Realist ontology of categories
(a work in progress)
Paul Thom
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Contents
Basic ontological relationships
ab
… the beautiful are beautiful by beauty.
Phaedo.
Thus, for example, the grammarian
gets his name from grammar,
the brave get theirs from bravery.
Categories 1a14-15
ab: is from
ab
Contents
Basic ontological relationships
de
de: said of
de
deG: said of as a genus
deD: said of as a differentia
deG de
What is said of a subject has its name
and definition predicated of the subject.
Categories.
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.
The genus [is said of] both the species
and the individual.
Categories 3a39.
For footed and two-footed
are said of man as subject.
Categories 5, 3a22-24.
Rule 1. If A de B, whatever is B is A
Rule 2. If A de B and B de C, A de C
Rule 3. If A deG B, A de B
Rule 4. If A deD B, A de B
Rule 5. If A deG C and B deG C,
either A deG B or B deG A
The differentiae of genera which are
different and not subordinate one to the
other are themselves different in kind.
Categories 1b16ff.
The Categories formula is equivalent to stating that if two genera
have a common differentia (thus a common species), then one
genus is subordinate to the other. That formula implies Rule 5.
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.
Contents
Basic ontological relationships
in
By ‘in a subject’ I mean what is in something, not as a part, and
cannot exist separately from what it is in.
Categories 1a24-25.
in
in: inheres in
in
ab
de
Rule 6. If A in B and C ab A, whatever is C is B
Rule 7. If A in B and A de C, C in B
… 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
Contents
Basic ontological relationships
ad
Relatives are what they are ‘to’ something.
Categories.
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.
Correlation
Kilwardby, De Natura Relationis 16:19-24
co
ab
ad: stands to
co: are a correlation
ad
Correlatives
ab
… 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 5:22-28.
Contents
Beings
Per se beings, denominatives
Definition 1. perse(A) iff for some B [B de A]
.
Categories.
Definition 2. denom(A) iff not perse(A),
and for some B: perse(B) and A ab B
Paronyms [denominatives] take their name from
what they are from but with a difference of ending.
Categories.
Per se beings
Denominatives
de
ab
perse: is a per se being
denom: is a denominative
Rule 8. If A de B, perse(A)
Rule 9. If A in B, perse(A)
Rule 10. If A in B, perse(B)
Definition 1 implies that
if A de B, perse(B)
Contents
Beings
… colour is in a body and therefore also in an
individual body. Categories 2b1-2
Universals, individuals
Definition 3. indiv(A) iff perse(A) and for no B [A de B]
Definition 4. univ(A) iff for some B [indiv(B) and A de B]
Things that are individual and
numerically one are, without
exception, not said of a subject.
Categories 2, 1b6-7.
Universals
… it is necessary that the things
predicated in what something is
are finite.
Posterior Analytics A22, 83a1.
univ: is a universal
de
indiv: is an individual
Individuals
Rule 11. If A de B, for some C
{A de C and for all D [if C de D, D de C]}
Rule 12. If A de B and univ(B), B de B
Definition 3 implies that if A de B
and indiv(B), it’s not the case
that B de B
Contents
Beings
Substances, accidents
Definition 5. subst(A) iff perse(A) and for no B, A in B
Definition 6. subst1(A) iff subst(A) and indiv(A)
It is a characteristic common to
every substance not to be in a
subject…. This is not, however,
peculiar to substance; the
differentia also is not in a subject.
Categories 5, 3a7-8; 21-22.
Definition 7. acc(A) iff for some B, A in B
Substances
Accidents
in
subst: is a substance
de
de
subst1: is a primary substance
acc: is an accident
A substance – that which is called
a substance most strictly,
primarily, and most of all – is that
which is neither said of a subject
nor in a subject.
Categories 5, 2a11-13.
in
Rule 13. If subst(A) and A de B, subst(B)
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.
A particular case of grammatical
knowledge would be, for example,
the grammatical knowledge that
Aristarchus possesses.
Porphyry, Categories Commentary 76,1.
Rule 14. If acc(A) and A de B, acc(B)
Rule 15. An individual accident inheres in exactly one individual substance
Contents
Derived ontological relationships
Definition 8. A in2 B iff for some C
[A ab C and C in B]
[Denominatives] are in a subject secondarily,
i.e., through their forms, which are primarily in subjects.
Garlandus, Dialectica 18:3-4
Definition 9. A was B iff for some C, D
[A ab C and C de D and B ab D]
‘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.
Definition 10. H sus C iff for some B
[H in B and B in C]
ab
in2: inheres in secondarily
(Garlandus)
was: wasfi predication
(Avicenna)
sus: sustenation
(Abaelard)
was
de
ab
sus
in
in2
in
Contents
Ontological dependencies
Among per se beings
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
de
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.
Rule 16. If a per se individual exists,
a specific per se universal (which is said of it) exists
Rule 17. If a per se universal exists, it is said of some per se individual
Contents
Ontological dependencies
Among relatives
Those relatives are said to be essential
whose being depends on the correlative.
