metaphysician7887

Firstly, I'm explicit in my essay that I'm neither claiming that the universe is infinite nor "extending." My essay draws out my entire argument, and I encourage you to understand it. Disagreeing with it is one thing, but flatly asserting the very thing that I wrote a whole essay to question renders debate impossible. Secondly, I only claim positives when something positive exists to claim. The universe lacks size and is not a quantity, and it happens to be these facts which allows one to integrate our knowledge about the universe. The fact that my essay makes a lot of negative claims is neither a fault nor my fault. Moreover, I stated in my last post the positive claims I do make in my essay, so to just assert once again that you can't find any positive claims in my essay is, quite frankly, bizarre. I devote a whole section to my essay to why the universe does not have an finite number of entities -- and why an infinite number is not the alternative. I explain why "number" and "quantity" don't make sense when applied to a whole which lacks boundaries. Again, you may disagree, but you must draw out why you disagree if you want to enable discussion.

Adrian, Your arguments against my essay rest on the supposition that the universe qua "hyperspheroid" is a viable alternative. But, as a fellow thinker, I must confess that I see neither evidence nor meaning in this contention. To say that the unbounded universe has a "shape" which "curves" or "wraps" back onto itself is to rely on stolen concepts proffered as metaphors. Concepts such as "curve" and "shape" are wholly formed with reference to boundaries, and simply have no meaning apart from them. You refer to the usage of such concepts as a "special case"; I refer it as using concepts which are stolen from their necessary context. This is why I must spread my hands out in honest disagreement when I hear you describe my position as not even "comprehensible." The universe qua "hyperspheroid" is, in my firm conviction, entirely incomprehensible. A "shape" or "curve" of an unbounded universe is literally just as meaningless and inconceivable to me as motion from point A to point B without traversing the points in between. In contrast, I have no problem comprehending the idea that the unbounded universe is "Euclidean," and nor have I been offered any reason why it is incoherent. It doesn't steal any concepts; it just asserts that the universe is an endless realm of three-dimensional, "Euclidean" space. (True, one cannot imagine an entire "expanse" of it at once, but that's not the standard for comprehensibility.) The most common impetus among Objectivists for entertaining a notion like a "hyperspheroid" is the claim that it is necessary to avoid the existence of a metaphysical infinity. But, I gave arguments in my essay for why an endless, "Euclidean" universe is finite through and through. Thus, I'm at a loss for finding any reason to regard the "hyperspheroid" hypothesis as anything more than arbitrary. Adrian, I'm interested in knowing: are your criticisms of my essay based on the supposition that the "hyperspheroid" alternative is correct? Or is the "hyperspheroid" idea attractive to you because every other alternative (mine included) is problematic? I want to go to the fundamental, here, so I can know exactly where you are coming from. (P.S. -- While you're right that my essay is largely negative in its claims, it is not entirely so. My essay doesn't merely deny size to the universe like atheism denies God to existence. I do deny size to the universe, and further claim that such a denial -- along with positive facts I mention about size, number, quantity, etc. -- is the means to integrating three facts we know about the universe: it is finite, it is unbounded, and it cannot contain an infinite number of entities. Whether this is a theory in the strict sense of the word, I'm honestly not that interested in.) -- Alex

