The Determinable-Determinate Relation
Eric Funkhouser
The properties colored and red stand in a special relation. Namely, red is a
determinate of colored, and colored is determinable relative to red. Many other
properties are similarly related. The determination relation is an interesting topic of
logical investigation in its own right, and the prominent philosophical inquiries into this
relation have, accordingly, operated at a high level of abstraction.1 It is time to return to
these investigations, not just as a logical amusement, but for the payoffs such
investigation can yield in solving some basic metaphysical problems. The goal in what
follows is twofold. First, I argue for a novel understanding of the determination relation.
Second, this understanding is applied to yield insights into property instance (e.g., trope)
individuation, how different property types can share an instance, the relation between
property types and property instances, as well as applications to causation (mental
causation, in particular).
1. Criteria for a Successful Analysis
The determination relation holds between property types. A successful analysis of
this relation should accord with the following truisms about determinables and their
determinates:
1. The following canonical pairs must turn out to be related as determinable to
determinate: colored/red, red/scarlet, and shaped/circular. The first two
examples show that properties are determinables or determinates only relative
to other properties. Red is determinable relative to scarlet, but determinate
relative to colored.
2. For an object to have a determinate property is for that object to have the
determinable properties the determinate falls under in a specific way. For
example, being scarlet is a specific way of being red, and being red is a
specific way of being colored. This notion of specificity with regard to
1
determinables-determinates can be compared and contrasted with other
standard specificity relations--e.g., the disjunction-disjunct, conjunctconjunction and genus-species relations.
3. An object instantiating a determinable must also instantiate some determinate
under that determinable. Colored objects must be red or yellow or blue, etc.
No object is merely colored simpliciter.2
4. An object instantiating a determinate also necessarily instantiates every
determinable that determinate falls under. Every scarlet object is also red and
colored.
5. The determination relation is transitive, asymmetric and irreflexive. Since
scarlet determines3 red and red determines colored, scarlet determines colored.
But since scarlet determines red, red does not determine scarlet. Furthermore,
scarlet, like all properties, does not determine itself.4
6. Determinates under the same determinable admit of comparison in a way
unavailable to pairs of properties with no determinable in common.5 For
example, an ordering or similarity relation obtains between determinate
colors--e.g., red is closer to orange than it is to green.6 But no such
comparison can be made between red and, say, circular.
7. The transitive chain of a determinable and the determinates under it does not
go on forever. At some point there is a property that does not allow of further
determination. Call such a property ‘super-determinate.’ Coca-Cola red
might be a super-determinate of colored. Similarly, the chain of
determinables a determinate falls under comes to an end somewhere. Let us
call a determinable property that itself falls under no determinables ‘superdeterminable.’ Colored and shaped might be super-determinable.
In addition to the above truisms, we should provide a further, but more controversial,
requirement:
2
8. Instances of determinables and their determinates do not causally exclude
each other.
It is reasonable to hold that property instances are the relata of causation.7 Minimally, it
makes sense to speak of a causally relevant property instance.8 A common constraint on
theories of causation is that they should not countenance too much causal
overdetermination. Only in rare cases does more than one sufficient cause converge on a
common effect. Two bullets may simultaneously strike a condemned man in the heart
and kill him, but this is surely a freak coincidence. The presence of one sufficient cause
is generally taken to exclude other causes for the same effect. Such exclusion principles
can be applied to property instances converging on a common effect, as well.9 It is
unlikely that there would be two (or more) causally sufficient property instances for some
effect. However, determinables and their determinates do not seem to causally exclude
one another.
Consider a pigeon trained to peck at red objects.10 A scarlet triangle is put before our
pigeon, and she pecks. It is truthful and appropriate to say that the sight of a red triangle
caused her to peck. And it also is truthful and appropriate to say that the sight of a scarlet
triangle caused her to peck.11 But it does not seem that this pecking is causally
overdetermined. Similar situations arise for other determinables and determinates.
Margie impressed her teacher by scoring an ‘A’ on her final exam. In fact, Margie scored
a 95% on her final exam. Margie’s ‘A’ performance caused her teacher to be impressed,
and her scoring a 95% is the specific way in which she scored an ‘A.’ But this is not a
case of overdetermination. Somehow determinables and their corresponding
determinates do not succumb to causal exclusion principles.
A successful analysis of the determination relation will accord with, and hopefully
explain, the above features.
3
2. Formalizing and Modeling the Determination Relation
2.1 A Two-Featured Analysis
Most central to the notion of determination is the idea that to have a determinate
property is to have the determinable properties that determinate falls under in a specific
way. However, this notion of specification can be easily misunderstood. Intuitively,
scarlet determines red, but red and square does not determine red. But, in some sense, to
be red-and-square is a specific way of being red, so not every sense of further specifying
a determinable counts as determination. Rather, determinates specify their determinables
with respect to only a limited number of features. This point is missed in current
discussions of determination, which often indiscriminately count cases of realization as a
species of determination (or vice versa)12, but was properly noted by both W.E. Johnson
and Arthur Prior in the first half of the 20th Century. Arthur Prior wrote:
Determinates under the same determinable have the common relational property,
presupposing no other relation between the determinates themselves, of
characterising whatever they do characterise in a certain respect. Redness,
blueness, etc., all characterise objects, as we say, “in respect of their colour”;
triangularity,
squareness, etc., “in respect of their shape.” And this is surely quite fundamental
to
the notion of being a determinate under a determinable.13
Proper understanding of a determinable requires discovering the features along which it
can be determined.
Following Prior’s lead, we can note that a determinable property X is determined only
with respect to its X-ness (or X-ity, or similarly appropriate grammatical construction).
Red and square is not a determinate of red, for the addition of the square constituent in no
way further specifies the redness. By placing proper emphasis we can see why this
conclusion is warranted. A determinate of red is red in a particular way. Redness, like
4
any color, can only be determined with respect to hue, brightness, and saturation. These
are the minimally sufficient criteria according to which all colors can be distinguished
from one another. Colors differ to the extent, and only to the extent, that they differ in
hue, brightness, or saturation. As such, these are the three variables along which colors
can be determined. As Johnson noted:
Our familiar example of colour will explain the point: a colour may vary
according to its hue, brightness, and saturation; so that the precise determination
of a colour requires us to define three variables which are more or less
independent of one another in their capacity for co-variation; but in one important
sense they are not independent of one another, since they could not be manifested
in separation.14
We should look for similar features of other determinables, for it is only according to
such features that a property can be determined. Let us call such features the
determination dimensions of a property.
