24293994-Descartes’s-Ontology

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The Meditations may have moved epistemology to the

center of modern philosophy, but Descartes himself

conceived it as a work of metaphysics: Meditations

on First Philosophy was his title for it. Still, the meta-

physics in the Meditations is mostly of the special

variety: natural theology, cosmology, and rational psy-

chology. There is not much general metaphysics or

ontology in it. Descartes does sometimes make onto-

logical remarks, as when he says in Meditation Three

that the mode of being by which a thing exists objec-

tively in the intellect by way of an idea, imperfect

though it may be, is certainly not nothing (VII. 41).

And he appeals to various ontological principles in

arguing for the existence of God: for example, that

there must be as much reality in the . . . cause as in

the effect of that cause (VII. 40) and that existence is

a perfection (VII. 67). But he undertakes no purposeful

investigation of being qua being, no systematic survey

of the modes and categories of being.

This neglect of ontology is remedied somewhat in thePrinciples. Here, in the articles comprising the final

third of Part I, Descartes does list and distinguish the

basic kinds of things he supposes there to be. He also

articulates a number of ontological doctrines which are

at best only implicit in the Meditations. I say at best

because it may be questioned whether Descartes actually

held certain of these doctrines at the time he wrote the

Meditations. In any case, some portions of the ontology

presented in the Principles cover topics that receive no

mention in theMeditations: the status of eternal truths,

for one. And in at least one instance Descartes takes a

position in the later work that seems directly to conflictwith a doctrine stated in the earlier one. I refer to his

account of universals in the Principles, within which

category he includes the numbers and figures which are

the objects of mathematical inquiry. By this account,

these entities are merely ideas in the mind, mere modes

of thinking which have no actual existence. But in the

Fifth Meditation, mathematical objects are held to be

things that have their own true and immutable natures

[which are] not invented by [any human being] or

dependent on [his] mind (VII. 64).

Questions about the relation between the ontology

laid out in the Principles and that, implicit if not

expressly stated, of theMeditations, provide one reason

for examining the text of the relevant Principles passage

quite carefully. Another reason is that this text by itself

is problematic. Descartess presentation in Articles 48

and following is rather sketchy and disorganized, and

his meaning is often unclear and indistinct. It is sur-

prising that scholars have paid so little attention to this

passage, and that some have read it so superficially.

There has, it is true, been some discussion of the

apparent conflict between the Principles account of

mathematical objects and that of the Meditations; but

the parties thereto have reached no consensus.

This paper has two parts. In the first I spell out andelucidate the ontology expressed in Principles I.4870,

explicating the text of this passage and resolving the

interpretive problems it presents as they arise. In the

second I consider the relation between the Fifth

Meditation account of mathematical objects and that of

the Principles. I shall argue that there is really no

conflict between these two accounts since the former

can be assimilated to the latter. A question I am not

going to deal with in this paper is that of the extent to

which the ontology of the Principles is implicit in the

Meditations, as opposed to being a later construction.

And of course a full treatment of Descartess ontologywould have to consider ontological doctrines expressed

or presupposed in works other than theMeditations and

the Principles. But that is a task for another paper.

Before beginning my examination of Principles

I.4870, I need to settle some terminological matters.

Descartess Ontology Vere Chappell

Topoi 16: 111127, 1997. 1997 Kluwer Academic Publishers. Printed in the Netherlands.


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First, ontologists require some way of referring, pre-

or extra-theoretically as it were, to all or any of the

things that in some sense or other have being, to the

items that are originally there to be divided up into onto-

logical categories. In English the word thing can be

used for this purpose; so can the common nouns being,

entity, and item. But thing is not a good word to

use in discussing Descartess ontology. The reason is

that he tends to take its Latin equivalent, res, to mean

substantia, and hence to restrict it to the members of

one ontological category. Nor is there any noun other

than thing that Descartes regularly uses as an extra-

categorical general term. His standard way of making

these pre-theoretical references is via pronouns and

pronominal phrases omnia, alia, ea quae . . . , quae-

cunque . . . , etc. a usage that is natural and

perspicuous in Latin but awkward and often ambiguous

in English. In this paper I follow the English custom of

using common nouns in this connection, being,

entity, and item, but not thing. Thing I reserve,

as Descartes largely does, for substances.

Second, Descartes sometimes uses the terms

attribute, affection, mode, quality, and property

interchangeably, as if they all stood indifferently for

entities of one general category. But sometimes he

distinguishes these terms by restricting some of them

to certain subdivisions of this general class. In what

follows I have opted for the latter practice. Thus I use

attribute and affection as more general terms

covering the whole class of entities in question, and

restrict mode, quality, and property to the specificsubclasses to which Descartes sometimes but only

sometimes applies them.

Finally, the word mode is particularly protean in

Cartesian texts. Apart from the two uses just noted, (1)

as a synonym for attribute and (2) for marking the

members of a subclass of attributes, two others are

commonly found. In one of these, (3) a mode is a

specific variety or form, a species, of something more

general; in the other, (4) it has the ordinary non-philo-

sophical meaning of manner or way. In all of these

senses the word mode often is followed by an of-

clause, but the prepositional object is different in dif-

ferent cases. When the mode mentioned is either an

attribute in general or a special sort of attribute (as in

the first and second of the senses just listed), the object

to which it is attributed via of is a substance; thus

mode of my mind and mode of an extended sub-

stance. By contrast, when it is a species or form of

something more general (third sense), the object is

an attribute; thus mode of extension and mode of

thinking (or thought). (There appear to be no restric-

tions as to what modes in the fourth sense may be modes

of.) The situation is complicated by the fact that

Descartes uses the phrase mode of thinking itself in

two different ways. In one the word mode occurs with

the third sense and the thinking refers to an attribute,

so that the whole phrase stands for a species of thinking:

perceiving or willing, or doubting, imagining, judging,

etc. In the other, the mode has the fourth meaning, and

the phrase is equivalent to way of regarding, manner

of conceiving, or some such. In my discussion I shall

have occasion to use the word mode in all but the first

of its four senses, and the phrase mode of thinking in

both of its two. I will do my best to make clear on each

such occasion which sense is being employed.

I. Exposition ofPrinciples I.4870

My exposition is keyed to the accompanying charts. I

distinguish three sections within this passage, com-prising Articles 48, 5156, and 5759, respectively. The

remaining Articles, from 60 to 70, refine and illustrate

but do not really extend the basic scheme that Descartes

presents in 4859. In addition, there is a portion of

Descartess ontology which, though not explicitly stated

in the passage, can easily and naturally be extrapolated

from it: this too is represented on my charts. The levels

I refer to in my exposition correspond to the lines of

text on each chart, counting from the top.

112 VERE CHAPPELL


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1. Level one: whatever falls under our perception

Descartes identifies his initial subject matter as

whatever falls under our perception. By doing so he

is not of course restricting it to the objects of sense per-

ception. He gives the term perception its maximum

scope, using it to cover every way in which a human

knower may apprehend or be aware of something.

We still might wonder whether the field of the

perceivable, even in this extended sense, exhausts the

whole field of being for Descartes. Does he hold that

the subject matter of ontology extends beyond what can

be humanly perceived, that there are entities apart from

those that we can think or be aware of? There is cer-tainly no indication in our passage that he does, and I

know of no text in any other work that points to this

position either.

