The Utility of the Tree of Porphyry

The disciple of logic has undergone a tremendous amount of change over time, including differences in how logicians view the goal of the disciple and also how they view the nature of syllogisms. For example, Frege’s conception of logic’s implications is very different from how Aristotle viewed it. Both philosophers knew that logic was related to metaphysics, but Frege thought that logic, at least in practice, was ontological prior to metaphysics and so logical truths had direct impacts on metaphysical truths, as can be seen in his conception of existence (Novotny and Novák 47). Aristotle, however, always viewed metaphysics as “first philosophy” and so, under his view, logic does not wield the same ontological power over metaphysics as Frege thought (Shields 1). Despite these vast differences, Aristotle’s system of logic has had an incredible amount of influence over all logic in the Western world that succeeded him, there are many definitions in his logic that seem odd to analytic logicians. For example, the term “doubt” within Aristotelian logic is given the definition of “a proposition … which … contains within itself both an affirmation and a negation,” by Cicero (Boethius In Ciceronis Topica 30). Or, the term “reason” is given the definition of an act of the intellect which can “produce a belief,” also by Cicero (Boethius In Ciceronis Topica 29).

One of the most important parts of Aristotelian logic which can confound contemporary philosophical minds is division, which deals with how concepts are broken down into smaller ones. Luckily, there is a common diagram that the medievals used to illustrate division and it is called the “tree of porphyry” (Michael O.P. 1). Here is an example of it: (Cohen 1)

This essay will be an exploration of the tree of porphyry and its role in logic and philosophical study more generally. It will begin by providing background context of how Boethius broaches the subject of the tree of porphyry in his Second Commentary on Porphyry’s Isagoge. It will then explore the purpose, usefulness, and limitations of the tree as a philosophical tool, in that order. This essay will argue that the fundamental purpose of the tree is to show how concepts are related to one another, the tree is useful insofar as it makes clear the hierarchy of being in Aristotle's philosophy, but it is limited in that it only applies to an Aristotelian metaphysics.

Before Boethius discusses the tree of porphyry, he provides a background context about logic in order to provide a better understanding of the tree when he ultimately explicates it. The first matter he discusses is his translation of Porphyry and explaining how it provides an accurate account of the human soul. He then speaks on the fact that:

Since the activity of the human soul is such that it is always occupied in the comprehension of present things, or in the understanding of absent things, or in the investigation and discovery of unknown things, there are two problems in which the power of the reasoning soul extends all its care: one, that it know the natures of things by a sure method of inquiry, and the other, that that which moral gravity may later perform, may come to be known beforehand. (Boethius Second Commentary on Porphyry’s Isagoge 72-73)

He then discusses whether philosophy “is absolutely a definite part of philosophy or … an apparatus or instrument by which philosophy seizes on the knowledge and nature of things” (Boethius Second Commentary on Porphyry’s Isagoge 75). Once he answers this question, he moves to a discussion of Aristotle’s Categories, which leads into his discussion of the tree of porphyry.

With this context in place, the purpose of the tree, which is to visually display how the relationship between different Aristotelian categories, will now be examined. There are many categories within Aristotelian philosophy, but the most important ones are genus, differentia, and species and they are conceptually ordered from highest to lowest. Boethius explains these categories and their hierarchical order in depth:

In each type of predication there are some most general items and again other most special items; and there are other items between the most general and the most special. Most general is that above which there will be no other superordinate genus; most special, that after which there will be no other subordinate species; and between the most general and the most special are other items which are at the same time both genera and species … . What I mean should become clear in the case of a single type of predication. Substance is itself a genus. Under it is body, and under body animate body, under which is animal; under animal is rational animal, under which is man; and under man are Socrates and Plato and particular men. Of these items, substance is the most general and is only a genus, while man is the most special and is only a species. Body is a species of substance and a genus of animate body. Animate body is a species of body and a genus of animal. Again, animal is a species of animate body and a genus of rational animal. Rational animal is a species of animal and a genus of man. Man is a species of rational animal, but not a genus of particular men - only a species. (Boethius Second Commentary on the Isagoge 205)

Boethius beautifully illustrates the relationship and hierarchy between different concepts in the Aristotelian framework in this passage. However, one thing that could be helpful in this passage would be a diagram which visibly displays the relationship between these concepts because it is clear that the relationships between genus, differentia, and species could be portrayed in a vertical diagram. This is the issue which the tree of porphyry is supposed to address as it shows the relationship between genus, differentia, and species in this vertical format and so is its purpose.

