aleph_0

Due to the constructibility of complex numbers from real numbers, real numbers from rationals, rationals from integers, integers from naturals, and naturals from sets, then if there is to be any philosophical issue at stake, the issue must be: Some objection to set theory or some objection to one of the constructions. If there is any objection to either, I can only imagine it comes in the form, why would we construct a mathematical system that is like that? Here, the answer must always be, "Because it serves a purpose." In the case of the natural numbers, it serves counting; in the case of integers, it serves counting quantity from a privileged point (namely, 0); in the case of rationals, it serves quantifying ratios; in the case of reals, it serves measuring without assuming a least unit of measurement, or imposing other geometrical constraints on the objects measured (thus making the system extremely general and applicable to many objects); in the case of complex numbers, I don't think I have such a succinct way of stating its purpose, but it is useful in representing rotations in R2 which appear in electrical engineering, quantum physics, and so on. How these mathematical structures succeed in representation is an interesting question, the answer to which is--I suspect--that there is, so to speak, an homomorphism between the behavior of our mathematical structures and aspects of reality.

Take the scenario where one person borrows another's book, accidentally destroys it, buys her friend a new copy, and says, "Sorry, but this is the same edition as yours and everything, they're identical, hope you don't mind." That's a natural context and natural use of the word, in which "identical" does not imply quantitative identity.

His account of explanation has been attacked pretty solidly, and he has since revised--then his revision was attacked, and he has no largely capitulated on the subject of scientific explanation. My version, I admit, borrows heavily from his, though.

Note: The days of Skype are kind of past, since they've taken down the feature where you can have a public chat room. However, there are a couple other programs out there where you can do this sort of thing, and I sometimes use PalTalk. If there's any interest in an O'ist chat room there, I'll set one up.

Perhaps not, but the question at issue seemed to me to be: Would a rational political society outlaw expressions of false propositions? I took it that the court case was a related issue which perhaps inspired the question. You may note that the only question-marks that appear in the original post, and in the text which I quoted when I made my response, occurred where individuals were asking about the proper legality of stating lies, so I don't think I'm in danger of posting off-topic. Unless, perhaps, the sale of the rights to view the news implies that the statements in the news are factual, rather than fictional? I think it would be fraud if I paid for cable or a newspaper, only to find that the "news" company (or, in this case, cable company which had promised the provision of cable news) had decided to cut the costs of hiring journalists by publishing a collection of Mother Goose stories. Ah! How silly of me, of course we should not ignore the pragmatics of the expressions of the contract, but instead we should ignore the propositional content! If you label a product as a "consumer report" for the purpose of selling it, but do not actually sell a consumer report, that seems like a quintessential act of fraud. If somebody tells me he will give me a consumer report in exchange for money, and then hands me a brick--I say he's a fraud. This echoes exactly what I wrote: So we do not disagree. Good. Nor do I, but even if there were some disagreement on this point, I don't think it's worth splitting hairs. This seems like the kind of thing that should either be left to explicit legislative act, or court decisions. In either case, when the rule is made explicit and companies are aware of the laws, they will write contracts with their consumers or broadcast their content with the appropriate restrictions, in order to avoid such problems.

I've been thinking a while about a question that Jon Stewart (yeah, yeah, shoot me for liking The Daily Show) asked of a Republican on his show: If you think that public healthcare and government programs in general are inept, then do you believe we should have private medical care for our military? The Republican was probably too stodgy and pressured by being in front of the cameras to be willing to consider the alternative. Personally, I'm not sure. I'm not entirely sure about the idea of the government granting private contracts in general, since this seems like government favoring some individual private enterprises over others. Besides the possibility for corruption, that seems like the kind of thing we shouldn't allow government to do for the same reason that we don't want government running businesses either. Monopolization tends to follow in the shadow of government "entrepreneurship". But if it's cheaper and we are to make decisions about how to most effectively use taxpayer money, then is it necessarily bad? If it's better care for the people who are risking their lives, is it still right to maintain a government medical program for our soldiers? Perhaps a third option. Give them insurance which they can use wherever they please. Perhaps--to encourage cost-effective behavior--give then better insurance if they prove that they've researched at least three locations to search for the lowest price. Whatever, point being, how should we administer benefits to government employees? A similar question is, should we contract out the construction of public buildings, like the courts and whatever roadways may need to be built for the police and military to effectively do their jobs? It seems like it might be wasteful to have a construction division in our government.

