Within the pages of his masterwork, Ethica, Spinoza drawed the outlines of his philosophical and theological conceptions. Since God was located in the core of his system of thinking, he played a central function both in the case of his metaphysical interpretation of the world and in the case of his understanding of the Christian God. Moreover, we can say that Spinoza failed to develop a classical theological conception, since his entire system of thinking was subordinated to the chief idea of explaining the reality using logical arguments exposed in a geometrical manner. Consequently, what resulted from his thoughts was a metaphysical doctrine and not the reiteration of a religious dogma. Taking in account the aforementioned conditions, I can say that his system was more akin with the onto-theology of Hegel than with the theosophy of Thoma D’Aquino, for example.
Ontologically speaking, Spinoza conceived God as being the only substance, while cosmologically God was understood as the everlasting and the all-encompassing cause of the world - the immanent cause -. Considering the philosophy of Spinoza after the number of the substances which were asserted as existing, his system was a monistic one. Also, analysing his philosophy using the criterion of the relation between God and the nature, his system was either pantheist, either panentheist. Was pantheist as far as it stated the perfect identity between the nature and God, and was panentheist as far as it enunciated that God possesses attributes which do not characterize the physical world, but which are compatible with his own nature, the attributes which correspond to the so-called transcendence of God (or at least to his epistemological transcendence).
In the first part of Ethica - which is otherwise entirely dedicated to the purpose of exposing his metaphysics - Spinoza confines theoretically the concept of substance. A substance is conceived as being something whose existence isn’t determined by something different by itself, or in other words a substance is a thing which 1) exist and 2) has the ability to deliver itself by itself to the existence: a substance have to be causa sui. The ontological autonomy of the substance constitutes, in the same time, its defining characteristic because a substance can be asserted as existing only and only if it is the reason of his existence, as it follows from Def. 1.
Also, a substance can be conceived only per se, that means that it cann’t be predicate - as an attribute - about another substance, as it results from Def. 3.
The attributes are defined as being the essences of a substance, more precisely, the attributes are essential properties of substance, as it follows from Def. 4. I can even say that prima facie the attributes are coextensive with the substance itself, namely, if the substance is infinite - and the substance must be infinite if we want to be objective analyzing the Spinozist metaphysics - then any of its considered attributes will be infinite as well. Still, the substance is far more complex than a single individual attribute, and the identity between substance and any of its defining attributes doesn’t confine the substance to the modally limited description provided by one particular attribute of it. In other words, I am tempted to subscribe to the belief expressed by Della Rocca regarding the relation between the substance and its attributes. That means that I agree with the explanation which pretends that the (only) cosmic substance has an indefinite quantity of attributes (essences, properties, propria), all of them being different from the substance itself, and each of them depicting the substance from a specific perspective, based on a given referentially opaque context.
Therefore, I state that the polyvalent nature of the substance - which make it descriptive by differite attributes - can be alternatively defined by each of them, as long as they satisfy the condition of coextensivity with their definiendum. For example, I don’t think that the attribute of extension may constitute one of the alternative descriptions of the substance (considered under the determination of extensivity) and, implicitly, that it may be conceived logically as one of its definiendo if we define extension as being a convergent series of geometrical elements (as vertices, edges, faces), namely, a definite volume, and not as being a divergent series of geometrical elements.
In other words, if we understand through ‘God’s extension’ a finite quantity of space or of occupied space, this word will fail to denote successfully the substance. Similarly, if we understand through ‘God’s thought’ a definite quantity of cogitationes or noemata, then the attribute of thought wouldn’t be able to describe properly its corresponding notional shade belonging to the concept of substance.
For a better illustration of the logical relations between attributes and the substance, I think that the notion of substance can be compared either with the divergent series of real numbers or with the divergent series of natural numbers, either with an heuristic polytope, having an infinite number of vertices, edges and faces.
In the case of any infinite series of numbers we will always have subordinate series, which are at their turn infinite. For example, the infinite series of natural numbers can be decomposed to the series of odd numbers and the series of even numbers, both of them being infinite. A special relation it is that one between the real numbers - the so-called numbers of the continuum - and any other infinite series of numbers because, alike the natural numbers in their specific relation with even and odd numbers, the series of real numbers includes all other series of numbers, for example, it comprises the series of natural numbers but, more than that, it even has a higher cardinality than this series.
