God and Individuals: The Porphyrian Tree in 17th/18th Century Philosophy
[In Italian in Rivista di filosofia neo-scolastica 91 (1999) 18-49 - plates are missing.]
One famous problem of so called possible worlds is that of Transworld Identity: Is an individual identical with itself in different possible worlds? I will not discuss the various solutions to this problem but just hint at a methodological implication. The question of theodicy, i.e. whether God could have created a world in which there is no (physical or moral) evil, makes sense only 'all other things being equal': Hitler and Mother Teresa, natural disasters and any vacation resort should be the same, just without murder and hurricane, ranging from the highest ideals of humanity down to the trifles. Otherwise, knowing or not knowing whether God could or couldn't have created a world different from the actual world, would tell us nothing about this actual world nor about God (e.g. divine and human freedom, evil). Making the argument in the framework of possible worlds, thus, makes it necessary to assume that "essential properties and essence" make up the individual and that this and only this individual instantiates its essence.
On the other hand metaphysics deals with something general. A statement is a metaphysical one
1. if it has "no restrictions of intended reference (...) in force",
2. if the author takes "responsibility for the strict and literal consequences of the words (...) used to make this statement", and
3. if this statement is "(...) 'sufficiently general'(...)".
The first requirement is meant to guarantee that such statements extend to real, actual, possible, and mental objects, if they are to be taken as metaphysical, since "metaphysics is an attempt to get at how things really are". The second requirement lays the burden of non-restriction and of awareness about the extension on the speaker or the analyst of that intentionally or supposedly metaphysical statement. But why is, in the third condition, the attribute of being sufficiently general put between quotation marks (scare quotes as they are termed colloquially)? Since "sufficiently general" is no quotation within the text, is it used in an improper, oblique way? In metaphysics? Well, because it is, indeed, about metaphysics, which is nothing but an "attempt" at reality with some claim for generality.
Metaphysics is reality wrapped in language. Furthermore, generality has degrees, some of them are "sufficient" for qualifying to be metaphysical. Actually there is (or at least historically was) a way of describing reality in a scale of generalities; I am referring to the differentiation of 'substances' and 'species'. Michael Loux, following Aristotle, presents these differences as the most promising philosophical tool for explaining individuation. But he has to admit by the very end that the "content [claimed for essences] is hidden from us as the consequence that reflection on individual essences will not contribute much to the ontologist's understanding of substance." Loux also shows that in this terminology 'substance' is the highest 'substance kind' which exists never apart but - as a genus and like all intermediary substance kinds or genera - only as infima species and not as individual. The problem of the individual persists, but this approach seems to open a way to attaining sufficient generality in metaphysical statements. The opposite approach, viz. taking substance exclusively as 'individual essence', is branded by him "Leibnitian essentialism". It is true that Leibniz does not accept any species which extends over more than one individual and hence the "specific difference" cannot work. Leibniz rejects the concept that substances are individuated numerically, and therefore he has no use for the hierarchy of genera and species, which is traditionally known as Arbor Porphyriana. Leibniz's opposition to generalization through a hierarchy of universals goes along with his idea that "every individual substance expresses the whole universe in its own manner" such that it entails "all its experiences together with all the attendant circumstances and the whole sequence of exterior events". We are evidently at the origins of the 'possible worlds' as one can see in parallel writings to that just quoted where Leibniz states: "We must, therefore, not conceive of a vague Adam (...) but we must attribute to him a concept so complete that all which can be attributed to him may be derived from this. Now, there is no ground for doubting that God can form such a concept or, rather, that he finds it already formed in the region of possibilities [dans le pays des possibles], that is to say, in his understanding [entendement]." This 'complete concept of Adam' in God's mind is called by Leibniz "conceived sub specie generalitatis", that is to say the whole of the individual as a general concept. This probably meets the requirements for a metaphysical statement, but its meaning nevertheless needs to be spelled out. This, however, is not my aim at present.
What is evident from these observations and what I want to show in the rest of the paper is that treating metaphysics as bringing about statements together with the claim of generalization on the one hand, and on the other hand of treating metaphysical problems with the tool of 'possible worlds' are conflicting philosophical languages. I will, however, not deal with modal logic because my sources don't do so. But I will show that the strain between different philosophical languages is an inherent conflict in the hierarchy of substances which became open in the 17th and 18th century. One key problem treated then was whether or not to include God into the hierarchy of genera, and it might be (but I am not competent to develop this idea) that closer consideration of this problem could help shaping the debate about the role of God in modal logic.While tracing the problem of present day metaphysics back to the Porphyrian Tree I have no intention to make old philosophers appear new or, vice versa, contemporary thinkers look old, nor am I just 'telling a story'; rather I hope to show – as I frequently hope – that facts of intellectual history do enlighten the ramifications of a current strain in philosophy.
The Aquinas' approach in De ente et essentia
The history of the Arbor Porphyriana from Thomas Aquinas to scholastic philosophers in the 17th/18th century is an interesting touch-stone for the development of basic philosophical assumptions. It has to do with ontological realism and gnoseology. Likewise it shows the power of schemes in philosophy. Representing philosophical concepts in graphical schemes can seduce to realist or conceptualist interpretations of an ontological problem - according to apparently slight changes in the presentation. Now, whatever the positions in philosophy might be at stake, realism is always to some extent a matter of decision as to how philosophical correctness can be achieved. If one assumes that ontology is a major field of philosophy, realism is its major challenge, supposed that 'reality' is what ontology is about. One can assume the position, however, that ontology is beyond the competence of philosophy, in this case 'reality' becomes an indifferent matter, but one has to admit that such a position can be the result of ontological questions. That is what can be shown by the career of the Arbor Porphyriana. I will start from some remarks on Thomas' De ente et essentia, relating it back to Boethius' interpretation of Porphyry's Isagoge. Then I will present a number of interpretations and representations of the Arbor (without any claim for completeness) in philosophy text books of the centuries around and after Descartes' metaphysics and gnoseology. It will turn out that the Arbor both underscores and simplifies the antagonism of realism and gnoseology.
In chapter 2 of his De ente et essentia, Thomas Aquinas says: "Similarly, the essence of a genus and the essence of a species differ as signate from non-signate, although in the case of genus and species a different mode of designation is used with respect to both. For, the designation of the individual with respect to the species is through matter determined by dimensions, while the designation of the species with respect to the genus is through the constitutive difference, which is taken from the form of the thing." It is worth noting the expression "per differentiam constitutivam" (through the constitutive difference), because we will have to ask in which way difference 'constitutes' the species. For he continues: "quidquid est in specie est etiam in genere ut non determinatum" ("whatever is in the species is also in the genus as undetermined"). What does 'being' ("est") mean in this case? Thomas' example is body which has different meanings if taken as part of the animal or if taken as genus. Here, "genus significat indeterminate totum id quod est in specie" (p. 8; "the genus signifies indeterminately the whole that is in the species "). Hence, the meaning of 'constitution' or 'being' depends on the question, whether genus is 'something' or just a concept: does genus signify a reality inherent in individual things, or does it refer to a concept which can be analyzed in a way that it leads to an understanding of things? Taking "indeterminate" ("indeterminately"; in ordinary language: 'indifferently') as a key, genus is indifferent to species. But can there be a thing which is indifferent? If genus is taken as identical in various species then it seems that there must be something identical, which stands in itself. These questions may sound naive to specialists of scholastic philosophy. But the problem arises in the concept of Being when applied to God and to spiritual beings, as we will see now.
The aim of the De ente et essentia is to clarify the modes of speaking about essence. Applying this concept to God Thomas says that "ipse non sit in genere" (5, p. 14; "he is not in a genus"). The difference of genus and species does not apply to God, because He is not included in the scale of perfections. The difference between esse and essentia does not apply in this special case, while it applies to all other cases of being. In God, Thomas goes on, all perfections are included "modo exellentiori omnibus rebus" (p. 15; "God has these pervections in a more excellent way than all other things have them"). And in created spiritual substances the difference between essence and being does apply but without going down from species to individuals, except for the human soul, due to its body. In this way the scale of individual, species and genus is referring to realities; they do not only signify ways of understanding but denote differences in real being. Furthermore, the De ente et essentia would be a mere logical treatise if it would not imply its value in determining the understanding of divine and spiritual beings. On the other hand, Thomas states that exactly the difference of esse and essentia are the precondition for reasoning about things at all, when he says: "Since in these [created intellectual] substances the quiddity is not the same as existence, these subtances can be ordered in a predicament". The other finite beings are composed of matter and form, and therefore their essence can be individualized in individuals, due to matter (p. 16); the form, which is both connected with essence and the higher grades of being, is not involved as itself in the individualization. One consequence of this approach is that both God and individuals are not objects of argumentation because in them the scale of differences has come to an end.
