Nate T.

Nah, no violation of identity-- this is an example of the same thing being given two different labels. It's no more contradictory than saying that 1/2 = 2/4; it's just that the concepts involved (limits) are more complicated. The real resolution to this is to recognize that while 1 is just that same unit that everyone knows and loves (?), .999... is actually the sum of a geometric series, and that when you sum the series you get 1, which is what .999... = 1 is really saying. I'm not sure how much math you've had, but I can probably give a quick proof if you're really interested.

What's statistical empiricism?

I have heard of a way to think of a particle interacting with its antiparticle as the same particle traveling forward and backward in time, but I don't think that physicists literally believe that's what's happening-- and it's a far cry to 'unleashing the power of our minds to remember the future,' that's for sure. I suppose that in a certain sense, humans fortell the future all the time-- using theories (scientific or more common-snese based) to predict what will happen in a given system. However, this probably isn't what the good professor was thinking of. There' a big problem with the idea that it's possible to remember the future. If you could remember the future, and you act to change it, did you really remember it?, etc. So on the face of it, this theory either contradicts the existence of volition or causality. That, along with statements like this: it's pretty clear that we shouldn't take these 'scientists' seriously, since they obviously have some kind of religious/social axe to grind.

Also, thanks, everyone, for your help with this!

Kevin, I think your resolution, that the problem is verbal, is the right one. I also think the question is trivial at best, whatever its solution. The reason I asked it is because I was studying IOE, and I wanted to know exactly how Objectivist Epistemology fits into all of this, in order to improve my understanding of the subject. Unlike most problems that fall under IOE's scope, I couldn't solve this one immediately, which is why I came here for help. This problem hasn't "obliterated my last brain cell," and so it does suffice to simply say that the answer to the problem is found by closely examining the context of the problem. If you think that considering this question is a waste of time, then I suggest you waste no more of your own on it. [edited for grammar and spelling]

Yeah, I agree, there's a subtle equivocation on 'same' going on here. The two houses are the same in the first sense but the house itself doesn't remain the same, since it was at one point destroyed. Since the question was phrased as though the first toy house constructed and the second were up for comparison, I'd say that the first definition applies and we ought to conclude that the two houses are the same. I don't really-- it's not as though Objectivist Epistemology hangs on this issue. But these little things irk me, especially when Objectivism applies so nicely to just about every other philosophical issue.

Hi, Andrew, Good point. Generally, we don't mention any kind of time-dependence when discussing entities, unless the change affects the attributes of the entity. For instance, if we take a scoop of dirt off of a mountain, it's still the same mountain, even though technically some of it's parts have been removed-- Rand succinctly defined a mountain as "a part of the earth that goes up", and removing a little dirt won't change that. However, if you take the roof off of a house, it isn't a house anymore, and what you have metaphysically is just parts of a house: a roof and the constructed walls and floor. Hence, we don't particularly care how long it has been from the construction of some table when we identify it as a table. Now to tie this into the identity of an entity as opposed to the definition of an entity, consider the human body. Since blood cells in the human body are circulating, among other things, does this imply that a human being is a different entity every moment a cell changes position? Evidently not, since the overall form of a human remains the same. It's the overall attribute of being a human being that we need to be concerned about, not necessarily the exact position of each and every cell. This seems like a good argument for the 'one house' view. I believe that it's metaphysical. I remember Rand drawing very careful distinctions about this issue in the workshops. An entity is epistemological in the sense that it exists as a relationship between parts, which man grasps. However, that relationship must itself be metaphysical, or we would have nothing to grasp, epistemologically. So entities are metaphysical. I'm starting to think that the entity which is the toy house in this example is the same toy house in both cases, and that it's proper to say that the adult in the scenario 'rebuilt' the house, as opposed to made a 'new' house out of exactly the same materials. My original reason for thinking this still holds-- the entity is its attributes, and so if it has exactly the same attributes it did before, it's the same house. But I'm still not entirely convinced by any of my own arguments.

