1. Realist ontology of categories (a work in progress) Paul Thom This is a Powerpoint presentation. You can navigate the slides by using the Browse menu. You can animate the images by clicking anywhere.

2. Basic relationships ab ab ab: is from … 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. Rule 1.

3. 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. Basic relationships de de For footed and two-footed are said of man as subject. Categories 5, 3a22-24. de: said of de D : said of as a differentia What is said of a subject has its name and definition predicated of the subject. Categories. Rule 2. If A de B, whatever is B is A de G 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 3. If A de B and B de C, A de C The genus [is said of] both the species and the individual. Categories 3a39. Rule 4. If A de G B, A de B de D Rule 5. If A de D B, A de B de G : said of as a genus de de G The differentiae of genera which are different and not subordinate one to the other are themselves different in kind. Categories 1b16ff. Rule 6. If A de G C and B de G C, either A de G B or B de G A de G

4. ab Basic relationships in in: inheres in Rule 8. 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 Rule 7. If A in B and C ab A, whatever is C is B de 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.

5. Basic relationships ad Relatives are what they are ‘to’ something. Categories. Correlatives ad ad: stands to Correlation ab 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 16:19-24 … 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 5:22-28. co co: are a correlation

6. ab Derived relationships in Definition 1. A in 2 B iff for some C [A ab C and C in B] Definition 2. A was B iff for some C, D [A ab C and C de D and B ab D] Definition 4. A sus B iff for some C [A in C and C in B] in 2 : inheres in secondarily (Garlandus) sus: sustenation (Abaelard) was: wasfi predication (Avicenna) [Denominatives] are in a subject secondarily, i.e., through their forms, which are primarily in subjects. Garlandus, Dialectica 18:3-4 ‘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. de in sus was in 2 exemp exemp: exemplification (E.J. Lowe) Definition 3. A exemp B iff for some C [B de C and C in A]

7. Beings SAYABLE BEINGS, DENOMINATIVES Definition 6. denom(A) iff not dic(A), and for some B [dic(B) and A ab B] denom: is a denominative Definition 5. dic(A) iff for some B [B de A] dic: is a sayable being DenominativesSayable beings What is said without combination is either a substance or a quantity or a relative or a quality or a time or a place... Categories. Paronyms [denominatives] take their name from what they are from but with a difference of ending. Categories. de ab Rule 9. If A de B, dic(A) Rule 10. If A in B, dic(A) Rule 11. If A in B, dic(B) Definition 1 implies that if A de B, dic(B) Definition 7. denom 1 (A) iff denom(A) and for no B [A was B]

8. Beings SUBSTANCES, ACCIDENTS Definition 8. subst(A) iff dic(A) and for no B, A in B Definition 9. subst 1 (A) iff subst(A) and for no B, A de B 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. 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. subst: is a substance subst 1 : is a primary substance de Definition 10. acc(A) iff for some B, A in B Rule 13. If acc(A) and A de B, acc(B) acc: is an accident de 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. in Rule 12. If subst(A) and A de B, subst(B) Substances Accidents Rule 14. An individual accident inheres in exactly one individual substance A particular case of grammatical knowledge would be, for example, the grammatical knowledge that Aristarchus possesses. Porphyry, Categories Commentary 76,1. Definition 11. acc 1 (A) iff acc(A) and for no B, A de B

9. Beings UNIVERSALS, INDIVIDUALS de Definition 12. indiv(A) iff subst 1 (A) or acc 1 (A) or denom 1 (A) indiv: is an individual Things that are individual and numerically one are, without exception, not said of a subject. Categories 2, 1b6-7. Definition 13. univ(A) iff for some B [indiv(B) and A de B] univ: is a universal Universals … it is necessary that the things predicated in what something is are finite. Posterior Analytics A22, 83a1. Rule 15. If A de B, for some C {A de C and for all D [if C de D, D de C]} Rule 16. If A de B and univ(B), B de B … colour is in a body and therefore also in an individual body. Categories 2b1-2 Definition 3 implies that if A de B and indiv(B), it’s not the case that B de B Individuals was

10. Dependencies AMONG SAYABLE BEINGS Rule 17. If an individual exists, a specific universal (which is said of it) exists de 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 18. If a universal exists, it is said of some individual 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.

11. Dependencies AMONG RELATIVES Rule 19. If A ad B and B exists and both correlatives are essential, A exists Both correlatives essential Those relatives are said to be essential whose being depends on the correlative. Kilwardby, De Natura Relationis 18:21-22 Correlatives ad Correlation ab

12. Dependencies INTER-CATEGORY Rule 20. An individual accident inheres in at least one individual substance de 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 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 ab in

13. Knowledge KILWARDBY, Notulae Knowable but not known R elative Knowledge Knowable and known de ad

14. Knowable Knowledge KILWARDBY, De Natura Relationis R elative Knowledge Quality Knower Medical knowledge Known de ad de ab

15. 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. Extreme conditions A RELATION IS A SUBSTANCE a ad 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. AB CD de … 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. 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.