Determinables and determinates often have features in addition to their values along
these determination dimensions. Let us call these, the second type of features, their nondeterminable necessities. Such features are so-called because they are features that each
instance of a determinable type must have, but which do not allow for variation. For
example, triangles are 3-sided, closed, plane figures—these features are required of all
triangles. While instances of triangular must have such features, these are not features
along which triangular is determined. As Johnson properly noted, determinates under the
same determinable differ in a particular way--i.e., along their determination dimensions.
But determinates under the same determinable cannot differ with regard to their nondeterminable necessities. For example, two triangles cannot differ in their 3-sidedness-such features do not admit of degree or variation. Determinates under the same
determinable have exact similarity in non-determinable necessities, but differ with regard
to their values under the same determination dimensions.
5
How do we discover the determination dimensions of a given determinable, X? The
easiest way is simply to inquire after the ways in which determinates under the
determinable X can differ from one another with regard to their X-ness. Since colors can
differ from one another only with respect to hue, brightness, or saturation, these are the
determination dimensions for colored. This may seem like a crude test15, but the
procedure can be supported with a scientific one. The scientific investigation of colored
and sound, for example, has led to distinctions among different color concepts and sound
concepts, as well as empirically discovered dimensions along which colors differ from
each other and sounds differ from each other. There is disagreement over the precise
determination dimensions for such properties, but the scientific pursuit of, and debate
over, these dimensions reveals a (perhaps tacit) commitment to the existence of some
such determination dimensions.16
According to some sparse property theorists (e.g., Scientific Realists), properties are
legitimized by making a unique contribution to a scientific law, or by marking a “real
similarity” in objects.17 Successful application of these laws and similarity judgments
requires input along only a limited number of dimensions--the determination dimensions.
With respect to the laws of geometry, it makes no difference if the rectangle under
consideration encloses a football field or a landing strip--only the side lengths matter.
Rectangles differ from one another only with respect to side lengths. When calculating
area, it does not matter if the area is covered with artificial turf or concrete. It is obvious
that geometry operates at this level of abstraction. And the other sciences operate with
their own abstractions. Some well-confirmed equations relate the acceleration of an
object to other properties. When inputting an acceleration, whether the object is heavy or
red or beautiful is irrelevant. An apple and a football can each fall with the same
acceleration--their difference in material constitution does not mark a difference in their
acceleration. So weight, color, aesthetic merits, etc., are not determination dimensions of
acceleration.
6
It may be helpful to provide a sample list of determinables and note the dimensions
along which they can be determined.
Determinable
Determination Dimensions
Triangular
3 side lengths
Colored
hue, brightness, and saturation
Temperature
degree
Mass
grams (or other mass unit)
Snapping
???
We can run through some examples to see why the above properties are determined along
these features only.
Triangle A and triangle B have the same 3 side lengths as measured according to
some metric. At most one triangle can be formed from 3 given side lengths, so we know
that these triangles do not differ in their interior angle measurements. All geometric and
trigonometric facts about a triangle can be derived from the 3 side lengths. With only the
information that A and B are triangles with the same side lengths, we can appropriately
conclude that A and B do not differ in their triangularity. Even if the realization bases of
these triangles differ in mass, transparency, material constitution, color, or some other
feature, they do not differ in triangularity. This shows that mass, transparency, material
constitution, color, etc. are not dimensions along which triangular is determined.
A childhood riddle asks, “Which weighs more: a pound of feathers or a pound of
gold?” Of course, they weigh the same. We should take this very seriously. The
feathers and gold in no way differ in weight, though they differ in density, material
constitution, monetary value, etc. Weight is not determined along these other lines.
Weights cannot differ but for being more or less along one dimension.
Because it can be determined along only one dimension, weight is a simple
determinable. Colored and triangular, since they have more than one determination
dimension, are complex determinables. But not all properties with constituent parts
7
should be thought of as complex determinables. For example, the linear momentum of an
object is the product of its velocity and mass. Still, velocity and mass are not
determination dimensions of momentum. Why?--Because objects with different
velocities and masses can nevertheless have the same momentum (e.g., a 4 kg. object
moving 6 m/s has the same momentum as a 6 kg. object moving 4 m/s). While
momentum may be complex in the sense of having constituents, it is not complex qua
determinable. Momentum is determined along one dimension only--e.g., that dimension
measured in kg.⋅meters per second units.
Sometimes a causal law relates individual determination dimensions to an effect. To
borrow an example from Fred Dretske, the pitch of a sound may be that in virtue of
which a glass shatters.18 Pitch is just one of the determination dimensions of sound. In
this case it seems plausible to take the pitch of this sound as a property instance in its own
right. This position is encouraged by the presence of a law, or counterfactual
dependency, relating the pitch (specifically) to the shattering, and a belief that property
instances are the causal relata. The legitimacy of complex determinables like sound
would be vindicated were there also laws relating the whole pitch-timbre-loudness bundle
to some effect. The status of complex determinables is a difficult philosophical problem
for which I have no answer. It may be that ideal science will countenance only simple
determinables. If not, we should be able to make a principled distinction between pitchtimbre-loudness bundles (i.e., the complex determinable sound) and shape-color bundles.
Pitch, timbre, and loudness may be properties in their own right, but many think they also
combine to form a unity--the property sound. Shape and color are also properties in their
own right, but they do not seem to combine to form a similar unity. It is not enough that
pitch, timbre, and loudness necessarily co-occur (i.e., whenever/wherever there is a
certain pitch there is also a certain loudness). For, every colored thing must also have a
shape, though we do not think color-shape is a unity on par with sound.
8
It has been fairly easy to find the determination dimensions for the examples we have
discussed thus far. But for some determinables it is harder to list the dimensions they can
be qualified along. A bolt snaps; it snaps suddenly. Intuition suggests that two bolts that
snap at different rates differ in their “snapping,” so we judge that the latter determines the
former. But along what other dimensions can snapping be qualified? Loudness?
Forcefulness? Material constitution? The dimensions are not as clear-cut as for
geometrical shapes, colors, temperature, and mass. This might be explained by the fact
that the property snapping is less scientific than these others. One hypothesis is that the
scientifically legitimate properties, the kind that really back causal judgments, are either
determinable along precise dimensions or are super-determinate. It would then be
inappropriate to worry about the identity of snapping instances, as they are not legitimate
causes.
While hints of our notion of a determination dimension can be found in Johnson and
Prior, neither develops such a notion (nor the complementary notion of a nondeterminable necessity). We have seen that limiting determination to our determination
dimensions accords well with our ordinary judgments about determinables, as well as
their scientific applications. It is now time to put this two-featured view of determinables
to work.
