EUROPEAN JOURNAL FOR PHILOSOPHY OF RELIGION 6/2 (SUMMER 2014), PP. 139-153 INHERENCE AND DENOMINATION IN THE TRINITY PAUL THOM The University of Sydney Abstract. The present paper describes an 'ontological square' mapping possible ways of combining the domains and converse domains of the relations of inherence and denomination. In the context of expounding and extending medieval appropriations of elements drawn from Aristotle's Categories for theological purposes, the paper uses this square to examine different ways of defining Substance-terms and Accident-terms by reference to inherence and denomination within the constraints imposed by the doctrine of the Trinity. These different approaches are related to particular texts of thinkers including Bonaventure and Gilbert of Poitiers. Given that the doctrine of the Trinity teaches a mystery that demands faith on the part of believers, it can be surprising that in the hands of certain medieval philosophers the Trinity becomes a logical puzzle, a puzzle how to reconcile the doctrine with certain tenets of Aristotelian philosophy. However, this development did not necessitate abandoning the requisite attitude of faith; it just meant that the faith of those who pursued this type of investigation was illuminated (or alternatively, encumbered) by philosophical theory. I. BACKGROUND A key component of the philosophical background to the logical puzzle of the Trinity can be found in the account of the various types of terms given in Aristotle's Categories. A privileged class of terms (let us say per 140 PAUL THOM se terms) divides into substance-terms and accident-terms. Beyond that class there are denominatives. The terms so classified are not construed as totally unmediated by language and thought; rather, they are construed as already having a certain conceptual content. Thus the terms man and the one approaching are different terms, and different types of term, even though in some context they stand for the same being. I take it that terms are picked out by abstract or concrete nominal expressions. But I make no assumptions about the ontological status of terms – whether they are mental or linguistic items, or whether they are objective entities. I do assume that various relations hold among terms, including relations of inherence and denomination. But when we say things like 'Colour inheres in body' or 'Coloured is denominated from colour', the truth of what we say is not dependent on the actual existence of colours, coloured things or bodies. Different configurations of inherence and denomination, discernible in the text of the Categories, give us necessary conditions for being a substance-term, and also for being an accident-term.1 Three necessary conditions for a term A being a substance-term are: (1) A does not inhere in any term as subject. This is a necessary condition of being a substance term, but it is not sufficient because it also applies to terms like rational that differentiate one species from another but do not themselves characterise a substance.2 (2) A second necessary condition is that A has accident-terms inhering in it.3 Aristotle calls this feature the most characteristic mark of substances. (3) A third necessary condition is not stated explicitly but may be conjectured as assumed in the text. It is noticeable that a differentia term such as rational is denominated from an abstract term, in this case the quality-term rationality, whereas we do not find any abstract terms in the Categories from which substance-terms are denominated. While man is a substance-term, no term humanity is mentioned. It seems then that a third necessary condition of substance-terms is that they are not denominated from any term. (4) Finally, it is clear that a substance term does not denominate anything. It seems then that we have three classes of terms as shown in Figure 1. 1 Paul Thom, The Logic of the Trinity: Augustine to Ockham (New York: Fordham University Press, 2012), pp. 13ff. 2 Aristotle, Categories 5, 2b21. 3 Aristotle, Categories 5, 4a10. 141INHERENCE AND DENOMINATION IN THE TRINITY Figure 1. Types of term in the Categories In distinguishing these three types of term, we have appealed to four relative states in which a term A can fi nd itself: (1) A inheres in some term, (2) A is inhered in by some term, (3) A denominates some term, and (4) A is denominated by some term. Each of these states can be present or absent in a given term. So there are in principle not 3, but 16 types of term – each one of which is characterised by the presence or absence of each one of the four relative states. Th ese types of term are shown in Figure 2, together with the locations of the types of term recognised in the Categories. Not denominated Denominated Denominating Denominating Not denominating Not denominating Inhering Not inhering Not inhered in Not inhered in Inhered in Inhered in A B C D 4 3 2 1 Substance Accident Denominative Figure 2. Th e ontology of the Categories Other ontologies based on notions of denomination and inherence ought to be able similarly to locate the types of term they recognise. 