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Understanding the Geometric Method: Hypothetical dialectic in Proclus, Abraham Cohen Herrera and Baruch d. Spinoza

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.

Geometric method; dialectic; metaphysics; epistemology; virtue; hypothesis; axiom; postulate; Euclid

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