2.2 A Mathematical Model
We can construct mathematical models for our determination theory. Each
determinable that can be modeled as such is determined along n determination
dimensions. For such determinables, by taking each dimension as an axis we can
construct n-dimensional spaces. Instances of those determinable property types
correspond to unique points in those n-dimensional spaces. Instances corresponding to
the same point exactly resemble each other in all aspects relevant to individuating that
kind, since they have the same determination dimension values (and cannot differ in nondeterminable necessities).19 The determination dimensions may be bounded on one end
9
(e.g., temperature has an absolute zero, but no absolute upper bound), bounded on neither
end, or bounded at both ends. Also, these dimensions may be continuous or discrete.
Our primary examples each involve continuous dimensions, but we can easily provide
cases in which discrete units are used. The property costing more than $100 is
determined by the precise dollar cost, and dollars come in discrete units (i.e., in
hundreths).
Color properties are 3-dimensional. Hue, brightness, and saturation provide us with
our x, y, and z coordinates. Call the n-dimensional space a property spans its property
space. Color property C determines color property D if and only if C’s property space is
a proper subset of D’s 3-dimensional property space. We can map these property spaces
as shown in Diagram 1.
Each point in this 3-dimensional color space corresponds to a super-determinate color
type. A point is the limiting case of a property space. Each instance of colored
corresponds to some point in this space (i.e., super-determinate color type), and instances
corresponding to the same point exactly resemble one another in all intrinsic aspects.
We can generalize sufficient conditions20 for determination as follows:
10
Property B determines property A if: 1) property A and property B have the
same determination dimensions, 2) property B has the non-determinable
necessities of property A, and 3) the property space of B is a proper subset of the
property space
of A.
Condition 1) is partly justified by condition 3). Since the property space of B is a proper
subset of the property space of A, property B must have values along A’s determination
dimensions. Furthermore, B cannot have any other determination dimensions. If A’s
determination dimensions were not exhaustive of B’s determination dimensions, then it
would be possible for instances corresponding to the same point in B’s property space not
to exactly resemble (i.e., they could differ in the determination dimension value(s) not
shared with A). But the property space of B is supposed to be a proper subset of A’s
property space, and all A instances corresponding to the same point exactly resemble
each other. Condition 2) is required in order that property B be of the same category as
property A. For example, triangular has determination dimensions for each side length.
Points within the property space of triangular must also meet the non-determinable
requirements for triangular--e.g., be a 3-sided, closed, plane figure. Finally, condition 3)
shows that property B is property A in a specific way. There are points in A’s property
space but outside of B’s property space, so having property B is just one way of having
property A.
2.3 Does the Mathematical Model Generalize to Cover All Determinables?
Not all determinables can be so handily modeled, however. Consider, for example,
the super-determinable shaped.21 Rectangular, triangular, and circular, are all
determinates of shaped, but they cannot be represented by a fixed number of
determination dimensions. The determination dimensions for shapes will need to include
features like the number of sides, lengths of sides, and their interior angles.
Corresponding to each side, there would have to be a distinct axis for its length. But
11
rectangles, triangles, and circles have different numbers of sides, and so they will require
different numbers of axes corresponding to their lengths. Since these determinates have
different numbers of determination dimensions, they are not embedded in the same model
and appear to have distinct property spaces. But they are all shapes!
Does shaped then provide a counter-example to our 2-featured analysis of
determination? Such properties22 do show the limitations of our simple method of
mathematical modeling. But, fortunately, our core analysis of determination applies
equally well for the relationship between shaped and its determinates. The property
shaped is an abstraction, characterized by its determination dimensions and nondeterminable necessities. The “laws” of geometry and trigonometry (and perhaps algebra
and calculus) provide us with the determination dimensions for shaped. We easily
recognize number of sides, side lengths, and interior angles as three such ways that
shapes can vary. But note that “side lengths” does not provide us with a fixed number of
determination dimensions, but dimensions that vary corresponding to the number of
sides. Still, we do have a schema for the determination dimensions of shaped. For
example, for each side let there be another determination dimension representing that
side’s length. The schema for the determination dimensions of shaped might be as
follows: the determination dimensions for a given shape property will be the minimal
dimensions by which the number of sides, their lengths, and their interior angles can be
distinguished. Shaped itself, the super-determinable, spans all compossible values for
number of sides, side lengths, and interior angles. Its determinates are limited values
along these 3 schematic determination dimensions (e.g., roughly, square corresponds to 4
sides, of any equal lengths, at closed right angles); precise values for the number of sides,
side lengths, and interior angles represent super-determinate shape properties. This
shows that the subset relation, in this case as applied to schematic determination
dimensions, is the key relation in our analysis.
12
While we cannot construct a simple n-dimensional model of the property space for
shaped, we still can provide an analysis of determination that covers shaped and other
properties that are difficult, if not impossible, to model mathematically. The general idea
is that super-determinables come with limited determination dimensions, or a schema for
producing such determination dimensions, which span a range of values. Determinates
are simply properties that fall under the (schematic) determination dimensions of some
determinable, but have determination dimension values that span a proper subset of the
determinable’s range. As with the mathematically modeled properties, ‘being a proper
subset of’ is the critical relation. We can then provide the following necessary and
sufficient conditions for determination:
Property B determines property A iff: 1) property A and property B have the
same determination dimensions (or are governed by the same determination
dimensions schema), 2) property B has the non-determinable necessities of
property A, and 3) the range of determination dimension values for B is a proper
subset of the range of determination dimension values for A.23
2.4 What Are Determinable/Determinate Instances?
We have spoken of determinable and determinate instances without yet defending a
particular understanding of property instances. Passing comments on this matter are in
order. The determination dimensions of our models are suited for taking abstractions
with ontological seriousness (though they can be adopted by the Nominalist as well), and
reflect the position of the Property Realist--i.e.,. believer in universals or tropes. A 15pound red bowling ball may exactly resemble a 15-pound black bowling in weight. In
making this comparison we are attending to abstract features of the bowling balls. Here
‘abstract’ does not mean outside of space and time. On the contrary, the weight of the
red bowling ball is located at the same place as the red bowling ball. Indeed, spatialtemporal properties should be part of our individuating conditions for property
instances.24 Our sense of ‘abstract’ derives from Locke, with the process of abstraction
13
understood as involving a subtraction.25 Strip away the ball’s color, hardness, and all its
other features, until you are left with only its weight.