142 PAUL THOM The class of substance-terms in the Categories can be characterised by the following configuration of inherence and denomination: these terms are inhered in, they don't inhere, they are not denominated, and they don't denominate. Accident-terms share one of these characteristics: they are not denominated. We do not find second-order terms like Rationality-ness in the Categories. But in respect of the other three characteristics, what substance-terms possess accident-terms lack. Thus accident-terms inhere in some term, they are not inhered in by any term, and they denominate. Before we proceed it will be useful to make some observations about the ways in which terms figuring in the ontology of the Categories are inter-related by inherence and denomination. (1) Every term enters into either a relation of inherence or a relation of denomination. (2) What denominates something inheres in something. (3) Denomination is irreflexive. (4) What is denominated is not inhered in. These observations can be spelt out as follows. Firstly, if we consider only substance-terms, accident-terms and denominatives, it is apparent that substance-terms are inhered in, accident-terms inhere, denominatives are denominated; so in each case the term in question stands towards something in a relation of inherence or a relation of denomination or the converses of these relations. Secondly, confining consideration again to substance-terms, accident-terms and denominatives, we observe that only accident-terms denominate, and only accident-terms inhere; thus what denominates something inheres in something. On observation 3, it might be thought that the irreflexivity of denomination is clear from the fact that when Aristotle introduces this relation he notes a linguistic difference between the denominating term and its denominative.4 But on the other hand, it might be argued that this linguistic difference is accidental to the ontological relation between denominating and denominated, and that consequently it cannot be a sound basis for concluding that the relevant ontological denomination is irreflexive. There is, however, another, ontological, argument that can 4 Categories 1, 1a12. 143INHERENCE AND DENOMINATION IN THE TRINITY be appealed to. Aristotle conceives of the denominated term as being derived from the denominating term; and under this aspect it seems that the relation must be irreflexive – at least, this is so if a term cannot be derived from itself. Regarding observation 4, it can be argued that (a) only denominatives are denominated (and denominatives are not substance-terms), and (b) only substance-terms are inhered in (to be inhered in is the mark of substance). Against this reasoning it might be argued that sometimes an accident-term inheres in another accident-term. For example, my pallor may change in its relational accidents, by spreading more widely over the surface of my face. If accident-terms can have accident-terms inhering in them, then it is not true that only substance-terms are inhered in. However, it remains true that only substance-terms or accident-terms are inhered in, and that denominatives are neither substance-terms nor accident-terms. These observations correspond to various possible states of our table. Observation 1 would be reflected in a table that has no terms in cell 1A. Observation 2 would be reflected in a table where there are no terms in cells 2A, 2B, 4A or 4B. Observation 3 does not require that there will be no terms in column 4 – but that any term in that column (a term that both denominates and is denominated) must denominate and be denominated in respect of two different terms. Observation 4 requires that there will be no terms in cells 3A, 3C, 4A and 4C. Thus there is some overlap between what is excluded by observations 2-4. II. THE TERM GOD In applying this kind of framework to the divine realm, the constraints imposed by the faith (in a broad sense that includes the teachings of the Church Fathers and Councils) are that among terms applying to the Godhead there be only one substance-term, no accident-terms, and that the Godhead exhibits simplicity. More specifically, God must be a substance-term, nothing else applying to the Godhead can be a substance-term, God must not inhere as an accident in anything, and nothing can inhere in God as an accident. The notion of divine simplicity can be interpreted in more than one way.5 On one interpretation, it excludes 5 Paul Thom, 'Shades of Simplicity', in Anselm Ramelow (ed.), God (Munich: Philosophia Verlag, 2013), pp. 323-340. 144 PAUL THOM any denomination within the Godhead. On another reading, it allows for denomination provided that this does not entail any dependency.6 Other constraints include logical consistency and interpretive sense and comprehensiveness. In some developments the account will seek to give an ontological grounding for all the relevant predications. The aims of the present investigation are more modest: I will confine attention to logical coherence. I will examine three different ways of introducing God into our framework. III. A GOD UNRELATED BY INHERENCE AND DENOMINATION The Categories scheme as it stands is ill-suited to representing a theology in which there is a substance-term in which no accident-terms inhere. If accidents are defined as what inheres, such a theology requires that there be a substance-term in row A or row B. If the term God is not denominated from anything and nothing is denominated from God then this term