VIRTUES OF GEOMETRY

The Ethics

Baruch Spinoza's "The Ethics", can be found in PDF form in any number of internet locations, none of which provide the document with a TOC beyond "Part I, Part2...etc." This iteration, however, has been carefully constructed with an active table of contents organized by Spinoza's "Propositions", with each TOC entry composed of the first sentence of the said proposition, allowing the reader to jump directly to that section. Spinoza's Definitions, Axioms, Postulates, etc. are also included under each Part heading.

in Charles Ramond and Jack Stetter (eds.), Spinoza in 21st-Century French and American Philosophy. Bloomsbury, 2019

The two manuscripts of the Korte Verhandeling that were discovered in the mid-nineteenth century contain two appendices. These appendices are even more enigmatic than the KV itself, and it is the first appendix that is the subject of this study. Unfortunately, there are very few studies of this text, and its precise nature seems to be still in question after more than a century and a half of scholarship. It is commonly assumed that the appendices were written after the body of the KV and I am not going to challenge this assumption. The first appendix is written in a geometric manner, and it contains seven axioms and four propositions. Strikingly, it does not include any definitions. This is in sharp contrast with Spinoza's Ethics and his 1663 book on Descartes' Principles of Philosophy, which are similarly written in a geometric manner but include both definitions and axioms. One could perhaps suspect that the text we currently have is merely a fragment from a more extensive work which included definitions. In my paper, I will show that this is not the case, and that the first appendix belongs to a genuine work of Spinoza that never contained definitions. I would further argue that the first appendix is most probably the earliest draft we currently have of Spinoza's magnum opus, the Ethics, but we have a long way to go before we reach that conclusion. I will conclude with a very brief discussion of the value of axiomatization in metaphilosophy.

The extensive parallels and affinities between Spinoza's philosophy and the philosophy of Platonism include, along with central characteristics of Spinoza's metaphysics and theory of knowledge, decisive aspects of the geometric method. Spinoza's presentation of the highest principle and source of being and knowledge, the substantia infinita, his arguments for its singularity, existence, infinity, eternity, causality, transcendence and immanence, its relationship to the attributes and finite modes, in particular to human beings, echoes essential features of Platonic and Platonist philosophy. His understanding of the paradoxical unity of freedom and necessity in the highest principle, and the aim of their reconciliation in the finite intellect by means of the ascent of cognition, culminating in scientia intuitiva and the intellectual love of God, is clearly prefigured in Plotinus and his model Plato, as well as in Renaissance Platonists such as Marsilio Ficino, Leone Ebreo and Abraham Cohen Herrera, the latter two of which may be shown to have directly influenced Spinoza's thought. Herrera anticipates Spinoza's critique of Jewish scriptural interpretation in Theological-political Treatise in attempting to provide rational illumination of the the Law, Prophets, Torah, Talmud, Mishnah and kabbalah or mystical tradition, and to reconcile their content with non-Jewish and philosophical tradition, taking as his primary topic "God the almighty First Cause, Creator and Sustainer of all things, 'Ein-Sof the Infinite, utterly perfect and elevated above every other existing thing." The same emphasis may be found in Spinoza's elaboration of the substantia infinita in the Ethics. Spinoza's division of the Ethics, comprising Part I, De Deo, Part II-IV, on the genesis of mind and derivation of its affects, and Part V, the ethics proper, dealing with the ultimate achievement of freedom, corresponds to Herrera's division of his interpretation of the Lurianic kabbalah in Gate of Heaven, according to the Neoplatonic system of hypostases, into consideration of the transcendent cause, principle and source of being, its procession (Hebrew hitpaštut) and reversion (Heb. histalqut). Like Spinoza, Herrera chooses "an expository style that, despite its difficulty for modern readers, was associated in his time with dialectical argumentation." As with Herrera, Spinoza's choice of the ordo geometrica is best understood within the context of a Platonic and Platonist understanding of dialectic. It is a method whose aim is not merely formalistic or epistemological, but comprises a type of spiritual exercise, leading us on the ascent by means of levels of knowledge originally defined by Plato's Analogy of the Line, whose end is realisation of the virtue proper to human beings. Spinoza's depiction of the levels of knowledge, their objects, and role in the attainment of true knowledge and unity with the source of being consistently reflects the characteristic epistemology of the Platonist tradition from Plato to Cusanus. His application of a method of hypothetical dialectic has its paradigm, ultimately, in Plato's conception of dialektike tehne as the method of philosophy, developed by later Platonist philosophers, in particular Proclus, and transmitted through Renaissance Platonists like Abraham Cohen Herrera. Taking as interpretative model the σχῆμα τριαδικόν, which is not of merely "formal significance, but a constitutive element of the movement of thought and of every being..." (Beierwaltes, Proklos 24), and its role in Proclus' "metaphysical method", the specific subordinative and hierarchical interrelationships of Spinoza's own trias of substantia infinita, extensio and cogitatio are thrown into relief. Much may yet be gained as regards a better understanding of Spinoza's geometric method by comparison with the method of hypothetical dialectic as developed by Proclus in his Elementatio theologica and in a more specialized form by Abraham Cohen Herrera. The "metaphysically structured method" of Proclus, based on a corresponding understanding of "system, " could be equally well applied to interpretation of Spinoza's system and method. Here, "system" is understood not as "schematic classification of thoughts", but as grounding in the One (substantia infinita), origin and end of the path of thought, which precedes and is present in each level of knowledge as its "initiating moment" and "all-pervading principle." This path follows according to the scheme of mone- proodos-epistrophe the procession of being from its source, the evolution of multiplicity and totality of its individual expression, and its turning back towards and reflection upon itself. "System" is thus an expression of the desire and intention of thought "to advance from what is grounded to the ground." The union of method and substance in the geometrical method does not however imply their simple identity in an idealistic or Hegelian sense. Thought proceeds methodically only when it receives its measure from the being of the thing, and insofar proceeds necessarily as relational unity, "correspondence of the meaning of thought and the existing thing." (Beierwaltes). This paper will explore prospects for a more complete understanding of Spinoza's geometric method by comparison of key concepts of dialectic such as hypothesis, axiom and postulate in Proclus and Spinoza and their role in a metaphysically grounded method.