I was in my Philosophy of Science class, and the topic of Metaphysics came up. The professor gave the following metaphysical problem. This was a remarkably cogent question in a class where I was used to hearing a lot of nonsense. Since it's clear that both of the toy houses were composed of blocks arranged in a form which resembled a house, both toy houses are entities. Obviously, both of these can't be right. Now on the one hand, when we're talking about entities, "the entity is its attributes." (IOE, 266). Hence, if we suppose that the first house and the second house are indistiguishable with respect to the placement of the blocks, then we'd ought to conclude that the two houses are in fact the same house, and that what the adult did was to 'rebuild' the house. However, it makes me very uneasy to say that an entity can come into existence, go out of existence, and then come back again. After all, during the entire last exposition, we were referring to the houses as distinct entities, i.e., as the first and the second toy house. So in this sense we should assume that the entities are distinct. I've read the workshop discussion of Entities in IOE, but it didn't answer my question. Given what I know, I'm tentatively concluding that the entities in question are the same house. What is the correct answer as to the status of the toy houses, and what am I doing wrong?

I'm in a philosophy of science course right now, and my professor deals with philosophy of language, and loves Wittgenstein. From what he told us, Wittgenstein holds that there are words which are so loaded with meanings and connotations that one shouldn't bother to try to define them, and instead rely on a 'family resemblance' to link together the different senses used for the same word. As far as I can tell, he also states that necessary and sufficient conditions for describing a concept (i.e., a definition), is not always possible. Objectivism, naturally, rejects such a vague theory of language. Frankly, I think Wittgenstein's just lazy. Rand herself mentions in IOE that "Wittgenstein's theory that a concept refers to a conglomeration of things vaguely tied together by a 'family resemblance' is a perfect description of the state of a mind out of focus." (2nd ed, 78)

IOE 2nd ed., 260.

Hi Craig, In Introduction to Objectivist Epistemology, Rand writes that "'Time', as the widest or parent abstraction of all subsequence and narrower measurements of time, is a change of relationship." (emphasis mine) The gist of the idea is this: it's evident that we have memory (since memory is a prerequisite to concept formation), and this allows us to notice that things don't stay the same-- we remember that things in the past are different than how they are now. It's from this that we get the concept of Change, and from there, the concept of Time. So there's no need to bring in the idea of a priori concepts at all (as indeed there never is a need), since time has a referent in reality. Also, as Bowser correctly points out, there really is no good reason to distinguish between a priori and a posteriori concepts. Even grasping that 1 + 1 = 2 requires concepts that have referents in reality. If Rand's concept theory is unfamiliar to you, you should definitely check out Introduction to Objectivist Epistemology as a primer. Nate T. [edited to correct spelling error]

I'm sorry, Josh, but an attempt to link Satanism, Ayn Rand and the Bush administration (of all things!) with one post is just too funny. If you want to link them together in the way that you have, you'd better back it up with more than vague analogies, 'satanic' principles and out-of-context passages.

"If you do not trust man to govern himself, why then trust him to govern others?" --Thomas Jefferson (paraphrased)

Relationships still exist, even without anyone there to observe their existence. However, if there were no observers at all, the concepts of the relationship (or the act of grasping the relationship) would not exist. For example, the physical laws of the universe would remain even if no one were around to observe them. However, the science we call physics would not. I'd like to add my two cents in on the "does the universe have mass" question, by asking whether this question has any relevance whatsoever. From a Newtonian standpoint, mass quantifies the amount of intertia a body is supposed to have (F = ma). Since the universe doesn't accelerate, and you can't apply a force to it either, why should we care whether the universe has mass or not?

Thanks! I try

No, in the hierarchy of knowledge, infinite is defined in terms of finite, since infinite just means not finite. So it doesn't follow that something infnite exists (and actually, nothing infinite does exist, metaphysically).

Yecch, don't get me started on Captain Planet. It's the worst example of Environmentalist propaganda yet. I remember a particularly telling episode in which the five eco-teens faced up against a counterpart team of "evil" businessman who themselves summoned some kind of super-villan thing that represents pollution. It's a real shame that kids watch this stuff. Terrible.

