Realist ontology of categories a work in progress

1
Realist ontology of categories (a work in
progress)

• Paul Thom

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Beings
Qualities
Other categories
Quantities
Potentialities
Universals
Substances
Denominatives
Relations
And since it is not theoretically necessary that
each object has similar ones that form a species
together with it, there can be isolated
individuals, without a species, and a fortiori
without a genus, which can not belong to any
category which doesnt prevent us from affirming
that the categories are only ten, since that
which is excluded from them is not a category by
itself, nor is it included in any new category.
If one says, for example, that there are only ten
towns in the world, the existence of nomads
outside these towns doesnt weaken that
assertion. Avicenna, Al Shifa fol.20a, 1-9.
Individuals
Nomads
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Basic ontological relationships intra-category
On the purely formal approach used here, this is
an undefined relation. We are not making use of
the Categories definition which requires that
both the name and the definition be predicated of
the subject.
Definition 1. A ess B iff A de B and for no C, A
de C and C de B
Definition 2. perse(A) iff either for some B, A
de B or for some B, B de A
de said of
ess is the essence of
perse is a per se being
deG said of as a genus
Rule 1. If A ess B and C ess B, A C
The species in which the things primarily
called substances are, are called secondary
substances,as also are the genera of these
species. Categories 2a14-17.
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Basic ontological relationshipsinter-category
Definition 3. acc(A) iff for some B, A in B
Definition 4. subst(A) iff perse(A) and for no B,
A in B
On the purely formal approach used here, this is
an undefined relation. However, Definition 2
defines accident in terms of in.
a is from
in inheres in
acc is an accident
subst is a substance
Rule 2. If acc(A) and A de B, acc(B)
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Ontological dependencies intra-category
For if one is to say of the primary substance
what it is, it will be more informative and apt
to give the species than the genus. Categories
2b8-10
Rule 3a. If a per se individual exists, a
specific per se universal in the same category
(which is said of it) exists
Rule 3b. If a per se universal exists, it is
said of some per se individual In the same
category
For example, animal is predicated of man and
therefore also of the individual man for were it
predicated of none of the individual men it would
be predicated of man at all.Categories 2a36ff.
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Ontological dependenciesinter-category
Thus, for example, the grammarian gets his name
from grammar, the brave get theirs from
bravery. Categories 1a14-15
Rule 4. If a denominative universal exists, a
unique universal accident (which it is from)
exists
By in a subject I mean what is insomething,
not as a part, and cannotexist separately from
what it is in. Categories 1a24-25. A particular
case of grammatical knowledge would be, for
example, the grammatical knowledge that
Aristarchus possesses. Porphyry, Categories
Commentary 76,1.
Rule 5a. An individual accident inheres in
exactly one individual substance
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Ontological dependenciesinter-category,
continued
All the other things are either said of the
primary substances as subjects or in them as
subjects. This is clear from an examination of
cases. Categories 2a34-36 Cf. Marenbon, The
Philosophy of Peter Abelard p.120-122
Rule 5b. An individual accident inheres in at
least one individual substance
He does not say that it is incapable of existing
separately from what it was in, but that it is
incapable of existing separately from what it is
in. The smell is capable of being separated from
what it is in but it cannot exist separately
and on its own. Porphyry in Cat. 79,23-34
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Derived ontological relationships intra-category
This rule leaves it open that A may be said of B
when it is not a genus of B, but doesnt specify
the nature of the relation in such a case. Rule 2
specifies that the differentia is said of the
species, but we have not specified any way in
which the differentia-species relation differs
from the genus-species relation. Nor have we
stated whether differentia and species are the
only types of said-of relation.
Whenever one thing is predicated of another as of
a subject, all things said of what is predicated
will be said of the subject also.Categories
1b10ff.
Rule 6. If A de B and B de C, A de C
The genus is said of both the speciesand the
individual.Categories 3a39.
Rule 7. If A deG B, A de B
A
B
The differentia also is not in a subject. For
footedand two-footed are said of man as subject
butare not in a subject.Categories 3a21.
C
Corollary 6.1. If subst(A) and A de B, subst(B)
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Derived ontological relationships
intra-category, continued
The differentiae of genera which are different
and not subordinate one to the other are
themselves different in kind. Categories 1b16ff.
Rule 8. If A deG C and B deG C, either A deG B
or B deG A
B
A
The Categories formula is equivalent to stating
that if two genera have a common differentia,
then one genus is subordinate to the other. That
formula implies Rule 3. Suppose that both A and B
are genera of C. If we assume that two genera
having a common species have a common
differentia, then A and B have a common
differentia. So, by the Categories formula,
either A is a genus to B or B is a genus to A. In
other words, the Categories formula implies Rule
3, on the assumption that two genera having a
common species have a common differentia.