In consequence, we can understand the interplay between substance and its attributes either in a pantheist way, as an immanent or coextensive relation of the attributes x,y...z with the substance Z, where x,y...z render different properties of Z, and the total amount of attributes defines exhaustively the substance; either in a panentheistic way, where attributes v,w,x describe the substance Z putting in light different features of it, but they perform this in an incomplete manner - the sum of the attributes doesn’t define exhaustively the substance, but they still succeed to confine it from certain perspectives. Though, an indefinite quantity of substantial features remains unspecified. Moreover, if I would use my analogy between the real numbers and any other series of numbers, I would say that any complete power-set of Z (where Z stands for the series of real numbers) is bigger than the sum of the atributtes v,w,z (where this subset can denote even an entire series of numbers, like that one of integers), but this consequence would place me in a totally different context than that one of Spinoza’s metaphysics, a context which would be more ideologically related to Hartshorne’s panentheism since it would imply that some of God’s attributes are relative perfections (and, consequently, they can be improved, at least the attribute of thought can increase its perfection, as it follows from Hartshorne’s doctrine), while other attributes represent absolute perfections: any subset of real numbers.
But if the ordered set of natural numbers stands for the attribute of extension, then any well-defined and complete subset of power-set Z - Z denoting the real numbers - which is ‘located’ between any two natural numbers will interfere with the set of natural numbers. This would be the same with saying that there are infinite attributes which can define substance in the base of its non-extensive properties (as thought), and some of them are ‘more infinite’ than extension (as love), but still the attribute of love may, somehow, interfere with extension or with any other attribute, all the substantial attributes being virtually contained in the attribute of love.
The conclusion isn’t though extremely inconsistent, reminding us that there have to be an area of intersection between res cogitans and res extensa, between mind and body Though, the main problem related to Spinoza is that he doesn’t allow any kind of interaction between minds and bodies, as it results from Def. 2, and this was made clear even in an extremely comprehensive manner because Spinoza writes there about the reports between the finite modes pertaining exclusively to the same substantial attribute. Still, I think that we can conceive this hypotethical ‘more perfect’ attribute as being divine love, which may pervade both the baryonic and the noetic matter. But I am afraid that all this is more a mathematical consequence, than an ontological one, therefore Cantor’s theorems don’t solve the main issues raised by Spinoza’s philosophy .
Of course, Bennett, in Study of Spinoza’s Ethics (pp.145-147), introduced as well a third term in the ecuation of the attributes, but the ontological implications were quite different. Basically, Bennett denied to the thought and extension their status-quo of attributes or essences, saying that exist a trans-attributive mode that connects simultaneously our bodies with our minds. More exactly, Bennett assumes that attributes aren’t essences of substance, but that the ‘intellect perceives [them] as constituting the essence of substance’. Therefore, all we thought that we knew as being fundamental properties of the substance, i.e, as thought and extension, are in fact just ‘necessary and sufficient conditions of existence’ and only the so-called system of trans-attributive differentiae, combining the trans-attributive mode with a given attribute, generates the knowledge of the external world.
I am not convinced at all by this alternative explanation of the nature of the attributes and of their specific relation with the substance, and I would prefer to think that the attributes really render the essence of the substance, even if they are not just many, but they are really an infinity, and I believe that the point of view of Della Rocca is more realistic in this matter, while Bennett just tried to shape the entire ontology of Spinoza so as to be compatible to his interpretation inspired by string theory: ‘Now, according to my ‘mode identity’ interpretation, there is a good sense in which the most basic properties of the one substance are not the attributes, but the modes, since they lie deep enough to combine with both attributes.’
The modes are described as being modifications of the substance, as it follows from Definitio 5.
Furthermore, at Def. 6, Spinoza presents God as representing a being absolutely infinite. Spinoza understands this ‘perfect infinity’ as a compositum made of an infinity of attributes, each of these attributes expressing an eternal and infinite essence. The substance is characterized as absolutely free, and determined by its own intrinsec necessity. The substance represents the necessary existence because its essence involves its existence. In consequence, all its actions and its very existence are originated in itself, the substance being causa sui, as it follows from Def. 7. Conversely, the created things are defined as having an external necessity, the reason of their existence being God, and not themselves. They represent the domain of creation, the so-called natura naturata, in opposition with natura naturans, which is the substance considered in its quality of cause.