In the background of these arguments is the Arbor Porphyriana, even though Thomas doesn't mention it literally. The Isagoge, that is the introduction into Aristotle's Categories by the Neoplatonic philosopher Porphyrios, has been commented on by Boethius and then has influenced scholastic teaching. Porphyry insists that the scale of genus, species and individuum is a means that works only on those levels where a genus can be specified, and Boethius, too, speaks of the intermediary levels when a species can be a genus of a lower level or a genus can be species when referred to the next higher level. Species specialissima, hence, is that species which has only individuals coming after it. Boethius continues saying that this series of genus and species has been developed by Porphyry only in the category of substance, and he puts substantia as "genus generalissimum" (103 A). Then he follows the well known divisions. Interestingly he divides animal rationale in immortale and mortale, i.e. "God and man". He justifies this by reminding that the pagans held God, as well as the heavenly bodies, to be corporeal. (103 B) This seemingly ephemeral occurrence will return in the 17th century in the form that Deus will occupy the same rank as Coelum (s. Plate 8).
In the traditional presentation of the Arbor Porphyriana in graphical form, as reproduced in a philosophy text book (Plate 1), we note that the genera and species are put in a sequence which is named "linea directa". This suggests that there is an order of beings ending in the individuals like Petrus and Paulus. The next observation to be made is: the difference is said "constituit" - and we have to ask if it constitutes in the sense of Thomas Aquinas. But the most striking feature should be that above "Substantia" there has been added "Ens". No doubt, the division of ens into substance and accidens is much different from that of e.g. corporeum and incorporeum: it doesn't make up a direct line, and the main feature of accidens is exactly that ens cannot be predicated of it in the same way as it can be of substance. This indicates clearly that the Arbor, stemming from a comment on a logical treatise, has developed into an ontological interpretation of the divisions. It now seems to represent realities such as Body, Animal, Man, etc. The fact that Thomas didn't mention the Tree suggests that he was aware of the shift, the Tree could work in his discussion of differences because the model would fade on the extremes: God and Individual.
One of the strictest critics of the Porphyrian Tree was the humanist Lorenzo Valla. In his Dialectica he confirms that the Tree as a model for genus and species comes to a logical end in the supreme being and the individual. But he criticizes the contraries of 'corporeal' and 'non corporeal' in the first division of substance, postulating that it had to be 'body' and 'spirit or soul'. This proposal comes from Valla's specific analysis of the modes of speaking, in which a concept (such as 'incorporeal substance') has to have a referent, i.e. a 'thing' (res) to which the concept refers. Consequently he suggests to put on the top of the scale "res" instead of "substantia". Hence follows that also 'incorporeal substance', spirit, has to be divided further, into "creantem" (God) and "creatum" such as angels and devils. He even considers Christ, stating that he – being God and human at the same time – does not fit into the scheme, too. This criticism is to a great part due to Valla's spirit of polemics against scholastic Aristotelianism and his humanist and philological approach to language, therefore he raises the question of whether the categories have a meaning with regard to reality or but to the ways of speaking. Even though his remarks are valuable, because most of the issues will return in the authors which will be discussed in the following paragraphs, I have no evidence so far that his Dialectics had any impact on them.
17th century scholasticism
But the Porphyrian Tree had a reappraisal in the 17th century among the Aristotelians, even though extensive commentaries on the Isagoge were rarely published, and as one can see from Thomas Aquinas and is confirmed by Cardinal Cajetan, commenting on Porphyry did not always include appreciation for the Tree as a scheme. The Dominican scholar Johannes a S. Thoma included a commentary on the Isagoge in his exposition of Aristotle's logic, but only summarizes the Tree with regard to substance without dignifying it a picture nor a comment. However, he bases his treatment of categorial being ("De ente praediamentali") on the subdivision of genus and species, an he gives five conditions for considering 'being' as category: "It has to be (1) in itself and not accidentally; (2) complete, (3) finite; (4) non-complex, and (5) univocal." The third condition excludes God from 'predicamental being'.
Franciscus Toletus, one of the earliest authors of Jesuit commentaries on Aristotle, mentions the habit of putting substances into tables and then enumerates the division of finite substance into corporeal and incorporeal and so on. From his wording: "De divisione seu coordinatione eorum, quae in praedicamento Substantiae continentur", and: "Pro cognitione harum substantiarum, solent aliquot tabellas assignare", we can gather that he takes the division of the concept of substance as an ontological and real division into different substances, such as angels, plants, stones etc., and consequently he excuses himself for presenting this in his commentary on logic, because these tables belong properly to "other sciences". This is also why he has to take precautions by excluding the concept of God from substance and from predicaments in general. As S. Thomas had said (e.g. Summa Theologiae I q. 3 a. 5) – and he is quoted duly – God as supreme being and source of being is not predicable, and if God is to be called substance then in a different way than all other beings.
An important step towards a revival of the Porphyrian Tree was made by the Spanish Jesuit Rodericus de Arriaga, who taught in Prague and published his Cursus philosophicus in 1632. He agrees with Toletus that the categories as a part of philosophical teaching do not belong to logic but rather to metaphysics, because logic is only concerned with the operations of the mind, while metaphysics deals with the things: "I stated earlier that the categories belong for the most part to metaphysics and in no way to logic, since logic deals only with the operations of the mind and not with things themselves." But Arriaga thinks there is no problem to include God in the category of substance, provided God obtains the top place: "Supposed these categories are so much ecclesiastical [i.e. widely accepted] (...) God may well obtain in them a place as supreme head." In order to justify this operation he has to stretch the concept of substance: "The concept of substance is, whatever constitutes a 'first thing' internally. By 'first thing' I mean, what first and in itself is intended by nature, viz. what exists first and in itself, or that which is the first root of what follows." First, substance is now realistically constituting things in the sense of a 'first intention', i.e., what something is as it is. Second, it is conceived as an inner principle. Third, it has its existence in itself - this is an ambiguous definition because in the creational and theological sense of the word, only God is per se existing, while in the logical sense of first intentions only individuals are existing "per se" whereas all other intentions depend gnoseologically from the perceived thing. Forth, existing beforehand ("primo") and "per se" is rendered additionally as being the first root of the following. This again has an ambiguous meaning as Albert the Great had pointed out: also the individuals are the 'roots' of all higher concepts in terms of species and genus, such as they are placed as 'roots' of the "tree".
From a medieval point of view Arriaga is two times confounding necessary distinctions: First he is combining the meaning of substance as (1) "ens per se existens" and as (2) "primum commune praedicabile"; in the first sense it belongs to the realm of metaphysics, in the second sense it is the object of logic. Second he is confounding "universale in essendo" with "universale in causando". To include God in the categories as the highest substance is justified only by assigning Him the function of creator and of the ontological root of all beings. But Albert had clearly assigned God a role outside the scale of beings, since God is "neither matter, nor form, nor the composite, nor universal, nor particular, nor individual, nor difference (...) but before any genus and above any genus". Thomas had even taken causality as the main reason to exclude God from the categories, because, as he says, genus extends only to the species the genus of which it is, while God as the cause of everything 'extends' over every being. Arriaga's identifying causation with being has a Neoplatonic ring which, however, cannot be confirmed by his text in the form of clear quotations. Nevertheless he eventually introduces into the hierarchy of being the theological notion of creation that is much akin to the Neoplatonic idea of the order of beings. It is Plotinus who describes the ascending from the species to the One which, as he says, then "spreads [skidnamenon] and extends [phthanein] to all things and comprises everything into one order [syntaxei mia]" (Enn. III 3, 1). But the Jesuit's strategy is certainly connected with Scotist influences, in as much as he adopts the univocation of the term 'being'. In his Theology he defends the inclusion of God in the categories by stating that the concept of being is uniform with respect to God and creation; therefore, he thinks, God might be considered the genus without eliminating His infinitude in comparison to created beings. Arriaga relies on the metaphysics of Francisco Suárez who defended the univocation of 'being' and expressly declared universal 'in essendo' and universal 'in causando' to be identical and even held that every 'universale in causando' in as much as it is the cause of more than one effect is "a single thing such as God, heaven etc."