C
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Derived ontological relationshipsinter-category
the individual knowledge-of-grammar is in a
subject, the soul . knowledge is in a
subject, the soul, and is also said of a subject,
knowledge-of-grammar. Categories 1a25-26 1b1-3
Rule 9a. If A de B and B in C, A in C
colour is in a body and therefore also in an
individual body. Categories 2b1-2
Rule 9b. If A in D and D de C, A in C
A
D
C
B
Corollary 9a.1. If acc(B) and A de B, acc(A)
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Defined relationships
Definition 5. E est A iff either for some B A a
B and B in E or for some B, C, D A a B and B in
C and D in C and E a D
Denominatives are in a subject secondarily,
i.e., through their forms, which are primarily
in subjects. Garlandus, Dialectica 183-4
est is accidentally
in2 inheres in secondarily Garlandus
F
G
E
H
was wasfi predication Avicenna
All moving things are changing is not to be
taken to mean that this is so absolutely, but
rather while the substance of the moving thing is
moving. Avicenna, Pointers 265.
sus sustenation Abaelard
B
Definition 6. E in2 C iff for some A E a A and A
in C
Definition 7. F was E iff for some G, A F a G
and G de A and E a A
Definition 8. H sus C iff for some B H in B and
B in C
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Ontological relationships among accidental
relations
ad stands to
A relation is an accident that is truly and
simply one, not requiring a multitude in which it
is, but just one thing only in respect of
another. A correlation is a pair of relations
mutually respecting one another. Kilwardby, De
Natura Relationis 1619-24
Correlation
paternity is not of filiation but father is
stands to son and son to father. A relation,
then, is not relative except through the
concrete being which it is in. And so a
relation is relative per accidens. Kilwardby, De
Natura Relationis 522-28.
Correlatives
Both correlatives essential
Those relatives are said to be essential whose
being depends on the correlative. Kilwardby, De
Natura Relationis 1821-22
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Ontological dependencies among accidental
relatives
Rule 10a. If A ad B and A exists, B exists
Correlation
A
B
Correlatives
Rule 10b. If A ad B and B exists and both
correlatives are essential, A exists
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Derived ontological relationshipsthe foundation
of a relative
Definition 9. A fun B iff A is a relative and B
is a non-relational accident and for all C if B
in C then A in2 C.
A
fun has as its foundation
B
C
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Rules
Rule 1. If A ess B and C ess B, A C
Rule 2. If acc(A) and A de B, acc(B)
Rule 3a. If a per se individual exists, a
specific per se universal in the same category
(which is said of it) exists
Rule 3b. If a per se universal exists, it is said
of some per se individual In the same category
Rule 4. If a denominative universal exists, a
specific universal accident (by which it exists)
exists
Rule 5a. An individual accident inheres in
exactly one individual substance
Rule 5b. An individual accident inheres in at
least one individual substance
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Rules continued
Rule 6. If A de B and B de C, A de C
Corollary 6.1. If subst(A) and A de B, subst(B)
Rule 7. If A deG B, A de B
Rule 8. If A deG C and B deG C, either A deG B or
B deG A
Rule 9a. If A de B and B in C, A in C
Rule 9b. If A in D and D de C, A in C
Corollary 9a.1. If acc(B) and A de B, acc(A)
Rule 10a. If A ad B and A exists, B exists
Rule 10b. If A ad B and B exists and both
correlatives are essential, A exists
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Definitions
Definition 1. A ess B iff A de B and for no C, A
de C and C de B
Definition 2. perse(A) iff either for some B, A
de B or for some B, B de A
Definition 3. acc(A) iff for some B, A in B
Definition 4. subst(A) iff perse(A) and for no B,
A in B
Definition 5. E est A iff either for some B A a
B and B in E or for some B, C, D A a B and B in
C and D in C and E a D.
Definition 6. A in2 C iff for some B A a B and B
in C
Definition 7. A was D iff for some B, C A a B
and B de C and D a C
Definition 8. A sus C iff for some B A in B and
B in C
Definition 9. A fun B iff A is a relative and B
is a non-relational accident and for all C if B
in C then A in2 C.
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Extreme conditionsAn accident inheres
essentially in a substance
Nothing in the definition of an accident
precludes an accident inhering necessarily in its
subject. Rules 6, 7, 9a, 9b remain valid if we
suppose such accidents. We mustnt confuse the
sense of accident as non-substance per se being
with the Topics sense of what may or may not
belong to a subject.
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Extreme conditionsDifferent universal accidents,
same individual accident
Rule 3. If A deG C and B deG C, either A deG B or
B deG A
Under these conditions, Rule 3 is invalid.