Definitio 8 is the topos where is emphasized the eternity of the substance, the (spatio-)temporal infinity being one of the infinite attributes and which is specified about substance in Definitio 6. Still, especially because I would like to think in accordance with the modern cosmological conceptions, I believe that spatial infinity or extension and, respectively, eternity or temporal infinity compose just one divine determination (proprium, essence, etc) which can be labeled ‘spacetime extension’ or in the spirit of Whitehead, ‘extensive continuum’, even if the latter expression doesn’t use explicitly the word ‘time’, which is presupposed instead tacitly. We know that, according to the modern views of science, will be hilarious to conceive space and time as being separate entities, and, consequently, that any duration needs a spatial frame where to be counted and where to be produced via changes of the material bodies placed in that space. Anyway, it seems that neither Spinoza didn’t have a problem with the ontological status of eternity, and he didn’t expose Aeternitas as a possible third attribute of God. Why? Maybe because was counter-intuitive to conceive an eventless nature, since everything, every res vera, must have a (physical) extension to be subjected even to the most static permanence.
Anyway, Spinoza distinguishes between sempiternity (or everlastingness, in aeternum) and eternity (or aeternitas), but he do not mention anything about aeviternitate. The first dichotomy allows him to separate one more time natura naturans by natura naturata, the complete or bidirectional temporal infinity (eternity) belonging just to the universal substance, which, being uncausal and indestructible, doesn’t have beginning or end, while the finite modes which make the existence could be in the best case everlasting, but they will never be eternal since was a moment when they didn’t exist.
The concept of aeviternitate, in spite of the fact that wasn’t used nominally by Spinoza within the logical articulations of his system, I think that would had been an extremely adequate theoretical way of expressing the relation between the substance and its modes, since this philosophical approach of the notion of time suggests that all the cosmic events have a matrix, where they are contained like Hesperian butterflies within the encompassing matter of a nugget of amber. I think that the concept of aeviternitate gives us something like an a posteriori image of the eternity, and has only a theoretical and eschatological reality.
As I stated before, God or the only cosmic substance it is the immanent cause of the world. The substance, thus understood, it is an eternal (macro-)cosmic process, defined - as several definite descriptions (or denotative phrases, in the terminology of Russell) describe a very complex reference - by a (potential) infinite number of attributes. All these attributes, from which just two of them, thought and extension, are known by humans, have an infinite quantity of finite modes. Therefore, the attribute of extension will have an infinite number of finite modes of extension, namely, physical bodies, the attribute of thought will possess an infinite quantity of finite modes of thought, namely, the ideas, and so on.
The finite modes are generating each other, that meaning that the organic system of the world maintains itself almost mechanically, being given the self-caused and autonomous nature of the one substance, as it follows from Propositio 28: ‘[...] everything which is finite [...] cannot exist or be conditioned to act, unless it be conditioned for existence and action by a cause other than itself, which also is finite, [...] and likewise this cause cannot in its turn exist [...] unless it be conditioned for existence and action by another cause, which also is finite [...].
The Spinozist metaphysics depicts a kosmos composed by a complete and mathematically in(de)finite series of functional and structural properties, the attributes, and by an infinite number of subsequent finite substantial alterations, the modes. Still, prior to the finite modes, we have the infinite modes. The infinite modes are, at their turn, immediate or direct, and mediate or indirect. The infinite immediate modes stand for extremely general and creative constituents of the world, like the infinite divine intellect, in the case of the attribute of thought, or the physical energy (more literally, the kinetic energy, the energy of the different degrees of motion), in the case of the attribute of extension. The infinite mediate modes designate general, but static and essentially non-productive components of the attributes, like the physical structure of the world as an infinite extensive container, in the case of the attribute of extension, - this would mean the fabric of spacetime considered by itself, which of course that constitutes a logical abstraction, especially because the system of Spinoza can be suspected by many things (as pantheism, panentheism), but it can not be suspected by pandeism because his world is subjected to a continuous process, and, consequently, an abstract and perfectly empty structure, non-superposed by any cosmic substantial event, wouldn’t have a concrete correspondent. God wouldn’t ever cease to be divine, and hence creative.
I would like to insist on Spinozist conception about finite modes, because I have the feeling that this part of his metaphysics represent the key for understanding the entire intellectual projection.