must be in cell 1A. The term God thus does not stand to anything in a relation of inherence or a relation of denomination or in the converses of these relations. Such a term clearly satisfies the requirement of divine simplicity: at least it excludes any complexity that might be due to the relations of inherence and denomination. The possibility of terms of type 1A is familiar to Aristotelians, though not because such terms form part of the Categories landscape. Negative terms like Non-man are of this type. To allow for such a term being a substance-term, the definition of substance-terms will have to be revised, dropping the requirement that a substance-term has something inhering in it. The ontology of Aristotle's Categories gives us an initial set of links (consequences and incompatibilities) between being a substance-term and various configurations of inherence and denomination. The task of adapting this ontology to a set of theological requirements is similar to that of adapting a theory to accommodate recalcitrant data. One has to place an ordering on the initial set of links, which will determine which links can be abandoned ahead of others. The link with the weakest strength in a context requiring that there be a substance-term in which 6 Paul Thom, The Logic of the Trinity: Augustine to Ockham (New York: Fordham University Press, 2012). 145INHERENCE AND DENOMINATION IN THE TRINITY nothing inheres is the link between being a substance-term and being inhered in. If that link is broken, a substance-term can be redefi ned as one that (1) does not inhere, (2) is not denominated and (3) does not denominate. Th e fi rst condition excludes rows C and D. Th e second condition excludes columns 3 and 4. Th e third condition excludes columns 2 and 4. Th e remaining cells are 1A and 1B. Created substanceterms belong in 1B, divine substance-terms in 1A. Not denominated Denominated Denominating Denominating Not denominating Not denominating Inhering Not inhering Not inhered in Not inhered in Inhered in Inhered in A B C D 4 3 2 1 Created substance Accident Denominative God Figure 3. Th e Categories ontology plus divine substance An accident-term can still be defi ned as one that inheres, is not inhered in, is not denominated, and denominates. Redefi ning substance-terms in this way brings us into confl ict with the fi rst of our observations about the Categories ontology, viz. that every term enters into either the domain or the converse domain of either inherence or denomination. Th e term God now appears as an exception to this observation. But this should not worry a hypothetical theologian who wants to fi t a term God into an ontology derived from the Categories. Aristotle's theory of categories gives an account of substance-terms that admit of temporally alternating accident-terms – an account in terms of inherence, denomination, and a couple of other relations. It is not surprising that all of the terms that are recognised in his account enter into these relations in one way or another. Once the account is extended so as to allow for other types of term, this restriction can no longer be expected to hold. 146 PAUL THOM IV. A SELF-RELATED GOD Let us now suppose that we want to make God a term which does stand in one or other of our relations, but only in a refl exive way. Th is account again satisfi es the demand for divine simplicity, at least in the sense that it excludes any multiplication of substance-terms in the Godhead. Some thinkers, among them Bonaventure, have thought of God in this way, claiming that God is a self-denominating term: Since quod est as well as quo est are found among lower things, by reason of which we have both concrete and abstract signifi cation (as when we say man and humanity), this is also our understanding in the divine realm, although we do not there understand these two to be diff erent. Accordingly, we signify abstractly by the name Deity and concretely by the name God. And thereby we give Him a name by which we signify quo est (and this is the essence), as well as quod est (and this is the substance).7 Th e terms God and divinity, denominated and denominating, have the same signifi cation. Th ese terms now appear in cell 4A. Not denominated Denominated Denominating Denominating Not denominating Not denominating Inhering Not inhering Not inhered in Not inhered in Inhered in Inhered in A B C D 4 3 2 1 Created substance Accident Accidental denominative God, i.e. divinity Figure 4. A self-related God 7 Bonaventure, Sent. I d.23 a.1 q.3. ... cum in communi in inferioribus inveniatur quod est et quo est, ratione cuius signifi catur in concretione et in abstractione, ut dicatur homo et humanitas: sic in divinis intelligimus, quamvis non intelligamus in diff erentia illa duo. Ideo et in abstractione signifi camus per hoc nomen deitas, et in concretione per hoc nomen Deus. Et ideo imposuimus ei nomen, quo signifi caretur ipsum quo est, et hoc est essentia; et ipsum quod est, et hoc est substantia .... 