2. Level two: things or affections of things vs.

eternal truths

This is Descartess first division within the field of the

perceivable, and here again the question arises: does this

division exhaust the field? That is, does it exhaust even

this field, never mind the (perhaps more extensive) field

of being? Again, there is nothing in the Principles

passage to suggest that it does not.Turning to the terms of the division, let us first

consider eternal truths. Descartes says that these have

no existence outside our thought, implying that they do

exist within our thought. He must regard them, there-

fore, as mere objects of thought, entia rationis, to use

the Scholastic term, or objective beings, to use his

own term from the Meditations. Note further that they

have no existence outside our, that is, human thought.

Descartes does not say that we human beings create

these truths: they need not be the products of our

minds. But it is in our minds and only there that they

reside.

One might well wonder how any mere object of

human thought, any entity existing in and only in a

human mind, could also be eternal. To be eternal is to

be outside time, but human minds exist within time.

Descartes sometimes used the word eternal to mean

not timeless but everlasting; but even if what he

means here is everlasting, it is hard to square a truthshaving that attribute with its having existence solely in

human thought. Descartes held that all human souls,

once created, never thenceforth cease to exist; but he

did not hold that any human soul began to exist at the

beginning of time. This is a problem I shall address in

Part II of this paper.

The other category that Descartes introduces at this

second level is things or affections of things. This is

not one single category but a compound of two, things

on the one hand, affections of things on the other.

Descartes eventually distinguishes these two, but not

until he reaches level five of his initial classificatoryscheme (in Section One), and then only implicitly; and

it is not until Section Two of the passage that he gives

them their proper names, substances and attributes

respectively. In the meantime he treats them as one

(and I shall henceforth refer to this compound via

the hyphenated title things-and-affections-of-things),

DESCARTESS ONTOLOGY 113

Eternal

Truths

Objects of Perception

omni-generic uni-generic

Things-and-

Affections-of-Things

intellectual material

Substances

= Bodies

AttributesSubstances

= Minds

ref to

Minds

ref to

M-B Unions

Emotions

Attributes

ref to

Bodies

Appetities Sensations

A. Section One: Article 48


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though some statements he makes at levels three and

four apply to one of the two categories and not to the

other.

Descartes takes eternal truths to be objects of

thought, that is, objective beings, in our passage. It

might be supposed that he regards things-and-affections-

of-things as entities existing outside human thought, that

is, as actual beings (to use a Cartesian term found in the

Meditations). The fact is that he does consider many

things (i.e. substances) and many affections of things

(i.e. attributes) to be actual beings, but not all of them.

In Section Three (Article 57) of the passage, he intro-

duces a distinction between attributes which are in

the very things of which they are said to be attributes

and those which are only in our thought. The same

distinction may be made, I believe, among substances,

though Descartes takes no notice of it here (this is the

main point of the extrapolation I referred to earlier). But

this is just the distinction between actual beings and

objective beings, between those that exist outside and

those that exist within our thought. I shall have more

to say about this distinction later on.

3. Level three: the most general things vs. those

confined to one genus

Descartes does not say much about these most general

things, in Article 48 or elsewhere in our passage,

although he invokes examples of them on several occa-

sions. The examples he gives here are substance,

duration, order, and number; later he appears to

add existence (Article 56) and perhaps time (Article57) to the list. We see at once that none of these, save

substance itself, is properly a thing; they are rather

attributes, that is, affections of things. But there is no

mislabeling here. The field that Descartes is dividing

at this level is still the compound things-and-affections-

of-things.

Duration, number, order, existence we have no

trouble conceiving these as attributes, and Descartes

clearly does so conceive them. But we do encounter dif-

ficulty in trying to think of substance as a thing, that

is, as a substance. This difficulty can be resolved, as we

shall see in due course. In the meantime I shall merelyassume that Descartess category of most general

things includes both substances and attributes.

Descartes says that these most general entities

extend to all genera of things; I call them, therefore,

omni-generic entities. He then immediately informs us

that there are only two genera of things (or at least

two summa such genera); and he identifies them as the

genus of intellectual things and that of material

things. One question that arises here is whether

Descartes is claiming that every being in both of these

genera has or is each of these most general entities,

that is, has existence, number, and duration and is a sub-

stance. Or is his claim merely that at least one being in

each genus has or is each of these general entities? The

answer is obviously the latter. It may be that every being

has existence (actual or objective) and number (at least

the number one) for Descartes. But not every intellec-

tual or material being is a substance, since some are

attributes. And God, who Descartes later says is a

thinking substance (Article 54), cannot have either

duration (since He is eternal) or order (since He is

simple). But then it follows that these most general

entities cannot be identified with the transcendentals of

Scholastic philosophy, as at least one recent commen-

tator has suggested.1 For the transcendentals are all

supposed to be convertible with being.

From what are Descartess omni-generic entities dis-

tinguished? Since there are only two genera of things,

the only alternatives (for a thing or an affection thereof)

to being found in all genera are (1) being found in

exactly one of these two, and (2) being found in neither

of them. But the latter is evidently not an option for

Descartes. On the one hand, there is not only no genus

of beings as such, but no genus of things-and-affections-

of-things, or of substances, or of numbered or enduring

things, given that the genera of intellectual and material

entities are the highest genera there are; and on thispoint Descartes is in accord with Scholastic doctrine.

On the other hand, there are no things or affections

of things existing outside genera, no extra-generic

such entities. The things-and-affections-of-things other

than those that are omni-generic, therefore, must be

uni-generic.

4. Level four: intellectual vs. materials things

Descartes distinguishes his two summa genera of

things at the same time that he says that there are two

of them. He does not at this point cite any basis or prin-

ciple for drawing the distinction: he merely names thetwo genera and gives examples of items included in

each of them. It needs to be noted again that though he

calls what he is distinguishing things, he means

things-and affections of things; and in fact the items

he cites as examples of intellectual things and

material things are all of them attributes. For he

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describes them as things . . . pertaining to substances,

to mind or to thinking substance in the one case, and

to extended substance [or] to body in the other. This

is one of his standard ways (and one of the Scholastics

ways too) of specifying attributes.

5. Level five: substances vs. attributes

Although Descartes mentions substances in describing

the items, that is, the attributes, that belong to the genera

of intellectual and material things, he does not explic-

itly say that these substances also belong to these

genera. But there is no doubt that he holds that they

do. Furthermore, although the distinction between sub-

stance and attribute that I represent him as introducing

at level five of my exposition is not in fact explicitly

made by him, at that point or anywhere in Article 48,

it surely is fair to claim that the distinction is implicit

there.

6. Level six: certain other [things] that we

experience in ourselves

Having distinguished intellectual from material things,

Descartes cites certain others [that] we experience in

ourselves. But his text at this point is obscure, and

commentators have had different opinions as to its

import. The main point at issue is the status of these

others, which, Descartes tells us, include appetites,

emotions, and sensations. These, he says, are not

to be referred either solely to the mind or solely to

the body, but arise from the close and intimate union

of our mind with the body. This could mean that

these entities, which are in fact attributes, constitute

a separate ontological category, a distinct kind of

attribute, apart from and on a par with the intel-

lectual and material attributes which are to be

referred solely to the mind and solely to the body,

respectively. On this reading, Descartes would not

be a dualist but a trialist, as John Cottingham has

put it, at least regarding attributes.2 Alternatively, it

could be Descartess view that these entities belong

to one or the other of the two categories, and differ

from its other members only at some sub-categorical

level.

