On the Isomorphism of Spinoza

Baruch Spinoza

In mathematics, an ismorphism is where you can map all the elements of Set A onto those of Set B, such that Set A and Set B can at least from a certain point of view be seen as actually being the same set. If (for example) Set A was {apple, orange} and Set B was {yabloko, oranzehevyy} I would be justified in sayingthat these sets were isomorphic to one another, since here Set B are simply the Russian words for the same items in Set A, "apple" and "orange."

Now, to go to Spinoza. Spinoza had a clever argument for why G-d and what we might call "The Universe" or Nature were in a sense isomorphic (although that is a more modern word than he would have used). Basically, Baruch Spinoza said that if G-d by definition is "the greatest thing" and if furthermore, G-d was seperate from Nature, then if we took the sum, G-d + Nature, we would have a totality that would be greater than G-d, contradicting the starting axiom of saying G-d is the greatest thing there is. Therefore (for Spinoza) G-d must in some way include Nature in Herself, perhaps in a sense establishing some sort of isomorphism between these two notions.

Now, this starts to get confusing, fast, and, indeed, has confused thinkers for going on four centuries. It would be easy (and, perhaps, arguably lazy) to accuse Spinoza of playing "word games" and simply using the "G-d" word as another word for Nature. However, I think what is going on here is a little more nuanced. Let us look at what Spinoza means by the word Nature or the Universe. He says there is one substance with infinite attributes. So, there is one "Reality" and what we have access to by experience and observation are these attributes of this one "Reality" or "Substance".

So, I think what Spinoza really means is that for him, "G-d" is this totality - the one substance that is, all that is, was, or will be, and Nature is if you will all the infinitude of attributes of this one substance. So this is not *quite* a perfect isomorphism. Rather, for Spinoza, "G-d" is "the whole thing", and "Nature" are those "attributes" which present themselves to empirical experience, which, in turn, are part of "the whole thing" or the "one substance" or what we might call "Reality".

Now, here I am going to get into more my own personal musing, which Spinoza may or may not have agreed with, but here we go. We have here, in a sense, a notion of "G-d" as if you will, the "Universal", and "Nature" as the particular attributes of this "Universal". But, by definition, I do not have access to experientially a "Universal", I can only "experience" particular things. So let us look more closely at the word "attribute". For example, say I am drinking chocolate milk. I "experience" the "attribute" of say the creamy texture of the milk, and the "attribute" of the chocolate taste of the milk. I may not directly "experience" say any additive vitamins that have been added by the manufacturer to the milk in terms of being able to taste them, but said additive vitamins are part of the totality of the chocolate milk that I am drinking. After the fact, I may look at the label and read about the vitamins, but I do not really "experience" them in the same way that I "experience" that chocolate flavor. So, without looking at the label, I would not list the additive vitamins as being among the "attributes" of the chocolate milk.

So, here I may say, that the "attributes" of the "One Substance" of Spinoza - Reality, say - are those aspects of this reality that I have some direct experience with and that furthermore I can label linguistically. But, I may not always be able to label all my experiences in terms of language. So, while I cannot (by definition) "experience" the "Universal", I can and do have experiences which sort of "call forth" this "Universal" by virtue of not being able to wholly pin down or capture these experiences in a linguistic manner.

Tersea of Avila

Now, the psychoanalyst Jacques Lacan referred to those experience of life which cannot fit easily or at all into language as what he called "The Real", and furthermore Lacan asseverated that this "Real" was the category of what are termed mystical or spiritual experiences. His canonical example was the mystic Teresa of Avila whose trances in which she claimed to encounter the Divine have long been cited as an example par excellance of the sublimity of the "other-wordly." Lacan's point was that the trances of Teresa of Avila could not be communicated by description, that they lay wholly outside the realm of language, but had a profound impact on her and her followers. Going back here to Spinoza's "one substance with infinite attributes," I would posit that Lacan's "Real" are those attributes which belong to raw experience and can never be wholly subsumed into a logical or mathematical framework, and, because of this, "point the way into" that Universal in which all resides, but is not (by definition) apprehendable in-and-of-Itself, anymore than a fish can "directly apprehend" the water in which it swims.

In a historical context, one thing that Spinoza was reacting to was the philosophy of Descartes, who was a thorough-going dualist, and so in a sense Spinoza's work can be seen as a rejoinder or counterpoint to Descartes, meaning Descartes held the notion that concepts such as "mind" or "consciousness" and "G-d" were wholly seperate from the world of empircal observation. Spinoza, working from the Jewish line of thought of the "one-ness" of the Divine, sought to work against this concept of dualism, as, full disclosure, do I. As a side-note, one of the many Jewish names for the Divine is "ha makom" ("the place") coming from the mystical tradition that the universe we experience and observe "resides" in some sense within the nature of the Divine, that is, the Divine is not "outside" the world we live in, but rather, the other way around, the world we live in is within the Divine. This I would  argue relates back to the ancient Jewish admonition regarding avoiding idol worship, an admonition that I think remains relevant to this day, where people make many things as central to their concern, such as, for instance, the economy, or a sports team, or some celebrity or other. What all "idols" or things in this world that retain people's central focus (or their "Ultimate Concern" to use the phrase of theologian Paul Tillich) have in common is these things all "live" in the world we experience, while Spinoza would have said that this approach has it completely backwards. The "Divine" is to be found in the Universal, not in a particular person or thing (like say the economy) within the Universal. "G-d" for Spinoza is not an object within the world, nor an object outside the world (as argued above) but is rather the Totality of the world, which always "over-flows" the ability of language to describe it. I would argue that Spinoza is the logical end point of the thousands of years of tradition regarding admonition against idols, namely, that the Divine is neither something within the world we experience, nor is it something apart from it (as say Descartes might have said) but rather is the totality of the world we experience, but this totality always is greater than the ability of humankind's most rarified systems of science or mathematics to wholly describe it.

