Eiuol

Please correct me then: is infinity a concept that refers to any pattern that goes on endlessly and also refers to the whole pattern at once? That is certainly reducible (in the Objectivist sense) to perceivable reality.

Actual in this context means that infinity is valid in a metaphysical way. There is no actual infinity any more than there is actual justice. There is a potential infinity in the sense that while at this point in time there is a definite amount, but abstractly, some patterns go on forever. I understand you're saying natural numbers are observable, and that's fine, but a *set* of numbers is necessarily abstracted from a natural number. So an infinite set is no problem. Oist philosophy is not inconsistent with the axiom of infinity. See post #91.

Going off ideas I had based on of what GrandMinnow explained (and if you can clarify if what I say is consistent, GrandMinnow, I'd appreciate that), it seems to me like a countable sets include all the types of numbers that can be counted in some consistent, known way. So, natural numbers go on forever, but certainly countable as n+1. If I give you a natural number, you'll always know what's next. 1000, 1001, etc. I don't know if this applies to rational numbers, or other numbers. What's next after 3.543? Is it 3.544? Or 4.543? Any notion of next doesn't make sense, so extend it into infinity, and you might not know what the next number is, and even measuring cardinality of a set with those numbers is a problem. You'd have to define the pattern better. With just decimals, it's not so bad, but get to complex numbers, prime numbers, irrational numbers, then the problem gets worse. I think you're saying that since there are no actual infinities, only potential infinities, it wouldn't make sense for infinity to have varying sizes. Justice doesn't exist walking around "out there" and it wouldn't make sense to ask if one justice is bigger than another justice. A numerical comparison between abstractions that have no physically measurable parts is hardly sensible. Certainly there is a metaphorical size, but no actual size. I can say if a tree has a bigger height than another tree, because they are actual; concretes are being compared. But I'm doubtful that such an approach is right. Concepts I think can be rightfully considered infinite sets, because an infinite number of members (referrents) can be put into a concept, and forever into past and future. For some concepts, a size between abstractions makes sense. I'd say mathematical concepts are the main type of concept where a size comparison can be made. A number basically abstracts everything about an existent except mere existence, so a "3" is just 3 objects of any size, shape, color, or anything else for that matter. Comparing small numbers could be perceptual, and a simple version of comparing tree height. With big numbers, how could you say 5000 is smaller than 90000? There must be abstract comparisons, and you are unlikely to find an actual 90000 of anything. Still, that's somewhat concrete. At levels of abstraction of algebra and beyond, which are derived from those simpler numbers and mathematical concepts, there won't be any concretes. Is 5000x bigger or smaller than 90000x? It's smaller of course, but you don't even need any concretes to answer the question. The value of x isn't even needed. Basically, any expressions (5000x, 90000x) are patterns that are bigger or smaller, at least when abstracting from numbers/math. Infinity is something I barely understand, I just see it as a way to capture how abstractions and patterns go on forever without regard to time. At the very least, two infinities can be of different sizes even if uncountable, provided that their patterns as sets differ in magnitude, cardinality, or some comparable way. If there are illogical conclusions, that would only mean the pattern in question is an absurd possibility, a floating abstraction. Of course, the thing to do is reduce a concept down to see where the problem occurred. I suppose the illogical conclusions don't matter in a literal way, as long as the person tries to resolve the contradiction.

http://books.google.com/books?id=VttF6CuC-cQC&pg=PT144&source=gbs_toc_r&cad=4#v=onepage&q=floating&f=false This is the best I found for "floating abstraction". Really there isn't a lot to say about it anyway, except that the abstraction is not connected to anything on the perceptual level. The link earlier for "stolen concept" is fine. Stolen concepts are all floating abstractions I'd say, because a stolen concept presumes that someone is using a particular concept in a totally untenable away. The bit about "rejecting sets" was part of GrandMinnow's response to me regarding greater and greater infinities. There are no actual infinities because that would imply an existent that is literally boundless and without physical constraint. Infinities only exist as mental entities, and not as anything that is perceivable. In that sense, infinity is an "artifact" because it is created for an epistemic purpose, even though there are no infinities "out there" metaphysically. (Some of this post is probably stated elsewhere, but this also partly answers Daniel's post #54.) Well, you were very unclear in your word choice for me, hence my clarification post. I think we're all on the same page now.

Ah, I got a little confused when you said artifact, earlier I read that as suggesting sets were invalid concepts with regards to math.