Arriaga's policy in transforming the discussion seems to be, on the one hand, to separate strictly the realm of logic and metaphysics, and in doing so he has to assign the categories to metaphysics while logic is restricted to the operations of mind. As we have seen, traditionally these fields where not methodically separated, but it had to be clarified in every case whether one was speaking in terms of logic or of ontology; this was one of the aims of Thomas' De ente et essentia. But by separating logic from metaphysics, Arriaga had to assign parts of logic to ontology, thus giving the categories more ontological weight than they had traditionally had. On the other hand, Arriaga's strategy aimed at a full description of reality, taking into account all levels and all details of what was to be said 'real'. Therefore he could not exclude God from categories, because otherwise they wouldn't have competence for all things which can be spoken about. In separating the philosophical disciplines Arriaga practically divides the world of philosophy into a realm of mind (logic) and a realm of being (metaphysics). From this point of view it is interesting to note how he deals with the possible divisions of substance. One possibility he offers is the distinction into created and uncreated, and furthermore into complete and incomplete substance; but he is not happy with this because evidently some of the branches would overlap. And now he offers the Porphyrian Tree: "Third, substance is divided into material and spiritual, living and non-living, and so on along all those differences which commonly are given in the 'predicamental tree', down to Petrus, for example, a division which is peculiar for 'being'."
The change is really drastic. The Tree is not anymore a line constituting predicable substances according a conceptual hierarchy but it is a series of beings, as it had been presented by Toletus, and the dividing side lines are not anymore made up of negative and positive distinctions (e.g. incorporeal vs. corporeal). The basic distinction into material and spiritual mirrors the separation of philosophical disciplines. But the most important reinterpretation is Arriaga's identifying substance with being: "Substantia potest dividi, sicut et ens", and "quae divisio etiam est propria entis". Identifying substance and being is possible only if the strategy of differentiating essence and existence as proposed by Thomas Aquinas is abandoned. This becomes clear in Albert the Great's commentary on the Isagoge, where he states, that substantia and ens are only identifiable if the mode of potentiality is disregarded, thus taking 'being' as "ens actu existens".
Even though Arriaga does not depict the Tree, we will see how his presentation leads towards the Cartesian interpretation of substance, and he comes very close to what Lorenzo Valla had purported as criticism to the scholastic teaching, namely the division of substance into spirit and body and the abolishment of the concept of substance. It should also be noted, that both Valla and Arriaga are prior in the order of time to any of Descartes' published writings.
There were plenty of philosophy texts books defending the traditional view. The Franciscan Johannes Poncius defends the impossibility of including God in the Categories. He also takes the categories as ordinating beings, but God, he says, cannot be "genus generalissimum" because this would include an imperfection, since by definition all grades of being mark an ability of further perfection. He subtly explains the major difficulty which arises if one tries to assign the concept of substance to God and finite beings: Applying the category of substance to God would affirm a difference in God, because grades of substances are made up by differences, which constitute finite beings. The only solution could be to oppose finite being to God by way of "modus", which, as he admits, is a well known approach with the Scotists, but he is afraid that such subtlety would not hold because then the category of "relatio" would interfere.
Only as an additional information ("Pro complemento" n. 30, p. 475) Poncius presents the Tree of Categories, insisting that this never can be complete because of the multiplicity of existing substances. His Tree presents only the series going down from "genus generalissimum ad individua humana", and he describes the lateral series, the differences, as "differentiae divisivae superioris, et constitutivae inferioris". His Tree however marks the differences as abstraction, such as "Incorporeitas/Corporeitas", and the individual "Petrus" does not stem immediately from "Homo", as we are used to see, but is mediated by "Petreitas" as distinguished from "Pauleitas" (p. 476).
A slightly different emphasis is given in the textbook of the Franciscan Scotists Bartholomaeus Mastrius and Bonaventura Bellutus. As is their habit they discuss the variety of opinions on this matter. For our purpose it is relevant that they divide the concept of substance into: "communissime" which includes God, "communiter" which refers to every created being including accidents, and "stricte" which excludes accidents and parts (n. 2, p. 215). These three meanings of substance represent also the possible interpretations of the genus generalissimum to the effect that those who take substance in the first sense include God in the categories, and this opinion is attributed to the nominalists ("Nominales omnes"; n. 5, p. 215) naming a.o. Arriaga. This text book prefers the 'strict' interpretation of substance; and in a concluding paragraph of the quaestio on substance it describes the Tree (n. 13, p. 217; without picture) starting with the finite substance. This is then divided into "spiritualem et corporalem" out of which the spiritual substance branches into the various species of angels, the corporeal substance ("corpus") into "corruptibile et incorruptibile". The non perishable substance denotes the celestial bodies while the perishable bodies are further split into living and non living etc. Even though these Scotists exclude God from the Tree they understand it - contrary to Poncius - as a complete division of what there is and consequently assign real beings to the negative branch of the incorporeal substance.
One of the most successful text books of the Thomist school was that of the Dominican Antonius Goudin, which he himself revised in 1692 and which was very frequently reprinted. He is well aware that substance has a logical and a physical meaning: "A physical subject is to which inheres any accidens (...). A logical subject is about which anything is being asserted, in the way as Petrus is the logical subject of man (...)." Repeating the loci classici in Thomas Aquinas, Augustine and others, he asserts that God is not included in the predicament of substance (p. 285). Finally Goudin presents a number of classifications of substances, warning the reader that "those are no physical but only attributive properties, that is, nothing really distinct from the substance but only kinds of second notions which one attributes to substance". He also closes his paragraph with the Porphyrian Tree, the function of which he calls "ordinare". His first distinction is "created substance in general as divided into spiritual and corporeal" ("substantia creata in communi, quae dividitur in spiritualem et corpoream"). Having excluded God from the category of substance, the division starts from finite created beings as in Poncius. In the 1686 edition Goudin's Tree ends with the individuals: "Man is divided into various individuals which cannot be divided further and serve in a way as basis of all degrees of predicates." ("Homo dividitur in varia individua, quae sunt ulterius indivisibilia, et veluti bases omnium graduum praedicamentalium.") The revised edition is more cautious in terms of logic, ending the Tree one degree earlier, without justification, but it is evident that Petrus and Paulus are not to be understood as logical 'divisions' of "homo" in the way in which every lower grade is a division of the superior grade. It was Pierre Gassendi who had explained why one could refrain from including individuals in the scale, namely according to Porphyry a species is always related to a genus, but "homo" is not the genus of individuals. Gassendi refers evidently to the text of the Isagoge itself, where the example of Socrates the son of Sophroniscus occurs, but the question of how to include individuals in the scale of genus and species has been rarely debated in the 17th century text books.
The Tree is presented as a mere logical tool in the Jesuit Melchior Cornaeus, who treats the categories in his Summula, where he offers a woodcut of the Tree (Plate 2). His Tree illustrates the logical divisions of genus and species in close reference to Porphyry's Isagoge. When discussing the categories, Cornaeus not only presents a new scheme "Paradigma praedicamenti substantiae" (Plate 4), he also follows the original intention of Porphyry and gives samples of all categories, which are divided from genus generalissimum down to individual things, marked as "hoc, illud", "hic, ille" and similar. To give an example he divides the category of quantum/quantitas into: continua--discreta, the continua into permanens--successiva, permanens into corpus--linea, and finally corpus into hoc--illud. In the text the author mentions even more divisions than given in that scheme, and he defines "quantitas continua permanens" as: "to which it is not repugnant that it has all parts really at the same time, as the line, surface or body (...)" ("cui non repugnat omnes partes habere simul existentes. Ut linea, superficies, corpus (...).") We may note in passing that he admits here to conceive body as defined by quantitative extension, as Cartesian physics would do. Coming back to substance, his new paradigm of dividing substance gives as a first distinction spiritus--corpus, and develops only corpus which finishes on one branch in Homo and Petrus--Paulus but also includes bees, lions, the four elements, the stars, and metals, which all is summed up as hic--haec--hoc ( 4 p. 17). But then we discover that he returns to the subject in his logic, and when discussing the question, whether God has to be included in the categories, he presents us with one more Tree, which starts from Ens, where on the division branch increatum hangs a leaf tagged: Deus (Plate 3). Now, this tree resembles again the Porphyrian shape, and goes down to "corpus etc.", indicating thus that this tree has to be planted on top of the traditional Arbor.
So far the general approach to the division of substance is no more controversial, the first division being now body and spirit even though the authors underline that this is to be seen as a logical and not 'substantial', or realist ontological resp. factual division of things. Also the protestant teacher Jacob Thomasius will follow that line, taking for granted that God is "superpraedicamentalis".
