Current to our way of thinking is that discrete spaces are purely virtual, that is, not real. To say that something is not real is to imply that it is not part of the material world and that it has no physical relevance, or that its physicality, if supposed at all, is contingent upon our perceptual rules or imagination. It’s “in your head”, as it were. For a Spinozist, this idea of “discrete space” is another way of saying the same thing as talking about “empty space”. For there to be discreteness, there must be emptiness between, which would imply further that there is space between spaces, and this leads us into a bit of silliness. So Spinoza himself defends the assertion that “nature abhors a vacuum”, which gets us to the idea that discrete space considered at all must be purely virtual. We are behooved to throw the idea out, or at least attempt to explain the illusion, or what “empty space” means when we use the concept behind the apparently self-defeating phrase.
Spinoza’s way of thinking was important to the cognitive revolution and to combating the “ghost in the machine” which was current to forms of empiricism at the dawn of the 20th century. To speak of cognition is to speak of representation: what’s in your head as some representation of what is in the world, and as to the rule-bound behavior that goes on between mental contents (ideas expressed like “the sky is beautiful” or “democracy is liberatory”) and non-mental (things denoted the words “the sky”, “is”, and “beauty”). Some non-mental things, we might say, do not depend on our ideas: it’s not just my idea what is liberatory or what is beauty, or else it would have to just be everybody’s “idea”, and so the question of beauty-in-itself and beauty-as-to-things becomes “split”.
As the story goes, the philosopher is often concerned with the conditions for the possibility of such “splits” between our concepts and their application or attribution to things, not just if the word fits, which is a problem for linguistics that itself must presuppose some idea about what cognition is in relation to our behavior and the rules of nature (i.e. physical laws). We think unicorns, shadows, dreams, greek gods, and the like, are “not real”, and the Spinozist might suggest that “discrete spaces” are not real in just the same way. So then, what is “represented”, what is “in” our mind when we use such terms? Spinozists might suggest that nothing is “in” the mind, but that the mind is configured a certain way when we use all language. A Spinozist might say this in order to avoid the view of cognition that depends on the brain being separate from the mind and which “contains” the mind like a cat in a box. Indeed, such a view of the mind would open us up to doubt in the way that Schrödinger’s paradox does: we’d have no reason to trust any thoughts are “inside” the mind, as they and their negations would be maintained if we do not open the box; i.e. ask a question. So the Spinozist radically changes the terms of cognition: thoughts, ideas, propositions are not “inside” the mind, since it also makes little sense to say the “mind” is “inside” the brain. The mind and brain are different expressions of the same thing, yet both conforming to rules; or we might say the brain conforms to laws and the mind to rules where laws and rules are different expressions of the same thing. So “cognition”, for the Spinozist, isn’t about representation as interior and exterior relations between two very unlike things: cognition is a matter of one thing, thinking and being, ascertained as a certain mode or configuration that is expressed in two ways which we can conceive, observe.
How are these laws and rules related? They are related through our conceiving that they are related; they are correlated through our conceiving that they are correlated; they are representative of one another through our conceiving that they are representative of one another. Sometimes we say smoke represents fire by virtue of being caused by it, other times we say beauty represents truth. Such ideas come about: do these concepts “contain” the other? No more than does the brain “contain” the mind: for the Spinozist, they’re all modes or configurations, namely of God or Nature. In this way, Spinoza affords us a philosophy of radical immanence. This is merely to suggest, by “radicality”, that a method is possible to apply to all such events to which questions smoke and fire, beauty and truth, and so on, are applied. These events may be decisions or relations: by the former, in that they involve our setting the matter straight for others to agree or disagree (deciding that “only speaking or drawing true things produces beauty or are beautiful”), and by the latter, in that they involve our being related to others (the President being elected relates me to others in my community in such-and-such a way). These are two kinds of events, constantly motivating us and prefiguring us.