However, if rule 3 is dropped, nothing in the
remaining rules precludes these conditions.
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Extreme conditions Different denominatives, same
accident
21
Extreme conditions Different relations, same
subject
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Extreme conditionsAequiparentia (different
relatives, same relation)
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Aequiparentia according to Auguistine
Friend of course has reference to friend, and if
they love each other equally, there is the same
friendship in each. Augustine, De Trinitate V.i.7
Rule 9a. If an individual accident exists, a
unique individual substance (in which it
inheres) exists
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Aequiparentia according to Kilwardby
Correlatives that agree in name and definition
respect one another by a relation that is one is
species but two in number. Kilwardby, De Natura
Relationis 1810-12
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Extreme conditionsA relation is a substance
Here is an alternative argument. Subst(A) iff for
some B, B de A. Reln(A) iff for some C,D, C a A
and C ad D. Thus, Subst(A) and Reln(A) iff for
some B,C,D, B de A and C a A and C ad D. The
constructive problem is to show that this is a
possibility.
And it is to be said that substance and accident
differ in this, that a substance subsists through
itself and an accident through a substance in
which it inheres. Hence accident has this
property that it inheres. Relation however, as
such, has this property, that it respects
another. So where these two (inhering and
standing toward something) concur, relation is an
accident not because it stands towards
something but because it inheres, since this
(namely that it inheres) is the nature of
accident. So take away the inhering and leave the
standing towards something, and you have taken
away the nature of accident. Leaving the nature
of relation, but taking away the nature of
accident, you necessarily leave the nature of
substance. And so a substance can stand toward
something and be a relative or relation, because
this is not repugnant to it. Kilwardby, De Natura
Relationis 3414-24.
paternity is not of filiation but father is
stands to son and son to father. A relation,
then, is not relative except through the
concrete being which it is in. And so a
relation is relative per accidens. Kilwardby, De
Natura Relationis 522-28.
A
B
C
D
Kilwardbys argument is flawed. It is relatives,
not relations, that are ad aliquid. So, the
most the argument could show is that a relative
may be a substance. However it cant even show
that, because a relative, being a denominative,
is neither substance nor accident.
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The Trinity according to Philoponus
God
Filius natum ex Pater unigenitum, hoc estex de
substantia Patris, deum ex deo,lumen ex lumine,
deum verum de deo vero,natum, non factum, unius
substantiae cum Patre (quod Graece dicunt
homoousion). Council of Nicea.
Holy Spirit
Father
Son
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The divine attributes according to Augustine
The power of course is identical with the wisdom
and the wisdom with the power. So it will be the
same, surely, with the other things mentioned,
and the greatnesswill also be identical with the
power . De Trinitate VI.i.2
Ess(God)
Thus we should understand God, if we can and as
far as we can, to be good without quality, great
without quantity . De Trinitate V.Prologue.2
God
Greatness
Gooodnes
Gooodnes
Greatness
im imitates,is an image of
for God it is the same thing to be as to be
great. The same must be said about goodness and
eternity and omnipotence and about absolutely all
the predicationsthat can be stated of God . De
Trinitate V.ii.11
when we think about God the Trinity we are
aware that our thoughts are quite inadequate to
their object, and incapable of grasping him as he
is De Trinitate V.Prologue.1
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The Trinity according to Augustine
every being that is called something by way of
relationship is also something besides the
relationship thus a master is also a man, and a
slave is a man . So if the Father is not also
something with reference to himself, there is
absolutely nothing there to be talked of with
reference to something else. De Trinitate
VII.i.2 the substance of the Father and the Son
is one. De Trinitate V.i.4.
How can the three relations inhere in God?
Nothing is said of God accidentally. So relations
can inhere in God only if (i) these relations are
not accidents, or (ii) they are inseparable from
their subject and inherences are sometimes
inseparable, or (iii) these relations are
accidents said of God or (iv) are identical with
God. Reply Definitions 3 4 exclude (ii). Rule
2 excludes (iii). Augustine excludes (ii). So (i)
and (iv) are the remaining possibilities.
What are these three relations? Boethius mentions
filiation and paternity presumably the third is
giving. But all these are accidents that can come
and go in a subject whereas God has no such
accidents. Reply It would be better to name the
relations as divine or preeminent filiation
(filiation), divine paternity (paternity) and
divine giving (giving).
There is at least no doubt that God is substance
. De Trinitate V.i.3
The Holy Spirit insofar as he isproperly or
peculiarly called the Holy Spirit is so called
relationship-wise, being referred to both Father
and Son, since the Holy Spirit is theSpirit of
the Father and of the Son. De Trinitate V.iii.12.