But are these property instances particular or universal? While this analysis could be
adapted to the needs of the believer in universals, as stated it best coheres with a trope
ontology. This is because the present model explains how different property types,
namely a determinable and its determinate, can share an instance. So, an instance of red
can be identical to an instance of scarlet. But, universals are supposed to be “wholly
present,” and strictly identical, in each of their instances. An instance of red can also be
identical to an instance of crimson. However, an instance of crimson cannot be identical
to, or even exactly resemble, an instance of scarlet. But a commitment to (Aristotelian)
universals and the transitivity of identity would require this. The believer in universals
can accept the present model only at the expense of according determinable property
types a lesser status, as in the manner of Armstrong’s denial of determinable universals. 26
In what follows I will simply assume that property instances are tropes. There are
several independent reasons for accepting a trope ontology, none of which will be
discussed here.27 For those not yet willing to accept tropes, the present view is offered as
a theory with great explanatory merit. If our property space analysis can account for the
8 desiderata of the determinable-determinate relation (given in section 1), while also
explaining other traditional features of properties (e.g., an understanding of how
properties are related to their instances), then we have made a strong, indirect case for
tropes.
2.5 Individuating Property Instances
Utilizing our property space models, we can now provide criteria for individuating
property instances (tropes). Borrowing familiar notation, let us schematize property
instances as follows: [(O, t), P].28 This is to be read as “O’s having/being P at t.” O is an
object or spatial location, t a time (span), and P a property type. Such property instances
occur if, and only if, O really is P at t. One such property instance might be ‘Tom’s shirt
14
being scarlet at noon.’ Because of problems with individuating objects (e.g., is Tom’s
shirt identical to the cloth that constitutes that shirt?), it might be thought easier to
understand ‘O’ as standing for a spatial location. Further, the spatial and temporal
components could be combined. Though we might individuate tropes by their spatialtemporal location in this way, I prefer to speak of objects (as opposed to the spatialtemporal regions themselves) as, generally, instantiating tropes. For many properties it is
an empirical matter whether their instances exclude one another from a given location
(i.e., at most one instance of that property can exist wholly in a given spatial-temporal
region). So, it would be inappropriate to build such exclusion into our individuating
conditions for property instances in general. Putting these complications aside, let us
continue to use the more familiar object-time schematization. From our understanding of
determinables we can conclude that [(x, t), P] = [(y, t’), Q] if and only if:
1. x = y,
2. t = t’, and
3. Q and P correspond to overlapping sections of a property space, in one of the
following 3 ways:
a) Q and P correspond to the very same region of a property space (type
identity), or
b) the property space of Q is a proper subset of the property space of P, or
vice versa (determinate-determinable relationship), or
c) the property spaces of Q and P partially overlap, and the property
instance corresponds to a point in the region of overlap (partially
overlapping determinates of a common determinable).29
These conditions yield the desired result that ‘Tom’s shirt being scarlet at noon’ is
identical to ‘Tom’s shirt being red at noon.’
One could complain against these conditions that at most we have shown that
determinables share instances with their determinates. However, with our trope identity
15
conditions we claim that only determinables and determinates can share an instance.
What justifies this further claim? The answer is short. Each trope corresponds to a
unique point in its determinables’ property spaces, so each trope has its non-determinable
necessities and determination dimensions essentially. Most properties will fall under
some determinable. Even if they do not, they are some kind of abstractions, with their
own accompanying determination dimensions. In extreme cases, there are properties that
fall under no determinables and have no determinates themselves. Instead, they possess a
property space that consists simply of a point. (Recall from section 2.2, a point is still a
property space.) A fictional example of such a property, for some particle, would be on.
A particle that is “on” interacts with other particles in predictable ways, but there are no
varieties of “on- ness” and no broader category (i.e., determinable) that on falls under.
Still, this property is some abstraction, with an unanalyzable determination dimension. I
take it that some microphysical properties are really like on in this regard.
Furthermore, tropes are abstract particulars, and they do not possess any features
apart from those given by their non-determinable necessities and determination
dimensions. For example, mass tropes do not have color. But tropes of types not related
as determinable-determinate differ in at least one determination dimension (i.e., they do
not share the same property space). Since tropes across property spaces differ in the
possession of at least one such determination dimension, they cannot be identical. So,
properties with property spaces not related as determinable-determinate cannot share an
instance.
3. Confirming our Analysis
The 8 truisms about determinables and determinates given in section 1 should be
derivable from a successful analysis of the determination relation. Let us see how each
truism follows from our analysis. For ease of explanation, the derivations that follow will
use mathematically modeled determinables as examples. But they generalize to cover
determinables/determinates that cannot be mathematically modeled, as well. The key
16
notion behind many of the derivations, “proper subset of determination dimension
values,” is shared by all determinables/determinates.
1. Our necessary and sufficient conditions do yield the verdict that our canonical
examples--like colored/red, red/scarlet and shaped/circular--are, in fact, related as
determinable to determinate. We can easily see this with our first pair. Colored and red
each has only 3 determination dimensions--hue, brightness, and saturation. Further,
whatever non-determinable necessities are had by colored are also had by red (though, it
is unclear what these would be). And finally, the property space of red is a proper subset
of the property space of colored (i.e., colored spans all compossible hue-brightnesssaturation values, whereas red spans a limited range of hue-brightness-saturation values).
2. Our conditions for determination require that the property space of a determinate
be a proper subset of the property space of its determinables. To be a proper subset the
determinate must specify a more limited range along at least one determination
dimension. Further, the notion of a determination dimension explains the limited ways in
which determinates specify the determinables they fall under. Proper subsets arise only
from a further specification along determination dimensions, so our analysis does not let
specifications like red and square count as a determinate of red. Red and square does not
have more precise values along the hue, brightness, or saturation dimension than does
red.
Nor is red a determinate of red or square. A sparse property theorist could reject this
possibility from the beginning by denying that there are such disjunctive properties.
However, even granting such properties, we can see that they are not determinables. Red
or square does not have a single property space. We do not admit disjunctive
determination dimensions.
3. An instance of a determinable corresponds to a unique point in that determinable’s
property space.30 Determinables necessarily admit of multiple specifications, so each
point in a determinable’s property space also belongs to a proper subset of the property
17
space. However, we have not yet said that each proper subset of a property space is itself
a property space. Our analysis allows us to be a sparse property theorist. Such a theorist
does not countenance a property for just any carving of the property space. For example,
take randomly disjoint subsets of the property space of colored. While a random
collection of disjoint subsets--e.g., the sum of a certain range of blues, oranges, and
lavenders--does constitute a proper subset of the property space of colored, we are not
required to judge the collection a property space. Our necessary and sufficient conditions
afford us this option by presupposing that A and B actually are properties. Since
determinates are properties and it is open to our theorist to accept a sparse property
ontology, we have not yet shown that determinable instances are also instances of
determinates.