The finite modes, and in particular de finite modes of extension, are important because they constitute the physical world as he know it and as we perceive it. The finite modes of thought aren’t available immediately in our current experience, or more precisely, is necessary to see the behaviour of a human population for being able to induce the existence of the finite modes of thought within the frames of our ordinary experience. But, since the human beings aren’t necessary, as it follows from metaphysics of Spinoza, neither are the aforementioned finite modes of thought. Of course, in a Kantian manner, we can assume the existence of an indefined quantity of ‘rational agents’, but as we all know, the introduction of this expression had only an epideictic function in respect to the categorical imperatives of Kantian moral philosophy, and even if the Kantian assertion would have a concrete correspondent, this wouldn’t impress to those hypotethical beings (aliens, angels) the character of (internal) necessity. The substantiality of a being is provided by his or its intellectual dimension, but by his or its extensive side. Therefore, I can state that the finite modes of thought don’t describe the most profound dynamics of the universe, as the finite modes of extension really can do it.
It is true that the things belonging to the same category of existence have the intrinsic tendency to reproduce each other, as the finite modes of extension do, conclusion which results from the already quoted Proposition 28. Of course that this natural law of causal identity between cause and effect can be applied to the mental processes as well, but at least for the moment, we don’t have any reason to infer that the mental processes are the ultimate physical interactions or that extension and thought are essentially undifferentiated, like in the case of Jung’s panpsychism.
It is true that the intuitive tendency - which is also the belief dictated by the common sense - is that the mental processes are superposed to corresponding physical processes, and that the mind is a function of the matter and the conscience is seen as an epi-phenomenon, but these wouldn’t change the logical priority of the finite modes of extension in understanding Spinoza’s metaphysics. If we will reduce the mind to be a determination of the extensive matter, and we will consider the thoughts as being a sort of subtle matter this wouldn’t modify the general theoretical landscape, but on the contrary, will make the comprehension of the finite modes of extension even more pregnant.
Then, I think that the finite modes of extension are paradigmatic for the intented-empirical concept of finite modes, qua modifications of the substance.
As Bennett said: ‘As for Spinoza’s thesis that all particulars - minds as well as bodies - are modes: I have to suppose that he started with a sound doctrine about the modal nature of extended particulars and then stretched it over mental ones as well on the strenght of a general thesis that the extended world is mirrored in detail by the mental world. [...] and it is indubitable that he did do most of his metaphysical thinking in terms of extension, and was willing to reapply his results to thought without working out the details’, I think that the priority of extension within the inferential frames of the demonstration offered by Spinoza was undeniable, and this becomes even more obvious if we admit that our daily experience gives us the hint that the physical facts - and not the mental ones - are the most elementary pieces of the puzzle called nature. In other words, the things behave as they were left alone, without being monitored by any thinking watcher and without exhibiting perceptible psychic features, i.e, a noetic field visible to everyone. Sure, quantum mechanics contradicts partially the indifference of things, but this doesn’t concern the present discussion.
One of the main issues faced by Spinoza’s metaphysics was the survival of his declared monism of one substance named nature or God upon the dynamical and manifold background constituted by the physical world. To enunciate formally the substantial identity between substance and all the particular phenomena represents only a theoretical or pretended monism, as all the philosophical, metaphysical and theological depictions of reality based on one substance were until Spinoza. But, in his specific case, the problem was that he effectively intended to justify his philosophical conception, reconciling it with the pre-existing Christian doctrine. Spinoza didn’t build shrines for those ones seduced by his arguments, he just necessitated to prove his metaphysical theory.
I think that one of the biggest novelties brought into the field of Spinoza’s exegesis consisted in the scientifical approach realised by Jonathan Bennett, which deserves to be quoted at least due to the courage of its author. He calls his interpretation ‘field metaphysic’. According with this understanding of Spinozist metaphysics, a motion of a body within the volume of the physical world is more like an alteration of the unique substance in which spatial regions have the property defined by us as ‘a body’. In consequence, all the cosmic processes are alterations, including the destruction or the creation of a thing, and everything is a change of a substantial state.
As Valtteri Viljanen wrote as well, in his article ‘Field metaphysic, power and individuation in Spinoza’, following the train of thoughts of the Dutch philosopher, the only way to understand Spinoza’s ontology and cosmology in a manner affected (or conciliated) by the modern science would be to accept that the only things which are changed - even divided or annihilated - are the modes of the substance, but not the substance itself, and accordingly, would be better to switch the notion of ‘an occupant of a space’ with that one of ‘a force or a wave’. Space, or more precisely the content of the space, or simpler, the extension, is understood as being one unified field of spatial power. The substantial power is thus conceived as a fundamental unity, which includes the finite modes in a real and conjunctive way, and not in an abstract and disjunctive manner, as are included the discrete and non-contiguous quantities (the numbers) into algebraic groups. Probably that the substantial power can be described as being a vectorial physical quantity. But, as notes Viljanen furthermore, the extension involves differences in power distribution in the spatial field, and consequently, the finite entities are made by differences of intensity or strenght of the spatial power. The duration of this differences of spatial power determines the lifespan of an extensive phenomenon.
