Taking as axiom that Reality consists of a single Substance as per Spinoza, and taking as another axiom Godel's Incompleteness theorems, from this we can conclude that Reality is not mathematical (as for example Tegmark would have it), because Godel's work suggests that any model requires an infinite regress of other models to prove the correctness of the first model, so, if Reality were mathematical, it would not be one Substance, but an infinite regress of substances. Thus from Spinoza and Godel, we show that Reality is not mathematical.
This being the case, it follows that there are always aspects of Reality that cannot be put into mathematics or language. Mathematics is itself a type of language, perhaps the most precise there is, but, at end of day, it does the job of any other language, that is, to categorize, or put labels onto things. Thus there are always aspects of what we call "Reality" that are outside of any language and that is to say, outside the ability to differentiate or to compare/contrast things.
As an aside, Spinoza spoke of how, since all is one Substance, that mind and material things were really simply different aspects of this Substance. This can be argued from General Relativity. As example, the sun can be seen to produce Ricci curvature which the earth experiences as gravity, but, equivalently due to equivalent reference frames, the Ricci curvature of the sun can be seen to produce the sun itself, it works both ways. The other type of curvature is Weyl cuvature, which is caused by the spinning of objects in spacetime, so, for example, the spinning earth causes precessing of orbits of small balls placed (in NASA experiments) into orbit above the north pole. Roger Penrose speculated that Weyl curvature is what gives rise to entropy, the familiar process that, as we move through time, there are ever more possible configurations for systems of particles to get into, leading to increasing disorder at the macroscopic level. If we take this as correct for the sake of argument, that Weyl curvature gives rise to entropy, and if we further assume that consciousness requires and indeed produces entropy, as some studies suggest, then we have a nice symmetry here, in that, just as Ricci curvature can be seen to give rise to matter, so Weyl curvature may be viewed as giving rise to entropy and hence to consciousness, showing Spinoza to have been correct here, that mind and matter are ontologically on the same footing, both consequences perhaps of different ways in which the spacetime metric can be curved / distorted.
Spinoza may be sometimes accused of "word games" by using the word "Nature" and "god" to mean more or less equivalent things. But there may be a distinction here. We might say that Reality when viewed from language, and most especially the language of mathematics and science might be thought of as "Nature" or related terms such as "Universe" or even, lately, "Multiverse". But if, as established above, Reality is at the end not mathematical, and therefore has aspects which cannot be put into the categories of scientific or mathematical or indeed any linguistic paradigm, then the word "Nature" indeed does not capture all of "Reality". So one might employ the "god" word to name those aspects of reality that cannot be subsumed into language (something like the initial and perhaps final singularities, for instance - as a related historical footnote here, the Jesuit and palentologist Teilhard de Chardin in his book The Omega Point identified god with the final singularity).
One is reminded of Heidegger's dichotomy of "reflection" and "engagement". We can have the modality of thought of "reflection" when we seek to understand something (for instance, figure out how the toaster works) and we have the modality of thought of "engagement" when we just interact with things in the world (e.g. just use the toaster, not analyze it). He averred that people are happier when they spend most of their time in the "engagement" mode rather than the "reflective" mode, which I will leave to others to debate, but, one can employ these terms to the Reality-as-Nature or Reality-as-god dichotomy - when one thinks about the world / universe etc., one confronts Reality-as-Nature, and when one simply engages in the world, one confronts Reality-as-god. Which creates a paradox or at least an interesting irony: one cannot - by definition - think about Reality-as-god, one can only engage with it - it is similar to Lacan's "Real", that category of experience that lies outside language (like seeing a UFO for instance) - one cannot ever "describe" or really "analyze" Lacan's "Real", one can only encounter it, or, to use Heidgger's term, engage with it.
So, I'd argue that the Nature/god dichotomy is not just a lazy equialence of terms on Spinoza's part, but at least could be seen as getting at a very real dichotomy of human experience - Reality is "Nature" when we think about it (such as in writing essays such as the current one!), Reality is "god" when it is engaged with sans reflection. But even in the "reflection" mode, Nature betrays its inherent non-mathematical, non-linguistic, "Lacanian Real" nature, "at the edges" if one likes, blatantly and profligately at the initial and final singularities, but, perhaps more subtly, in the very fact that in any model of Nature whatsoever, including the familiar / canonical DeSitter or anti-DeSitter spacetime of general relativity, is itself unprovable / incomplete etc. per Godel. So, yes, "Nature" and "god" are both words to describe "Reality" but in different modes thereof - "Nature" describes if you like good old fashioned anti-DeSitter spacetime - "god" describes (in "reflective" mode) where all that breaks down, becomes incomplete, etc., and is also another way to name the immediacy of sentient experience that is pre / post / non linguistic, that is to say, to name the Lacanian Real. Quod Erat Demonstrandum.
- Francis Erdman, May 20, 2023, Sagamore, Cape Cod, Massachusetts
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