My own position is that Descartes holds the latter of

these two alternatives, as is shown on my chart. I take

the others in question to belong ontologically to the

category of intellectual attributes, and not to constitute

a distinctive third kind of attribute. They differ from the

other members of this category in that they require

causes of both the mental and the material kinds in order

to exist, whereas the other intellectual modes require

none but mental causes. (Correspondingly, attributes in

the material category require none but material causes.)

But it is not the kind of cause an entity has that deter-

mines the ontological category it belongs to, at least at

the level of the categories of intellectual and material

beings. For causes according to Descartes operate across

these categorical boundaries.

I know that this position needs defending, but I shant

defend it here, since to do so would divert me from the

task of surveying Descartess whole ontology.3


B. Section Two: Articles 5156

uncreated

uni-gen

G

omni-gen

S M B

uni-gen

uncreated

uni-gen

d

created

uni-gen omni-gen

nn

uni-gen omni-gen

nn

?

uni-gen omni-gen

nn

uni-gen

i m i m i m

?

i m

Modes

created

Qualities

created

?

principal

created

constant variable

AttributesSubstances

Things-and-Affections-of-Things

non-principal

created


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1. Level one: things-and-affections-of-things

In Article 51, Descartes returns to the ground he has

covered in Article 48 and begins tracing a different

path through it. The new scheme he produces is not in

conflict with the earlier one; rather, it interpolates new

divisions within it and adds detail under existing divi-

sions. The resulting structure can be mapped on to that

Section One in different ways; the way I have chosen

is shown by my charts.

2. Level two: substances vs. attributes

This time through, Descartes draws the distinction

between substance and attribute explicitly, and indicates

the basis on which he does so. By a substance, he

says, we understand a thing which so exists that it

requires no other thing for its existence. Implicit in

this formula is a definition of an attribute as a thing

which does require another thing for its existence,

and this is spelled out in a clause added to the

French translation of the Principles (at Article 51):

things [that] are of such a nature that they cannot

exist without other things, we . . . call . . . attributes

(IXB.47).

There are well-known problems with these defini-

tions. At the least it seems that, in order to understand

them, we must already have some understanding of the

terms being defined. We need to know what a substance

and what an attribute is, and to grasp the specific (non-

causal) kind of dependence the one has upon the other.

As Descartes might have put it, we need to understand

that special way of depending in which attributes arewont to depend on substances.

3. Level five: uncreated vs. created substances and

attributes

Immediately upon defining substance, Descartes pro-

ceeds to distinguish one particular substance, God, from

all other substances. The latter, he says, are the crea-

tures of God, whereas God himself is uncreated. His

point is that God is the only being that strictly satisfies

his definition of substance. Instead of concluding,

however, that it is false or inaccurate to call creatures

substances, Descartes announces that the term sub-stance does not apply univocally to them and to God,

meaning that God and created things are substances in

different senses of the word.

We should note that not only is God an uncreated

for Descartes, but that His attributes must be uncreated

too. And so are the attributes of created substances the

creatures of God.

4. Level three: constant vs. variable attributes

Descartes next moves to consider attributes, making a

number of divisions among them and adding, along the

way, details to his account of substances. From now on,

however, my discussion will proceed in a somewhat dif-

ferent order from that of his presentation.

The division between (what I call) constant and

variable attributes is merely implicit in Descartess text,

but it is presupposed by two divisions that he does make

explicitly.

An attribute is constant iff it is never absent from

the substance that possesses it, that is, in the case of an

enduring substance, iff it inheres in or is exemplified by

that substance at every moment of its existence. It is

important to notice that this definition is satisfied by

two different kinds of attribute for Descartes, those he

calls principal attributes and those I am calling omni-

generic ones. Thus not only extension in a corporeal

substance and thinking in a mind, but existence and

duration in an existing and enduring thing are constant

attributes.

A variable attribute, by contrast, is either one that

an enduring substance has at certain times and lacks at

others, an attribute that is gained or lost; or else it is one

that, though never lost, undergoes change in the course

of its existence. Thus if an apple turns from green to

red, its greenness is a variable attribute according to the

first clause of the formula just stated; its color is oneaccording to the second.

5. Level four: principal vs. non-principal attributes

In Article 53, Descartes lays down a fundamental prin-

ciple of his ontology. A substance, he declares, has

many attributes, but for each substance there is one

principal property, which constitutes its nature and

essence, and to which all the others are referred. By

one principal property here Descartes means one

exactly, not one at least; and for a property to be

referred to another, he tells us two sentences later, is

for it to presuppose it (Latin praesupponere). Butwhen he says that all the other properties of a sub-

stance are referred to its principal one, he does not mean

all without qualification. He means all of its uni-

generic properties, for the point does not hold, for

example, for existence or duration. From the fact that

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something exists, nothing whatsoever follows as to what

its principal property is.

The principal property of minds, of course, is

thought; of bodies it is extension; and Descartes fre-

quently, throughout his writings, identifies thought and

extension as the essences of these substances, respec-

tively. He has some trouble defining the term essence,

however. One problem is to distinguish essences from

omni-generic attributes, since these too are always

present: a substance (that once has them) never lacks

them. And not only does it never lack them in fact but

it could not lack them and still exist. Indeed, Descartes

goes so far as to say (in Article 62) that a substance

and its duration are distinguished merely ratione, which

means that the substance cannot be understood without

that attribute. This is exactly what he holds about the

distinction between a substance and its essence: a body

or a mind cannot be understood as lacking extension or

thought, respectively.

So then what is the difference between an essence

or nature and an omni-generic attribute for Descartes?

For one thing, an essence or principal attribute deter-

mines a genus of things, indeed a highest genus (there

being only two such attributes), in the sense that the

class containing all and only the substances that

have it constitutes a genus, whereas an omni-generic

attribute does not. Again, the essence of a substance is

entailed by each of its uni-generic attributes or, to

put it in a more Cartesian way, the concept of the one

is contained in that of the other whereas its omni-

generic attributes are not so entailed. These are not ofcourse surprising points, since they are built into

Descartess definitions of these terms genus and uni-

generic.

Distinguishing essences from omni-generic attributes

is one problem we encounter in trying to define

essence in the Cartesian sense. But it is not the only

such problem. For omni-generic attributes are not the

only non-principal constant attributes that Descartes

recognizes. There are also those that fall under the tra-

ditional Aristotelian heading of properties. Descartes

does not mention these properties until he comes to

discuss universals, in Article 59: they constitute one ofthe five types of universal that he says are commonly

listed. Nor does he provide any characterization of

them even then. But it is clear from the example he

gives, viz. that the square on [the] hypotenuse [of a

right-angled triangle] is equal to [the sum of] the

squares on its sides, and from what he says about it,

viz. that it belongs to all and only right-angled trian-

gles, that properties meet the same condition that

essences do: they are attributes without which the sub-

stances possessing them cannot exist. The Aristotelians

of course have a similar problem of distinguishing

essences from properties. But they also have more

resources for dealing with this problem than Descartes

has at his disposal: a richer conception of essence

grounded in a theory of scientific explanation. Note that

I say: resources for dealing with the problem, not for

successfully solving it.

6. Level four: qualities vs. modes

In Article 56 Descartes notes that he has been using the

terms quality and mode as synonyms for attribute.