I certainly agree that infinity doesn't exist in a metaphysical sense any more than concepts in general exist in a metaphysical sense. Insofar as they are epistemological though, sets seem quite important for epistemology. If my math terminology is wrong here, anyone can correct me. I could call all objects that fall under the concept apple as Set{A}, and everything else as Set{~A}. Obviously Set{A} is things that are similar, and Set{~A} is things that are not similar to Set{A}. In other words, Set{~A} is just the set of everything else outside of Set{A}. Not only that but concepts refer to past, present, and future, so Set{A} can grow and change infinitely. I fail to see where sets are even a possible issue for Objectivist epistemology if concepts seem to behave as any set possibly could. I fail to see an issue with infinite sets, too, because, well, concepts are sets that go on forever in both time and number of referents, used for an epistemologically purposeful end.

Since you are certainly willing to explain yourself and it has helped me understand, what is in fact wrong with accepting greater and greater infinities in the first place? What I'm thinking is that while some patterns can go on infinitely, the magnitude in which patterns go on infinitely can vary, which seems to suggest that "greater infinities" makes sense. Some magnitudes can be greater than others depending upon your level of abstraction.

Moralist, would you please stay on topic for once? You're not even remotely on topic.

Yeah, but the action you advocate is basically pragmatism. There's a lot of extreme assertion of individual dedication and possibility to do *anything* they set their mind to. This is pragmatism in the sense of "hey, I can't do anything about it, so I'll use my bodyless mind to overcome these obstacles". To you, it is moral certainty and confidence. To me, this is total pragmatism because people are *absolutely* constrained by force, and they cannot overcome the obstacles in any reasonable way except eliminating the obstacle, which is difficult. Pragamatism I see as giving into a situation and simply to act within the constraints of a bad system. You basically said in post 110 there is a loss of freedom because there aren't enough people that deserve freedom, which is pragmatic in the sense of "bad people will be bad, so I'll go sit in my personal Gulch until people learn!!!" Sure, living to the best of our ability is great, but it isn't room enough to say it's just one's own fault that anything negative happens. You call some things bad, but only advocate dealing with it because nothing else can be done at all.

I don't think this is called AmericanCapitalist.com This is pragmatism at its finest, particularly because you make no moral objection whatsoever to taxation, nor are you asking a single question about it. The nature of force is that you are not in control of whether you pay taxes. If you have a point, then make it, but if your only point is pragmatism where any possible injustice is one's own fault for not reasonably responding to actions, because force is at best an illusion, then you are in the wrong forum. I judge this from 500+ posts of yours. Anything you've ever espoused is pragmatism and never even talk about Objectivism except that you really really like Atlas Shrugged. I may be out of line here, but really, this forum is not merely your soapbox.

Indeed, so why don't you provide a justification then? I may be a broken record here, but I really am curious.

Yes, but why must LEM contain meaninglessness? Why is having distinct infinities a problem any more than complex numbers, as Grames suggests? You keep saying there is an issue with this, but not why it is an issue for LEM. What is the meaninglessness you are referring to?

Presumably if LEM implies the existence of different cardinal infinities is problematic; you were saying rejection of LEM is proper because LEM leads to that conclusion. I get that much of your position. But... why is having different cardinality infinities a problem anyway? Maybe a formal definition of LEM would help here.

LEM isn't a tenet to Objectivism so much as it is crucial to logic. All LEM really says is that there is no third option for certain concepts. For Objectivism and its epistemology, the only implication really is that there is no third option for existing or not existing. What would the third option plausibly be? Beyond that, it's possible to use LEM wrong, and false dichotomies are examples of LEM being used wrong. Secondly, how does Cantor's theorem have any implication on the way I described LEM? I really don't know, so I'm asking you to spell it out.