But Cornaeus' "paradigm of substance" makes use of a different pattern of division, which is historically derived from the Platonic dialectics (as Porphyry's Tree was, though independently from that), but was largely developed by Petrus Ramus and his followers. The most influential of these was Johann Heinrich Alsted who in his Encyclopedia summarizes every chapter with his system of dichotomies. There substance is to be divided into "Increata: Deus" and "Partim increata, partim creata: Christus", and "creata", which then splits into Corpus and Spiritus (Plate 5). Again this author opts for including God in the substance. What is interesting for the further development is that "spiritus conjunctus" denotes "Anima humana" while "Corpus completum mixtum perfecte animatum" leads to "animal" which is subdivided into bestia--homo. That is to say that human being appears three times: 1. in Christ, as partly created substance, 2. as a derivative of spirit, and 3. as derivative of body. The soul in the finite form of "animatum" finds a second place in addition to its proper place under spirit. This obvious inconsistency is not justified but explicable by Alsted's assumption that categories divide beings into substances and accidents, and that substance is divided both in 'degrees' and in things: "The category shows specifically the division of being into substance and accidens. (...) Substance is the thing subsisting in itself; the division of it is derived from different degrees and different things." Alsted turns back to a mixture of logical and ontological understanding of the categories, and we will see that his line was to be successful in the future.
Another author who was influenced by Ramism was the Cistersian Eustachius a Sancto Paulo, known since Étienne Gilson's studies on his influence on Descartes. Ramist dichotomies make up the whole Summa, and are also applied to all ten categories, not much different from Cornaeus, even though a direct influence on him is still to be sought for. He also shows an engraving of the traditional Arbor Porphyriana, called "paradigma". The series of substances (corpus, vivens, animal, homo, Petrus-Paulus) is marked as "genera intellecta". Consequently the logical-ontological uncertainty is resolved by defining category as "appropriate disposition of the nature of things" ("naturae rerum apta dispositio", p. 51), a wording that sounds like humanist dialectics on the traces of Rudolph Agricola. In addition to that, he interprets the 'constitutive' power of the series of genus and species in the terms of analysis and synthesis: "Moreover the direct line [of the Tree] is constituted in two ways: (1) upwards by synthesis or composition, (2) downwards by analysis." While the text of Porphyry uses the metaphor of descending with respect to the genera and species, it is unusual to connect this with the method of analysis and synthesis. We cannot trace back the humanist sources of this interpretation of the categories, but rather should have a look at the category of substance itself.
After having dichotomized ens into "Subsistit, diciturque Substantia" and "Non subsistit, diciturque accidens" (q. 2, p. 56), Eustachius makes sure that God is not included in the categories basing himself, without naming sources, on the argument, which we found in Thomas' De ente et essentia that all perfections are in God "nobiliore modo" (q. 3, p. 57). Thus the way is open to enumerate the divisions of substance into "spiritualis seu incorporea" and "corporea" etc. (q. 5, p. 64 sq.). In a very similar way like Cornaeus he tries to give a full account of all existing substances which include not only in the branch of bodies the stars, or gems, and not only individual angels (in Cornaeus it was Michael and Gabriel) but even the celestial hierarchies of Seraphim, Cherubim, Thrones etc. and "spiritus mali" such as "Lucifer, Beelzebub et alij". The most general differentiation in Eustachius is substantia finita/infinita, which includes - contrary to what he himself had said - God (p. 66). He also adds a division of the "substantia finita incompleta" (Plate 6). This dichotomy is extraordinary because it presents the well known features of the series of Porphyrian substances as incomplete parts of the substances: Since all corporeal beings are composed of matter and form, the soul is classified as the incomplete essential physical form of animated beings, as in plants, animals and humans. On an other branch animal and rationale in human beings is classified as the incomplete essential metaphysical part, which is said to be equivalent to genus and differentia. Even though Eustachius, who as we have seen is well aware of the logical problem, does not discuss it, we have to state that he returns to an ontological interpretation of the categories, when he classifies genus and difference as 'metaphysical'; the only way out of this surprising turn would be that Eustachius takes 'metaphysical' in a strict nominalist sense. His metaphysics seems indeed to have some nominalist inclinations, but this would deserve further study.
For the present study we may conclude that in the first half of the 17th century the Arbor Porphyriana had a revival thanks to a variety of interpretations of the realm of logic and ontology and served rather to show the intertwining of logical and ontological problems than to solve them. This uncertainty was to change under the influence of Descartes.
Descartes and Cartesianism
René Descartes did not appreciate the Aristotelian categories and he intended to replace them in logic with his rules of inference. Consequently he mocks about the Porphyrian Tree. In his Recherche de la verité‚ one speaker calls the "gradus metaphysici" a labyrinth and full of obscurity, because they create more problems than they can solve and lead form one statement to another "like the branches of a genealogical tree": What is at stake is the methodical and gnoseological service to be obtained from the scheme. The defender of scholasticism responds that the Tree presents successively "ante oculos" the grades which constitute individual being and knowledge of this depends on knowing what is common and what is different. The dialogue reveals that Descartes takes the Tree as a mechanical device to generate knowledge. The ironic reply by Descartes' spokesman is that he owes his conviction about the uncertainty of knowledge to his school masters, and this uncertainty is due to the general lack of precision in the meaning of words; consequently the author opts for a reduction and clarification of basic and experience related words the meaning of which is both evident and common to all, such as: "when I said I am a man, I spoke about those things the most simple man and the greatest philosopher know likewise."
As is well known Descartes reduces all divisions of substance to res cogitans and res extensa. Nevertheless in his Principia Philosophiae one can trace the Arbor Porphyriana. When speaking about substance Descartes, too, starts from the supreme being, God. So in a first approach substance, understood as something that "nulla alia re indigeat ad existendum", is identified with God; but with explicit reference to scholasticism it is made clear that in this concept substance is not univocal, since there is no meaning of substance which covers both God and creature. Only after having laid this ground Descartes introduces the two all-inclusive substances "substantia corporea et mens, sive substantia cogitans, creata" ( 52, p. 24 sq.). For any reader raised like Descartes in scholasticism the following "modi" ( 55, p. 26): duration, order, and number, are introduced in order to replace categories. And whoever intended to reconcile Cartesianism and scholasticism could find a good starting point here.
The most influential book of logic of Cartesian setting was the so called Logic of Port Royal by Antoine Arnauld and Pierre Nicole. The authors abolish the dialectics of negative distinctions (such as: incorporeal) and expressly favor classifications through direct positive oppositions referring to Descartes' "division de la substance en celle qui pense, et celle qui est étendue" (II 15, p. 163). Substance is treated here in the chapter on the five "idées universelles", i.e. genus, species, differentia, proprium and accidens (I 7, p. 59). Their definition (p. 60) is: "On appelle genre, quand elles sont tellement communes qu'elles s'‚tendent … d'autres id‚es qui sont encore universelles (...): la substance est genre … l'‚gard de la substance ‚tendue qu'on appelle corps, et de la substance qui pense qu'on appelle esprit." In accordance to the rationalist or conceptualist approach genus is a special case of the idea of species, which is defined as: "idées communes qui sont sous une plus commune et plus generale" (I 7, p. 60). Now the universals are discussed as ideas and mere ideas. Truth is consequently defined (I 2, p. 49) as a correct relationship between ideas and the objects they represent: "Que si les objets représentés par ces idées, soit de substances, soit de modes, sont en effet tels qu'ils nous sont représentés, on les appelle veritables (...)"; and Aristotle's categories are but some of them (I 2, p. 49).
This solution to the ambiguity in the universals between logic and ontology was still perceived by the scholastics as a problem. And it seems that in this atmosphere which shows its symptoms in the various and sometimes contradictory presentations discussed above the Porphyrian Tree was rediscovered in order to come to grips with it. Taking it as describing reality some scholastics criticized - like the Cartesians Arnauld/Nicole - that in the linea indirecta there are only negative statements, but they demanded that God as the highest substance should be included. While the original scholastic concept had to exclude God for theological as well as logical reasons, from a realist point of view they now felt themselves encouraged to search for a place within the scheme. On the other hand, for Arriaga, Eustachius, to some extent for Cornaeus and definitely for the Cartesians of Port Royal the difference between being, substance, and thing tended to vanish. This perspective had probably been opened by Renaissance-Aristotelians like Lorenzo Valla, who had said that substance and being are no operable concepts because all thought and knowledge is about "res". Probably the univocal concept of being in the Scotist school helped to identify substance and being, too, because as soon as there is no difference in the concept of being between God and created beings, the major barrier against including God in the scale of being was removed, this is also evident in Poncius who can exclude God from the categories only by subtlety, admitting that in an ontology of "modes of being" this would not hold any more, as it also happened in Arriaga.
