not by way of their mental properties" (1992: 249).
Moreover, type identity seems at odds with the multiple realizability
of mental properties.



Some, including MacDonald and MacDonald (1986), Yablo (1992), Wilson
(1999), and Shoemaker (2001), have suggested that a better response
proceeds by taking mental properties to be determinables of their
physical
 realizers.[44]
 The appeal to determination reflects various features of determinates
and determinables, including *Causal compatibility*. As Yablo
says,



> 
> 
> [W]e know that [determinables and determinates] are not causal rivals.
> [...] Determinables and their determinates, like objects and
> their parts, are guaranteed to be on the same team. (1992: 259)
> 
> 
> 



Moreover, as per *Multiple determinates*, determinables are
multiply determined, and given that determinables and determinates are
type- and perhaps also token-distinct, one can argue
 (see SS3.5)
 that determinables are distinctively efficacious. If mental
properties are determinables of physical realizers, these features are
inherited: as causal non-competitors, overdetermination is avoided
while accommodating multiple realizability, compatible with the
distinctness and distinctive efficacy of mental properties. Similar
considerations apply to other higher-level goings-on, in which case
realization might be determination, more generally.



A determinable-based approach to realization is subject to two main
concerns (besides those generally targeting a powers-based account;
 see SS3.5),
 each aiming to show that realization cannot be determination, on
grounds that realization lacks some key feature of determination (see
Ehring 1996; Funkhouser 2006, 2014; Walter 2007; Worley 1997). First
is the argument from mental multiple realizability, according to which
such realizability effectively violates *Determination 'in
respect of' determinables* (entailing that determinates
differ in respect of determinables), since



> 
> 
> Mental properties are said to be multiply realizable precisely because
> distinct physical realizers can be exactly the same with respect to
> the mental property they realize (Walter 2007: 219)
> 
> 
> 



in which case



> 
> 
> [T]he physical realizers of the mental will not differ mentally at
> all, as they should if they are determinates of the requisite mental
> states. (Ehring 1996: 474)
> 
> 
> 



Second is the argument from mental superdeterminates, according to
which a mental property could be maximally specified *qua*
mental--as, e.g., a precise state of searing pain (Ehring), or a
belief maximally specified along the dimensions of content and
confidence (Funkhouser); but if realization is determination, this
would falsely imply that mental super-determinates could be further
determined.



One response to these concerns, offered by Wilson (2009), proceeds by
analogical attention to color metamerism, in which colors of the same
hue, saturation and brightness can differ in respect of color, and are
moreover reasonably taken to have physical determination dimensions.
One 'metameric moral' is that properties such as
*color* may have physical determination dimensions; a second is
that the determination dimensions had by a given higher-level property
may be science-relative. Applying the morals: there is no in-principle
problem with mental properties' having physical determination
 dimensions;[45]
 moreover, which dimensions are associated with mental properties may
be science-relative. This allows accommodation of mental multiple
realizability: mental properties with diverse physical realizers can
be exactly alike, relative to the determination dimensions associated
with psychology, compatible with these mental properties being
different, relative to a lower-level physical science distinguishing
these realizers. And given that different sciences may treat a single
determinable as having different determination dimensions, mental
properties may be super-determinate relative to a purely psychological
science, while being further determined relative to a lower-level
science.



A powers-based implementation of the metameric
 morals[46]
 also provides a basis for a response to a third objection, due to
Worley (1997), according to which the constituents of beliefs are not
constituents of their physical realizers, as they would have to be if
(as per Worley's constitution-based account;
 see SS3.5)
 beliefs were determinables of physical
 determinates.[47]
 Supposing that constituents are associated with sets of powers, the
content of a belief may be a constituent of its physical realizers,
after all--not *qua* content *per se*, but
*qua* the relevant subset of powers.


### 5.3 Metaphysical indeterminacy



Many phenomena appear to be indeterminate: macro-objects (clouds,
mountains) appear to have imprecise boundaries; the future, it seems,
might be genuinely open; on many interpretations of quantum mechanics,
some properties of a system (e.g., position and momentum, orthogonal
spin components) cannot jointly have precise values. In these and
other cases there are reasons to think that the indeterminacy is
metaphysical, as opposed to merely semantic or epistemic. Elder (1996)
suggests that determinables might be useful for purposes of making
sense of "the idea that corresponding to (at least some) vague
predicates there really are, in the world, vague properties"
(1996: 150). Wilson (2013) more specifically argues that determinables
and determinates provide the basis for an attractive account of
metaphysical indeterminacy
 (MI),[48]
 as follows:




*Determinable-based MI*: For a state of affairs to be
metaphysically indeterminate in a given respect \(R\) at a time \(t\)
is for the state of affairs to constitutively involve an object
(entity) \(O\) such that (i) \(O\) has a determinable property \(P\)
at \(t\), and (ii) for some level \(L\) of determination of \(P\),
\(O\) does not have a unique level-\(L\) determinate of \(P\) at
\(t\).