Concrete as in perceivable entity as opposed to abstractions of those perceivable entities. Galaxies, cats, rocks, atoms, bananas, books, mountains - these are all examples of what I mean by concrete. We can discuss ways to classify these entities in terms of needing tools in order to perceive them, but the point I'm making is that these don't require abstraction to be able to observe. Existence by its very nature can't be grasped in this way, because it is an abstraction of everything. All measurements except mere existence is omitted, establishing the concept "existence". So what I'm saying about philosophy is that it deals with reaching wider abstractions and detailing the general "framework" of those abstractions. Science, on the other hand, is about getting into the specifics of reality, not trying to abstract per se - even if science involves a lot of abstraction. For example, science answers how consciousness works (the cognitive science fields), while philosophy abstracts in order to present a framework of just what consciousness is (philosophy of mind). Of course, both science and philosophy involve induction, but they are not identical. That could be a taxonomic question: if I see a new set of characteristics in a generation of lab-grown bacteria, then I'll figure out if it needs a specific classification. But what does evolution suggest about the idea of change? Are there just definite lines between everything that exists? This new species could actually be classified as that previous species in an important aspect, but what is an important aspect anyway? How can I take into account the newly evolved animal without obliterating how I understand the world? Answering that I'd say is philosophy, just used in a biology context! So, it is not strictly taxonomy. Actually, it even says a lot about how to approach Objectivist epistemology (borderline cases, essential characteristics, concepts aren't intrinsic or subjective, concepts as tools of understanding). These questions are quite different than asking what the specific causes of change are. I know this wasn't addressed at me, but this is important to expand on. Some ambiguity is fine, considering the conceptual limitations of all people. One-to-one concept-word correspondence is a lot of information to keep track of and remember. For the sake of conceptual economy, there needs to be some ambiguity, but fortunately, the human mind is really good at disambiguating word meanings. Not that accuracy is intrinsic, but a conceptual mind is good at this. If I say "I'm going to the bank to cash a check", do you think I'm going to a river bank, or a bank *building* filled with money? If I talk about a right to bear arms, do you think I'm talking about a right to the arms of a grizzly bear? These are all great examples of ambiguity, but they are not problematic most of the time. Those examples suggest your principle is unnecessary and probably makes language more difficult if you get rid of all words with more than one definition in favor of one concept and only one concept. What works better is no more than one word per concept. The concept of a large mammal that hibernates in winter (amongst other characteristics) is given the word "bear". But what about other languages? The concept of a bear is given the word "oso" in Spanish. Even my own principle is problematic. Rather than limiting how words can be used, maintaining an effective conceptual economy is important. Like unit economy for a basis to form concepts, I'm suggesting a conceptual economy as a basis for multiple concepts per word and even multiple words per concept in some cases. Regardless of what happens with words, though, concepts don't change. That's why "oso" makes just as much sense to me as "bear". I'm saying that the so-called communist postmodernists are just plain ol' postmodernists. They are categorically different from communists, even if some of the consequences are the same. Communists can be combated at least with evidence, and at least a communist would say you are wrong. A postmodernist would just say my truth is different than their truth. Nothing can be said to that. I point this out because it's important to understand one's enemy. (As an aside, I think the only way to combat postmodernism is to mock it with humor and the absurdities that it implies).

Would it be just as valid for you to say "As a woman, you need the experience of being able to stop back and say, 'I did that'" ?

Which concept(s) is Rand confusing with the concept value? All you said is that there is more than one sense to use the word value.

I'll try to be brief. Even tea has some psychological consequences, as does every action. Mind and body are inseparable. Consequences may be positive. I'm saying sex has greater consequences even in the positive sense because of the degree it is pleasurable, partly due to dopamine release and all that which *doesn't* happen with drinking tea. Greater consequences doesn't always mean bad consequences. I simply don't buy evolutionary psychology regarding sexual preferences though, so leave that out. It's a nonissue anyway, because we are specifically talking about how to evaluate sex and its consequences on life, not why some people are irrational.

This is begging the question. You are implying a fetus is a person, which is the whole part of abortion that is debated. Also, the practical effects aren't even the same - preventing something from coming into being isn't the same as ending the being of something.

No, evolutionary psychology hasn't shown that conclusively as far as I know, those are just taking presumptions of modern Western standards of beauty and making up some story where the standard promotes reproductive fitness. Furthermore, that is for sexual attraction and not necessarily attraction in a romantic sense, at least if you distinguish between the two. I wouldn't construe anything Rand said that would suggest that character qualities are all that's needed to establish attraction. At most they are necessary, but not sufficient. If a person lacks any good character qualities, they are not a person to start a relationship with. But then there are also character qualities that people value at different levels, values unique to individuals, or any assortment of other factors. The journal entry you mentioned seems like Rand was rationalizing her jealousy, but we're talking about jealousy and attraction basically, not to what degree Rand is being consistent with her own stated views. No two people will or even can have identical values, so it's not bad if there is difference. People vary in the value they "see" in one another. This is a lot to assume about a person. Maybe it's true, maybe it's not, we can't ask her, so we won't know. I don't think Rand defined promiscuity really, so I think all she's saying is that sex should not be treated as simply as what to watch on TV at night. Tea and conversation doesn't really have any of the psychological consequences that sex does, and are two very different kinds of action. Pleasure is fine, but that isn't all one should use to judge if an action is beneficial to your life. Apparently heroin has a hell of a lot of pleasure to it, but other consequences must be taken into account since it causes addiction and medical problems. Tea and conversation doesn't have really much to consider as bad, unless you're doing it because your family told you to and you don't even want to go (which would be second-handed). These type of questions are why pleasure shouldn't be the guide to action, because possible impact on your life is just as important. Hedonistic utility is not the measure, even if pleasure is important to living a happy life. Sex clearly doesn't have the consequences as heroin, but it is not as straightforward as tea. More or less, all Rand implied is that if you have sex with someone, they ought to be really important to you, but I'm afraid that Rand didn't talk about *why* extensively except for one section of AS. I don't think this response has anything to do with jealousy actually. So, if you would like to talk about what makes for attraction and/or a discussion about casual sex, please make a new thread. You probably could do a search on either term and use an old thread.