147INHERENCE AND DENOMINATION IN THE TRINITY In order for God to be counted as a substance-term in the same sense as non-divine substance-terms, the definition of a substance-term will have to be altered. This can be done by redefining a substance-term as satisfying the following three conditions. (1) It does not inhere, (2) it is inhered in iff it is not denominated, (3) it is denominated iff it denominates. The first condition rules out rows C and D. The second rules out 1A, 1C, 2A, 2C, 3B, 4B, 3D, 4D. The third condition rules out columns 2 and 3. The remainder is 1B and 4A. 1B is the profile of a created substance-term, 4A of a divine substance-term. The definition, however, may be too wide because it includes everything falling into cell 4A, including terms that are denominated by something other than themselves. The difficulty can be met by replacing the third condition by the specification that the term is not denominated by anything other than itself. A difficulty with this account arises from our earlier observation that there are no self-denominating terms in the Categories. Bonaventure is aware of this difficulty. In order to meet it he makes a distinction within the class of denominatives: To compare one thing to another as informing it or denominating it, is not thereby to posit a diversity or distinction between them; for, Deity is compared in this way to God. To compare things as a principle and that of which it is the principle, is a different sort [of comparison]: this is to import a distinction.8 In other words, denomination has to be irreflexive if it is understood as treating the denominating term as a principle from which the denominated term flows. But if we remove this element from the notion of denomination, there is no objection to a term's being denominated from itself. The definition of accidents is unaffected. A line of objection could be raised against Bonaventure's idea of isolating an element in the notion of denomination which renders the relation irreflexive, and by abstraction generating from the relation a transform of it which lacks that element. First of all, in order to be sure that the abstracted relation is not itself irreflexive, one would need to be sure that one had removed all elements that would render it irreflexive. 8 Bonaventure, Sent. 1.25.2: Quando aliquid comparatur ad aliud ut informans sive denominans, non ponitur propter hoc diversitas sive distinctio unius ad alterum; sic enim comparatur deitas ad Deum. Alio modo comparatur alterum sicut principium ad principiatum; et tunc de necessitate importatur distinctio. 148 PAUL THOM A sound argument leading to the desired conclusion requires a universal premise. Bonaventure does not address this point; and it is not at all clear how he, or anyone, could do so. Secondly, even if by this kind of process one could arrive at a suitably abstracted description of a non-reflexive relation, that would not yet prove that the description was satisfiable. One would still need a consistency (satisfiability) proof for the description. In any case, Bonaventure's specification of the content of the relation of denomination is too specific. Rather than being primarily a relation of what is principled to its principle, the relation of being denominated from what denominates it seems better described as that between something derivative and that from which it is derived. Given this, it's clear that the conclusion at which Bonaventure wishes to arrive can indeed be arrived at. Since mutual inter-derivability is a limiting case of derivability, and since denomination shorn of its linguistic marker is reducible to derivability, mutual denomination may be accepted as a limiting case of denomination. Derivability is a process of transformation in which each step is in accordance with a predetermined set of rules. If there is a single instance in which a rule is reversible, then the derivability relation is non-reflexive. That doesn't mean that all sub-relations of derivability are non-reflexive; but Bonaventure clearly thought that the specific kind of derivability that connects a denominated with a denominating term is non-reflexive. Bonaventure and his contemporaries were happy to allow that a term for a created substance, such as man, had a corresponding abstract term humanity – even though such abstract terms do not figure in the Categories. A full account of his views would have to take that into account. However, my present objective is not to analyse Bonaventure's views, but to illustrate how our framework accounts for a term God as self-related by denomination. V. A GOD RELATED TO OTHERS Let us turn to a third way of construing the term God – as entering into relations of inherence or denomination with other terms. Gilbert of Poitiers, who died in 1154, is a famous exponent of such a view. Gilbert holds that God and divinity have different significations and are connected by a non-reflexive relation of denomination. On the face of it, such a view conflicts with divine simplicity. But Gilbert has a response to this charge, which we will see presently. 