As long as this approach is inspired by the modern physics, by quantum electrodynamics and superstring theory, more exactly, the explanation of the cosmic dynamics lies at the infra-atomic level (the level of strings) and therefore we cannot anymore make a difference between an artefact (like a chair) and a living organism when we are interpreting the reality in the proposed terms of extensive modes in their qualities of expressions of the ubiquitous spatial power. This theory implies that all the universal things, all the res verae, represents relative stable spatial patterns or transient modes of extension. Moreover, it seems that the metaphysical truth - which coincides with the physical one - is hidden at the unseen level of physical fields, and, as Gary Zukav said in his book ‘The dancing Wu Li masters’, ‘fields alone are the real substance of the universe, and not ‘matter’. Zukav sustains that the material particles are just the momentary manifestations of the interacting fields, and these interplays receive a material appearance because fields interact very abruptly.
But, returning to Bennett’s view, I would like to underline that he basically associates each object - finite mode of extension, res extensa - from Spinozist metaphysics ‘with a spatio-temporally continuos set of place-times, which I call a string of them’. Practically, Bennett defines the notion of motion (in spacetime) in terms of qualitative identity and difference. More precisely, if we have a string composed by some definite chronospatial coordinates, R₁ - T₁…. R n - T n, then ‘such that each R₁ is qualitatively unlike its spatial neighbours at T₁, and is qualitatively like the other regions on the string, then that string defines the trajectory of what we call an object in space [...]’.
But strings, as they were thought by Bennett, are temporary differentiated regions of the extensive continuum, which host dynamic objects or events - as they may be called according with process metaphysics -. Therefore, the strings of place-times are nothing more than patterns or configurations having a relative permanence whereon events occur. The strings are static, unlike the objects which are placed on their coordinates, the latter exhibit themselves as being constitutive to the strings. In conclusion, all the physical transformations which reveal the dynamic dimension of the nature take place at a deeper level of reality, while the exterior division of the world shows us only the objectual concrescences - with a certain degree of temporal continuity or even of everlastingness, as it is the case in some special situations - . In other words, what appears to be for the genuine experience of common people nothing more or less than a well-confined material being it is in fact the result of the intense interaction between fields of power, while the imagined irreducible and etimologically atomic and corpuscular components of reality are conditioned and shaped in their definite forms from deeper levels, which correspond to the diachronic and uniform movements of the different densities of substance from the infra-atomic layers.
What can be derived from this is that, in the words of Valtteri Viljanen as well as in those of Bennett, the only one substance hasn’t substantially distinct parts, but just different modes of extension. The substantial differences are only modal, and not real. The terminology chosen by Bennett isn’t random, since strings conceived by him, as an alternate explanation of Spinoza’s metaphysics, have similar properties with the homonymous theoretical concept from string theory and superstring theory. Namely, as in quantum physics each type of elementary particle is determined by a specific quantum state of the strings, analogously, according to the ‘field metaphysic’ developed by Bennett, each type of finite extensive mode is produced by a specific intensity of the immanent spatial power, power which pervades the entire space.
Of course that the entire digression made by me into the technical details of Spinozist metaphysics didn’t change anything by real significance in its understanding, but at least I tried to pour a new light upon some of the ontological and cosmological issues raised by his system. Also, I developed the conviction, which is more or less subjective, that the newest scientifical approaches of the metaphysics of Spinoza touched the most vital problems of it in the most apparently successful manner, but still without having the pretention of exhausting the whole sum of philosophical and scientifical questions which were generated by the publishing of his Ethica, in Anno Domini 1678.
Bibliography
Spinoza, Baruch - Ethics, Curley’s edition
Spinoza, Baruch - Ethics, Elwes’ edition
Bennett, Jonathan - A study of Spinoza’s Ethics
Cottingham, John - The rationalists
Della Rocca, Michael - Representation and the mind-body problem in Spinoza
di Poppa, Francesca - Spinoza and process ontology
Viljanen, Valtteri - Field metaphysic, power and individuation in Spinoza