But these terms, he announces, also have a narrower

use, in which they apply only to a restricted subclass

of attributes those I call variable attributes. Descartes

then undertakes to distinguish modes and qualities from

one another. Unfortunately, his attempt to explain the

narrower use of these terms is unilluminating. When,

he says, we consider a substance to be affected or

modified [variari] by [its attributes], we call [these

attributes] modes; when it can be designated as such and

such [talem] by this modification we call them quali-

ties. Cottingham in his translation puts an Aristotelian

spin on the last part of this statement by rendering talem

a substance of such and such a kind, and if Descartes

were invoking an Aristotelian theory of species and

genera here, it would be appropriate to interpret hiswords in this way. But I see no justification for

Cottinghams reading in the text itself, and no other

reason to think that Descartes is alluding to Aristotle

here.

Descartes gives no example of qualities in the

narrower sense and (I believe) never uses the term

quality again in this sense, in the Principles or else-

where. Hence I shall having nothing specific to say

about these qualities. The situation is different, however,

with respect to modes. Not only does Descartes often

use the word mode, in the narrow way; he also gives

several examples of modes in this sense; so we are ableto get quite a firm grip on his conception of them. Thus

in Article 61 he cites as examples of modes proprie

dicta the square shape and the motion of a square

moving stone. In Article 64 he says that thought and

extension, which have been identified as the principal



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attributes of minds and bodies respectively, can also be

taken as modes of substances, in that one and the same

mind can have many different thoughts, and one and the

same body can have, at different times, many different

sizes and shapes. He then makes it clear that it is the

different thoughts and the different sizes and shapes

themselves that are the modes of the substances in

which they inhere.

Finally, in Article 65, he lists intellection, imagina-

tion, recollection, volition, etc. on the one hand, and

all shapes, the positions of parts, and the motions of

parts on the other, as modes of the things in which

they inhere that is, of thinking and extended sub-

stances respectively. The text here is a little confusing,

in that Descartes first describes the items on the first list

as modes of thought and those on the second as

modes of extension. This is a case in which he is using

the word mode in two different senses, without any

indication that he is doing so. The point he wants to

make in the Article is that intellection and the other

items he lists are modes in the sense of attributes (i.e.

in the second of the four senses I distinguished earlier).

But he identifies the items in question by referring them

to the more general principal attributes of which they

are species, calling them modes of the latter (in the third

sense of mode).

One further point about modes and qualities. In God

there are attributes, Descartes observes, but no modes

or qualities, because in God there is no variation. Hence,

as is shown on my chart, the only modes and qualities

there are, are created ones, that is, ones belonging tocreated substances.

7. Level six: omni-generic vs. uni-generic attributes

and substances

Descartess distinction between omni- and uni-generic

attributes, first introduced in Section One of our

passage, is invoked on several occasions in Section

Two. We encounter problems, however, when we try to

fit this distinction into the more elaborate system of dis-

tinctions that Descartes constructs in Section Two.

Some points are clear enough, but others are not. (a)

It is clear that no principal attribute is omni-generic,since it is principal attributes that determine the genera

there are. (b) It also is clear that an uncreated attribute

must be uni-generic, since it is a principal attribute. But

to what genus does it belong? One possibility is, to the

genus of intellectual entities, since God is a thinking

substance. On the other hand, the term thinking, pre-

sumably, is not applied univocally to God and his crea-

tures; and this could mean that God and they cant

belong to the same genus after all. (c) It is clear that

Descartess main examples of omni-generic entities,

duration, number, order, and existence, fall into the

category of constant non-principal attributes, although

he has no common name for them (which is why I

label them nn on my chart). But what are the uni-

generic members of this category? One answer is, the

Aristotelian properties that he includes among the

five common universals in Article 59. This is plau-

sible, given his example there, and on the assumption

that such properties are to be found not only in geo-

metrical entities but also in bodies and minds. (d) In the

case of qualities, nothing is clear: whether they are all

omni-generic, all uni-generic, or come in both varieties.

(e) And it is clear, finally, that all of Descartess

examples of modes, which we surveyed a moment ago,

are uni-generic. But are there any other modes that are

omni-generic, and if so, what are they? Here again is

one possible answer: there are such modes, and they are

modes of number or order in the way that a particular

thought and a particular shape are modes of thinking

and extension. (Note the shift in sense between the first

modes and the other two in the foregoing sentence.)

The latter, Descartes says, are modes of the substances

to which they belong; and so, we might say, are the

former. But what would such a mode of number or of

order be? How about a particular number or order, for

example, the number two and the order in a straightline? (I am not sure that this move would work for

duration, much less for existence.)

The most vexing question that arises at this level,

however, concerns substances rather than attributes.

There is no doubt that all the substances Descartes iden-

tifies as such, created and uncreated, are uni-generic,

though we have not yet determined which genus it is

that the uncreated substance, along with its attributes,

belongs to. What is uncertain is whether there are

any substances that Descartes would recognize as omni-

generic. In favor of an affirmative answer is the fact that

Descartes includes substance, along with durationand number, on his list of most general things when

he first introduces this category. Furthermore, it is

obvious that the term substance applies to both minds

and bodies (and that it does so univocally). On the other

side, although duration and number are attributes, it

118 VERE CHAPPELL


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sounds gibberish to say that substance is a substance.

Second, even if we can allow this substance to be a sub-

stance, we are hard put to say which substance it is. It

cannot be God, or any body or mind, since these are

all uni-generic. And what other substances are there for

Descartes? Finally, it appears that an omni-generic sub-

stance would have no principal attribute. But this

violates Descartess fundamental requirement that every

substance have exactly one principal property.

I think I know how to answer this question, but I need

to lay out Descartess theory of universals before doing

so.

8. Level seven: God, minds, and bodies and the

attributes thereof

We come now to the level at which individual sub-

stances and fully specified attributes appear. Let us run

through their various categories in the order in which

they are represented, left to right, on my chart, begin-

ning with God.

God is of course the uncreated substance, the one and

only such substance there is, and all the divine attrib-

utes are uncreated too. Every divine attribute, moreover,

is a principal attribute. This might seem surprising, for

isnt existence a divine attribute, and yet doesnt it

extend to all genera of things? The answer is, Yes and

No. Gods existence is one of his attributes, but his exis-

tence is special, as is his thinking and the substance he

is: the term existence is not said univocally of God

and of the created beings existing in genera. Descartes

states explicitly of Gods existence (in the FifthMeditation) that it pertains to [His] essence (VII.68),

and the same is true of every one of his attributes. That

is why every divine attribute is a principal attribute.

We might even conclude, in view of Descartess insis-

tence in the Third Meditation on the unity and sim-

plicity of the divine attributes, that these all reduce

somehow to one single attribute. In any case, it is clear

that the divine attributes are not only uni-generic, as we

have already noted they are, but unique to the single

individual substance who is God. This suggests an

answer to the question raised earlier, concerning the

genus to which God belongs. It is that his genus too isunique to God, that he is its only member. If so, we

cannot place God in the genus of thinking beings,

despite Descartess characterization of him as a thinking

substance.

I come now to the created substances, first the

mysterious, omni-generic substance, then individual

minds and bodies, and finally the different varieties of

created attributes. The first I pass over, pending my dis-

cussion of universals. About minds and bodies I have

only one point to add to what I have already said about

them, viz. that each individual mind is, as Descartes

affirms in Article 60, really distinct [both] from every

other thinking substance and from every corporeal sub-

stance. This last point is one that Descartes explicitly

argues for in the Sixth Meditation. Here he seems to

regard it as a straightforward consequence of the onto-

logical doctrines he has been presenting.

