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Realist ontology of categories (a work in progress)

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. Rule 1. Basic relationships ab. … the beautiful are beautiful by beauty. Phaedo.

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Realist ontology of categories (a work in progress)

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  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. . Rule 1. Basic 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 ab: is from

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

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

  5. ab ab ad Basic 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. Kilwardby, De Natura Relationis 16:19-24 Correlation co … 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. ad: stands to Correlatives co: are a correlation

  6. de ab ab in in exemp Derived relationships [Denominatives] are in a subject secondarily, i.e., through their forms, which are primarily in subjects. Garlandus, Dialectica 18:3-4 Definition 1. A in2 B iff for some C [A ab C and C in B] ‘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 2. A was B iff for some C, D [A ab C and C de D and B ab D] Definition 3. A exemp B iff for some C [B de C and C in A] Definition 4. A sus B iff for some C [A in C and C in B] in2: inheres in secondarily (Garlandus) was was: wasfi predication (Avicenna) sus exemp: exemplification (E.J. Lowe) in2 sus: sustenation (Abaelard)

  7. BeingsSAYABLE BEINGS, DENOMINATIVES 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. Definition 5. dic(A) iff for some B [B de A] Definition 6. denom(A) iff not dic(A), and for some B [dic(B) and A ab B] Definition 7. denom1(A) iff denom(A) and for no B [A was B] Sayable beings Denominatives de ab dic: is a sayable being denom: is a denominative Definition 1 implies that if A de B, dic(B) Rule 9. If A de B, dic(A) Rule 10. If A in B, dic(A) Rule 11. If A in B, dic(B)

  8. de BeingsSUBSTANCES, ACCIDENTS 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 8. subst(A) iff dic(A) and for no B, A in B Definition 9. subst1(A) iff subst(A) and for no B, A de B Definition 10. acc(A) iff for some B, A in B Definition 11. acc1(A) iff acc(A) and for no B, A de B 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. Substances Accidents in subst: is a substance de subst1: is a primary substance The species in which the things primarily called substances are, are called secondarysubstances,as also are the genera of these species. Categories 2a14-17. acc: is an accident in A particular case of grammatical knowledge would be, for example, the grammatical knowledge that Aristarchus possesses. Porphyry, Categories Commentary 76,1. Rule 12. If subst(A) and A de B, subst(B) Rule 13. If acc(A) and A de B, acc(B) Rule 14. Anindividual accident inheres in exactly one individual substance

  9. de was … colour is in a body and therefore also in an individual body. Categories 2b1-2 BeingsUNIVERSALS, INDIVIDUALS Definition 12. indiv(A) iff subst1(A) or acc1(A) or denom1(A) 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] Universals … it is necessary that the thingspredicated in what something is are finite. Posterior Analytics A22, 83a1. univ: is a universal indiv: is an individual Individuals Rule 15. If A de B, for some C {A de C and for all D [if C de D, D de C]} Definition 3 implies that if A de B and indiv(B), it’s not the case that B de B Rule 16. If A de B and univ(B), B de B

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

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

  12. ab de in 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 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

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

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

  15. a de ad 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 34:14-24. … 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. A B 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.

  16. SABELLIANISM The Trinity 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. God, Divinity Son Father ab ab Filiation Paternity

  17. ARRIANISM The Trinity 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. God Divinity ab Father, Paternity Son co ab ad Filiation

  18. in in in a a a ad ad The Trinity 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 withGod. 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 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. 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

  19. a a a ad ad ad The Trinity 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.35:303-315. 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.42:16-24.

  20. =,de a ad ad The Trinity 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 God’s knowledge God’s 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 God’s understanding, the Word should be compared to God, of which it is the Word, as son to father. Compendium Theologiae 39

  21. in in ad co ab ab Extreme conditionsCORRELATIVES ARE SUBSTANTIALLY IDENTICAL In the doctrine of the Trinity, certain conditions arise which do not (usually) obtain among created beings. These are: • Correlatives are substantially identical (Father and Son are both substantially God) • Multiple denominatives are from a single abstract, e.g. multiple relatives are from the same relation (Father and Son are both from Divinity) • Self-predication of certain abstracts (Divinity is God) • A relation is a substance (Paternity is God) 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’.

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

  23. Extreme conditions SELF-PREDICATION 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, Am = A. Where there is self-predication, Â = A. If A = Â, what is the value of Am?

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