Spinoza offers various definitions, explanations (of certain definitions), axioms and premises in Part 1 of Ethics. The most note-worthy concepts that Spinoza provides are the premises, which serve as foundations for his arguments in establishing certain truths. Before Spinoza starts his arguments, he reinforces the validity of his premises with the provided definitions and axioms lest he wishes for others to accuse him of arguing on pre-supposed premises.
The point here is not so much as to examine and analyze the validity of his Spinoza’s premises, but rather, to point out the ambiguities and confusions that appear in his work. His most outrageous of claims lies with P8 in which Spinoza states that “all substance is necessarily infinite” (p.6). He defends this claim on the ground that everything has its own substance, that is, everything has its own unique essence and with essence comes existence. From there, he elaborates that the existence in question must be either finite or infinite and he rejects the notion of finitude because other substances of the same nature can only limit substances. However, because there are no such substances being of the same nature, then substances cannot fall under limitations and is therefore infinite. As deductively sound as that may be, the mere notion that everything is ultimately infinite is completely baffling. When speaking of substance, do people not automatically assume something of the physical nature? If that is so, how can physical objects such as a human body, an air conditioner, or a bag of Skittles be infinite? For these physical objects to be of the infinite nature, does it not mean that one cannot ever estimate their exact sizes? However, many, if not all, people have a clear idea of just how big their bodies or a bag of Skittles are. The problem here is either that the premise is simply absurd or there is a misunderstanding of the terms “finite” and “infinite”. Since Spinoza does not define such terms, one cannot help but find this premise to be confusing.
Spinoza later uses the same notion of infinity to claim in P11 “God, or substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists” (p.8). Those with a belief in the existence of God will readily agree to His infinite being, but and it is not to say that the existence of all things known to be real ought to be doubted of their realness. The problem here is once again the supposition of these things being of an infinite nature. Once again, the size of a person’s body or a piece of Skittles is of a calculable size, that is, a size of limitations. Why can it not be that certain objects of finitude also necessarily exist as well? The bag of sweet smelling Skittles seated across the room seems awfully real and in existence. Once again, what exactly does Spinoza mean for something to be “finite” or “infinite”?
I think the most confusing part of P8 is his use of the word substance. We look at the word substance to mean something in the physical. Something that is measurable by means of weight, takes up space and has mass. Spinoza attempts to avoid confusion, unsuccessfully, by first defining what he wants to convey to the reader. It can be found in definitions 2, 3 and 5 (p3-4). To somewhat summarize, definition 2 states… “A thing being physically finite vs. a thing in itself IE the thought of a thing not having physically finite substance, it having a concept that cannot be measured anyway or otherwise.”
ReplyDeleteNow if we look at it this way your bag of Skittles, yes having the sensible appearance of color, taste, weight texture sweetness etc., changes into something a more transcendental and since the concept of a thing of skittles cannot be weighed or limited by any physical means, it must be infinite, in a philosophical sense. So maybe the word substance has either two meanings or a very broad one and what he means by (in)finite.
Spinoza focuses on the nature of finite and infinite substance to analyze and bring forth the idea of what is necessarily true and essential. The idea you bring forth of an air conditioner or skittles being “real” because of their quantitative and measurable nature is interesting. This is so because as rational humans, we instinctively yearn to see, touch and measure what we encounter every day. But we must detach ourselves from this scientific method to delve into this dichotomy of finite and infinite substance. According to Spinoza, substance is so unique because of its paradoxical nature of genesis. Meaning, Substance has no beginning or creation, it has always existed without needing a creator or needing another object to stem from. Infinity exists in a sphere that as humans we will never truly grasp because of its lack of needing a creating force behind it. “God” is the true and only substance because of this. Air conditioners and skittles, although seem most real to us because we can measure their existence, are the least real to Spinoza because of their known source of origin. This paradoxical nature of substance leads one to only more questions about the distinction between the finite and infinite but to truly understand their distinction one must extract their consciousness from a certain space-time perspective in viewing the infinite substance of God and bring ourselves to distinguish known objects of origin such as skittles from the idea of the infinite substance, “God”.
ReplyDeleteGiven the difficulty that you are having accepting that substance, which you identify with physical things (save Tom, I think), is infinite, perhaps you need to reexamine this conclusion that substance is a physical thing. I mean, there seems to be no sense in which we can attribute infinity to a bag of skittles (the endless bag of skittles ... that sounds like torture) sensibly, so maybe the example is flawed, or your understanding of substance, and not the concept of infinity.
ReplyDeleteI think the idea is that through substance, your bag of skittles participates in the infinite, which is existence itself. To exist is to be part of God / the infinite. It's like a property of all existing things.