First off, and as I pointed out in my essay, the proper phrasing of the question at hand is not whether the universe is finite or infinite, but whether the universe's (alleged) size is finite or infinite. We are not discussing the age or density of the universe; we are discussing its spatial extension (size). Secondly, I agree that most people would think that my ideas amount to claiming that the universe has an infinite size. But, I don't agree that such a popular vote is relevant. My ideas are to an extent original, so of course they will be different from what "most people" believe. The number series, unlike the universe, is not a metaphysical thing existing "out there"; there are only as many actually existing numbers as the human mind has conceived of. As such, even assuming that we could count indefinitely, there would not be an infinite number of integers. A potential to count indefinitely is just that: a potential, not an actual infinity. So, in a way, your point is even stronger than what you intended: the universe has a _better_ claim at being infinitely long than the number series, since the universe is an actual, currently existing endless thing. Of course, I have arguments for why I reject that the universe has an infinite size, but they have not been addressed here yet. No, I'm not just arbitrarily using words differently; I gave arguments, trying to make a real differenation between infinity and the universe. This is why I did explain in my essay what it would mean for the universe to possess an infinite size (or any infinite attribute). I wrote: "The concept of infinity is metaphysically invalid because it attempts to describe an existent (e.g., an attribute) as existing, but as nothing in particular." For the universe to be infinite, it must have some infinite attribute or characteristic; for an attribute (i.e., size) to be infinite, it must actually exist, but as nothing in particular. To achieve an infinity, the universe must have a size, but have no particular size (which is a contradiction). My theory is to deny that the universe has either a finite size or an infinite size -- i.e., to reject the claim that the universe has a size in the first place. I see no a priori reason why the universe must possess a size, anymore than I see an a priori reason why the universe must possess an age, density, weight, or shape. What is the arugment that the universe actually possesses any of these characteristics? I would be interested in hearing one. Have you stopped beating your wife? After all, either you have stopped beating her or you have not stopped beating her; to claim anything other would be an outright denial of the Law of the Excluded Middle. In philosophy, one must be very careful not to pass off complex questions as iron instances of the Law of the Excluded Middle. If a question assumes a false premise (and therefore a false context) to begin with, throwing in a negation within this context does not amount to the Law of the Excluded Middle. "Have you or have you not stopped beating your wife?" is an invalid question, because either alternative will assume the false premise that one has beaten one's wife in the past. Similarly, when you ask whether the universe has an infinite or non-infinite number of atoms, you are obviously assuming that the concept of "number" applies to the universe and its contents to begin with. And this is a premise that I explicitly reject in my essay. I gave arguments for why concepts such as "number," "quantity," and "size" are wholly inapplicable to an unbounded universe, so to just assume that such concepts apply to the universe from the outset does not do justice to my arguments. -- Alex

I don't see why one should assume that either philosophy or science would come to that conclusion. (For the record, I'm the author of the essay being discussed here.) Via philosophy, we know that all existents of consciousness (e.g., emotions) do not possess any size at all. With regard to time, the ultimate constituents of the universe would have to be eternal, and thus would not be temporal or possess an age. The universe, being all that exists, similarly must be eternal: the universe (i.e., existence) has always existed, since nothing can exist before existence. I don't see why the universe as a whole has to be able to be ascribed measurable, quantifiable attributes for it to have identity. It's not rationalistic to say that the universe has identity, since every piece of knowledge consists in knowing the identity of the universe (i.e., the universe), and I don't see how such knowledge ever assumes that the universe as a whole has a measurable, quantifiable attribute. I'm not saying that the universe is this thing with an identity that we are ignorant of; I'm saying that the universe has identity, the objects of our knowledge consist in it, and the universe as a whole does not have size or age (and probably lacks every other measurable, quantifiable attribute as well, although this is more debatable and not explicitly argued for in my essay). Again, many things possess a size and an age, but it's simply not the case that everything does. So, my question is: why assume that the universe has either attribute? What would it mean to say that, for example, the universe has only existed for a specific time, and thus came into existence at one point? The universe can't "come into existence"; it is existence. The main question of my essay centers around the attributes of size and age, and one must have a specific argument to show that the universe possesses these attributes. The claim that such attributes are universal simply isn't true, and does not address my positive arguments that operate in the context of knowledge that size and age are not universal attributes. One must examine the nature of the existent in question to see if it has a size or an age, rather than assume that such attributes must be present. With regard to the universe, I'm questioning a widespread (and very understandable) assumption that it does in fact have a size, so the mere fact that it is an assumption is not a sufficient objection. It really isn't. But even if it was, I did try to draw out my argument (in my essay) for why it is the case that the universe cannot possess a size or an age. I did not simply make a question-begging exception to a universal law of reality; I made an argument, based on the nature of size, time, and the universe, that the latter is incompatible with the other two. If it is objected that size and time are universal and thus must apply to the universe, then -- if anything -- it is this objection (rather than my argument) which begs the question. One could probably well say that the universe is a sui generis "exception" in the following sense: as far as I can tell, it is only in the context of the universe as a whole that one has something which lacks a size, while still having parts that do possess a size. I think (although am not entirely sure) that this is a phenomenon unique to the universe. But, either way, uniqueness is not proof of falsehood. If anyone has any further questions on and/or objections to my essay, I'd be more than happy to respond. -- Alex