On a personal note, I (independently) for reasons too long to get into in this essay had the notion some time back that entropy plays a role in human consciousness. Some time after I had this thought, Canadian scientists doing brain scans on epileptic patients found that indeed patients in states of "higher wakefulness" (as opposed to being in say a seizure state) do have brain states corresponding to higher levels of entropy. So beyond the validation that this was in line with my own thinking, I find this interesting because here we see in a sense a confirmation of Spinoza's intuition, because entropy is something that "ties together" subjectivity and the objective world. Entropy is found everywhere, including in the principles of physics that enable the internal combustion engine used in automobiles to run. If entropy is also involved in consciousness / subjectivity, as the evidence now seems to be suggesting, we have these two seemingly seperate realms being tied together. Entropy may form a "bridge" between the world of empirical experience and our innermost subjective feelings. This gives support I would argue to Spinoza's main thesis of monism, that there is but one Universal whose various as he called them "modes and attributes" form our experience, and what we call the Divine or "G-d" is in a sense this same "Universal" which (I would contend) is "encountered" in the experience of mystery, what Lacan in his analysis of the story of Teresa of Avila and elsewhere referred to as the "Real".

An artistic rendering of Lovecraft's "Azathoth" metaphor

To give a literary example here which may I think help explain what I am driving at, the writer H.P. Lovecraft had many fictional monsters or space-alien type creatures in his stories, the most famous perhaps of which was Cthulhu, an octopus-like entity living on the Pacific Ocean floor. One of his lesser known perhaps but more interesting creations was a being he called "Azathoth" that lies somehow outside of the known dimensions, which he dramatically writes "is that amorphous blight of nethermost confusion which blasphemes and bubbles at the center of all infinity." Scholars have often thought that Azathoth was different from Lovecraft's other characters, not meant to be taken as a literal space-alien type thing (like, say, Cthulhu) but was a metaphor for the cosmic Unknown. In some readings, the universe we live in is part of a dream which Azathoth projects. As a life-long Lovecraft afficianado, I take the view that Azathoth is indeed a metaphor for our limited understanding of the ultimate nature of Reality (and, indeed, in one story, "The Whisperer in Darkness," Lovecraft explicity states that Azathoth is indeed a metaphor for the "outside", or that which is unknown to the sciences but which may now and again enter human experience). Azathoth basically is a metaphor for the fact that the Totality of Reality is always greater than whatever models science can come up with, and the idea of our world being somehow "within" the dream of Azathoth further reinforces this notion of the limitations of human knowledge. So Azathoth perhaps can be seen as a metaphor for the Universal and specifically for the failure of language or mathematics to fully pin it down.

To summarize, I would posit that the isomorphism of Spinoza between the Divine and the Universe is more nuanced than it is often portrayed. When I think of the word, "universe", I often (instinctively) visualize in my mind's eye some sort of space-time diagram of (for example) anti-DeSitter spacetime, one of the solutions to General Relativity which is used often to describe the development and expansion of our observable cosmological horizon. How Spinoza would use terms like "Universe" or "Nature" is arguably different. By "Divine" he does not mean (say) anti-DeSitter spacetime, or any particular mathematical model of the world we live in, but rather, he means the totality of Reality itself, which always outstrips human ability (even in principle due to Godel's Incompleteness Theorums) to be able to comprehend it. Therefore the "Divine" for Spinoza is something like the totality of the mystery of being (one could phrase it thusly perhaps) and "Nature" is that part of being of which we can perhaps say something about, but we can never describe what we might call "Reality" completely. There is, I would argue, an ethical dimension to all of this. If indeed we as human beings are part of this one universal Substance we might call "Reality" then - by definition - we are each of us connected (literally in an ontological sense) to everything else, all other people, all rocks, plants, animals, stars, black holes, Higgs boson particles. Thus (as for example Buddhist or Quaker philosophies also say) to harm others is to harm ourselves, for we are all inextricably linked together in the cosmic nature of things. The lesson of Spinoza then is that at the end of the day, dualisms (of whatever sort) are deceptive for each particular thing is part of an infinite and indivisble Universal which is never static, but is always in a creative state of becoming, bringing new realities into being each and every moment, a Universal that can only be apprehended indirectly at the edges of language, and about which we can only say (with the prophets of old) that She will be what She will be.

Because it is my blog and I will picture Spinoza's Universal however I bloody well please :)