Fortunately, this conclusion can be reached in a few ways. The easiest way is to
admit super-determinate properties corresponding to each point in a property space. This
approach is friendly to even the sparse theorist. In fact, most judge super-determinates to
be more acceptable than determinable properties. David Armstrong is one sparse theorist
who accepts only super-determinate properties.31 If all points correspond to superdeterminate properties, instances of determinables are then instances of some determinate
(specifically, some super-determinate property). But many determinables are also
divided into exhaustive sets of non-super-determinates. Each instance of colored, while
being some super-determinate shade, also falls under some non-super-determinate, for
example. And, of course, we could be an abundant property theorist and simply grant
property-hood to every subset of a property space.
4. An instance of a determinate corresponds to a point in that determinate’s property
space. Because the property space of a determinate is a subset of each of its
determinables’ property spaces, each point in the determinate’s property space is also
located in each determinable’s property space as well. So, necessarily, an instance of a
determinate is an instance of each determinable that determinate falls under.
18
5. We can prove transitivity as follows. Assume C determines B, and B determines
A. Then the property space of C is a proper subset of the property space of B. Also, the
property space of B is a proper subset of the property space of A. ‘Being a proper subset
of’ is a transitive relation, so the property space of C is a proper subset of the property
space of A. Similarly, they each share A’s non-determinable necessities. Therefore C
determines A, and the determination relation is transitive.
Our analysis also entails that the determination relation is asymmetric and irreflexive.
B determines A only if the property space of B is a proper subset of the property space of
A. No property space can be a proper subset of a proper subset of itself (e.g., A cannot
be a proper subset of B if B is a proper subset of A), so the determination relation is
asymmetric. Furthermore, the property space of A cannot be a proper subset of the
property space of A, as nothing can be a proper subset of itself. So, the determination
relation is irreflexive.
6. Ordering and/or similarity judgments among determinates under the same
determinable are also explicable on our framework. As a first pass, similarity between
such determinates can be understood as nearness of their corresponding points in the
property space. Our mathematical model offers an explanation of why orange is more
similar to red than it is to blue: orange property space points are closer to red property
space points than they are to blue property space points.
These judgments of nearness are difficult, though, when more than one determination
dimension is involved. We quickly discover that we cannot make judgments of
similarity/ordering simpliciter for such determinables, but only similarity/ordering
judgments relative to one determination dimension. This is particularly evident when one
determination dimension makes more subtle distinctions (e.g., as measured in the pure
number of such distinctions) than another. For example, assume a world in which there
are only two super-determinate values for the brightness of colors: dim and bright. In
this world, there is still the same spectrum of hues as in the actual world. Pick a point in
19
this property space. This point has a neighbor that is one over on the hue scale (leaving
brightness and saturation fixed) and another neighboring point one over on the brightness
scale (leaving hue and saturation fixed). Is the color represented by the first point equally
similar to each of these neighbors? It appears not. Why?--Because the move along the
brightness dimension is much greater than the move along the hue dimension. And even
when there are numerous possible values for each dimension, a similar problem still
arises. Namely, there is no common scale according to which values along the different
determination dimensions can be compared.
Similarity of determinates is best understood when limited to a single determination
dimension. There is a common metric along which nearness of, say, hue can be
evaluated. Minimally, when point B lies between points A and C according to hue, then
the hue of A is more similar to the hue of B than it is to the hue of C. Obviously, simple
determinables do not pose an incommensurability problem, as they admit only one
determination dimension.32
7. Our model also clarifies the notions of a super-determinable and superdeterminate. Super-determinables correspond to entire property spaces (i.e., the full
gamut of values along the determination dimensions). Values along these determination
dimensions may be unbounded. In that sense, a determinate may fall under an infinite
number of determinables. For example, having a 4 kg. mass appears to fall under the
determinables having under 5 kg. mass, having under 6 kg. mass, and so on ad infinitum.
As before, a sparse property theorist can reasonably deny that there such determinable
properties. But it does seem that there is a super-determinable property governing this
property space--i.e., having a mass simpliciter. Entire property spaces are the superdeterminables.
Every trope corresponds to a point in a property space. Points in property spaces
have precise values along each determination dimension. Therefore, every trope is superdeterminate. While each trope is an instance of a super-determinate property type, it is
20
also an instance of every determinable that super-determinate falls under. In holding
every property instance to be super-determinate, we follow in the tradition of Locke and
Berkeley. Though they disagree about the status of general ideas, both agree that
everything out in the world is super-determinate.33 There are no triangles lacking precise
side lengths. Similarly, our abstractions should not be confused with indeterminates.
8. Stephen Yablo has held that even though determinable events are not identical to
their determinate correlates, these events do not causally exclude one another.34 Yet, he
provides no explanation for this non-exclusion. As such, it appears to be an ad hoc
exception to exclusion principles. It would be better if we could explain why determinate
instances do not causally exclude instances of the determinables they fall under.
The easiest explanation for this lack of causal exclusion is to establish an identity. If
the determinable instance just is identical to the determinate instance, then obviously
there can be no exclusion. This justification for determinable-determinate non-exclusion
has been advocated by Cynthia and Graham Macdonald, as well as Douglas Ehring.35
Ehring correctly criticizes the Macdonalds’ position that property instances are
exemplifications of universals, yet different universals can still share an exemplification.
Ehring instead opts for the trope view that we favor. The present theory is an
improvement on Ehring (1996) in that it more precisely specifies the requirements for
different properties to share an instance. Our development of determination dimensions
and property spaces is critical to this specification.
We should also take this trope identity more seriously than do some trope theorists
who allow for different property types to share a trope. If tropes are the causal relata, as
most trope theorists (including myself) believe, then they are causes however described.
So, when a scarlet trope causes a pecking, then a red trope and colored trope cause a
pecking as well (because the scarlet trope is identical to a red trope, and the scarlet trope
is identical to a colored trope). This is to accept the Davidsonian line that causes are such
regardless of how they are described. It would be explanatorily misleading to say that the
21
pigeon pecked because she saw a colored object (since it suggests that she would have
pecked at blue or orange things as well). Yet it is nevertheless true that the pigeon
pecked because of the color of this thing (since the color of this thing is scarlet).