Oh right, getting back to the point, would it be a violation of contract to sell media which publishes false claims? I'm not entirely certain, but I do feel confident in saying that, if we lived in a capitalist society where this was somewhat uncertain, then media companies would add provisos in their contracts, stating that they will not be held accountable for any claims which may be false--or they would qualify all claims with "a source has informed us that...", so that their claims are generally immune from falsification.

I think, perhaps, this might be in the spirit of what Turing had in mind: When making a claim to another person, does this constitute a verbal contract that your claim is truthful, thereby making lies a form of fraud? I don't think so, but it's a good idea or exercise in analysis to discuss the matter. Under most circumstances, I see no reason to suppose that any given claim comes with any implicit contractual agreement of truth. Contracts have to be stated in language that makes it clear to all parties involved that there is a mutual agreement of exchange, and that's not the case by mere assertion. However, some situations may seem harder to adjudicate. For instance, if you publish consumer reports, and claim that a given product is defective when it's not--or vice versa--one might argue that this violates a contract. I believe that you commit (something like) fraud when you sell meat that has spoiled (without letting the consumer know that it's spoiled), or a car with no engine. We can dispute this if others disagree, I'm not sure what the Objectivist consensus on this is. But when you call something meat without additionally qualifying that statement, standard English rules in normal contexts cause your listener to understand that the meat is edible when cooked in some standard way. If it is rotten or laced with poison, this is fraud because you were led to believe something about the product which is false. Likewise, if you sell someone a car, because of the pragmatics of English, you lead your listener to understand that the car has an engine. Where to draw the line seems difficult, and the appropriate discussion for a court which spends decades and centuries establishing case law, as well as any kind of specific laws enacted by a legislature. We might argue that pragmatics should not be taken into consideration when forming contracts, but then take the following scenario: Somebody commits adultery with another man's wife, and the husband learns of it without telling either of the other two, then invites the other man over for dinner and serves him poisoned food. This isn't terribly far-fetched, things of this ilk are reported in the news fairly often in a given year. If we don't call this murder, that seems outlandish, and if we call it murder then it would have to be because the person identified the food as "food" rather than "poisoned food". If he had presented the food to the other man, calling it "poisoned food", then we probably shouldn't charge him with murder. So if I'm convincing in this argument, then by identifying a publication as a "consumer report" implies that the publication tells facts about the performance of a product on the market. In that case, to do otherwise deliberately seems like a breech of contract. [Editted for better wording.]

I found this interesting: Let us consider different possible interpretations of this. First, let us be naively literal. No bosses? So a very radical form of anarchism, in which no person has any influence upon any other human being in any way. After all, to even speak to another person is to impose one's thoughts upon him. This is echoed in more mainstream communist arguments against free market freedom of speech. This would be amazing. Every individual has to live equidistant from every other, so that no individual can influence another. As soon as one person decides he's tired of hanging out on his plot of land, I guess he'll go take something from his neighbor and wham-bam government established (after all, he will now be wielding force against another person, and so de facto be the one organizing resources [namely, taking them for himself] and controlling the use of coercion [he goes around doing whatever he wants]). Well that didn't last long. Maybe we need a notion of boss and superior that's a little thicker-skinned. Let us say that a boss is someone who uses coercion against those who initiate violence--in this sense, a CEO wouldn't be a boss. But, er, yeah, this is already too much like capitalism since we're letting there be CEOs and punishing all and only the initiation of violence. Let's try again. Well maybe the sense in which there is no boss, is the sense in which EVERYBODY is a boss! Everybody votes about what laws go into place, with uninhibited control over every aspect of everyone else's life, as well as the means (and ends! ... Communists always seem to leave out that part...) of production. Now we're cooking with gas, this is starting to look like the communism we know and love. I wonder why it wasn't worded this way in the article. *shrug* Anyway, in this utopia, the religious majority of the population will undoubted want to put an end to homosexuality, atheistic college education, and... well... eh, this is kind of embarrassing. They'll probably vote communism away in favor of theocracy. Hmm... In order for Communism to perpetuate itself, maybe a different notion of "boss" is still needed. ... ... OH! I get it! There is no boss from the perspective of the author, because HE has no boss--because he IS the boss! Now it makes sense. He just dictates the way he wants things, and is hoping he'll convince enough dolts that it's a good lovey-dovey plan for the betterment of everyone everywhere, even though he hasn't the slightest credentials for running the cash register at a nickel-and-dime store let alone all of the industries and lives of a nation. NOW it makes sense, NOW I understand communism. Thanks!