Another scale of beings was popularized in the Renaissance through Neoplatonism and Lullism. In a 1512 edition of a book of Raymond Lull a wood cut shows a ladder on which the intellect steps up from stones over animals, Man, etc. to God and down again (Plate 7). There is no evident border between individuals and genera and universals and God. Regardless of the peculiarities of Lull's art, for a real order of beings which is mirrored in the intellect this scale is as suggestive as the Arbor.
It was the Paris Professor Edmund Pourchot (Purchotius), who first designed a Tree of Categories according to Descartes in a school book (Plate 8). His Arbor Purchotiana or Cartesiana had a remarkable career in catholic philosophy text books of the 18th century. As we see immediately, God has found his place in a dead end of spirit. One finds him on the same level as the earth and the stars. Further more, the logical differences of the traditional Arbor have been turned into powers and chances (vim habens, praeditum, destinatus). And after having seen the discussion in Arriaga and in Descartes, we are not surprised to find ens, res, and substantia identified. One feature Pourchot is most proud of is the new position of Man in the middle of the order of beings. The human soul - which was a special case also in Thomas - is now one item joined with corporeality and constitutes the particular human place in the world. Pourchot manages to avoid the double identity of human soul and human body as it happened to appear in Alsted's scheme. The philosophical background is obviously the Cartesian distinction of 'extended thing' and 'thinking thing'. Therefore one can find the first distinction of "being, thing, or substance" marked as extensa vs. cogitans. The ideological background of this solution is certainly the Renaissance speculation on the dignity of man, which of course was foreign to scholastic logic. What is also striking is the absence of the individuals. We had observed the same absence in the second version of Goudin's order of categories, who did not explain why he omitted the usual Petrus and Paulus. In Pourchot it is evident that if the substances are taken to be ideas (as in the Logic of Port Royal, and Pourchot expressly refers to it), individuals are not to be included in such a table. In this respect they all return - paradoxically enough - to the Thomist way.
Given the authority of scholastic thought one can expect an attempt to reconcile the old and the new Tree, and we find it in the Piarist Donatus a Transfiguratione Domini. In his Arbor Porphyriana accuratius disposita (Plate 10) the linea directa that represents the degrees of substances is split into two lines, the upper divisions forming with Homo below the shape of a heart. These two lines represent two parallel scales of beings on each side outside the heart shaped lines: Deus-Angelus-Anima post mortem and: Lapis-Planta-Brutum which join again in Homo. On contemplating the two lines it is evident that the line Homo-Animal-Vivens Corpus represents the old linea directa in which the superior grade can be predicated of the lower, while the line Homo-Anima rationalis-Mens angelica vel humana-Spiritus is made up of spiritual substances. Looking at the horizontal levels the inconsistency of this solution is evident, because – if the items were realities - stone and God were of the same rank. The conceptualist and the realist reading of the Tree are fused again. The pretended 'accuracy' consists in displaying the problem, not in solving it.
At the same time a Jesuit teacher in Dillingen, Berthold Hauser, reproduces the two trees with the same arguments as Pourchot (Plate 11). Yet he added his own new tree which he calls "analysis idearum" (Plate 12). Needless to say that his logic adapts as much as possible from the Logic of Port Royal. The linea directa consists now of inferences: "Plato est homo ergo animal ergo vivens (...) ergo ens." The side branches which are almost all truncated represent distinctions and arguments which repeat one another. Albert the Great had also meditated the possibility of reading the line from the individual up to substance as a series of inferences, but he warned not to go on from substance to 'being': "It follows: if it is a man it is an animal, if an animal it is a living body, if a living body it is a body, of a body a substance - because of the inclusion of the genus in [the concept of] species. But it doesn't follow: if it is a substance it is a being, because the genus - regardles whether it is something or not - follows always if a species is postited." Genus can refer to non-existing merely possible or mental 'things' and therefore does not necessarily include actual being. It seems this distinction ceased to work with Cartesianism to which every concept is just an idea.
Thus finally the Arbor has been set back to a logical instrument, but to the logic of Descartes. And the whole sequence is turned upside down: Being is now at the lower end and the individual is on the top. This is paradoxical again, because traditionally the individuals marked the root because the scale of genera started from there by way of abstraction. On the other hand, an ontological interpretation could have marked being as the root. Right now, when the series is turned into method, the inference runs from top to bottom. Reality is not anymore a question since the philosophy of reality is conceived as the analysis of ideas; ontology has become gnoseology. We are on the threshold of Kant.
To conclude this survey of several variations on the theme of the Tree: From a Thomist point of view this presentation should assume a polemic tone, since it shows that the development of philosophy was achieved at the price of reducing and simplifying the problem. In Thomas Aquinas God was the major problem of metaphysics because God escapes linguistic and semantic as well as logical solutions to the philosophy of being. Early modern philosophy also was not free to chose a solution without God, since philosophy would have been poor without a supreme being that is at the same time the most exceptional case of being and its source or creator. But in Thomas God is also the opposite extreme to the individual being, therefore without God - in natural theology and apart from revelation - the table of beings or the order of the substances would not be complete if on the end opposite to the individuals there would not be one being that exceeds the entire scale. This is proven by Thomas' argument that God is not to be conceived as that universal that comprises formaliter all things, because this solution would not comply with the logical line of the order of being in which individuation is the ultimate perfection: pantheism excludes God's excellent way of being a person. Thomas refers to the theology of Amalrich of Bena which has been repeated by Spinoza - following and transforming Descartes -, who held that there is only one substance, God, and that all other beings are but accidentals. This was, of course, a further step towards unification at the price of simplification, at least from the point of view of the early and the late scholastics who didn't think that philosophy was called upon making things easy. The Arbor Porphyriana as it was received in the 17th and 18th century was partly used to keep the standard of complexity and partly to reduce it.
From the perspective of the history of Cartesianism, we discover once again that Descartes' theory of substance and his method had its preparations in both scholasticism and Ramism, and that even these two early modern strains could be intertwined in thinkers like Arriaga or Cornaeus. If one dares to say that Arriaga and Eustachius were Cartesians ante Descartes, then only on the basis of the philosophical problem carried forward from Aristotle's Categories through their ancient and medieval interpretation. On the other hand philosophers could be non-Cartesian after Descartes without losing any contact to the debates of early modern philosophy exactly because, from the scholastic perspective, Descartes' was just one solution of the persistent problem of realism and gnoseology that can also be paraphrased as the problem of essence and individuals.
The graphical representation was revived in order to ban the complexity of the problem and eventually it was dissolved it into an plausible scheme. The Arbor Cartesiana is an indicator of the problem that was at the origins of modern philosophy of mind and substance. The last example in this paper shows that the inference of universals from individuals has an epistemic status only if we bear in mind the Porphyrian Tree in its double meaning as ontological hierarchy and gnoseological tool. Hauser's Tree tries to present the individual as the complexion of higher ideas or concepts. The problem is that these 'superior' or 'more basic' levels lack a specific ontological status - and this is one reason why (as shown in the introduction) modern metaphysics wrestles both with the meaning of generality and the constituencies of the individual.
 Versions of this chapter were discussed at the Philosophy of Religion Colloquium at The University of Notre Dame and at the Institute of Philosophy at the Università Cattolica del Sacro Cuore, Milan, in 1999: I am indebted to the audiences for various corrections and suggestions.
 Michael J. Loux, Introduction, in: Michael J. Loux (ed.), The Possible and the Actual, Ithaca and London 1979, pp. 36 sqq. David Lewis, On the Plurality of Worlds, Oxford 1986, chapt. 4.
 This seems to me the reason why Plantinga treats philosophical theology with an extensive discussion of the concept and method of possible worlds: Alvin Plantinga, The Nature of Necessity, Oxford 1974.
 Plantinga p. 88.
 Peter van Inwagen, Introduction: What it Metaphysics?, in: Peter van Inwagen and Dean W. Zimmerman (eds.), Metaphysics: The Big Questions, Oxford 1998, p. 5.
 P. van Inwagen, p. 3.
 Michael J. Loux, Substance and Attribute: A Study in Ontology, Dordrecht 1978, p. 178; it is the last paragraph of his final chapter on "Individual Essences", which is preceded by the exposition of "Genera and Species". A summary in Idem, Metaphysics: A contemporary introduction, London-New York 1998, pp. 117 ff.