4. An Application: Determination and the Mental
By arguing that mental properties are determinable relative to their physical realizer
properties, Stephen Yablo has revived interest in the determination relation.36 The claim
is, for example, that being in physical state P1 is a determinate of being in pain. If true,
this conclusion would be of extreme importance--for, given the present analysis, mental
and physical properties could share an instance and the mental would avoid causal
exclusion worries.
Yablo argues that two commonly accepted features of the mental-physical relation-multiple realizability and supervenience--entail that they are related as determinable to
determinate. From multiple realizability, being in physical state P1 is just one specific
way in which a person can be in pain, just as being scarlet is one specific way of being
red. This observation is supposed to show that criterion 2 from section 1, the key feature
of determination, is met. Further, criterion 3 is met because a person in pain must have
one such physical realizer or other. By supervenience, if one is in physical state P1, then
one must37 be in pain. (Compare: If something is scarlet, then it must be red.) This
claim purportedly shows that the mental-physical relation fits criterion 4.
There is a beautiful simplicity to Yablo’s reasoning that the mental and physical are
related as determinable to determinate and that, just like red and scarlet do not causally
exclude each other, mental properties are not causally excluded by their physical
realizers. But despite the initial attraction of this view, by applying our understanding of
the determination relation we can see that the mental and physical are not related as such.
To discover the determinates, if any, of being in pain, believing that p, or any other
mental property, we need to discover the determination dimensions for such mental
properties. That is, we need to uncover the ways in which pains can differ from one
22
another in their pain-ness, beliefs can differ from one another in their belief-ness, and so
on for other mental properties. It makes sense to speak of people having exactly
resembling pains or beliefs. Plausibly, two people who believe the same content with the
same confidence level do not differ with regard to that belief. It can be difficult to
determine if such sameness of content and confidence level holds, but it is still the case
that beliefs differ from one another only along these lines. Jack believes that ‘Nebraska
has a panhandle,’ and Jill believes that ‘Nebraska has a panhandle.’ Each believes this
content with 90% confidence. From this information alone, I submit that Jack and Jill
exactly resemble each other with regard to this belief. This parallels the way in which
Jack and Jill would have exactly resembling hair color if their hair shared the same hue,
brightness, and saturation values. Content and confidence are the only determination
dimensions for believing that p. This is supported by the fact that folk psychological
laws (and/or the laws of cognitive science and/or decision theory) care only about these
two dimensions of beliefs.
The laws of intentional psychology are blind to the physical hardware that
implements these beliefs. Suppose Jack and Jill are on a game show and asked to name
all the U.S. states that have a panhandle. We can confidently predict that Jack and Jill
will each include Nebraska on their list. Why?--Simply because we know that Jack and
Jill each believe the content ‘Nebraska has a panhandle’ with 90% confidence. Note that
we do not have to inquire after the physical hardware realizing their beliefs. Our
prediction would in no way be altered if we discovered that Jack’s belief is realized in
physical state P1 and Jill’s in physical state P 2. These differences are simply irrelevant as
far as our psychological generalizations go. And there is nothing peculiar about this
game show example. Any psychological law relating that belief to another mental state or
to action would be indifferent to the physical hardware. And this observation generalizes
to other mental states: content, attitude, phenomenology and similar psychological-level
features are the only determination dimensions for mental properties.
23
On this understanding, believing that p is similar to our earlier examples of triangular
and mass in that the material constitution is not a determination dimension for any of
them. Just as a steel triangle can have the exact same triangularity (i.e., side lengths) as a
wooden triangle, and a steel ball can have the exact same mass as a wooden block, Jack’s
belief (in physical hardware P1) can have the exact same belief-ness as Jill’s belief (in
physical hardware P2).
Some might reject our conclusion and insist that the physical realization of a belief is
a determination dimension on par with content and attitude toward that content. Others,
more moderately, may opt for an agnosticism that leaves them open to the possibility of
an empirical reduction of folk-psychological kinds to, say, neuroscientific kinds. This
raises a general concern about our approach. Surely some reductions have occurred in
the history of science. In cases of reduction the properties of some science, with their
distinctive determination dimensions, are identified with the properties of some more
basic science, with different determination dimensions. But, it seems that the present
approach would rule this out, as difference in determination dimensions is difference in
properties. How is reduction possible on this model? And given that reduction is
possible, how can we be confident that the folk-psychological and neuroscientific
property spaces are not such a case?
Discovering determination dimensions is an empirical matter and, as such, folkpsychological reduction cannot be ruled out a priori. There is not enough space to
present a full explanation of reduction of property spaces here, but let us sketch a picture
of how reduction of property spaces is to be understood. It is (or was) epistemically
possible that the property spaces of higher-level sciences, like psychology, would be
supplemented with the determination dimensions of a lower-level science. Or, the
higher-level determination dimensions (epistemically) could even be completely replaced
in favor of the lower-level determination dimensions. Applying this point to our
example, the folk-psychological determination dimensions (epistemically) could have
24
been supplemented with physical realizer determination dimensions, or (epistemically)
could even have been replaced in favor of purely neuroscientific determination
dimensions.
The critical question is: What would justify such supplementation or replacement?
Supplementation would be justified if the predictive and/or explanatory powers of the
higher-level science could be increased by adding lower-level determination dimensions,
without too great a loss in simplicity and generalizability of the higher-level laws. This
last clause reveals that we are dealing with vague standards. Of course we could gain
more accurate predictions of human movement by utilizing the determination dimensions
of chemistry, but doing so would involve us in complexities that folk-psychology can
conveniently overlook. Though it is an empirical matter, it seems that the details needed
to increase the predictive and/or explanatory powers of folk-psychology would come at
too great a cost to the generalizability of such laws. Replacement would be justified if
the generalizations of the higher-level laws could be captured purely in terms of the
determination dimensions of a lower-level science, where these lower-level determination
dimensions have proved their worth with respect to other predictive/explanatory tasks.
This is another empirical issue, but it again seems that the robust patterns picked out by
the “laws” of folk-psychology cannot be captured utilizing only lower-level
categorizations. In this sense, the special science and their property spaces are
autonomous.
It is important to note that on this picture of property spaces and reduction, the
properties are “out there” in the world, with determination dimensions to be discovered.
There is not necessarily a property corresponding to each possible combination of
determination dimensions we can concoct. In more familiar terms, there is not
necessarily a property corresponding to every possible predicate.