Having some first-hand familiarity with the selection process, this is certainly not a reason. Perhaps in a freer market, private universities would impose demands on selection committees that the people they hire espouse free-market ideals, but it's not the case that people in modern philosophy (outside of political philosophy, anyway) select based on the desire to promote a political agenda. Derrida hasn't really affected American philosophy at all. Only the extremely few continental departments. Kant and Rawls, and Kit Fine are far more influential. So did logical positivism, but it had a place in academia. A fortiori: As noted, Objectivism is a growing presence in academia and shows now signs of slowing. I am one of several graduate and undergraduate students very influenced by Objectivism, and there are already several powerful departments already populated by Objectivist professors, one of which is in America's top-five philosophy departments: The University of Pittsburgh.

Definition of Norms The sense you're familiar with is a more colloquial sense. The sense used in philosophical conversations refers to concepts that are characterized by "ought statements". So my question is, is there ever a true, minimal sentence expressed as "You ought to do x," which is not a statement of moral requirements?

I'm reading the keynote speeches for the APA West and East (I think) from last year, given by Nancy Cartwright and Christine Korsgard. In Cartwright's article she proposes that we pursue a philosophy of science wherein we consider the creation of causal laws. I cannot understand this. She claims not to mean that the causal laws, which she proposes we make, are just special cases of more general laws. But the examples she gives seem just like that: "My accelerator causes the car to move faster, when sitting in a working automobile." She takes this to be its own causal law, which to me sounds absurd, and I cannot see what sense there is in talking about the creation of causal laws except to create certain conditions under which certain causal laws apply in a particular way (such as in the example of the car, where we construct the car so that laws of conservation of energy and angular momentum, and electrodynamics, and so on, work in the ways necessary for the car to move when the accelerator is pressed). In Christine Korsgard's work, she asks the question, "Why do reasons exist?" She proposes one explanation, which she believes motivates the rest of her views on the nature of reason, but I'm not convinced the question even makes sense. She says that reasons exist because we are able to reflect upon our own possible choices and to choose between the grounds we have for making these choices. Each ground we have for an action, in a non-reflective animal intellect would just be a cause--in a reflective animal like humans, it is a reason, a consideration in favor of the action. Thus reasons exist because we are reflective. At least, I think this is what she's saying, I'm going to go re-read this soon to make sure. In any case, she says that a competing view of reasons is committed to the claim that either reasons exist because the universe is logically unified, or that there is no reason for reasons to exist. I can perhaps see how logical unification would make reasons possible--I don't see how they make them necessary. But in the end, I'm left wondering what could possibly constitute an explanation for the existence of reasons. Are these two concepts nonsense?

Good example. I believe I agree with you, Odden, in the big picture. Do you believe that the choice to play chess is a(n im)moral one? What life-supporting purpose does it serve? It doesn't seem like the kind of thing to be an end in itself.

I actually didn't answer the question, which in part of your message you seem to recognize, though with the first two sentences you don't seem to. How I determined that your question is full of blatant jealousy: The jealousy is blatant (meaning apparent for all to see), and the question is full of it. Pretty simple. America is not a continent. True story. Look it up. There's North America (a continent), South America (a continent), the Americas (composed of two continents), and America (a colloquial name for the United States of America). The non-American Americas are not unidentified, for the most part. They're just stupid. The "we" is the English-speaking community. We've agreed to this. Also a true story. Answering the question would not be significant. I spend my time answering worth-while questions, for the most part. If we want to be particularly formal in our English, we could refer to Americans as "United States citizens" or "citizens of the United States of America". But hell, we're Americans.

When people were speaking of it not as an improper name, it was "united states of America" since "united states" acted as a modified noun, but so long as it's been a proper name it has always been "United States of America", which I believe is ever after the ratification of the Constitution if not before. Personally, I find the question so full of blatant jealousy it's not worth responding to. Do something significant with your country and we'll consider giving you a special name.

When I said mathematicians have figured this out, I wasn't making an argument, I was being a little flip. My analysis came from what was above it. And I'm not sure in what argument I've claimed that something is understood because it's no less understood than something else. I've claimed that we understand complex numbers because we understand real numbers, and I assume that people don't have a problem with real numbers. If that's not true, then we can talk about those, but since we started at complex numbers I think it was a fair assumption that real numbers were not in question.