 The evidence quoted by Loux is: Gottfried Wilhelm Leibniz, Discourse on Metaphysics, Correspondence with Arnauld, Monadology, Lasalle 1901, 14th printing 1994, § IX, p. 14. Cf. Reinhard Finster et al., Leibniz Lexicon, Hildesheim 1988, pp. 336 sq. for more references.
 Discourse, p. 14 headline of § IX.
 Leibniz, Remarks upon Mr. Arnauld's letter (...), [May, 1686], ed. as quoted, Letter VIII, p. 103, cf. the final version of this letter, July 14, 1686, Letter IX, p. 129. Leibniz, Discours de métaphysique et correspondance avec Arnauld, ed. Georges Le Roy, Paris 1984, pp. 108, 119 sq.
 Ibid. Letter IX, p. 129.
 Some hints concerning free will and values in: Frederick Sontag, Being and God: Universal categories and one particular being, in: Religious Studies 9 (1973) 437-448.
 The terms 'gnoseoloy/gnoseological' do not exclude ontology, whereas in modern parlance 'epistemology/epistemological' are restricted to problems of conditions of cognition and understanding, while metaphysics focuses on knowledge of reality without correlation to sensation. See "Gnoseology" in The Oxford Companion to Philosophy, ed. Ted Honderich, Oxford 1995, p. 314.
 Hans Wagner, Begriff, in: Handbuch philosophischer Grundbegriffe, ed. Hermann Krings et al., vol. 1, München 1973, 191-209, esp. 204-206. A more recent study of the Prophyrian Tree is Ian Hacking: Trees of Logic, Trees of Porphyry, in: Advancements of Learning. Essays in Honour of Paolo Rossi, ed. by John L. Heilbron, Firenze 2007, pp. 219-261. Hacking is interested in part in the metaphysical, in part in the graphical aspects.
 Thomas Aquinas, Opuscula philosophica, ed. R. M. Spiazzi, Torino Marietti 1973, p. 7: "Sic etiam essentia generis et essentia speciei secundum signatum et non signatum differunt, quamvis alius modus designationis sit utrobique: quia designatio individui respectu speciei est per materiam determinatam dimensionibus; designatio autem speciei respectu generis est per differentiam constitutivam, quae ex forma rei sumitur." English translations of this text are taken from: Medieval Sourcebook: Thomas Aquinas: On Being and Essence (De ente et essentia), Translation E 1997 by Robert T. Miller, http://www.theologywebsite.com/etext/aquinas/beingandessence.shtml. Of course, I am not intending an exhaustive interpretation of Aquinas.
 A rather logical interpretation is given by Karl Werner: Der heilige Thomas von Aquino, 3 vols., Regensburg 1858-1859, vol. 2, p. 27-29. This is quite an extraordinary and still informative study on Thomas himself and the history Thomism. Concerning the necessary distinction of "il piano logico" and "reale" see for instance Pasquale Porro, Introduzione, in: Tommaso d'Aquino, L'ente e l'essenza, Milano 1995, p. 20 sq.
 De ente, p. 15: "quia in istis substantiis [sc. creatis intellectualibus] quidditas non est idem quod esse, ideo sunt ordinabiles in praedicamento".
 Thomas Aquinas: De natura generis (Opusculum 42) gives an extended discussion on the logical and ontological, as well as methodological implication of universals. One key passage is in chapt. 4: "Sciendum est ergo quod, sicut in quarto Metph. [1004 b 20 sq.] 'Logicus et Metaphysicus circa omnia operantur, differenter tamen' (...). quia Philosophus procedit ex certis et demonstrabilibus, Logicus autem ex probabilibus: et hoc ideo est quod ens dupliciter dicitur, scilicet naturae et rationis. Ens autem rationis proprie dicitur de illis intentionibus, quas ratio in rebus adinvenit, sicut est intentio generis et speciei, quae non inveniuntur in rerum natura sed sequuntur actiones intellectus et rationis: et hujusmodi ens est subjectum Logicae, et illud ens aequiparatur enti naurae quia nihil est in rerum natura, de quo ratio non negocietur." (Thomas Aquinas, Opuscula [cf. note 14] p. 180.) Even in this treatise, the authenticity of which is being debated, Porphyry with his Tree is not mentioned.
 Boethius: In Porphyrium commentariorum lib. III, in: Migne, Patrologia latina 64, 102 D.
 Laurentius Valla: Repastinatio dialectice et philosophie, ed. Gianni Zippel, Padua 1982, 2 vols. (Thesaurus mundi 21-22); vol. 1: Retractatio totius dialecticae cum fundamentis universe philosophie [this text quoted here]; vol. 2: Repastinatio dialectice et philosophie; Retractatio I 7, pp. 46-50: "Substantie distributio contra Porphyrium et alios" (also in: Laurentius Valla: Opera omnia, Basel 1540; Reprint ed. Eugenio Garin, Torino 1962, I pp. 657-658).
 Valla p. 46 sq.: "'Substantia' summum genus ponitur, utpote predicamentum; 'corporea' et 'incorporea' differentie dicuntur, que semper bine constituuntur: que cum rediguntur in substantivum faciunt speciem, ut ex 'corporea' fiat 'corpus'. Verum 'incorporea' non est suum substantivum sortita apud hos [sc. Prophyrios and his commentators]: ad meam autem legem erit 'spiritus' sive 'anima'."
 Ibid. p. 49 sq.
 It does not appear in Francisus Suarez: Disputationes metaphysicae (first. ed. 1597) even though the categories and especially substance are treated there at length.
 The last edition of the Isagoge seems to have been published in 1600, and the last commentary on it is recorded in 1606: Wilhelm Risse, Bibliographia logica, I: 1472-1800, Hildesheim 1965, 264, 280.
 Thomas de Vio Cardinalis Caietanus: Commentaria in Porphyrii Isagogen ad praedicamenta Aristotelis, ed. Isnardus M. Marega, Romae (Institutum Angelicum) 1934; see chapt. 9, p. 61-69.
 Johannes a Sancto Thoma: Cursus philosophici Thomistici (...) pars prima. Continens ea quae ad artem logicam spectant (...), Coloniae Agrippinae (Münich) 1638, pars. 2, qq. 6-14.
 Ibid. q. 15, in fine, p. 250. The summary is headed: "Coordinatio praedicamenti substantiae"; similar 'coordinations' are given for the remaining categories. There is no graphic scheme in the editions I used: Wolfenbüttel Xb 2613, and Cursus philosophicus Thomisticus, Lugduni (Borde, Arnaud) 1663, Microfiche edition by IDC, Leiden 1987 (The Catholic Reformation CA 20).
 Ed. 1663, Logica, qu. 14, art. 1, pp. 205f.: "qinque enumerantur conditiones, quae requiruntur, ut aliquid sit in praedicamento (...). Prima, ut sit ens per se seu non per accidens. Secunda, ut sit ens completum. Tertia, ens finitum. Quarta, ens incomplexum. Quinta, ut sit univocum." In qu. 9, following Thomas Aquinas, Johannes presents a distinction of the individual into "designatum et determinatum" and "in communi seu vagum". Even though it is beyond the purpose of this paper it is worth mentioning that Johannes refers the concrete individual ('designatum') to the first and second intention to the effect that the individual considered in the first intention simply cannot be split up in to further properties (this is the literal meaning of individual), while according to the second intention, the individual is a twofold relationship ("constat duplici relatione rationis") and thus either it can be related to the superior degrees of substance, such as "hoc animal, hoc corpus", or it is selfreferential (Ed. 1663, p. 170). The "individuum vagum" refers to the concept of individuality and is as such not "praedicabile": it does not refer to any specific being and does not belong to any hierarchy of universals ( p. 174). The 'Leibnizian essence' overrides these distinctions.
 Franciscus Toletus: Commentaria, una cum Quaestionibus, in universiam Aristotelis logicam, Coloniae (Birckmann) 1573 [1st. ed. 1572], cap. 5, qu. 4, p. 113.
 Ibid. qu. 3, p. 112.
 "Metaphysics", in the case of later scholasticism, means the body of teaching in the Philosophy course (s. P. R. Blum: Philosophenphilosophie und Schulphilosophie, Stuttgart 1998), which has its medieval roots as one can see in the passage quoted from Aquinas, Opusc. 42, above note 14; it comprises the problem of being as being (later called ontology) and the 'being' of spiritual beings.