As for the created attributes, about them I have

nothing to add to my earlier accounts of them. But there

is a further point about the whole scheme I have been

presenting. It is that this scheme could be continued;

that is, the categories of substances and attributes at

which we have arrived could be further subdivided. Or

at least some of them could. We could introduce sub-

genera of bodies and of modes, certainly, though the

other cases arent so clear. But there is this interesting

difference, from the Cartesian perspective, between the

two tasks of subdividing bodies and subdividing modes.

The former Descartes would likely assign to the natural

scientists, physicists and biologists as we should now

call them; whereas the latter he might still regard as a

proper pursuit for ontologists. There is certainly a basis

in his works for distinguishing, within the category ofmodes, subcategories of standing as opposed to

occurring properties, dispositions vs. states, activ-

ities vs. events (my terminology, not Descartess),

among others. And these are, I believe he would grant,

ontological distinctions.

C. Section Three: Articles 5759

The chart representing this third Section continues that

of Section Two; its first six levels coincide with levels

two through seven on the attribute side of the SectionTwo chart.



10/17


11/17

course have been the subject of philosophical contention

for many centuries. Some philosophers have argued that

there simply are no such entities; some commentators

have claimed that Descartes did not believe in them. For

my part, I believe that Descartes did believe in them,

and further that it is no philosophical sin to do so. I also

believe and here am acting on the belief that

Descartess theory of objective being can be used to illu-

minate his doctrine of universals.

Before proceeding to that, I need to note that

although Descartes introduces the distinction between

actual and objective beings in his discussion of attrib-

utes, it is clear that the same distinction can be extended

to substances. I shall provide details of this extrapola-

tion, as I call it, just below.

2. Level eight: particular vs. universal attributes

Descartes does not say a great deal about universals in

the Principles, but it is past doubt from what he does

say that he regards them, all of them, as mere objects

of thought, that is, as ideas in the objective sense and

hence as objective beings. True, he doesnt quite express

this in so many words. What he says (in Article 58) is

that when number, for example, is considered not in

any created things but only in the abstract or in general,

it is no more than a mode of thinking, and the same

holds, he continues, for all [the entities] we call uni-

versals. Here the term mode must be understood as

having the fourth of the senses I distinguished earlier,

and the phrase mode of thinking the second of its

two senses. Even so, Descartess meaning is far fromobvious. But then he goes on, in Article 59, to explain

how these universals come about (fiunt). They do so,

he says, from the fact that we use one and the same

idea for thinking of all the individual [entities] which

are similar to one another. We then apply one and the

same name to all the things represented by this idea,

which name, he says, is universal. It might appear

from this last remark that it is only the name and not

the idea that is universal. But this appearance is dis-

pelled by Descartess description of an example of this

process. When we see two stones and attend not to their

nature but only to the fact that they are two, we form(formamus) the idea of their number, which we call two;

and later when we see two birds or two trees and

consider not their nature but only that they are two, we

recall (repetimus) the same idea as before, which thus

is universal. And so, he adds, we designate this

number by the same universal name of two. Hence it

is the idea that is the first or basic universal; and the

name is called a universal name because it designates

this idea. As for the mode of thinking which gives rise

to the universal idea, Descartes must mean by that the

abstract or general way of thinking, the key to which

he evidently takes to be selective attention. Notice how

much like Locke Descartes sounds in this passage.

Of course the similarity between Descartess and

Lockes view of universals is only partial. Locke holds

that when we form an idea of two upon seeing two

stones, we are in effect creating that idea: it first comes

to be in our minds by the process of abstraction.

Descartes, however, believed that ideas such as that of

two are innate, having been installed in our souls by

God at the time he created them. Hence the idea of two

is already there when we see the two stones, and what

the ensuing abstraction process effects is not the

creation of that idea but merely its discovery or activa-

tion: abstraction brings it not into being but into con-

sciousness. (Descartes elaborates on this theme in his

Reply to Gassendis Objections at VII.382.) Descartes

does not mention his doctrine of innate ideas in his

discussion of universals, or anywhere in this part of

the Principles. But he does do so earlier in the same

work (VIIIA.9, 13), and there is no reason to suppose

that he is abandoning it here. We must therefore append

this doctrine to his account of abstraction in order to

reach a full understanding of the Cartesian theory of

universals.

Having laid out this theory in general terms,

Descartes proceeds to apply it to the five commonuniversals of the Aristotelian tradition: genus, species,

differentia, property, and accident. Only the last three

of these are universals in the category of attributes; for

genus and species, as we shall see, are substance

universals (another source for my impending extrapo-

lation). But there is no reason to think that these three,

together with the constant non-principal attributes exem-

plified by number and duration, are the only universal

attributes that Descartes recognizes. There must in fact

be universal attributes in all the categories of attributes

that have been distinguished, essences as well as modes,

both uni- and omni-generic. To generate a universalprincipal attribute all we have to do is think of thought

or extension in general or in the abstract; a universal

mode results when we think in this same way of imag-

ination or rectilinear motion; and so for the others.

All universals are objective beings for Descartes;

hence all actual beings are particular. This is not an



12/17

unusual view when the beings in question are sub-

stances. But Descartes introduces his theory of univer-

sals as a theory about attributes; and since according to

that theory only attributes in our thought are univer-

sals, the contrasting attributes in things must be partic-

ular. And this is an unusual view: not many philosophers

have held it. It may not seem implausible that some

Cartesian attributes, for example, modes such as indi-

vidual occurrent thoughts and motions of bodies, should

be regarded as particulars. But even the essence of a

particular mind, the essence that Descartes says is in

that mind, is a particular in his view; it is an attribute,

but one that is unique to that one mind. By contrast,

the essence that one mind shares with others, indeed

with all minds, is found in our thought; it is there and

only there that that universal attribute exists.

All universals are objective beings, that is, ideas in

the objective sense of the word. But it doesnt follow

that all objective beings are universals, that is, that every

idea we have is the idea of a thing or things considered

abstractly or generally. We often do think of things indi-

vidually and as particulars, and the ideas by means of

which we do this must be particular too. This point

holds not only for particular substances Descartess

sun in the sky and its objective counterpart but also

for attributes. Since actual attributes are particular for

Descartes, and since we can think of them as such, there

must be objective attributes that are particular as well.

3. Extrapolation: universal substances

The account of universals that Descartes gives in thePrinciples is cast and illustrated in terms of attributes.

But it is reasonable to extend this account to cover sub-

stances as well, as I have mentioned several times now.

Most of the details of this extrapolation can be gathered

from my chart.

As the chart shows, no actual substance is a uni-

versal, neither God nor any mind nor any body. But we

sometimes think of these particular substances, and

when we do we have ideas of them, ideas in the objec-

tive sense, so that for each actual substance we think

of there is an objective substance existing in our mind.

Hence there are objective as well as actual substances.

Now we can think of substances individually, in which

case the ideas we have of them are as particular as they

are. Or we can think of substances generally and in the

abstract, and when we do our ideas of them are uni-

versal. We can think of the whole genus of minds or

bodies, or of some species of them, in this way, in which

case the idea we have, the universal that exists in our

thought, just is that genus or species.