149INHERENCE AND DENOMINATION IN THE TRINITY Gilbert radically overhauls the conceptual scheme of the Categories. Instead of speaking of the relation of denomination he uses the opposition between quo est and quod est (or alternatively, that between a subsistence and a subsistent): So he says Being, i.e. the subsistence which is in a subsistent, is different from what-is, i.e. the subsistent in which the subsistence is: for example, corporeality and body, humanity and man.9 Both types of term can stand for substances. For not only a subsistent but also a subsistence is called 'substance' in that both stand under accidents, though for different reasons.10 Gilbert also has a novel way of conceiving of the Aristotelian relation of inherence. He understands inherence to be the relative product of two relations, the first of which relates an accident-term to a subsistence, while the second relates that subsistence to a subsistent. He calls the former relation accompaniment, the second being the relation of denomination. Thus, instead of saying that colour inheres in body, Gilbert wants to say that colour accompanies corporeality which denominates body. He explains the relation of accompaniment as follows: And we say that colour and line follow corporality, rather than corporality following colour and line. For they don't cause corporality; it causes them. It is the very being of a body; but they accompany it in a body. So it exists at first, after which it is a body (for it is indeed their substance). They are accidents first of corporality, and through it of body. For they stand under it – both corporality (which they accompany) and body (in which they inhere).11 9 Gilbert of Poitiers, Expositio in Boecium librum De Bonorum Ebdomade §35. Ait ergo: Diuersum est esse i.e. subsistentia, que est in subsistente, et id quod est i.e. subsistens in quo est subsistentia: ut corporalitas et corpus, humanitas et homo. 10 Gilbert of Poitiers, Expositio in Boecium librum primum De Trinitate 4 §99. Non enim subsistens tantum sed etiam subsistentia appellatur 'substantia' eo quod utraque accidentibus, diuersis tamen rationibus, substant. 11 Gilbert of Poitiers, Expositio in Boecium librum primum De Trinitate 4 §26. Et dicimus quod non corporalitas colorem aut lineam sed color et linea corporalitatem secuntur. Non enim hec corporalitatis sed horum corporalitas causa est. Qua ratione illa corporis est esse: hec uero in eodem corpore illi adsunt. Ideo primum illa, deinde quod ea corpus est, uera ratione est horum substancia: hec uero primum corporalitatis et per eam corporis Taccidencia. His enim uere substat et corporalitas, cui assunt, et corpus cui insunt. 150 PAUL THOM The language Gilbert uses here suggests that he views the relation of accompaniment as holding only when that which is accompanied provides a metaphysical substratum for that which accompanies. As a result of his innovations, Gilbert is committed, even in conceptualising the created world, to terms of types 2B and 3B, neither of which is found in the Categories. 2B are not denominated but do denominate. 3B are denominated and do not denominate. 3B is how substance-terms appear in a language that admits abstract terms derived from them. 2B is how those abstract terms appear in such a language. Gilbert treats divinity and God as being of types 2A and 3A. This treatment is perfectly analogous to his treatment of the abstracts of created substance-terms and the created substance-terms themselves. However, the created substance-term is inhered in while the divine one is not, and the abstract created substance-term is accompanied by something while the abstract divine one is. For that by which He is – the essence (which in Greek is called ousia) – cannot be non-simple. Nor can something other in it accompany the same essence, by which it is. For God would not be simple if His essence were established from several essences, or if forms accompanied the same in it, of which either God Himself truly was (or His essence were with reason said to be) the subjected matter.12 Even though God is not the same as Divinity, there is nothing other than Divinity by which God is, and Divinity is only because God is from it.13 This is Gilbert's reinterpretation of what divine simplicity requires. We already know of terms that satisfy the profile of 3A, namely accidental denominatives. As for 2A, a term of this type must not inhere in anything nor have anything inhering in it, not be denominated by anything but must denominate something. In other words, such a term does not enter into inherence relations in any way, and enters into denomination relations only by denominating not by being denominated. There doesn't appear to be anything ruling out such a state 12 Gilbert of Poitiers, Expositio in Boecium librum primum De Trinitate 2.37: Neque enim ea, qua ipse est, essencia – que Grece usia dicitur – potest esse non simplex. Neque in eo eidem essencie adesse aliud aliquid potest quo ipse sit. Non enim Deus simplex esset si uel eius essencia constaret ex multis essenciis uel eidem adessent forme in illo quarum uel ipse Deus uere esset uel eius essencia ratione diceretur 'subiecta materia'. 