Indeed, the tree of porphyry is very useful as a way to see how concepts are related to one another within an Aristotelian framework. The purpose of the tree is to effectively and clearly communicate how genus, differentia, and species relate to one another, and it accomplishes this very well. It accomplishes this goal so well that Beothius himself acknowledged this fact: “great” is “the utility of this book in regard to the categories” (Boethius Second Commentary on Porphyry’s Isagoge 84). Here is an example of the tree of porphyry:(Michael O.P. 1)

“This illustration” clearly “explains how Aristotle’s ‘Categories’ are divided from the ‘genus most general’ down through all subalternate genera and species, down to the ‘species most special’ and individuals” (Michael O.P. 1). This is a particularly high quality tree because there are two lines at each level which connect to the next level of concepts, displaying how the lower levels are syntheses of the higher ones. Moreover, the tree does an excellent job of visualizing how differentia are conceptually derivative of genuses, and also how species are conceptually derivative of differentia. Furthermore, it displays, very apparently, how the lower level concepts are conceptually, although not actually, present in the higher level concepts, thus visually representing Aristotle’s notion of a great chain or hierarchy of being, which is intrinsic to his categorical analysis of being. So, the tree of porphyry is a very useful philosophical tool because it visually communicates how genus, differential, and species relate to each other, thereby communicating the hierarchy of being in Aristotelian metaphysics.

However, the main drawback of the tree of porphyry is also its biggest strength, which is that it is limited to an Aristotelian framework and has trouble being applied to other philosophical theories. This almost goes without saying, but it is a point that makes the tree of porphyry difficult to accept for many contemporary analytic philosophers. The tree of porphyry only functions within an Aristotelian metaphysics framework because the tree was developed in order to account for the Aristotelian categories of genus, differential, and species and how they relate to each other. Thus, it is very difficult to apply the tree of porphyry to other metaphysical views since it was not designed for these views. Indeed, this fact is most actually felt when one attempts to apply the tree to analytic metaphysics, at least that metaphysics which figures like Frege, Russell, and Quine contributed towards because their views of modality are synchronic, rather than diachronic. Within the tree is an implicit diachronic view of modality, even if medieval thinkers did not write about this topic, because possibilities derive their being from that which is already actual. This is represented in the tree in the fact that species are derivative of genesis and differential, at least conceptually. Moreover, this correlates to a contemporary analytic notion of modality, which is frequently called the Aristotelian account of modality because it holds that possibilities derive their being from that which is actual. Nevertheless, the synchronic views of early analytics would render the tree of porphyry utterly useless. However, this fact may not be such a strike against the philosophical legitimacy of the tree as more and more analytic philosophers return to Aristotelian ideas, particularly in metaphysics. So, while the tree of porphyry does not fit into a framework that is not Aristotelian, the fact that an increasing number of analytic philosophers identify themselves as Aristotelian metaphysicians ensures that the tree of porphyry is still a relevant philosophical tool.

In conclusion, the tree of porphyry is a very important philosophical tool to understand in order to understand Aristotelian and later Medieval metaphysics. Within Boethius’s Second Commentary on Porphyry’s Isagoge, the purpose of the tree is to show how concepts are related to one another within an Aristotelian framework. This means that he shows how species are conceptually derivative of differentia, with differentia being further derivative of genuses. The usefulness of the tree of porphyry is found in the fact that it accomplishes its purpose very effectively as it communicates both how distinct concepts are related to each other, but also how certain concepts are prior to, or more fundamental than, others. Moreover, the Aristotelian chain and hierarchy of being is very clearly displayed by the tree. The primary limitation of the tree is the fact that it is hard to apply it to other philosophical frameworks, which can make it difficult for contemporary analytic philosophers to use the tree of porphyry because it will require them to, in some way, affirm Aristotelian metaphysics. However, this limitation is not so troublesome when one realizes how well-liked Aristotle’s metaphysics is in contemporary analytic philosophy and that many popular positions today, such as an Aristotlian account of modality, could be more easily understood with the tree in place. It is interesting to see how a philosophical tool which is so old can still be useful today, not only for understanding the history of philosophy, but also for pursuing the truth in philosophy and the tree of porphyry is one such tool.

Works Cited

Boethius. “Book 1.” Boethius’s In Ciceronis Topica, translated by Eleonore Stump, Cornell University Press, Ithaca, NY, 1988, pp. 25–36.

Boethius, and Richard McKeon. “Second Commentary on Porphyry’s Isagoge, Book 1.” Selections from the Medieval Philosophers, vol. 1, Charles Scribner’s Sons, London, UK, 1930, pp. 70–99.

Boethius. Second Commentary on the Isagoge. Translated by Samuel Brandt, Corpus Scriptorum Ecclesiasticorum Latinorum (CSEL), 1906.

Cohen, S. Marc. “Definitions and the Tree of Porphyry.” Definitions and the Tree of Porphyry, 2015, faculty.washington.edu/smcohen/433/PorphyryTree.html.

Michael O.P., William C. “The Porphyrian Tree or Tree of Porphyry.” Classical Liberal Arts Academy, 14 Jan. 2022, classicalliberalarts.com/classical-trivium/classical-logic/the-porphyrian-tree-or-tree-of-porphyry/.

Novotny, Daniel, and Lukáš Novák. Neo-Aristotelian Perspectives in Metaphysics. Routledge, Taylor & Francis Group, 2016. 

Shields, Christopher. “Aristotle.” Stanford Encyclopedia of Philosophy, Stanford University, 25 Aug. 2020, plato.stanford.edu/entries/aristotle/.