Can we also apply this mode of thinking to God;

that is, can we think of God in this abstract and general

way? If so, then when we do so think of Him, we have

a universal idea of God, an objective universal God

existing in our intellect. It may be questioned whether

we can have such an idea of God; for uniqueness is not

only a necessary property of God, it is entailed by each

of his other properties, hence by any property which is

included in any idea we have of God. But what this

means is not that we cannot think of God abstractly at

all; only that we cannot so think of him clearly and dis-

tinctly. So there is, or could be, a universal God existing

in a human mind, as my chart shows.

There is only one problem that remains to be solved,

the problem we noted earlier concerning omni-generic

substances. The problem is that there are reasons both

for and against supposing that such entities are included

in the Cartesian ontology. The main reason against sup-posing this is that every substance Descartes mentions

God and every mind and body is uni-generic. Now,

however, having considered Descartess account of uni-

versals and the extension of that account to substances,

we can see, first, that all the substances that Descartes

mentions are particulars, and second, that there are,

besides these, substances that are universal, for example,

the genus mind or that of body. And we can also see

that there is nothing to keep Descartes from recognizing

a universal substance itself, that is, an idea of substance

which applies to all particular (created) substances, both

minds and bodies. This universal substance wouldindeed be omni-generic, since it would extend to all

genera of substances. Hence our problem is solved if

Descartes does recognize this universal substance. And

I see no reason to believe that he does not.

This concludes my exposition of the Principles

passage. I turn now to the apparent discrepancy between

122 VERE CHAPPELL

a

p p u

o

uncreated

uni-gen

God

omni-gen

Substance

o

u

a

p p u

o

Minds

a

p p u

o

Bodies

uni-gen

created

Substances


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Descartess account of universals, including numbers

and figures, in this passage, and what he says about

mathematical objects in the Fifth Meditation.

II. The objects of mathematics

According to the Principles, universals are merely

modes of our thinking, which is to say, ideas in human

minds. They are ideas in the objective sense of the word,

and hence objective beings, though Descartes does not

use this terminology here. Among the examples of uni-

versals he cites are the number we call two and the

figure . . . we call . . . triangle. To be sure, this number

and this figure can turn up as modes of individual

material substances. But in this case they are particu-

lars, as much so as are the substances in which they

inhere. The universal two or triangle is the number or

figure considered, as Descartes says, simply in the

abstract or in general, and not in any created things

(Article 58). And it is this two and this triangle that

belong to the subject matter of pure mathematics.

In the Fifth Meditation, however, Descartes charac-

terizes the objects of pure and abstract mathematics as

things which even though they may not exist anywhere

outside me still cannot be called nothing; for although

in a sense they can be thought of at will, they are not

my invention but have their own true and immutable

natures. When, for example, I imagine a triangle, he

goes on, even if perhaps no such figure exists, or has

ever existed, anywhere outside my thought, there is stilla determinate nature, or essence, or form of the triangle

which is immutable and eternal, and not invented by me

or dependent on my mind (VII.64). The implication of

these remarks is that, though geometrical figures may

exist in human minds, they must have some way of

being in addition to and independent of such existence:

otherwise they could not have essences which are

eternal and immutable.

This at any rate is how this passage has been inter-

preted by certain commentators, most notably Anthony

Kenny. In one article Kenny calls Descartess philos-

ophy of mathematics thoroughly Platonic and declaresDescartes to be the founder of modern Platonism

(Kenny, 1970, pp. 692693). Elsewhere Kenny com-

pares Descartess view of mathematical objects to that

of Meinong (Kenny, 1967, p. 155; Kenny, 1969, p. 25).

In both cases Kennys point is that for Descartes a

triangle, for example, has a kind of being that [is]

sufficient to distinguish it from nothing (Kenny, 1970,

p. 699), but is different both from actual existence and

from existence or being in thought. Kenny calls this

third kind of being being given (dari) (Kenny, 1969,

p. 21).

Kenny bases his case for Descartess Platonism (or

Meinongianism) almost entirely on the Fifth Meditation.

He makes no mention of Descartess discussion of uni-

versals in the Principles, so of course he takes no notice

of the conflict between its view of mathematical objects

and the one he attributes to Descartes. By contrast, Alan

Gewirth finds both Platonism and Aristotelianism in

Descartes, the one in the Fifth Meditation (and the First

Reply to Objections), the other in Principles One (and

the Fifth Reply) (Gewirth, 1970, p. 678). Gewirths

Platonic Descartes, however, is not the extreme realist

that Kennys is. Gewirth has Descartes holding that

mathematical entities have their own determinate

natures or essences regardless of whether any such

entities exist (Gewirth, 1971, p. 299), but not that these

entities enjoy some kind of being other than that of

existence, nor that they are, as Kenny puts it, real

thing[s] lacking only the perfection of actual existence

(Kenny, 1970, p. 697). Nor is Gewirths Aristotelian

Descartes the explicit, thoroughgoing conceptualist

that the Principles passages show him to be. To his

Descartes Gewirth attributes the Aristotelian doctrines

that mathematical essences are quantitative abstrac-

tions from natural substances and that mathematical

essences in their ontological status are not indepen-

dent of physical existents (Gewirth, 1970, p. 678), butnot the doctrine that these entities are ideas existing in

peoples minds. It is thus not surprising that Gewirth

finds it not too difficult to reconcile [the] Aristotelian

doctrines of Descartes with his Platonic [ones]

(Gewirth, 1971, p. 299). For the doctrines that Gewirth

has in mind are indeed logically compatible. But it is

not on account of Descartess holding these doctrines

that there is a conflict within his thought, at least not

the conflict that I am concerned with. Besides which,

Kenny claims that Descartes does not hold the

Aristotelian doctrines that Gewirth attributes to him;

and I agree with Kenny on that.On Gewirths view of Descartes, there is no real

conflict between the Principles and the Fifth Meditation

concerning the status of mathematical objects. But

Gewirth fails to grasp the full import of Descartess

position, at least that of the Principles. On Kennys view

the conflict is real, but Kenny himself fails to address



14/17

it: he doesnt consider the Principles position. Another

recent scholar who has tackled these issues is Tad

Schmaltz. Unlike Kenny, Schmaltz does consider the

Principles position; and unlike Gewirth, he does under-

stand its conceptualist message, a message he rightly

associates not with Aristotle but with Gassendi and

Locke. For Schmaltz the problem is to find a reading

of Descartes that avoids the Scylla of Kennys Platonic

interpretation without thereby falling into the Charybdis

of the abstractionist interpretation (Schmaltz, 1991,

pp. 162163). By abstractionist here Schmaltz means

conceptualist, and he attributes this interpretation

mistakenly, as I believe to Gewirth, as well as

to Martial Gueroult. According to Schmaltz, mathe-

matical entities are neither independent real beings nor

merely ideas in human minds but something else: viz.,

immutable essences belonging to the essence of God.

Indeed, Schmaltz goes so far as to claim that Descartes

identifies [these] immutable essences with God

himself (Schmaltz, 1991, p. 135).

One might object to Schmaltzs interpretation on the

ground that it is not the immutable essences of numbers

and figures that Descartes takes to be the objects of the

mathematicians inquiry, but numbers and figures them-

selves, the immutable entities that have these essences.