13 Gilbert of Poitiers, Expositio in Boecium librum primum De Trinitate I,2,89. Non enim est a diuinitate aliud quo Deus sit. Nec est unde diuinitas ipsa sit nisi quod ea Deus est. 151INHERENCE AND DENOMINATION IN THE TRINITY of affairs: the fact that A denominates B doesn't require that something should denominate A (we know this from the case of accident-terms). Nor of itself does it require that A should inhere in anything (it seems that any abstract term denominates, but privative abstract terms, such as blindness, do not inhere). Nor does A's denominating something entail that something should inhere in A (again, in the case of accident-terms we know that they denominate, but do not have anything inhering in them – at least, this is true of accident-terms of the highest order). On Gilbert's reckoning God turns out to be a denominative just like created accidental denominates such as brave (but different from created substance-terms). At first sight this seems unacceptable. However, even within the slender resources to which we have limited ourselves, we can draw a distinction between two types of denominative. Terms like brave are denominated from accident-terms, the term God is denominated from the non-accidental term Divinity. Or, confining ourselves to what can be expressed solely through inherence and denomination: brave is denominated from a 2C-term not from a 3A-term; with God it is the other way round. Another apparent difficulty with Gilbert's idea of God is that this term is denominated but is not inhered in – contrary, so it seems, to one of our observations about the Categories, viz. the observation that in the Categories what denominates something inheres in something. But actually, the objection is misconceived. To say that what denominates something inheres in something is not to say that what denominates A inheres in A. And in the Categories what is denominated is never what is inhered in. The denomination relation connects what is abstract with what is concrete. The inherence relation connects what is abstract with a substance-term. So, even in the Categories it is not the case that every denominated term is inhered in. So, from the point of view of the Categories there is nothing untoward about God being denominated but not inhered in. A third difficulty concerns Gilbert's construal of divinity. Contrary to what we observe in the Categories, this term denominates but does not inhere. Its failure to inhere follows, in Gilbert's view, from the fact that it is not an accident-term. However, the coextension of denominating and inhering terms that we observe in the Categories does not appear to be have a principled basis. If we assume that what inheres must be an accident-term, we can argue that what inheres must denominate. For, an accident-term must denominate: all accident-terms are abstract, and 152 PAUL THOM thus can be made concrete, in which case they denominate some term. So there is a reason why what inheres must denominate. But there doesn't seem to be any reason why, conversely, what denominates must inhere. Rather, any term – even a term beyond the limits of what is considered in the Categories (e.g. terms for negations, privations, compounds, Platonic Forms) – so long as it is abstract, must denominate. But terms falling outside the range of what is considered in the Categories cannot inhere, because they are not accident-terms. Gilbert's innovations necessitate a revision of the definition of substance-terms. A substance-term satisfies the following two conditions (which are the first and third of the three conditions defining substanceterms in a Bonaventure-style scheme). (1) It does not inhere, (2) it is denominated iff it denominates. The first condition excludes rows C and D. The second condition excludes columns 1 and 4. What remains are the cells 2A, 3A, 2B, 3B. These are the profiles respectively of the abstract and concrete expressions for divine substance-terms, and the abstract and concrete expressions for created substance-terms. VI. WHAT DOES THIS TYPE OF ANALYSIS SHOW? The type of analysis used in this paper may have a use in reconstructing the conceptual schemes that structure certain strands of medieval theological thought. It may even help in understanding the changes that are evident when one of these schemes gets supplanted by another. Acknowledgment. This paper was delivered to the conference Analytic Theology: Faith, Knowledge, and the Trinity held in Prague on 19-20 September 2013. My warm thanks go to the organisers of the conference for their hospitality, and to those who participated in the discussion of my paper for their helpful comments. The conference was generously funded by the John Templeton Foundation and this publication was made possible through the support of a grant from the John Templeton Foundation, grant #15571 ('Analytic Theology'). The opinions expressed are those of the author and do not necessarily reflect the views of the John Templeton Foundation. 153INHERENCE AND DENOMINATION IN THE TRINITY BIBLIOGRAPHY Aristotle, Categoriae et liber de interpretatione ed. L. Minio-Paluello (Oxford: Clarendon Press, 1949) Bonaventure, Commentaria in quatuor libros sententiarum Magistri Petri Lombardi (The Fathers of the Collegii S. Bonaventura (eds.), Florence: Quaracchi, 1882) Gilbert of Poitiers, Expositio in Boecium librum De Bonorum Ebdomade, in Nikolaus M. Häring (ed.), The Commentaries on Boethius by Gilbert of Poitiers (Toronto: Pontifical Institute of Mediaeval Studies, 1966), 183-232. Gilbert of Poitiers, Expositio in Boecium librum primum De Trinitate, in Nikolaus M. Häring (ed.), The Commentaries on Boethius by Gilbert of Poitiers (Toronto: Pontifical Institute of Mediaeval Studies, 1966), pp. 62-160 Thom, Paul, 'Shades of Simplicity', in Anselm Ramelow (ed.), God (Munich: Philosophia Verlag, 2013), pp. 323-340 Thom, Paul, The Logic of the Trinity: Augustine to Ockham (New York: Fordham University Press, 2012)