Journal of Undergraduate Mathematics at Puget Sound, 2009

Ever since Euclid first laid out his geometry in the Elements, his axiomatic approach to geometry has been widely praised and admired. For centuries geometry was considered the only sure and certain “science,” for precisely the reason that the axiomatic method used to prove its propositions seemed so irrefutable in its logic. However, geometry is not the only area in which the axiomatic method first developed by Euclid has been put to use. One of the most noteworthy examples of an employment of the axiomatic method far outside the reaches of pure geometry comes in Baruch Spinoza’s famous work: the Ethics. While much of the Ethics is concerned with, as the title might suggest, normative claims about the proper form of human behavior, Part One “On God,” especially, purports to prove a number of very interesting assertions. Spinoza begins this section with a set of eight definitions and seven axioms (he leaves none of his terms undefined).

Essays on Spinoza's Ethical Theory, 2014

"Essays on Spinoza's Ethical Theory" is a collection of original essays by leading scholars in the field today. These essays address a wide range of issues concerning Spinoza's ethical theory and, in doing so, deepen our understanding of this relatively neglected but richly rewarding facet of his system. Given its importance to his philosophical ambitions, it is surprising that his ethics has, until recently, received relatively little scholarly attention. Anglophone philosophy has tended to focus on Spinoza’s contribution to metaphysics and epistemology, while philosophy on the continent has tended to show greater interest in his political philosophy. This tendency is problematic not only because it overlooks a central part of Spinoza’s project, but also because it threatens to present a distorted picture of his philosophy. Moreover, Spinoza’s ethics, like other branches of his philosophy, is complex, difficult, and, at times, paradoxical. The essays in this volume advance our understanding of his ethics and also help us to appreciate his ethics as the centerpiece of his system. In addition to resolving interpretive difficulties and longstanding debates, these essays point the direction for future research. Spinoza’s enduring contribution to the development of ethical theory and to early modern philosophy—and to early modern history generally—provide us with good reason to follow the lead of these essays.

2015

2017

Mind, 2005

1991

There are very few studies devoted specifically to the ethical teaching of Spinoza's Ethics. Instead, commentaters have focussed their attention mainly on the metaphysical and epistemological doctrines found chiefly in Parts I and II. Nevertheless, ethics was Spinoza's primary concern and the metaphysical and epistemological doctrines were intended by him to support and culminate in a practical doctrine of the best way of life. Despite its title, however, the Ethics is silent about what Spinoza means by ethics; indeed, nowhere in this work does he define or explain what ethics is. With this in mind, my chief objective will be to determine what Spinoza himself means by ethics and the significance of this for an understanding of both his ethics and his philosophy as a whole.