Kenny makes the same point against Gewirth (Kenny,

1970, p. 692); and it is true that the texts of both

Meditation Five and Principles I.5759 specify trian-

gles and not their essences as the targets of mathemat-

ical concern. (Note that by treating figures and numbers

as entities that have essences Descartes must beregarding them as substances abstract and universal

ones but substances nonetheless.) But this point is

hardly damaging to Schmaltzs position. For as we have

seen, Descartes holds that an entity and its essence are

neither really nor modally distinct, and that it is only

ratione that they can even be distinguished. So the dif-

ference between saying that the mathematician studies

figures and numbers and saying that he studies the

essences of figures and numbers is inconsequential.

A more significant difficulty with Schmaltzs inter-

pretation concerns the relationship of the mathemati-

cians objects to God. Schmaltz agrees with Kenny inmaintaining that such objects are, in Descartess view,

the creatures of God. But for Kenny Descartes takes

them, once created, to be distinct from their creator,

whereas Schmaltzs Descartes conceives them to be

identical therewith. On this point Schmaltz cannot be

right: as Kenny points out, Descartess mathematical

entities [must be] distinct from God, since they stand

in a causal relationship to him (Kenny, 1970, p. 696).

And of course Schmaltzs Descartes is at odds with the

author of the Principles regarding the ontological locus

of numbers and figures. According to the former, such

things are in God; for the latter, they are in human

minds.

Schmaltzs interpretation does have some virtues.

For one thing, it provides an easy explanation of the

eternality of mathematical objects, a feature Descartes

explicitly and repeatedly attributes to them. Offsetting

such advantages, however, is the fact that Schmaltz is

unable to cite a single Cartesian text in direct support

of his position. And his efforts to show that various texts

and historical precedents support his reading indirectly

are at best unconvincing, and in some cases are seri-

ously flawed.

Is there then no way of reconciling Descartess

account of universals in Principles I.5759 with what

he says about the objects of mathematics in the Fifth

Meditation? Must we suppose that he held and pub-

lished two contradictory doctrines within a three-year

period or else that he radically changed his view some

time between 1641 and 1644? My own belief is that

the doctrines in question are perfectly consistent, and

that, despite appearances, they can be reconciled,

without either violating or ignoring the plain meaning

of Descartess texts. I shall now proceed to show how

such reconciliation is to be accomplished.

My reconciliation project is in fact quite simple: it

can be completed in two steps. The first is to note theclose affinity that Descartes posits between the objects

of mathematics and eternal truths. In the ontological

scheme of the Principles, entities of both these kinds

are assigned to the general category of objective beings;

but the affinity I have in mind is more intimate than that.

Descartes discusses eternal truths at several places in

his writings. Outside the Principles , his most striking

claim about them is that they are created by God, and

that they would not have the content they do, or even

exist, had not God indifferently chosen to establish

them. They are, Descartes sometimes says, the product

of Gods free decrees, and they depend absolutely onGod for their being and nature. Now in a number of

passages Descartes explicitly links eternal truths to

mathematical objects. Some such truths, he is wont to

say, are truths about(Latin de) numbers and figures, or

about the essences thereof. More to our purpose, he indi-

cates that these objects, no less than the truths about

124 VERE CHAPPELL


15/17

them, are the creatures of God. Thus in responding to

Gassendis Objections, he says that both the essences

of things and the mathematical truths which we can

know about them were originally established (condita)

by God and hence that neither is independent of him

(VII.380). Again, in an early letter to Mersenne he states

that God is no less the author of creatures essence than

he is of their existence, and goes on to characterize this

essence as nothing other than the eternal truths (I.151).

Both Kenny and Schmaltz, as we have seen, interpret

Descartes as definitely holding what these passages

suggest: that God has created not only truths about

triangles, for example, but triangles (or their essences)

themselves. On this point I think we must agree with

them.

The second and final step is to recall the connection

I noted earlier between Descartess account of univer-

sals and his doctrine of innate ideas. The former entails

that mathematical objects are objective beings, which is

to say, ideas in human minds. The latter explains how

these ideas came to be in the minds that have them,

viz. by being placed there originally by God. What I

now wish to claim is that, for Descartes, Gods creation

of numbers and figures consists in his creation of

minds containing the ideas of numbers and figures.

Mathematical objects just are ideas, according to the

ontology of the Principles; and God creates them,

according to the doctrine of innate ideas, by including

them within the minds that are the direct products of his

creative action. These ideas need not be consciously

present to the minds in which they are housed, eitherfrom the beginning or at every moment thereafter.

They may exist originally or intermittently as uncon-

scious dispositions, as Descartes acknowledges in his

Comments on Regiuss Programma (VIIIB.357f., 361).

But doesnt this position destroy the objectivity of math-

ematics by making its objects differ from mind to mind?

And doesnt it render these objects mutable, since minds

grow and wither and the ideas within them change? No,

for Descartes holds that God installs the same ideas in

every mind that he creates; and no again, since the ideas

that God makes to be innate in us are constant and never

change. So the position I am attributing to Descartessecures both the objectivity and the immutability of

mathematical objects.

If I am right about Descartess conception of the

objects of mathematics, then given the affinity between

them and eternal truths, what holds for the one must

hold also for the other. Hence Gods creation of the

eternal truths must also consist in his creation of human

minds containing such truths. We should have no trouble

extending the doctrine of innate ideas to cover eternal

truths, considering that Descartes often applies the term

idea to propositions as well as to simple concepts (cf.

III.395, 417). And in any case he frequently cites truths

sometimes calling them axioms or common notions

as examples of items that we are born with or that

have been placed in us by God: on one occasion he

explicitly says that mathematical truths . . . are all

inborn in our minds (I.145). So the same considerations

that account for the immutability and objectivity of the

objects of mathematics account also for the

immutability and objectivity of the truths that hold of

them, and indeed of the eternal truths in general.

This view of eternal truths bears some resemblance

to a thesis defended in a recent article by Jonathan

Bennett. Bennetts topic is not the ontology of

Descartess eternal truths but their modality. His

problem is to understand how such truths can be the free

creations of God and yet be true of necessity. To solve

this problem, Bennett argues, we must attribute to

Descartes a conceptualist or subjectivist analysis of

modality. On this analysis the necessity of a truth is

taken to consist in our being unable to conceive its being

false, so that modal facts are reduced to facts about our

mental capacities. Hence God is responsible for these

modal facts because he is responsible for our minds

having the capacities they do: God created modal truths

by making us unable to conceive of impossibilities

(Bennett, 1994, p. 646). Bennetts view of Descartessunderstanding of the modal status of eternal truths thus

parallels my view of his conception of their ontolog-

ical status; and it was in fact while reading Bennetts

article that my view first occurred to me.4

It should be clear that the reconciliation I am

proposing is not one of compromise. I am not claiming

that Descartess true doctrine of mathematical objects

either combines or lies between the conceptualism of

the Principles and the Platonism of the Fifth Meditation.

Rather, I am denying that the view expressed in

Meditation Five is Platonic: I am in effect assimilating

that view to the position of the later work. And I thinka close reading of the text of Meditation Five bears me

out. Nothing in that text amounts to an explicit state-

ment that triangles have any being apart from human

minds. What is said is that a triangle may not exist

anywhere outside me or outside my thought, and that

its nature or essence is not invented by me. Descartes



16/17

does add that the triangles essence is not dependent on

my mind; but what he means is merely that it is not my

own creation, or indeed the creation of any human

being. He does not in this passage make the positive

claim that this essence (and its possessor) is the creation

of God, or that it is, in that sense, dependent on God

a claim he does make, in exactly those terms, in other

texts, as we have seen. But he does not deny, here or

anywhere, that triangles and their essences depend in

another sense on the minds in which, as ideas, they have

been created, and to which, as attributes, they belong.

