iouswuoibev Posted June 16, 2004 Report Share Posted June 16, 2004 There are two mutually exclusive statements that can be said of an existent. Existent X is composed of something that exists. Existent X is composed of nothing. If the latter is true, then X does not exist, in which case X is not an existent, which is a contradiction. Therefore, in order for an existent to be an existent, the first statement must always be true. The first statement works recursively. X is made of an existent, and that existent is also made of an existent, which is also made of an existent, and so on. This recursion is infinite. Does this mean that infinity is real? I read an article linking from this site which asserted that infinity cannot be real, but I have lost the page. I am wondering if it is the consensus among objectivists that infinity is not real except as a relational concept, and if so, does that not contradict the facts I have described? Quote Link to comment Share on other sites More sharing options...
stephen_speicher Posted June 16, 2004 Report Share Posted June 16, 2004 The first statement works recursively. X is made of an existent, and that existent is also made of an existent, which is also made of an existent, and so on. This recursion is infinite. No. The recursion is not infinite. There is an ultimate constituent for which there is nothing more fundamental. Does this mean that infinity is real?If you mean physically real, then absolutely not. I read an article linking from this site which asserted that infinity cannot be real, but I have lost the page. I am wondering if it is the consensus among objectivists that infinity is not real except as a relational concept, and if so, does that not contradict the facts I have described? The existence of an actual physical infinity is not an issue for which a "consensus among objectivists" is required. The Objectivist position on infinity has been quite clearly stated by Ayn Rand. For instance, Introduction To Objectivist Epistemology, pp. 148-149: "The concept of 'infinity' has a very definite purpose in mathematical calculation, and there it is a concept of method. But that isn't what is meant by the term 'infinity' as such. 'Infinity' in the metaphysical sense, as something existing in reality, is another invalid concept. The concept 'infinity,' in that sense, means something without identity, something not limited by anything, not definable. Therefore, the measurements omitted here are all measurements and all reality." Quote Link to comment Share on other sites More sharing options...
danielshrugged Posted June 16, 2004 Report Share Posted June 16, 2004 See the current thread on rationalism. Your deduction is not valid because your original alternative is not mutually exclusive. What makes you think that every existent is composed of something else? Quote Link to comment Share on other sites More sharing options...
DPW Posted June 17, 2004 Report Share Posted June 17, 2004 See the current thread on rationalism. Your deduction is not valid because your original alternative is not mutually exclusive. What makes you think that every existent is composed of something else? Uh oh. Leibniz returned from the dead! Quote Link to comment Share on other sites More sharing options...
danielshrugged Posted June 17, 2004 Report Share Posted June 17, 2004 Wait a minute...I'm not sure why you bring up Leibnitz. Quote Link to comment Share on other sites More sharing options...
MinorityOfOne Posted June 17, 2004 Report Share Posted June 17, 2004 I don't think it's mutually exclusive either. Composition is a concept which applies only to things which have parts. If something has no parts, it isn't composed of anything. But that's quite different from saying "It's composed of nothing and therefore does not exist." The problem is an equivocation in the meaning of "nothing" as used above. In the first use, it means lack of parts; in the second, it means lack of anything. If an existent is indivisible, it will have no parts and thus not be composed of anything; but it is not therefore nothing. Quote Link to comment Share on other sites More sharing options...
stephen_speicher Posted June 17, 2004 Report Share Posted June 17, 2004 Wait a minute...I'm not sure why you bring up Leibnitz. Yes, you are right to question that. Leibniz' monads had no parts and were not composed of anything more fundamental. However, the real irony lies in that Leibniz condemned the new science of his time, and that was the science of the natural philosopher who actually did accept the possibility of particles being divided infinitely, none other than Issac Newton himself. Quote Link to comment Share on other sites More sharing options...
Evangelical Capitalist Posted June 17, 2004 Report Share Posted June 17, 2004 The statements are mutually exclusive. A is A; a thing cannot be composed of something and nothing at the same time. However, they are not collectively exhaustive. There are existents to which the concept of composition does not apply, i.e. they are indivisible. These statements do not cover such existents, as has already been discussed. Quote Link to comment Share on other sites More sharing options...