This gets us back to the original point about “discrete spaces”, and as we’ve just mentioned “immanence”. Immanence contrasts with the transcendental: what is transcendental stands outside of all experience or is presupposed by experience. It is the conditions for the possibility of experience as that which is outside of all experience. Immanence is the attribute to which all experience is accorded: it is not prior to all experience but inheres all experience. Spinozists really want us to understand the role of our conceiving things to be thus-and-so, not just perceiving things to be thus-and-so. Materiality is wedded to our practice of conceiving and merely supported by our perceiving: but perception is obviously bound by our imagination, so we must appeal to conceiving that which is the case, as by our reason. The Spinozist’s epistemology ranks reason above the imaginary, intuition above reason, and beatitude above intuition: imagination, reason, intuition, beatitude.
When it comes down to “philosophy” and “non-philosophy”, the former is a transcendental hallucination of the Real constantly at odds with the latter, so maximally conceived, a globally transcendental discipline. Hallucination and discipline are the operative terms here: a person can certainly exist as a superposition of both, or more so one than the other depending on their stage in life. But it might also be said that “discrete space” is something more like a “hallucination” to which our discipline teaches us better, whatever that discipline amounts to insofar as it dissolves the hallucination as such. If we assert that discrete space is real, what are we committing ourselves to? The Spinozist might say “a hallucination, for whatever reason that might benefit you” and this might be true, at the cost of the equally present potential understanding of what is discipline. In most cases in our life, we behave according to some kind of discipline or another, rather than some hallucination, unless the skeptic about the world wishes to defeat their very own language in order to produce an infinite regress, which would imply that no regularity is permitted despite the obvious fact that it is. So the skeptic may only deploy “local” skepticism, and we’re fine with this, rather than “cosmic” or “arch-”skepticism (so much for simulation theory, unless you’ve got a whim about you). None of this isn’t to say certain local skepticisms cannot be useful, but yet they are merely expansions within the Spinozist’s framework of thinking about modes and configurations (does a sun of a certain color represent impending dangerous astro0chemical processes like smoke represents fire? can we know this within our lifetime?)
But I suppose I’ve digressed. To say “discrete space is real” entails either that we are truly separate or that separateness is illusory. What could this mean? We are either a unified field of subjectivization (separateness is illusory) or not. We are like the points on a lattice, and the “space” between us, like in the lattice, is purely virtual, not part of the material world and has no physical relevance. We might say that certain “things” are between us, but this is like saying, to one who upholds radical immanence as a doctrine, that because we hold a pencil on two different ends that the pencil is “between” us: it’s only “between” is insofar as we conceive it so, where at the same time and in more ways, we might say that it connects us like links in a chain. If Alice says “hold onto this pencil” to Bob, I might look at them and come to the conclusion that it is their pencil. Do this with a classroom of students to build an “immanent” (or decentralized) network, and we could suggest that the pencils are not doing the connecting at all and certainly that there is no “empty space” between them, concluding that their field is an outcome of their subjectivization. To suggest that discrete space is real, ultimately, commits one to the idea that we are not a unified field of subjectivization. It’s not just that “if you were in my shoes, you’d see it this way”, that’s rather a different doctrine which might be added on. Since there is nothing that in fact separates us, we are connected through space’s fabric. We are situated on a cosmic blanket or in a global pool such that our actions and thoughts ripple throughout according to laws and rules. Our subjectivity is constantly protected or exposed to the waves. To suggest that discrete space is purely virtual, or “not real” just is to imply that we are a unified field of subjectivization, the things between us only “separate us” insofar as our conceiving and thinking so.
What’s important to understand here is that Spinoza’s rejection of angels, supernatural miracles, a personal god that loves individuals and the rest were not the grounds of his excommunication: it was the position that if God is as he described, everyone should eventually arrive at his conclusions. Recall how Christians tell atheists, “You’ll grow out of it and see things the Right way.” That is, if God is as described, only through reason should others arrive at such conclusions, which are more excellent as they are rare than any supernatural miracle, whereas the appeal to supernatural miracles only could be an appeal to the imagination. So Spinoza developed a method for epistemological unification which has cropped up in cognitive sciences as well as treatments of quantum field theory’s formalization. To take away the belief in vacuums (“discrete spaces”) just is to commit oneself to a unified field of subjectivization where the spaces between lattice sites are purely virtual and objects only separate us insofar as we imagine, whereas reason shows us that such separateness is not the entire story, that seeing objects as extensions of ourselves is just as negotiable or grounded as seeing objects as divisions between us.