As a further note, while you can give some semi-intuitive reasons why multiplying with negatives gives a positive in terms of counting, you can't give any such understanding for what you get by multiplying irrational numbers.

Only the part of the concept that actually doesn't matter to what you're studying. Point is, not all mathematics is meant to count or measure. Complex numbers don't do this--they, among other things, chart directed line segments. It turns out the way it turns out, because the properties I mentioned above are useful in the situations they're useful in. For example, applications in number theory and questions like, "Given a tetrahedron, count the number of ways of coloring each face black or white, such that no two instances of the counting could be viewed as the same tetrahedron considered from different perspectives. (E.g. you could color the whole thing white except one face, and you could color the whole thing white except some other face, but they'll look like exactly the same coloring if in both cases you look at it from the angle of the black face. However, coloring it black on one side cannot be made to look the same as coloring it black on two sides.)" If you replace your domain of numbers with sides of a tetrahedron, and just stick to the requirements of closure, associativity, and so on, you can answer this question by means of an algebra.

I think the point he's making is that, if multiplication is repeated addition, how do you multiply two negative numbers? If 5 x 5 is five plus itself five times, and 5 x -5 is -5 plus itself five times, then what is -5 x -5? -5 plus itself -5 times? How do you have -5 instances of anything? More problematically, what is 5 x pi? How do you have 3.14... infinite non-repeating decimal expansion instances of a thing? Or multiplication of complex numbers, and so on. Turns out, when you study purer maths, particularly algebra, that we're not really interested in numbers in the first place. What we wanted all along, in the roll of multiplication, was just some operation on some set that satisfied certain basic properties (like closure, associativity, commutativity, having a zero-element for one of the operations [+], and a distinct 1-element for the other [x], and so on). Multiplication in the sense of repeated addition satisfied these properties, but then when we generalize mathematics, we keep the properties and let go of this common-sense way of understanding the operation.

I just found out about him by finding some articles on JSTOR--what is the general O'ist impression of him? Favorable or un-?

I'll take a phenomenon to be any event, regularity, or disposition. Examples: A flagpole casts a shadow of a certain length; a person treated with penicillin recovers quickly from strep throat; the atoms of a sodium sample have certain properties, which determine their characteristic spectrum; a barometer's water-level drops suddenly, followed by a storm outside; a planet sweeps out a defined orbit in space. All the independent variables is in contrast to just some of them (a minimal explanation). In my account, I consider only one dependent variable, but I'm glad you brought it up, because I might ought to revise at some point to make a more nuanced presentation that considers multiple dependent variables. This shouldn't affect the substance of the presentation, though it would allow for more expressive power. The claim is not that this is an account of how explanations do or have occurred, precisely in this notation. The claim is that this account is an explication of the concept of explanation--i.e. an analysis of a concept, about which we had some rough understanding in the past, and now seek to make more explicit. In doing so, I introduce more explicit vocabulary. I have explained myself in thorough detail. I imagine you presenting this objection to a physicist or mathematician, demanding that he not use so many damn symbols. And then I lol. Their audience, and mine, is clearly not you. My audience is the philosophy of science community, manned by people with far more technical acumen than I have, who have themselves written formal accounts of scientific explanation WAY more detailed and formally complicated than my own. See, for example, Kitcher's Explanatory Unification (1981), which defines no less than 15 terms of art, with reference to such fields as algebra, model theory, and logic. Moreover, the study of explanation is traditionally less formal than the field of, say, belief revision. I suggest, if you have such complaints, you direct them to Gardenfors, whose literature is so steeped in statistical analysis that I--with a decent though imperfect background in advanced mathematics--find the more exoteric literature unreadable. There is at least one person on this forum who understands more math than I do, and has written about it. I know that there is at least one other distinct person who is comparably familiar with advanced philosophical literature. Moreover, I began the post in such a way that most anybody could contribute (the basic question: what is an explanation), and then delivered a more rigorous presentation. If someone has a more general objection to the association of explanation with the identification of independent and dependent variables, one which does not depend on a grasp of the details of the account I've provided, then I welcome it. I do so when it suits me, and sometimes I communicate with still more advanced people. I repeat my challenge to you, to present a more clear presentation of the same material. Provide an account of explanation as the identification of independent and dependent variables at least as precise as the one I gave, which makes no such use of notation. If it is comparably economical, I will concede that you are a better writer than I am, and envy your skill. And in which case, you could make millions writing scientific and mathematical textbooks explaining the confusing formalisms currently in use. Don't hide behind your insecurity about not understanding or having anything worthwhile to say, by lobbing accusations at me. [Edit: grammar]

[Edit: I'm removing my previous post--it was written in regard to Ifat, and I somehow didn't see the long list of people who posted after her.]