Can anything else be said about the irreducibility of psychology, apart from what has
already been said about the laws of psychology being blind to the implementation
25
details? Ironically, one of Yablo’s explicit premises in arguing for the physical
determining the mental--multiple realizability--is sufficient to show that the physical does
not determine the mental. Further, the multiple realizability of the mental in the physical
is almost universally held by philosophers, so a non-determination conclusion should be
widely accepted. The amazingly simple argument goes as follows.38 When we say that
the mental is multiply realizable in the physical, we mean that the same belief type can be
realized in many physical types. Note, in particular, that even super-determinate belief
types are multiply realizable. That is, beliefs corresponding to the same point in the
property space of beliefs can nevertheless differ in physical realization--there can be a
physical difference without a mental difference. Since the mental property instances
exactly resemble, but the physical property instances do not, the mental property
instances are not identical to the physical property instances. The mental and physical
differ with regard to at least one determination dimension, so they cannot be related as
determinable to determinate.
A general conclusion to draw is that higher-level properties are not generally
determined by their lower-level implementing mechanisms (realizations). Here we break
with many who mistakenly judge the realization relation to be a species of the
determination relation. Examples of higher-level properties include having temperature
X, transparency, believing that p, and being such-and-such computer program. Each one
of these has a lower-level implementing mechanism (realization). But, differences at the
lower-level do not necessarily mean that there is a difference at the higher-level.
Functionalists have long observed that the same belief or computer program can be
realized in various lower-level mechanisms. Such multiply realized beliefs do not differ
in their belief-ness, so the lower-level mechanisms do not determine the belief. Heat,
transparency, mental states, and computer programs can all be super-determined by the
determination dimensions of the higher-level at which they reside. Similar points hold
for “abstract” properties, like mass and shaped, and their surrounding concreta. A
26
wooden triangle can have the exact same shape as a steel triangle. The addition of such
concrete features does not determine the shape property. Such shape properties are
super-determined without paying heed to the concrete features.
The application to the mental is just one of many that could be made. Our analysis of
the determination relation distinguishes it from the realization relation and provides us
with an apparatus for determining when different property types share an instance. This
is an especially important contribution if, indeed, property instances are the causal relata.
Regardless, our property spaces and determination dimensions provide a novel way of
understanding the relation between property types and their instances.39
ENDNOTES
1. The first systematic account of the determination relation belongs to W.E. Johnson,
Logic, Vol. 1, (Cambridge University Press, 1921), pp. 173-185. Johnson also introduced
the terms of art ‘determinable’ and ‘determinate.’ The most sophisticated and extensive
treatments of the determination relation since Johnson are found in: Arthur Prior, “I.
Determinables, Determinates, and Determinants,” Mind Vol. LVIII, No. 229, (January,
1949), pp. 1-20; John Searle, “ Determinables and the Notion of Resemblance,”
Proceedings of the Aristotelian Society, Supp. Vol. 33, (1959), pp. 141-158; and David
Armstrong, A World of States of Affairs, (Cambridge University Press, 1997), pp. 48-63.
Prior (1949) documents discussion of similar relations by John Locke, as well as in the
extensive literature on the genus-species relation.
2. One might object that something can possess a determinable property, be specified by
a disjunction of determinates, though not have any one determinate in particular. For
example, quantum indeterminacy might allow for determinables with indeterminate
determinates. While this may be true of microphysical phenomena, the macro-properties
we are normally concerned with do have some determinate or other. That is, even
27
granting quantum indeterminacy, in normal cases criterion 3 still holds. For example, it
is still the case that if something is colored it has some particular color, and if something
is shaped it has some particular shape. And even quantum indeterminacy is
probabilistically qualified. An amendment for the quantum level might be that every
object instantiating a determinable also instantiates certain determinates to certain
probabilities. Settling this debate would take us too far afield. Criterion 3 is typically
taken as a prerequisite for determination, and will be assumed throughout.
3. ‘Determines’ (and its variants) is used throughout as a term of art meaning “is a
determinate of,” rather than its more common use as signifying a causal or supervenience
relation.
4. Irreflexivity follows from criterion 2.
5. The presupposition is that there aren’t generic determinables--like being some
property or other--that all properties fall under. Determinables mark a genuine category
of difference. Things genuinely differ in their color or shape, but things do not genuinely
differ in their “being some property or other.”
6. I am assuming a subjectivist understanding of color as defended by, say, C.L. Hardin
in his Color for Philosophers, (Indianapolis, IN: Hackett Publishing Co., 1988). In later
appearances of this example, I suggest how objectivist reinterpretations can be made.
7. Arguments that property instances are the causal relata can be found in: Douglas
Ehring, Causation and Persistence: A Theory of Causation, (New York, NY: Oxford
University Press, 1997), pp. 76-77; and L.A. Paul, “Aspect Causation,” Journal of
Philosophy, (2000), pp. 235-256.
8. This is the lesson to be learned from criticisms of Donald Davidson’s Anomalous
Monism. The worry expressed there is that according to Davidson’s theory only the
physical property instances are causally efficacious. As just a sampling, see: Fred
Dretske, “Reasons and Causes,” Philosophical Perspectives 3 (1989), pp. 1-15; Jerry
Fodor, “Making Mind Matter More,” Philosophical Topics, 17 (1989), pp. 59-80; Ted
28
Honderich, “The Argument for Anomalous Monism,” Analysis 42 (1982), pp. 59-64;
Terence Horgan, “Mental Quausation,” Philosophical Perspectives 3 (1989), pp. 47-76;
and Frederick Stoutland, “Oblique Causation and Reasons For Action,” Synthese 43
(1980), pp. 351-367.
9. See my “Three Varieties of Causal Overdetermination,” Pacific Philosophical
Quarterly 83 (2002), pp. 335-351.
10. This example is taken from Stephen Yablo, “Mental Causation,” The Philosophical
Review, Vol. 101, No. 2, (1992), p. 257.
11. We should distinguish, however, between those properties that are causally
efficacious (a metaphysical notion) and those properties that are causally relevant (an
epistemic/explanatory notion). The triangle’s being scarlet might have been causally
efficacious with regard to the pigeon’s behavior, but this property of the triangle might
not be relevant with regard to explaining the pigeon’s behavior. This is especially true if
citing the scarlet color suggests contrasts with other shades of red. This distinction
between causal efficacy and relevance will arise later as well. I thank an anonymous
referee for stressing the relevance of this distinction.
12. Examples of such confusion are found in Yablo (1992); Sydney Shoemaker,
“Realization and Mental Causation,” in Physicalism and Its Discontents, eds. Carl Gillett
and Barry Loewer (New York, NY: Cambridge University Press, 2001), pp. 78, 80 and
85; Douglas Ehring, “Part-Whole Physicalism and Mental Causation,” Synthese 136
(2003), p. 375; and Lenny Clapp, “Disjunctive Properties: Multiple Realizations,”
Journal of Philosophy XCVIII, 3 (March 2001), p. 125.