16. The Trinity SABELLIANISM God,Divinity Father Son ab Paternity Filiation The Sabellians also have dared to affirm that there are not three separate Persons but only one, saying that the Father is the same as the Son and the Son the same as the Father and the Holy Spirit the same as the Father and the Son; and so they declare that there is but one Person signified under the diversity of names. Boethius, De Fide Catholica 35-41.

17. The Trinity ARRIANISM ARRIANI QUI TRINITATEM i.e. host res quorum unus Pater alius Filius alius Spiritus sanctus vocatur VARIANTESi quibus GRADIBUS MERITORUM atque dicentes Patrem esse maiorem Filio et Filium Spiritu sancto DISTRAHUNT i.e. non modo personalium proprietatum verum etiam naturam numero distingunt dicentes solum Patrem veritate essencie Deum, Filium vero creaturam, et Spiritum sanctum creaturam creature. Que nimirum diversitas ex meritorum gradibus necessario intelligitur qui, nisi in diversis, etiam eiusdem generis natura esse non possunt. Illorum igitur opinione cum Pater dicitur Deus et Filius dicitur Deus et Spiritus sanctus dicitur Deus, Filius intelligendus est alius deus quam Pater, et Spiritus sanctus alius deus quam Filius vel Pater. Neque hanc posse fieri coniunctionem qua dicitur: “Pater et Filius et Spiritus sanctus sunt unus Deus”. Sed intelligendum quod ipsi sint plures dii quandoquidem Filius est alter deus quam Pater, et Spiritus sanctus alter deus quam Filius vel Pater. Gilbert, DTrin I, 1, 15-17. ad God Divinity Father, Paternity Son Filiation ab co

18. The Trinity AUGUSTINE a Father Son God Gift (Holy Spirit) in a 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. … 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. [The Holy Spirit] insofar as he is properly or peculiarly called the Holy Spirit is so called relationship- wise, being referred to both Father and Son, since the Holy Spirit is the Spirit of the Father and of the Son. De Trinitate V.iii.12. 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, giver Son, giver There is at least no doubt that God is substance …. De Trinitate V.i.3 ad a 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 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. 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*). 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. ad 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. “Even though some modifications are called inseparable … like the color black in a crow’s 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. “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. “… for God even being born is everlasting, so that the Son can be coeternal with the Father.” De Trinitate VI.i.1.

19. The Trinity KILWARDBY God a a a ad Holy Spirit Father* = spirator* Son* = spirator* Filiation* Paternity* Spiration* = = = … 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.35:303- 315.

20. The Trinity AQUINAS God God’s knowledge God’s love =,de ad Divine Known, i.e. Word Divine Knower, Lover i.e. Father Divine Loved i.e. Holy Spirit a God understands and loves himself. Moreover, his understanding and his loving are identical with his being. Compendium Theologiae 37 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 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 … the manner whereby God is in himself as beloved in lover is described by the terms breath or spirit. Compendium Theologiae 46 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

21. Extreme conditions CORRELATIVES ARE SUBSTANTIALLY IDENTICAL In the doctrine of the Trinity, certain conditions arise which do not (usually) obtain among created beings. These are: 1.Correlatives are substantially identical (Father and Son are both substantially God) 2.Multiple denominatives are from a single abstract, e.g. multiple relatives are from the same relation (Father and Son are both from Divinity) 3.Self-predication of certain abstracts (Divinity is God) 4.A relation is a substance (Paternity is God) in This situation is consistent with our Rules. It occurs with correlatives (such as Lover and Beloved) that are from a correlation (Loving and Being-loved) whose 2-place predicate (‘… loves …’) has instances such as ‘x loves x’. co ab ad

22. AEQUIPARENTIA (different relatives, same relation) ad de 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 ab in Extreme conditions This situation is consistent with our Rules. It occurs with correlatives that are aequiparentia, such as neighbour and neighbour.

23. SELF-PREDICATION Extreme conditions This situation is consistent with our Rules. It occurs with second-order abstract terms (such as ‘universal’) that are self-predicable. But here we do not have a sayable being. Erkenntnis 40/1 1994

24. Dynamic ontology The Categories ontology does not include notions of matter and form, potentiality and actuality. It does not distinguish changeable from unchangeable beings. Thus, principles drawn from it should apply equally to God and creatures. If, however, we formulate ontological principles drawn from the Physics, then we should find some that apply only to creatures – as Gilbert of Poitiers thought. Can self-predication occur among changeable beings? In the realm of the unchangeable, A m = A. Where there is self-predication, Â = A. If A = Â, what is the value of A m ?