 Rodericus de Arriaga: Cursus philosophicus, Antverpiae 1632 [Microfiche edition by IDC, Leiden 1987 (The Catholic Reformation CA 2)], Metaph. disp. 3, sect. 2, n. 11: "Praedicamenta maiori ex parte proprie ad Metaphysicum spectare, nullo modo ad Logicam dixi supra, eo quod Logica solum agit de actionibus intellectus, non vero de rebus ipsis."
 Ibid.: "Quod si haec praedicamenta sunt tam Ecclesiastica (...) bene posset in illis Deus ut supremum caput locum habere."
 Ibid. disp. 4, sect. 4 n. 32: "Conceptus substantiae est quidquid intrinsece constituit primam rem. Nomine autem primae rei intelligo id quod primo et per se intenditur a natura, vel primo et per se existit; vel, quia est prima radix ceterorum."
 Albertus Magnus, De praedicabilibus, tr. 4, c. 4, in: Opera omnia, ed. A. Borgnet, I, Paris 1890, p. 67: "Et ad hunc modum figura per modum arboris scribi consuevit, quae si secundum esset et essentiam consieratur, radices quibus principiatur, superius habet. Si autem secundum esse actuale consideratur, radices quae sunt in individuis, habet inferius." - References to Albert as a contemporary to Aquinas are of systematic order and cannot claim 'influences' or 'receptions', also because Albert is never quoted by the philosophers treated here.
 Albertus Magnus, De praedicamentis, tr. 2, c. 1, in: Opera omnia, ed. A. Borgnet, I, Paris 1890, p. 166.
 On this distinction see Ronald P. McArthur, Universal 'in praedicando', universal 'in causando', in: Laval théologique et philosophique 18 (1962) 59-95.
 Albertus Magnus, De praedicamentis, tr. 2, c. 12, p. 189.
 Thomas Aquinas, Summa theologiae I q. 3, a. 5 c: "Quod autem Deus non sit in genere per reductionem ut principium, manifestum est ex eo quod principium quod reducitur in aliquod genus, non se extendit ultra genus illud: (...) Deus autem est principium totius esse."
 Rodericus de Arriaga, Disputationes Theologicae, vol. 1, Antverpiae (Plantin) 1643, disp. 2, sect. 8, subsect. 3, p. 47: "Admittitur autem communiter unus conceptus obiectivus entis communis Deo et creaturis, in quo proculdubio ut sic concepto non explicatur differentia Dei: ergo est univocus, ergo genus. Neque timeant inde impediendam in Deo differentiam infinite perfectiorem creaturis, aut inducendam aliquam imperfectionem."
 Franciscus Suárez, Disputationes metaphysicae , in: Opera omnia, Paris 1856-1878, vol. 25-26, disp. 6, sect. 8, n. 2, p. 232: "Nam causa quae universalis dicitur, quia varios effectus potest producere, res aliqua singularis est, ut Deus, caelum, etc. (...) Tertium autem universale, quod vocatur in essendo, vel nullum est, vel in re coincidit cum quarto [sc. in praedicando], solumque nomine et habitudine rationis differunt." - Suárez does not discuss the Porphyrian Tree.
 Arriaga, Cursus, metaph 3, disp. 4, sect. 7, n. 41: "Substantia potest dividi, sicut et ens, in creatam et increatam (...). Ulterius substantia creata potest dividi in completam et incompletam. (...) Divisio haec non est rigorosa, quia unum membrum includitur in alio (...)."
 Ibid. n. 42: "Tertio dividitur substantia in materialem et spiritualem, viventem et non viventem, et sic per omnes illas differentias, quae in arbore Praedicamentali poni solent usque ad Petrum v.g. quae divisio etiam est propria entis."
 Albertus Magnus, De praedicabilibus, tr. 4, c. 3, p. 65: "Cum autem didtur ens absolute, non intelligitur nisi ens actu extistens: et ideo non sequitur si substantia est, ens est, quia esse ens accidit omni ei quod est."
 Johannes Poncius: Integer philosophiae cursus ad menten Scoti, prima pars complectens Logicam, Romae (Scheus) 1642, disp. 10, concl. 2, n. 24, p. 446.
 Ibid. p. 446 sq.: "sed quia est valde difficile assignare discrimen inter modum intrinsecum contrahentem ens ad Deum, ac differentiam, et quia non minus difficile est ostendere quod relatio ut sic, quae est summum genus praedicamenti relationis, non contrahatur per modos ad sua inferiora, si substantia, ut sic, contrahatur per tales modos ad Deum et creaturam."
 Poncius' treatment belongs to the Scotist tradition which seems to avoid the scheme of genus/species; see: Ludger Honnefelder: Scientia transcendens, Die formale Bestimmung der Seiendheit und Realität in der Metaphysik des Mittelalters und der Neuzeit, Hamburg 1990, p. 233 (on Francisco Suárez and Scotus).
 Bartholomaeus Mastrius, Bonaventura Bellutus: Disputationes in Organum Aristotelis, Venice 1638; edition quoted: Philosophiae ad mentem Scoti cursus integer, vol. 1, Venice 1708, disp. 7, q. 1.
 Cf. the claim maid in the same text book, vol 4, Metaph. disp. 1, q. 3, n. 49, p. 15: "Sed Metaphysica dividit ens, et alia suprema genera, et ex his divisionibus colligit particulas entis".
 Antonius Goudin [Goudinus; also: Gaudinus]: Philosophia juxta inconcussa Divi Thomae dogmata quatuor tomis comprehensa, Urbeveteri 1859; edition used, but checked against the editions Bologna (Longus)1686 and Venetiis (Lovisa) 1736. Earliest editions known to me: Paris (Couterot) 1674 and Mediolani (Vigonus) 1674; latest edition known to me: Paris (Sarlit) 1886. On Goudin see Ignazio Narciso, Alle fonti del neotomismo, in: Sapienza 13 (1960) 124-147.
 Ibid. vol 1, Logica maior, pars 1, disp. 2, qu. 2, art. 2 p. 283: "Subjectum Physicum est, cui inhaeret aliquod accidens (...). Subjectum vero Logicum est, de quo aliquid praedicatur; ut Petrus est subjectum logicum hominis (...)."
 Ibid. art. 3, p. 291: "eas non esse proprietates physicas, sed solum attributales; id est non esse aliquid realiter distinctum a substantia, sed solum esse quasdam notiones secundas, quae attribui solent substantiae."
 Petrus Gassendi: Institutio logica, pars 1, canon 6, in: Opera omnia, I, Lugduni (Anisson/Devenet) 1658; Reprint Stuttgart-Bad Cannstatt 1964, p. 95 A; there p. 94 Gassendi gives a scheme which goes from "Ens seu Res" via "Substantia" down to "Homo", and the last is divided into three: "Hic Filius Sophronisci etc. --Alius--Socrates".
 Melchior Cornaeus: Curriculum philosophiae Peripateticae, uti hoc tempore in scholis decurri solet, multis figuris et curiositatibus e mathesi petitis, et ad physin reductis, illustratum, Würzburg (Zinck) 1657, Summula Dialecticae, cap. 3, p. 12.
 The following authors also apply the tree on all categories: Caietanus Felix Veranus OTheat., Philosophia universa, 4 vols., Monachii (Iaecklin) 1684-1686, I, p. 486 sq.; Coelestinus Sfondrati OSB, Cursus philosophicus monasterii S. Galli, I, St. Galli (Müller) 1695 1696, I 3.
 Cornaeus, ibid. 5, p. 17 sq.
 For Cornaeus' relationship to Cartesianism see: Paul Richard Blum: Sentiendum cum paucis loquendum cum multis: Die aristotelische Schulphilosophie und die Versuchungen der Naturwissenschaften bei Melchior Cornaeus SJ, in: Aristoteles Werk und Wirkung (Festschrift Paul Moraux), ed. By Jürgen Wiesner, vol. II, Berlin 1987, 538-559 (cf. Blum, Philosophenphilosophie, chapter 4.5); abridged version as: Science and Scholasticism in Melchior Cornaeus SJ, in: Acta Conventus Neo-Latini Guelpherbytani, Binghamton/New York 1988 (Medieval and Renaissance Texts and Studies 53), 573-580. On Cornaeus's relation to modern science see Marcus Hellyer, "Because the Authority of my Superiors Commands": Censorship, Physics ad the German Jesuits, in: Early Science and Medicine 1 (1996) 319-354; 343-346 (cf. Idem, Catholic Physics. Jesuit Natural Philosophy in Early Modern Germany, Notre Dame 2005, chapter 2.
 NB: Summulae, i.e. the technical part of definition and argumentation, and logic as the scientific treatise on the topics of Aristotle's Organon, are frequently separate in catholic text books.