Correlation
ab
Both correlatives essential
Kilwardby, De Natura Relationis 18:21-22
ab
ad
Correlatives
Rule 18. If A ad B and A exists, B exists
Rule 19. If A ad B and B exists and both correlatives are essential, A exists
Contents
Ontological dependencies
Inter-category
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
ab
de
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
Rule 20. An individual accident inheres in at least one individual substance
Contents
Knowledge
Kilwardby’s account, Notulae
Relative
de
de
de
Knowable and known
ad
ad
Knowledge
Knowable but not known
Contents
Knowledge
Kilwardby’s account, De Natura Relationis
Quality
Relative
de
de
Knowledge
de
de
ad
ab
Knowable
de
de
Knower
ad
Medical
knowledge
Known
Contents
Extreme conditions
Different denominatives, same accident
ab
ab
Contents
Extreme conditions
Aequiparentia (different relatives, same relation)
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 18:10-12
ad
de
in
de
in
Contents
Extreme conditions
A 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.
… 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 5:22-28.
A
B
de
a
ad
C
D
Kilwardby’s 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 can’t even show that,
because a relative, being a denominative, is neither substance nor
accident.
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
34:14-24.
Contents
The Trinity
Augustine’s account
… 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
How can
theisthree
relations nothing
inhere in God?
is said of with reference to something else.
to himself,
there
absolutely
thereNothing
to be talked
What are these three relations? Boethius
of GodVII.i.2
accidentally. So relations can inhere in God only if
De Trinitate
mentions filiation and paternity;
(i) these relations are not accidents, or (ii) they are
… the substance
of the Father and the Son is one.
presumably the third is giving. But all these
inseparable from their subject and inherences are
There is at least no doubt that God is substance …. are accidents that can come and go in a
De Trinitate
V.i.4. inseparable,
sometimes
or (iii) these relations are
[The– Holy
Spirit]
as he is
subject
whereas
God insofar
has no such
De Trinitate V.i.3
accidents said of God or (iv) are identical with God.
properlyaccidents.
or peculiarly called the
Reply: Definitions 3 & 4 exclude (ii). Rule 2 excludes (iii).
Reply:
It would
to name
the
Holy
Spiritbeisbetter
so called
relationshipAugustine excludes (ii).
relations
as
divine
or
preeminent
filiation
wise, being referred to both Father
So (i) and (iv) are the remaining possibilities.
(filiation*), divine paternity (paternity*) and
anddivine
Son,giving
since
the Holy Spirit is the
(giving*).
God
Spirit of the Father and of the Son.
De Trinitate V.iii.12.
“Yet when you ask ‘Three what?’
in
human speech labors under a great
of words.
So we and
say of
three
He dearth
is the gift
of the Father
the Son
a
persons,
not
in
order
to
say
that
… . So when we say ‘the gift of the giver’
ad
precisely,
in order
not say
to be
and
‘the giverbut
of the
gift’, we
each with
Father giver
Father,
Gift (Holy Spirit)
reduced
to
silence.”
“…
for
God
even
being
born
is
Son giver
reference to the other.
Son,
Trinitate
V.ii.10.
everlasting,
so
that
the Son can be
De De
Trinitate
V.iii.12.
“Even though some modifications are
coeternal with the Father.”
called inseparable … like the color
De Trinitate VI.i.1.
God, though,
blackWith
in a crow’s
feather,nothing
… the is said modification-wise, because there is nothing changeable with him.
Andityet
not everything
is said
moment
ceases
to be that that
animal
or of him is said substance-wise. Some things are said with reference
How
can
two
correlatives
have
a
to something
else,oflike
Fatherthat
with reference to Son and Son with reference to Father.
that feather
… it loses
courses
Son and giver are different relatives; similarly, Father
single subject (if the corresponding
De
Trinitate
V.i.6.
color….relations
So there
is
no
modification
in
and giver. So there seem to be five or six relatives,
are asymmetrical)?
God because
there
is
nothing
in
him
not three. Reply: Father and giver may be different
Reply: Paternity* is not
Thus
the
Father
is
God
and
the
Son
is
God
and
the
Holy
Spirit
is God,
and no-one
that person.
this is said substance-wise ….
that can
be changed
or subject
lost.” De
asymmetrical.
Every
that
considered
as notions,
but they denies
are the same
De stands
Trinitate
V.ii.9
in the
relation to something
Trinitate
V.i.5.
(viz. God) stands in the relation to
itself.
Contents
The Trinity
Kilwardby’s account
God
a
=
Filiation*
Spiration*
Paternity*
a
ad
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.42:16-24.
… 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.35:303315.
Contents
The Trinity
Aquinas’s account
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.
God understands and loves himself.
Moreover, his understanding and his loving
are identical with his being.
Compendium Theologiae 49
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
God
=,de
God’s
knowledge
ad
Divine
Known,
i.e. Word
a
God’s
love
ad
Divine
Divine
Knower, Lover
Loved
i.e. Father
i.e. Holy Spirit
… the manner whereby God is in himself as
beloved in lover is described by the terms breath
or spirit.
Compendium Theologiae 46
Compendium Theologiae 37
When the mind understands itself, the word conceived is related to mind as offspring to father. Therefore in
dealing with God’s understanding, the Word should be compared to God, of which it is the Word, as son to
father.
Compendium Theologiae 39