13. Prior (1949), p. 13.
14. Johnson (1921), p. 183.
15. I do not want to give the impression that determination dimensions can be known
purely a priori, say, by conceptual analysis. For more on this, see section 4.
29
16. Sometimes color theorists use alternative vocabulary, but generally the same
individuating criteria are roughly accepted. For example, on the Munsell Color System
these same 3 criteria are termed ‘hue,’ ‘value,’ and ‘ chroma.’ Alternative models of the
color space are provided by the Ostwald and C.I.E. color systems. Objective color
theorists provide alternative determination dimensions--e.g., wavelength, purity, and
luminance. Similarly, sound is typically analyzed into three components: pitch, timbre,
and loudness. It is controversial whether this list is exhaustive. But, timbre is sometimes
characterized negatively such that other determination dimensions are excluded. For
example, timbre is sometimes simply defined as that feature which allows listeners to
distinguish sounds of the same pitch and loudness. Each of these alleged determination
dimensions may itself have determination dimensions, further complicating matters.
17. The classic statement of Scientific Realism with regard to properties is found in
David Armstrong’s Universals and Scientific Realism (2 Volumes), (New York, NY:
Cambridge University Press, 1978).
18. Fred Dretske, Explaining Behavior, (Cambridge, MA: The MIT Press, 1988), p. 80;
and Dretske (1989).
19. Relational features that are irrelevant to individuating that kind, like space-time
location, are not included as determination dimensions.
20. These are only sufficient conditions because not all determinables can be modeled as
such. For the others, and the more general necessary and sufficient conditions, see
section 2.3.
21. I am indebted to an anonymous referee for bringing this example, and the problem it
represents with regard to mathematical modeling, to my attention.
22. There are many other properties, like shaped, that cannot be (easily) mathematically
modeled. Just as shaped has different determination dimensions corresponding to the
number of sides of the particular shape, there can be different determination dimensions
for genetic properties corresponding to the number of chromosomes for the particular
30
DNA, different determination dimensions for chemical properties corresponding to the
number of elements forming the molecule, etc. Still, there is a schema for picking out the
determination dimensions corresponding to the abstractions of each science.
23. ‘Property space’ will now be used to cover such ranges in determination dimension
values, as well as the n-dimensional spaces discussed in section 2.2.
24. Jonathan Schaffer argues that tropes are to be individuated by spatial-temporal
location (as well as resemblance) in his “The Individuation of Tropes,” Australasian
Journal of Philosophy Vol. 79, No. 2, (June, 2001), pp. 247-257. The criteria for
individuating tropes provided in section 2.5 follow Schaffer in (partially) individuating
tropes by spatial-temporal location. However, we also offer an explanation, in terms of
our property spaces, of the resemblance component of trope individuation.
25. Locke, An Essay Concerning Human Understanding, ed. Peter H. Nidditch, (Oxford:
Clarendon Press, 1975), II.xi.9.
26. See Armstrong (1978, 1997).
27. The following present the most systematic and/or influential accounts of tropes:
D.C. Williams, “On the Elements of Being I,” reprinted in Properties, eds. D.H. Mellor
and Alex Oliver, (New York, NY: Oxford University Press, 1997); G.F. Stout, “Are the
Characteristics of Particular Things Universal or Particular? II,” Aristotelian Society
Supplementary Volume, 3, (1923), pp. 114-127; Keith Campbell, Abstract Particulars,
(Oxford: Blackwell, 1990); J. Bacon, Universals and Property Instances: The Alphabet
of Being, (Oxford: Blackwell, 1995). For some prominent disagreements, see Chris
Daly, “Tropes,” in Mellor and Oliver (1997), as well as almost any work by David
Armstrong on property theory.
28. This is borrowed from the notation Jaegwon Kim uses for his events (i.e.,
exemplifications of universals) in Kim, Supervenience and Mind, (Cambridge University
Press, 1993), p. 9. My adoption of this schematization should not be seen as judging
31
property types to be ontologically prior to their tokens (tropes). Like most trope theorists,
I take property types to be classes of resembling tropes.
29. I wish to thank an anonymous referee from this journal for bringing this third
possibility to my attention. The example he/she gave is of two overlapping color types
that might share an instance--say, orangish red and yellowish red. Clearly, neither is a
determinate of the other.
30. Or, given the possibility discussed in footnote 2, each instance of a determinable may
correspond to various points in that determinable’s property space, to various
probabilities.
31. Armstrong (1978, Vol. I), p. 117.
32. It is a merit of the present analysis that it explains why we cannot issue absolute
similarity judgments regarding complex determinables. Such judgments must always be
relative to a determination dimension. I wish to thank an anonymous referee for drawing
this merit of the analysis to my attention.
33. Locke, Essay, III.iii.6, and Berkeley A Treatise Concerning the Principles of Human
Knowledge, ed. Kenneth Winkler, (Indianapolis, IN: Hackett Publishing Co., 1982),
Introduction.
34. Yablo (1992), p. 259; pp. 273-279. While holding that determinables and
determinates do not causally exclude one another, Yablo does hold that one of them can
nevertheless be a better candidate for occupying the role of cause than another. For
example, if the pigeon pecks at only scarlet things, the triangle’s being scarlet is more
appropriately judged the cause than its being red (i.e., since there are shades of red that
the pigeon would not peck at). But this is another point at which the distinction between
causal efficacy and causal relevance, as used in footnote 11, is relevant. Contrary to
Yablo’s emphasis on the explanatory aspect of causation (causal relevance), causal
exclusion principles concern the metaphysical notion of causal efficacy.
32
35. Cynthia and Graham Macdonald, “Mental Causes and Explanation of Action,” in
Mind, Causation, and Action, ed. L. Stevenson, R. Squires, and J. Haldane (Oxford:
Basil Blackwell, 1986); and Douglas Ehring, “Mental Causation, Determinables, and
Property Instances,” Nous 30:4 (1996), pp. 461-480.
36. Yablo (1992). Cynthia and Graham Macdonald (1986) provides an earlier
application of the determination relation to mentality.
37. This ‘must’ can be read with varying strength (e.g., mere nomic necessity,
metaphysical necessity, etc.), depending on one’s view of supervenience.
38. A similar argument is made in Ehring (1996), p. 473.
39. Thanks to Tamar Gendler, Karson Kovakovich, Jonathan Schaffer, Ted Sider, Robert
Van Gulick, and two anonymous referees for very helpful comments.
33