 Cornaeus: Logica, tr. 3, q. 1, dub. 5. - A full version of this kind of tree can be found in: Carolus Josephus a S. Floriano OFMobs., Joannis Duns Scoti philosophia nunc primum recentiorum placitis accomodata, I, Mediolani (Typ. Morelliana) 1771, appendix; here it is named "Arbor Sanctofloriana" and compared with the traditional Tree and that of Purchotius, about which in the following. This is also the latest scholastic philosophy text book with the Tree I have encountered so far.- The Swiss Capuchin friar Gervasius Brisacensis presents two times the Porphyrian Tree in the identical traditional version, the difference is that the Tree in the Summula is poorly printed, while the one in the Logic is a more decorated and explicit engraving: Gervasius Brisacensis, Cursus Philosophicus, Coloniae Agrippinae (Schlebusch) 1699 (edition used, 1st. edition 1696), elem. logic, art. 8, p. 21; Logica, pars 1, q. 4, art. 6, p. 189.
 Jacobus Thomasius: Erotemata logica pro incipientibus, editio secunda, Lipsiae (Frommann) 1678, cap. 6, p. 13: "De Specie et Genere", and cap. 11 on substantia.
 G. Martano: Albero di Porfirio, in: Enciclopedia filosofica (Centro di studi filosofici di Gallarate), I, Firenze 1982, 149 sq.; Cajetan (cf. note 24***) p. 53, 67.
 Ramus' friend Talaeus commented on the Isagoge criticizing it's "confusio" and rejected the series of substances: Audomarus Talaeus, Dialecticae praelectiones in Porphyrium, edition used: Praelectiones in Ciceronem, Porphyrii Isagogen, et Aristotelis primum librum ethicorum, Francofurti (Wechel) 1583, 946-1001; esp. 970 n. 7, 1001.
 Johann Heinrich Alsted: Encyclopaedia, Herborn 1630, reprint Stuttgart-Bad Cannstatt 1989, vol. 2: tom. 3, metaph. pars. 2, cap. 2, p. 621 sq.
 This classification is rejected by Franciscus Suarez, Disp. metaph. 33, sect. 1, 12.
 Alsted, ibid.: "Praedicamentum in specie exhibet divisionem entis in substantiam et accidens. (...) Substantia est ens per se subsistens. Ejus divisio petitur e diversis tum gradibus tum rebus."
 Eustachius a S. Paulo: Ocist: Summa philosophiae, Paris 1609; I quote from the edition Coloniae (Zetzner) 1616.
 E. Gilson: Index scholastico-cartésien (1. ed. 1913), Paris 1966. But note recent studies on the subject such as: Marjorie Grene: Descartes among the Scholastics, Milwaukee 1991; Roger Ariew: Descartes and Scholasticism: the Intellectual Background to Descartes' Thought, in: Cambridge Companion to Descartes, ed. John Cottingham, Cambridge 1992, 58-90; André Robinet: Aux sources de l'esprit cartésien, Paris 1996, 182-184. Cf. Blum: Philosophenphilosophie, chapt. 2.1.
 However, Cornaeus spent some time of his career as a professor of philosophy in Toulouse.
 Eustachius: Dialect. pars 1, tr. 3, disp. 1, q. 1, p. 52.
 Eustachius, p. 52 sq.: "Porro series directa duplici ratione constituitur: Altera per synthesim seu compositionem ascendendo, altera per analysim descendendo."
 Cf. Cajetan (cf. note 24***) p. 53: "descendere autem per media dividentes".
 Eustachius' text book is different from the other scholastics also in that he almost never quotes his sources when discussing contrasting opinions.
 Eustachius: Metaphysics, pars 1, disp. 1, q. 3, p. 8: "Formalis conceptus entis est re unus in unoquoque intellectu concipiente. Probatur, quia notitia quam efformat intellectus, audito nomine entis, est una numero similitudo actualis in ipso intellectu residens." The usage of metaphysical as opposed to physical or real is present in Franciscus Suárez, Disp. metaph. 33, sect. 1, 13 on substantia incompleta: "hujusmodi subsantiam metaphysice seu potius logice esse completam"; and on the distinction between completa and incompleta, 24, p. 337: "aliter enim est de illa loquendum, si membra sumantur secundum metaphysicam considerationem, aliter vero si sumantur secundum physicas realitates."
 René Descartes: Regulae ad directionem ingenii, reg. 6, AT 10, p. 381: "res omnes per quasdam series posse disponi, non quidem inquantum ad aliquod genus entis referuntur, sicut illas Philosophi in categorias suas diviserunt, sed inquantum unae ex alijs cognosci possunt."
 René Descartes: Recherche de la verité, AT 10, p. 516. Gervasius Brisacensis (cf. note 48***), much later, said: "[linea Praedicamentalis] inde juvantur Philosophi ad construendas definitiones: Cum enim hae fieri debeant ex Genere et Differentia, et quidem ex genere proximo (...) inservit haec tabula etiam ad inveniendum genus proximum (...)."
 Ibid. p. 517: "cum me hominem esse (...) dixi (...) de ijs, quae vel omnium simplicissimus hominum, aeque et maximus (...) Philosophus, scit, locutus sum."
 Descartes: Principia Philosophiae, I 51, AT p. 24.
 Antoine Arnauld and Pierre Nicole: La Logique ou l'Art de Penser, Paris 1662; quoted edition: ed. Pierre Clair and Fran‡ois Girbal, Paris (Vrin) 1993.
 Michael Angelus Fardella: Universae philosophiae systema, Venetiis 1691, I 172 sq.; according to: Wilhelm Risse: Die Logik der Neuzeit, 2: 1640-1780, Stuttgart-Bad Cannstatt 1970, 124.
 It should be noted that Eustachius was acquainted with Bérulle: F. Ferrier: Eustache de Saint-Paul, in: Encyclopédie philosophique universelle, III: Les Oeuveres philosophiques, Paris (PUF) 1992, 1132; Roger Ariew, Eustache de Saint-Paul, in: Dictionnaire des philosophes, Paris (PUF) 1993, 967 sq. Hence a mutual influence between the Cartesians and the Cistersian deserves further research.
 Reproduced in Frances A. Yates: The Art of Memory, London (Routledge) 1972, 180.
 Edmundus Purchotius: Institutio philosophica ad faciliorem ac recentiorem philosophorum lectionem comparata, Paris (J. B. Coignard) 1695, 5 vols; edition quoted: Patavii (Manfr‚) 1737. On Purchotius see: Risse (cf. note 68***) 126-129, and Paul Richard Blum: Pourchot, Edmund, in: Foisneau, Luc (ed.), The Dictionary of Seventeenth-Century French Philosophers. London: Thoemmes Continuum, 2008, 1029-1031.
 An Augustinian Canon even identified "Res=Natura=Essentia=Substantia", see Plate 9 from Werner (cf. note 15***), III, p. 641, taken from: Julius Franciscus Gusmann: Dissertationes philosophicae, quibus philosophia rationalis et naturalis (...) illustratur (...), Graz 1755 sqq.
 Gallus Cartier OSB: Philosophia eclectica, Augustae Vind. et Wirceburgi (Adam et Veith) 1756; Logica p. 34, tabula 2. This was a text book for the Benedictine abbey of Ettenheimmünster (Breisgau, Germany).
 Donatus a Transfiguratione Domini Opiar: Introductio in universam philosophiam (...), Rastadii (Scheel) 1751 (this edition quoted, first ed. 1748), Table in I, after p. 141.
 Bertholdus Hauser: Elementa philosophiae Ad rationis Et experientiae ductum conscripta, I, Augustae Vind. et Oeniponti (Wolff) 1755, tables in the annex. On Hauser see Barbara Bauer: Experimentalphysik und Theologie. Die Embleme im mathematisch-physikalischen Museum zu Dillingen und die Physik des P. Berthold Hauser SJ, in: Scientia Poetica. Jahrbuch für Geschichte der Literatur und Wissenschaften 5 (2001) 35-89.
 Hauser mentions that this tree has been designed by a certain "P. Laurens" (p. 53).
 Albertus Magnus, De praedicabilibus, tr. 4, c. 3, p. 65: "Sequitur enim, si homo est, animal est: et si animal est, corpus animatum sive vivum est: si vivum est, corpus est, et si corpus est, substantia est, propter intellectum generis in specie. Sed non sequitur, si substantia est, ens est: quia sive sit aliquod, sive non, semper genus sequitur ad speciei positionem."
 De ente et essentia, c. 5, p. 14 sq.