One application of *Determinable-based MI* is to macro-object
boundary MI; here the conditions are satisfied in 'glutty'
fashion, reflecting that macro-objects typically have multiple
overlapping realizers, as with Mount Everest and the multiple
overlapping aggregates of rock in its vicinity at any given time. On
the suggested approach, Mount Everest has a determinable boundary
property, but no unique determinate boundary property, since there are
too many candidate determinates of the determinable, associated with
the comparatively precise boundaries of its realizing aggregates, to
non-arbitrarily pick out any one as the 'unique'
determinate boundary had by the mountain. At best, these determinate
boundaries can be attributed to Mount Everest in relativized (or
degree-theoretic)
 fashion.[49]
 That ordinary objects typically have metaphysically indeterminate
boundaries provides, in combination with a determinable-based account
of realization
 see SS5.2,
 the basis for an argument that such objects are emergent--that
is, distinct from and distinctively efficacious as compared to the
lower-level configurations upon which they cotemporally depend (see
Wilson 2021, Ch. 6). Another application is to open future MI: here
the conditions may be satisfied in 'gappy' fashion,
reflecting that, while there might be present grounds for the future
instancing of a given determinable (say, *being an outcome of a sea
battle*) there may be no present grounds for the future instancing
of any specific determinate of that determinable.



*Determinable-based MI* is also usefully applied to cases of
value indeterminacy on (various interpretations of) quantum mechanics,
associated with superpositions, incompatible observables, and
entangled states. Darby (2010) and Skow (2010) argue that metaphysical
supervaluationist accounts of MI (see Akiba 2004, Barnes 2010, and
Barnes and Williams 2011) cannot accommodate quantum MI on the
orthodox interpretation, for on these accounts MI is effectively a
matter of primitive unsettledness about which maximally precise world
or state of affairs obtains; but such an approach cannot model quantum
MI, since the Kochen-Specker theorem rules out simultaneously
assigning definite values to all properties of a quantum system.
Calosi and Wilson (2019 and forthcoming) defend this result against
certain objections, and extend the concern with supervaluationist
accounts to cases of MI on the GRW and Everettian interpretations,
associated with GRW's 'tail' problem (see Lewis
2016) and ineradicable incompatible observable MI within Everettian
branches (see A. Wilson 2020), respectively.



By way of contrast, *Determinable-based MI* is compatible with
the Kochen-Specker theorem, and more generally, with insuperable or
(as Skow puts it) any 'deep' quantum MI associated with
quantum phenomena. Whether individual such cases are best treated in
gappy or glutty determinable-based terms remains controversial.
Bokulich (2014) and Wolff (2015) see a gappy implementation as most
promising for the target case of spin value indeterminacy; as Wolff
observes:



> 
> 
> Permitting the instantiation of determinables without determinates
> helps to describe this phenomenon, because we can say that \(x\)-spin
> and \(y\)-spin are determinables with two determinates each, and
> [after a spin-\(z\) measurement] neither of these determinates is
> instantiated even though the determinables "spin-\(x\)"
> and "spin-\(y\)" are. (2015:
>  385)[50]
> 
> 
> 



(See also Schroeren 2021.) However, a glutty implementation has
certain advantages, including being able to preserve information
associated with coefficients of components states in a superposition.
Calosi and Wilson (2021) advance a glutty implementation as providing
the basis for an intelligible explanation of the distinctive
interference patterns characteristic of the double-slit experiment,
reflecting that a single particle in the experiment can (in
relativized or degree-theoretic fashion) go through both slits in such
a way as to be able to interfere with itself (as per Dirac's
original suggestion).



That said, whether the value indeterminacy on (available readings of)
available interpretations of quantum mechanics should be understood in
metaphysical terms, and if so, whether it should be treated in
determinable-based terms (or relatedly, whether a supervaluationist
approach can be fixed up so as to do the job), remains an area of
active
 research.[51]
 The debate continues; still, here and in other cases of seeming MI
there is a case to be made that our experiential and theoretical
familiarity with determinables goes at least some distance towards
rendering MI intelligible--offering, along the way, a nice
case-in-point of how determinables may be useful for purposes of
illuminating the structure of natural reality.