Sir Issac Newton was born on Christmas day, so I like to joke that with his birth (and subsequent invention of classical mechanics and the technology that ensued) came the Enlightenment, where most of the ideas of reason, rights, etc., were historically germinated. However, maybe not such a bad idea.

Hi, McGroarty, Actually, I'm studying a certain integer associated with every convex polygon (which for lack of a better name I call the degree of the polygon). The degree turns out to be an invariant over linear isomorphisms (if not some more general kind of transformations-- I'm looking into it), and so may distinguish some more familiar properties of convex polygons. As Stephen already mentioned, such a thing would be useful since convex polygons come up in lots of other contexts in mathematics.

Godel's Incompleteness Theorem states that, given a collection of axioms powerful enough to describe arithmetic, there are statements describable in the language of the system which are true, but not provable in terms of the axioms. A lot of my math buddies are really upset by this, since they're used to "truth" and "provability" being the same thing-- that is, if something isn't true, you can find an instance of it being false (a counterexample). Some even go so far as to say that it disproves the Law of Excluded Middle. If Godel's Result applied to reality, I might agree with them. However, it does not. Reality isn't based upon a set number of axioms-- you can't "derive" reality from just "A is A" (which is a common misconception that I struggled with for a long time). Sense perception is also axiomatic, and there's no limit to the kinds of things that one can observe. So trying to apply Godel's Theorem to reality is just being Rationalistic. So, I actually take GIT as a nice refutation of Rationalism-- there is no guarantee that you can prove every single statement to be true or false with a limited number of assumptions (axioms), and truth and falsehood has meaning outside of the mathematical system in which one happens to observe them, i.e., it has meaning in reality. You may have to include outside information to determine whether something is true or false, even if you can describe it in the language of the system. Needless to say, GIT does not prove the existence of God.

Hi Stephen, Okay, that makes sense.

Hi Stephen, Wow, that's impressive! Do you recommend that I try applying there for grad school? I'm making my final decisions about where I'm applying now.

Hi, Stephen, Well, not to say that mathematical theories that have no direct connection to reality aren't useful or never will be. Just that I personally enjoy researching mathematics that has a visual or otherwise physical interpretation, as opposed to, say, abstract group theory. Certainly they all have their purposes, though. The prgram itself feels like it should be grad school since they go very fast, except that they grade much easier. I really like the more relaxed approach of learning mathemtics through optional homework, even though it does put a lot of stress onto the final exams. Also, I like the fact that everything is so cheap over here, since the forint is so inflated. The students are all very smart, of course, and the part I like the most is that I haven't really run into the hyper-competetiveness that can be part of a group of really smart students. I like it better when I can collaborate with my peers on homework assignments and bounce ideas off of them in general. Something that I've been meaning to ask (if you don't mind, that is): Are you a professor? If so, in what subject and at which school?

Hi, Stephen, I agree that memory as a function of consciousness is a primary, since we need memory to form concepts. And I think that's it's worth stating explicitly, since one could try to attack concept-formation through the 'unreliability' of memory much as in the same way as one could try to attack sense perception. And that's why it made me nervous that Rand didn't mention it in IOE. But what do you mean when you say that memory as a physical component is not axiomatic? I wouldn't think that a physical component of anything could be axiomatic or not, since it isn't a concept but a physical existent.

Hi Stephen, Bingo! I didn't know this program was that well known. To be honest, most of your explanation on Finsler spaces was above my head. I'm just now taking Differential Geometry, and we've just gotten to the Riemann metric and the Levi-Civitra connection. I'll certainly look into Finsler spaces when I have the background for it, though. And I completely agree with your sentiment about the interconnectedness of math and physics-- and in fact I better enjoy studying areas of mathematics that are directly motivated by physics and physical objects as opposed to some of the highly nonconstructive areas of mathematics where all you have to go on are axioms. How about yourself?