God
Yet when you ask Three what? human speech
labors under a great dearth of words. So we say
three persons, not in order to say that
precisely, but in order not to be reduced to
silence. De Trinitate V.ii.10.
He is the gift of the Father and of the Son .
So when we say the gift of the giver and the
giver of the gift, we say each with reference
to the other. De Trinitate V.iii.12.
Father
Father, giver
Gift (Holy Spirit)
for God even being born is everlasting, so
that the Son can be coeternal with the Father.
De Trinitate VI.i.1.
Son
Son, giver
Even though some modifications are called
inseparable like the color black in a crows
feather, the moment it ceases to be that animal
or that feather it loses of courses that
color. So there is no modification in God
because there is nothing in him that can be
changed or lost. De Trinitate V.i.5.
With God, though, nothing is said
modification-wise, because there is nothing
changeable with him. And yet not everything that
is said of him is said substance-wise. Some
things are said with reference to something else,
like Father with reference to Son and Son with
reference to Father. De Trinitate V.i.6.
How can two correlatives have a single subject
(if the corresponding relations are
asymmetrical)? Reply Paternity is not
asymmetrical. Every subject that stands in the
relation to something (viz. God) stands in the
relation to itself.
Son and giver are different relatives similarly,
Father and giver. So there seem to be five or six
relatives, not three. Reply Father and giver may
be different considered as notions, but they are
the same person.
Thus the Father is God and the Son is God and the
Holy Spirit is God, and no-one denies that this
is said substance-wise . De Trinitate V.ii.9
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A psychological model of the Trinity according to
Augustine
Just as you have two somethings, mind and its
love, when it loves itself,so you have two
somethings, mind andits knowledge, when it knows
itself. Themind therefore and its love and
knowledge are three somethings, and these three
are one thing, and whenthey are complete they
are equal.. De Trinitate IX.i.4.
Mind
Love
Knowledge
this color, or the shape of this body, cannot
belong to another body too. Butmind can also
love something besidesitself with the love it
loves itself with.Again mind does not only know
itselfbut many other things as well.
Thereforelove and knowledge are not in the mind
as in a subject, but they too are
substantially, just as mind itself is. De
Trinitate IX.i.5.
Mental word
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The Trinity according to Kilwardby
gignens, genitus et procedens sunt relativa,
sed relationes non sunt accidentia, sed
substantia. Qualiter autem relatio possit esse
substantia, patet illis qui noverunt quomodo
prima principia substantiae compositae ad invicm
referuntur, scilicet materia et forma, quomodo
etiam creatura Relativa ad creatorem. Potest
autem hoc esse tali ratione Relatio accidens
aliunde est accidens et aliunde relatio accidens
enim est unde inest, relatio unde ad aliquid
extra se respectum habet. Tolle ergo hoc ipsum
inesse et tulisti accidens. Quod ergo remanet,
substantia erit. Ubi ergo Nihil est inhaerens,
non est accidens. Et tamen bene potest inesse
respectus ad aliquid, et ille erit
substantia. Kilwardby, Sent. 1 q.35303-315.
God



Spiration
Filiation
Paternity
Holy Spirit
Son spirator
Father spirator
potius vocatur Spiritus Sanctus quam
donum, Sicut Filius potius vocatur Filius quam
Verbum. Cui enim imponitur Spiritus Sanctus,
est hypostasis rationalis, sed cui imponitur
donum, infinitae substantiae quae dari potest,
unde et nomen doni communius est de prima
impositione quam nomen Spiritus
Sancti. Kilwardby, Sent. 1 q.4216-24.
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The Trinity according to Aquinas
Since the Word is the Son when God understands
and loves himself, which Word is uttered by the
Father, we must infer that the Holy Ghost, who is
of the love whereby God is in himself as th
beloved in the lover, proceeds from the Father
and the Son. Compendium Theologiae 49
God understands and loves himself. Moreover, his
understanding and his loving are identical with
his being. Compendium Theologiae 37
God
Gods knowledge
Gods love
A thing as understood in the mind is, as it were,
a word of mind for what we signify by an
outward word of speech is what we have understood
within. Therefore, within God we set down the
existence of a Word. Compendium Theologiae 37
the manner whereby God is in himself as beloved
in lover is described by the terms breath or
spirit. Compendium Theologiae 46
DivineKnown, i.e. Word
DivineKnower, Lover i.e. Father
DivineLoved i.e. Holy Spirit
When the mind understands itself, the word
conceived is related to mind as offspring to
father. Therefore in dealing with Gods
understanding, the Word should be compared to
God, of which it is the Word, as son to
father. Compendium Theologiae 39