I agree with what you say about jealousy. I do think Rand acted jealously given what I know, which is improper of her. I'm not sure what to add that's new, except perhaps that jealousy is an indicator of a lack of trust in another person. If you are concerned that someone is going to abandon you due to mistakes or failing to see the value in you, something is wrong with the relationship that needs to be fixed. Jealousy is primarily about a possible loss of a value, so this applies to even friendships. Someone acting in their own interests and spending time with people in addition to you is not a threat to you. Their good is your good, and does not indicate that you are worth any less. More or less, I do not think there is any rational basis to jealousy, unlike some emotions like fear or anger. Those emotions may have a rational basis sometimes. Not that it should be suppressed; jealousy is something to deal with and hopefully fix. Hmm the only sentence I see is this one, which I didn't know about: "that a right is the property of an individual". That doesn't make sense to me, and I don't know where else she implied that terminology. I'll discuss it in another thread if you want.

Actually, I just think it needs to be pointed out, evolutionary psychology is flawed in many ways, most of all because we don't have any observations of primitive humans. That would be impossible without a time machine. At least in this context, people have such considerable control over behavior due to cognition that speaking of desires in the same way as say, chimpanzees, is not applicable to the same degree.

Well it makes no difference in that context, "woman" in place of "morally good female". I'll just place "woman" in place of that *each time* I say morally good female. You said Ayn Rand is a woman thinks like a man more or less, and said it's rare. You explain how a man thinks rationally and objectively, therefore Ayn Rand thinks like a man. Basically, I'll phrase it this way: How does a woman think? You said rationally and objectively. Okay... is there any difference from how men think, then? If so, what is the difference? If there is no difference, then "Ayn Rand thinks like a man" is a meaningless phrase. I know you didn't say what you bolded, but it is implicit in what you are saying, whether or not you realize it.

That doesn't make any more sense than saying than asking if the Internet can operate without objective rules to its operation. The Internet has protocols and all that without a central, monopolized agency. In some sense there is a market, but little deviation exists precisely because no one would get along. That would especially be applicable to violence - people don't *want* to be killed, unless we want to presume a Hobbesian world. Rules can and do exist without a central agency, so certainly police agencies/courts/laws are reasonable. If anything, this is how the world works right now. Multiple governments means multiple standards of law and of course a variety of people wielding force, and some governments wielding force wrongly. I see no difference from just saying "anarcho capitalist private agency" and "government". At least today, in 2013. My point is not that I think anarcho-capitalism is right, but that your arguments are bad. If you want to really demonstrate how government should be distinguished from private agencies, go through an example of it in practice. An thought experiment I like is consider how a "slave contract" would be dealt with. Suppose I decided to sell myself to you for you to control my life, doing this with a contract. People may think I'm crazy to do that, but hey, it's my choice I'll claim. Would this contract by respected in any sense, and if not, what would be done about it?

I saw this mentioned in a class I'm taking, and since I'm basically involved with libraries, data storage like this is pretty cool to me. The first thing I thought of was something from the scifi book Count Zero (William Gibson!) called biochips. The biochips are used for extremely advanced computing, but the DNA storage here is like a primitive version of those. Even if primitive, clearly it's the beginning of biologically-compatible data. If I really want to get wild, DNA storage can supplement human memory or perhaps extract information right out of someone's brain! Or if someone invented a "DNA drive" for a computer, then that may totally alter computer architecture as we know it. Really, a scifi imagination can go many places with this. Of course, this has to be put in perspective. I read the actual paper, and not even that mentioned how long decoding took. If Bluecherry hadn't mentioned that link, I would not have found that it took "more than two weeks". Thinking back to 1960 that's probably not too bad, but 739 kilobytes in 2+ weeks is very slow compared to what any of us are used to. A 50kb document of mine would probably take a day and a half to load, while my computer loads it within seconds. The article said two weeks to read the data, and it probably took longer for the whole process. They had to mail the test tube of data to Germany, and then of course time to prep the equipment. I'm a bit confused by the wording, so I'll have to see what the total time was. What the scientists did sounds like it was mainly a trial shot that worked out pretty nicely. Quadruple layers of error-checking is definitely taking the safe route. Although, one of the pieces of data couldn't be decoded, so the scientists had to figure out what was missing and reinsert the data themselves to complete an accurate decoding. But hey, at least we know DNA storage can work. That's what counts right now.