Depend in this other sense stands for the relation that

any attribute bears to the substance that houses it; and

in that sense, according to the Principles, mathemat-

ical objects do depend upon human minds.

My position is that Descartes believes that mathe-

matical objects, that is, the universal numbers and

figures that constitute the subject matter of the mathe-

matical sciences, are objective beings residing in minds,

and that they have come to be where and as they are

by the creative action of God. But I am not claiming

that there are for Descartes no real numbers and figures

in the material world, and that mathematics is merely a

mental construction that is imposed arbitrarily on an

indifferent reality. On the contrary, I am sure that

Descartes believed that God creates not only minds

having mathematical ideas residing in them but also

bodies having numbers and shapes inhering in them,

bodies possessing mathematical properties and standing

in mathematical relationships. The difference is that the

products of this latter creation are particulars; andalthough the mathematicians results apply to these

entities, the true objects of his study are the universals

which are the fruits of the former creation.

I have argued that the immutability of mathematical

objects, and of eternal truths too, is provided for on the

view that I am taking of them. But Descartes maintains

that these entities are eternal as well as immutable, and

I have not yet said anything about their eternality.

Indeed, it may be objected that these entities cannot be

eternal if they really are merely ideas in human minds,

even if ideas are taken to include (the contents of ) long-

term unactualized dispositions as well as (of) occur-rent events. This is obvious if eternal means timeless,

for no human mind exists outside of time. But the objec-

tion has force even if eternal is taken, as it frequently

is by Descartes, to mean sempiternal or everlasting.

For Descartes certainly held that no human mind has

existed from the beginning of time, even if he did

believe that every mind that is created exists forever

after its creation. This means that he would have had

to grant that there was a time at which no universal

numbers and no truths about such numbers existed,

because there were no minds for them to exist in.

Bennett avoids this objection (or its analogue) by

claiming that the term eternal in the phrase eternal

truths means no more than unchanging and thus picks

out the same property that immutable does (Bennett,

1994, pp. 663665). I think that Bennett may be right

about this. But Descartes also speaks of Gods having

created such truths from all eternity (I.152). This

might suggest that these truths have been around, so to

speak, either from the beginning or as long as God

himself has; and if so the objection is applicable after

all. Strictly, however, what God does from all eternity

is will or decree that the truths in question obtain, and

it is his acts of will or decrees that are contemporaneous

with him: indeed, Descartes says, these decrees are not

really distinct from God himself (V.166). But the crea-

tures that come to exist by Gods decrees, whether truths

or human minds or the whole universe, are distinct both

from God and from the pertinent decrees. (Schmaltzs

failure to appreciate this point is one of those flaws in

his argumentation that I alluded to earlier.) And though

the decree may be issued at (or before) the beginning

of time, the creature does not begin to exist until the

decree is, as Descartes says, enacted (V.166).

Descartes has, as far as I can see, no way of meeting

this objection without admitting that by calling themeternal he did not mean that either the truths or the

objects of mathematics themselves exist from all

eternity. He cannot claim that these entities exist implic-

itly or potentially in Gods decrees, which are eternal in

whatever sense Descartes takes that term to have. For

these decrees are in, or rather are, God himself, and

Descartes is clear that nothing belonging to God is

implicit or potential. Nor does the Cartesian ontology

provide any place for potential or merely possible

beings as such: for Descartes, any entity that is not

actual is an objective being, and hence requires the exis-

tence of at least one human mind. I see no way, there-fore, of allowing entities (other than God) that are

strictly and literally eternal within the confines of

Descartess ontology. The objection stands; but the con-

clusion I draw from it is not that either Descartess

ontology or my rendition of it must be rejected, but

126 VERE CHAPPELL


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rather that the objects and the truths of mathematics are

not, for Descartes, strictly and literally eternal.5

Notes

1 See Schiffer, 1976, p. 22 et passim.2

Cottingham attributes such trialism to Descartes in Cottingham,1985, although he does so on the basis of texts other than this one

in the Principles. Other scholars have taken the stronger position that

Descartes is a trialist regarding, not (or not merely) attributes, but

substances, i.e. that he recognized three distinct kinds of substances,

at least in some texts; see Broughton and Mattern, 1978, Hoffman,

1986, and Schmaltz, 1992.3 In another paper, however, I have defended the view that Descartes

is a dualist regarding substances against the claims of Hoffman et

al. that he espouses substance trialism: see Chappell, 1994.4 Bennett has since informed me that he is much in agreement with

my ontological extension of his position, and that he strongly agrees

with my dissolution of the worry about the Fifth Meditation.5 Shorter versions of this paper were read at (1) the Early Modern

Philosophy Conference, in honor of Willis Doney, at DartmouthCollege, July 1995; (2) the Sixth Annual Philosophy Conference at

the University of California, Riverside, January 1996; and (3) the

University of Western Ontario, April 1996. I am grateful to my

auditors on those occasions for helpful suggestions and criticisms.

At the Riverside Conference I was delighted to learn that views very

like mine on the status of Descartess mathematical objects had been

arrived at quite independently by Larry Nolan, who was then com-

pleting his dissertation at Irvine. Nolan gives an elegant statement

and a persuasive defense of these views, not only in his dissertation

(Nolan, 1997a) but in a paper (Nolan, 1997b) he had read the previous

May at a conference at Stanford, and which is now in the course of

being published.

References

Bennett, Jonathan: 1994, Descartess Theory of Modality,

Philosophical Review 103, 639667.

Broughton, Janet and Mattern, Ruth: 1978, Reinterpreting Descartes

on the Notion of the Union of Mind and Body, Journal of the

History of Philosophy 16, 2332.

Chappell, Vere: 1994, Lhomme cartsien, in Jean-Marie Beyssade

and Jean-Luc Marion (Ed.), Descartes. Objecter et rpondre,

Paris: Presses Universitaires de France, pp. 403426.

Gewirth, Alan: 1970, The Cartesian Circle Reconsidered, Journal

of Philosophy 67, 668685.

Gewirth, Alan: 1971, Descartes: Two Disputed Questions, Journal

of Philosophy 68, 288296.

Hoffman, Paul: 1986, The Unity of Descartess Man, Philosophical

Review 95, 339370.

Kenny, Anthony: 1968,Descartes: A Study of his Philosophy, New

York: Random House.

Kenny, Anthony: 1969, Descartess Ontological Argument, in

Joseph Margolis (Ed.), Fact and Existence, Oxford: Blackwell,

pp. 1836.

Kenny, Anthony: 1970, The Cartesian Circle and the Eternal Truths,

Journal of Philosophy 57, 685700.

Nolan, Lawrence: 1997a, Descartess Theory of Essences. PhD

Dissertation, University of California at Irvine.

Nolan, Lawrence: 1997b, The Ontological Status of Cartesian

Natures, Forthcoming.

Schiffer, Stephen: 1976, Descartes on his Essence, Philosophical

Review 85, 2143.

Schmaltz, Tad M.: 1991, Platonism and Descartess View of

Immutable Essences,Archiv fr die Geschichte der Philosophie

73, 129170.

Schmaltz, Tad M.: 1992, Descartes and Malebranche on Mind and

Mind-Body Union, Philosophical Review 101, 281325.

University of Massachusetts, Amherst


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