MinorityOfOne Posted June 17, 2004 Report Share Posted June 17, 2004 The statements are mutually exclusive. A is A; a thing cannot be composed of something and nothing at the same time. However, they are not collectively exhaustive. Heh. Yeah, that's what I meant. Sorry, I was being careless. Quote Link to comment Share on other sites More sharing options...
danielshrugged Posted June 17, 2004 Report Share Posted June 17, 2004 Heh. Yeah, that's what I meant. Sorry, I was being careless. Me too. Quote Link to comment Share on other sites More sharing options...
danielshrugged Posted June 17, 2004 Report Share Posted June 17, 2004 I don't think it's mutually exclusive either. Composition is a concept which applies only to things which have parts. If something has no parts, it isn't composed of anything. But that's quite different from saying "It's composed of nothing and therefore does not exist." The problem is an equivocation in the meaning of "nothing" as used above. In the first use, it means lack of parts; in the second, it means lack of anything. If an existent is indivisible, it will have no parts and thus not be composed of anything; but it is not therefore nothing. As you put this, you're missing an alternative. I'll list the THREE alternatives here: 1.) Something is composed of something else more fundamental. 2.) Something has no parts; it is not composed of anything. 3.) Something is homogenous (I'm thinking of the continous theory of matter, here). It has parts, but those parts are not something different in kind from the whole. One might reject the third alternative on scientific grounds, but it can't be rejected on philosophic grounds. The potential for matter to be divided infinitely is just that, a potential, not an actual. Quote Link to comment Share on other sites More sharing options...
DPW Posted June 17, 2004 Report Share Posted June 17, 2004 Wait a minute...I'm not sure why you bring up Leibnitz. It wasn't aimed at you but him. He's beginning his rationalistic deductions from the same place Leibnitz did, more or less. Quote Link to comment Share on other sites More sharing options...
danielshrugged Posted June 17, 2004 Report Share Posted June 17, 2004 It wasn't aimed at you but him. He's beginning his rationalistic deductions from the same place Leibnitz did, more or less. Ah, that is true. I thought that might be what you were getting at. Leibnitz, though, says it would be absurd to have an infinity and concludes there must be monads, though...at least that's what I remember from Dr. Peikoff's lectures. The good news (or bad, depending on the perspective) is that I get to read Leibnitz himself next year. Quote Link to comment Share on other sites More sharing options...
DPW Posted June 17, 2004 Report Share Posted June 17, 2004 Ah, that is true. I thought that might be what you were getting at. Leibnitz, though, says it would be absurd to have an infinity and concludes there must be monads, though...at least that's what I remember from Dr. Peikoff's lectures. The good news (or bad, depending on the perspective) is that I get to read Leibnitz himself next year. B. Russell has a lot of interesting things to say about him, which is suprising when you consider that "interesting" and "Russell" are two things that seldom go together. Quote Link to comment Share on other sites More sharing options...
icosahedron Posted November 16, 2010 Report Share Posted November 16, 2010 There are two mutually exclusive statements that can be said of an existent. Existent X is composed of something that exists. Existent X is composed of nothing. If the latter is true, then X does not exist, in which case X is not an existent, which is a contradiction. Therefore, in order for an existent to be an existent, the first statement must always be true. The first statement works recursively. X is made of an existent, and that existent is also made of an existent, which is also made of an existent, and so on. The logic so far is pristine. However, have you considered the fact that "Existent A is composed of Existent A", i.e., "A is A", is consistent with "Existent X is composed of something that exists? In other words, the sequence may begin to repeat after some focal depth. Heisenberg bites you in the behind at some level of resolution, so whether or not it is true, it indeed IS true at any given point in history that the sequence is finite for any given conscious individual, or collection of individuals -- even if they extend their forbears' knowledge as efficiently as possible (and so on with each successive generation -- the sum total of knowledge is still finite). What is true and undeniable is that changes keep occurring around us, and our grasp of those changes is necessarily in the form of discrete sensory inputs, which, however woven, cannot produce continuous percepts, nor continuous concepts (as opposed to concepts of continuity, which are the basis of judgment of concepts as discretely hierarchical, like a type graph in Java). Nonetheless, there is a "ticking", something that doesn't stop functioning, moving, changing around us in ways not wholly within our grasp, yet. Time causes all things to be bred, including innovations in thinking that lead to better grasp of Existence in all its forms. So, it is fair to note that the ticking doesn't stop, i.e., change is eternal (time is the essential dimension by which we account change ... or is it the other way around?). This recursion is infinite. Does this mean that infinity is real? But, eternal and infinite are two different concepts. That's why we have different words for them. Eternal is a perfectly good concept: "change occurs eternally" is not something that can be argued with whilst living and breathing and thinking. However, "infinity" is an invalid concept, because you cannot represent it in your mind with respect to existents in any consistent way. Even more fundamentally, this is where your induction got disconnected: You pointed out the process of iterative mental reduction (a form of induction), and then attempted to use it as a synonym for infinity. You can never visualize whatever it is that infinity means via an iterative method, because you only have a finite amount of time to work with, and each iteration takes effort. Eternal process of change, fine. Infinity, bogus. Cheers. - ico Quote Link to comment Share on other sites More sharing options...
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