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ReplyDeleteAs I sat back and read Kevin’s post and the material over and over, I kept looking for the pot of philosophical gold at the end of the Skittles infinite rainbow. Unfortunately, my clarity was as clear as dense London fog. I then decided to close my eyes and clear my mind of everything, with a quest to rebuild knowledge on pillars of truth, just as Descartes did. When that didn’t work, I just went to Google :o) I did find some helpful links which I want to share. Spinoza much like Descartes, builds philosophy on a mathematically based definition, axiom, and proof system. (http://www.drury.edu/ess/history/modern/spinoza.html). In def. 2, Spinoza tells us ‘That thing finite in its own kind which can be limited by another thing of its own nature. For example, a body is called finite because we always conceive of another which is greater’. He then lays out the groundwork for the discussion on infinity stating in P8 that ‘every substance is necessarily infinite’, in my eyes throwing finite things out the window. In P13 he states that ‘absolutely infinite substance is indivisible.’ We can go back to Kevin’s blog and infer that Skittles is not a Descartesian substance but instead a ‘mode or modification’ of ONE substance which can be considered infinite. But much like a 2AM raid on an unlicensed strip club, this sexy stuff is going to get REAL UGLY! One link I found punched holes in the Spinozan premises using simple mathematical truths. (http://home.comcast.net/~csides2/philosophy/spinoza.html). First bombshell, let’s say you were somehow able to take an infinity ruler and measure an infinite length first in inches, and then use it again to measure that infinite length in feet. The measurement in infinite feet would be 12 times larger than the measurement in infinity inches. This would invalidate Spinoza’s premise, as you can’t have something larger than infinity. Another great example that was shown uses infinite WHOLE numbers versus infinite REAL numbers. REAL numbers can be larger than a WHOLE number, but how according to Spinoza can an infinite REAL number be larger than an infinite WHOLE number, when they are both INFINITE?!? Kevin, rest assured, the Skittle induced madness was not in vain!
ReplyDelete@JHart
ReplyDeleteI think your examples of infinity measured in inches vs feet (and likewise for real #s vs whole #s) are examples of constructed infinities
When Spinoza talks about the one substance (e.g. God), he is talking about an absolute infinity, not a constructed one. It's important, then, to remember that one of the key aspects of an absolute infinity is that it is eternal and perfectly simple, which is to say that it cannot be broken down into smaller parts or destroyed in any other similar way.
So to go back to your example with numbers: yes, there are an "infinite" number of real numbers between say, 99.999 and 100 (and likewise for any two real numbers), which is crazy because obviously if you keep counting up from 100 there's an even further "infinite" number of real numbers extending upwards (and thus an infinite number of numbers to choose a pair from, like 99.999 and 100, between which there are an infinite number of infinities). But this is only because these are CONSTRUCTED infinities, which lend themselves to such decompositions (like the famous Greek paradox where you can never get from A to B by repeatedly walking half the distance between them).
Absolute infinity does not, thankfully, behave in this way.
Many thanks for commenting on my blog response, you have definitely stimulated further thought (and subsequent and extensive cognitive dissonance lol). I’m not sure I can make a distinction of constructed versus absolute infinity, nor do I see Spinoza use the concept of constructed infinity in Ethics (maybe I missed it). Are you suggesting that constructed infinity is a ‘false’ infinity or are you suggesting that it is a DIFFERENT type of infinity? Going back to the use of real numbers, if I have the ‘thought’ of trying to find the center of two real numbers, isn’t the ‘means’ continual even though the answer is unreachable, eternal, and therefore absolutely infinite (back to P8, P12 and P13)? Is Spinoza suggesting that mathematical rules which have the effect of separating things into parts via division or counting, can NEVER be used in reference to something which is absolutely infinite? If we must rule out counting as a means of referencing the absolutely infinite, how can humans use a subset of two, with two being a subset of an infinite whole, attributes or essences to have knowledge of God (P47)? Doesn’t the concept of separating, categorizing, or partitioning attributes violate P8 and P11?
ReplyDeleteI mean that they are different kinds of infinity, with absolute infinity being the greater kind and constructed infinity being lesser. Although I suppose you could argue that since it is a lesser infinity, it is false in some sense, but I don't think of it in that way. In fact, mathematics grants larger and smaller infinities all the time. Just think of the two functions, y = x and y = x^2, in their limits as x goes to infinity. The former will be infinity, whereas the latter will be something like infinity squared, which is obviously much larger.
ReplyDeleteI think that constructed infinity just means something like, "REALLY REALLY BIG, so much so that it is unimaginable." This is the garden variety of infinity that we find in mathematics all the time, or the type of infinity that physicists mean when they say the universe is infinitely large. It's an infinitely large sum of smaller, discrete / finite parts.
ReplyDeleteThe only example in Spinoza of absolute infinity is the substance. It is immutable, eternal, perfect, and perfect simple. It cant be broken down into smaller parts, nor defined in any simpler way. It just... is.
Oscar I like your use of REALLY REALLY BIG to describe constructed infinity, but what happens when you have something like SUPER DUPER REALLY REALLY BIG lol. In terms of different types of infinity, that sounds more like Cantor than Spinoza. So my question remains, can the use of mathematics, which is a partitioning science, be applied to the Spinoza infinity and if not how can you apply the concept of discrete attributes?
ReplyDeleteAny infinity that is composed of discrete parts is a constructed infinity, whether it's bigger or smaller than other constructed infinities. That's why it has the name; it is constructed by the addition of discrete parts.
ReplyDeleteAs far absolute infinity and it having discrete attributes, I'm not 100% on that myself, but I think it's something like they are aspects of the same absolute infinity, and not really different parts of it at all. I think that any notions of discretion or limitation in the substance are purely illusional. It's still all just the one thing.