Complex numbers have a geometric interpretation; they are, with the exception of definitions of derivation and continuity and the like, just pairs of real numbers. Don't worry about them, we have this thing figured out. Take a slightly more abstract mathematical concept, that of isomorphism. This actually corresponds to nothing at all, and is--in a sense--a way of reading off mathematical structure imposed on a set. (That's not really what it is, but that's what it's used for, so close enough.) So sometimes our mathematical structures are just devised in order to organize our other mathematical structures. This kind of phenomenon, that of mathematics for the purpose of mathematics (not in the Platonic sense) comes up a lot in foundations. These are not troubling concepts, in my opinion. In the philosophy of mathematics, I think there are a few related, seminal questions: What is a mathematical entity, what is mathematics as a whole, how does mathematics figure in explanations, and how do we bridge the gap between the physical world and it (i.e. problems of model theory)? These have, by far, much harder answers.

This is, essentially, what I'm going to try to publish: 1) Let X = {x1, …, xn} be a non-empty set of independent variables. These are intended to be the variables upon which our phenomenon depends. 2) A = {a1, …, an} ⊂ C = {cr| r ∈ ℝ} where xi can take each value cj and A a set of (approximately) true sentences. A is to be the facts which obtain and help to explain the explanandum, and C will contain all the elements of the contrast classes for each ai. 3) For d ∈ ℤ, πd ∈ π = {πr| r ∈ ℝ} where π is the contrast class for πd, and πd is the explanandum (and so it is [approximately] true). In a sense, X is the domain and π the range. d is restricted to the integers in order to ensure that the formulae are of finite length, though really, we should think of d as merely an index to pick out a statement asserting that particular phenomenon in which we are interested, did in fact occur. 4) p is your probability function, p(πd|x1 ∧ … xn) = px(πd) is defined and for each xi, upon fixing some x1 = cs, … xi-1 = cs′, xi+1 = cs′′, … xn = cs′′′, the probability is different for at least two distinct values which xi may take (i.e. πd depends on each xi), and pa(πd) = p(πd|a1 ∧ … an). ε = <X, A, B, C, π, πd, p> is just the septuple of these. I claim that ε minimally explains πd just in case the context of inquiry determines the classes and probability function of ε and there is at least one cj ≠ ai such that p(πd|a1 ∧ … (ai ∨ ~ai) ∧ … ai ∧ cj) < pa(πd). ε maximally explains πd just in case the same holds, and is true for every cj ≠ ai. ε completely explains πd just in case X is the set of all the independent variables upon which πd depends. Note that there can be no scientific explanation of a tautology or contradiction because the probabilities will be the same on every condition, and πd will never explain πd since there can be no context which makes it appropriate to explain something by merely reiterating that it is true. If you can think of a good objection and I reply to it successfully, I'll cite you.

a=a, it sounds like you think there is no exact cut-off between moral and not-moral-but-nice, that it's a smooth spectrum from neutral to shades of better choices, topped off at perfectly fully moral. No? I've always thought these kinds of rationales were bad. I don't do many things just to avoid other people's disappointment or to see them smile--if I do, this is extremely minimal. I would do such things because I want to live in a society where people help each other when the cost-benefit analysis is so slight that actual money exchange for values isn't worth-while. This picture sees each of the options as somehow equal, though, whereas I want examples where there are some options which are better than others though they are all basically good and moral. I want to know whether there is ever a case where you can have a set of options where some subset are not only moral but moral + something extra which is nice, but which has no moral character. In this picture, there is only superbly, radiantly, starkly moral, and then flatly immoral. That doesn't seem right to me--can't there be people who do well enough? Eddie Willers or that construction worker friend of Roarks who probably didn't do everything he could, but did a lot, and that was pretty good. Maybe they chose to focus their minds on the best that they could achieve, but didn't focus as much as they could have.