Hal

I think that this is a bad definition. Mathematics can certainly be used to measure things, but saying that it is 'just' about measuring things (or even mainly about measuring things) is incorrect. What measurements are involved in complex analysis? Or number theory? Are these not valid areas of mathematics? What do you mean by calculus is "made possible by reality"? I suppose this is trivially true in the sense that if nothing existed then noone would have been able to come up with calculus, but calculus can be (and usually is) defined in a purely formal manner that makes no mention whatsoever of physical or geometric objects, and it still works perfectly well. Calculus is useful because of certain aspects of reality, yes.

If it describes existing phenomenon with tidier and more elegant math than any competiting theory, why shouldnt it be classed as physics? If the math works as well as many who champion string theory claim, I would take that as prima facie evidence of its validity - if things are that neat, there's probably some underlying reason. What new predictions does TEW make, out of interest?

Well I dont claim to be familiar with the science in question, but I think it's difficult to make predictions with any degree of accuracy when it comes to speculating about technology over that period of time. If I were in 1970 and trying to guess what life would be like in 2005, I think I would have expected us to have had a far higher life expectency than we currently do, but then I wouldnt have guessed the extent to which computers changed the world. Sometimes all it takes is one significant discovery and then the rest come poring in, completely transforming the world in an incredibly short period of time - take what happened in physics during the first 20-30 years of the 20th century for instance. Who could have predicted that? Or the moon landing, 15-20 years before it happened. 4 litres is fine, and that's generally the recommended minimum for people who take creatine (as I do). I think the volume you need to drink for it to become dangerous is around 10-12 litres a day.

That's a brilliant puzzle. I gave up after about 20 rolls then came back a few hours later and got it in aroud 5 minutes.

But he didnt apply any conditions on what a, b were. He only managed to arrive at the a+b=b step because of the fallacy in the preceding line. Worked through with a=3: Let 3 = 3 3^2 = 3*3 3^2 - 3^2 = 3*3 - 3^2 (3-3)(3+3) = 3(3-3) 3+3 = 3 the reason we have arrived at 3+3=3 is because of the (invalid) cancellation of (3-3) in the previous line.

Yes, and 0.999~ is 1; they both refer to the same thing - we can use different labels to denote the same number. The infinite repeating thing here is just a quirk of the decimal system - as someone else said it's basically the same as saying that 1/2 = 2/4 (or that Samuel Clemens = Mark Twain).

But lots of libertarians believe that it is necessary for a political philosophy to have a moral basis, Robert Nozick for one.

Good call, having 2 threads on the same subject seemed a bit silly. No, it's 1. I gave the formula for calculating the sum of the series in the other thread. I agree, but we arent talking about cups of coffee, we are talking about numbers in the abstract sense. The square-root of -1 doesnt exist in reality, but it's still a perfectly valid number. There is perhaps a smallest number that has significance in reality (Planck), but this doesnt mean that there is a smallest real number, mathematically speaking.

It would be a bit risky to 'live forever', as erandror pointed out - I'd definitely want to be able to end my life if I wished to. At the moment I think a lifespan of 500 years would do me fine, but I imagine I'd want to double it when I reached 400. I think that immortality is certainly impossible if you consider a human, as we know them now, living forever, but there are other ways I could conceive it happening, although it depends on precisely what you mean by immortal. If human cloning/'consciousness-uploading-into-computers' technology were to reach the point where a person could be brought back to life if he died, would this be classed as immortality? A few others have made similar predictions (not immortality, but superlong lifespans). Here's a geneticist from Cambridge talking about the likelihood of people living till 1000. How much is a cup? I drink about 4 litres a day and a few people I know drink 6-8.

There is no largest number less than 1, as I said the real numbers are infinitely dense. I'm not sure what you mean by 0.99~ doesnt exist in reality. It makes more sense (to me at least) if you think of 0.999~ as being an infinite series (0.9 + 0.09 + 0.009 + ...), which is how it's defined mathematically, rather than being a big long list of 9s

Not if you put infinite 9's there.

The proof using calculus. 0.999~ is the infinite series 0.9 + 0.09 + 0.009 + ... which is a geometric progression with initial term 0.9 and ratio (1/10). From calculus, the sum of an infinite series is (initial term)/(1 - ratio). Substituting in here we get (0.9)/(1-(0.1)) = 0.9/0.9 = 1.

Yes you can, at least in the standard construction of the real numbers where you don't have infinitesimals. The real numbers are dense, which means that in between any 2 real numbers is a third. If 0.999~ is not equal to 1, then which number is between then?

it isnt 0.99999, it is 0.9999~ where the sequence of 9's is infinite. If you use a calculator (or do it by hand) youre not going to get the right answer because you'll have to terminate the sequence at some point - you need to manipulate the (non-truncated) infinite series to get the correct result.

1/3 doesnt equal .333333333, it equals .33333~ where the ~ signifies that the sequence of 3s repeat to infinity (some people write three dots, as in 0.33333... instead). All real numbers can be represented by an infinite decimal expansion in this way. When you multiply .33333~ by 3 you get .9999~, an infinitely recurring sequence of 9s, which is equal to 1. The argument given in the other thread to show that .999~ = 1 is informal and not particularly rigorous, but you can prove it properly using elementary calculus. 1/3 is a rational number. Any number of the form p/q where p and q are integers is rational. The difference between rational and irrational numbers is that the decimal expansion of a rational number is periodic, ie your infinite sequence will repeat a certain pattern over and over again. For instance, 2/7 = 0.285714285714285714, which is just '285714' repeating to infinity, and 1/6 = 1.66666~ where the 6 repeats to infinity. However an irrational number such as root(2) or pi will have a non-periodic decimal expansion, ie there is no sequence that repeats over and over again (for instance, the number represented by the decimal expansion 0.101001000100001000001etc, where the number of zeros inbetween the 1s gets larger and larger, will be irrational since there is nothing that repeats).

While I despise Kant's morality, he most certainly wasn't a Utilitarian. Kant believed that obedience to the moral law was a contextless moral absolute, regardless of any specific factors, such as what would make people happy. When presented with the argument that his system would imply that it was morally wrong to lie to a serial killer about the whereabouts of a person he wished to kill, Kant agreed that this followed from his beliefs and stated that telling the truth would indeed be the moral action. For Kant's actual discussion of this topic, click here

A word refers to many different actions and objects, and this can lead people to believe that they must have something in common ("if I can describe these things using the same word, then they must be similar, right?"). This is not always the case. To go back to the word selfishness, the normal usage of the word is not just 'different' from the Objectivist one, but it completely obliterates the distinction which Ayn Rand always emphasized when discussing morality, namely that the 'selfish' act of a man who produces a good is entirely different from the 'selfish' act of the thief who steals it from him. In ordinary language this distinction does not exist - the two acts will both be described as 'selfish' and this causes people to believe they have something in common. Another example would be 'illegal drugs', which is a pseudo-concept, since there are no clearly defined properties which seperate 'illegal' drugs from 'legal' drugs other than the sole fact that they are illegal (cannibas and ecstacy have more in common with alcohol than they do with heroin or LSD, but the 'legal/illegal' classification system obscures this). People generally get the idea that 'legal' drugs are ok whereas 'illegal' drugs aren't, and I think this is largely because of the way they are grouped together in everyday talk.

Almost all fields (whether indiividual disciplines like philosophy or physics, or individual schools within these disciplines such as Objectivism or will need technical terms in order to identify concepts which they believe need to be identified, but for which no word exists in normal language. There are two options - either use words in a slightly different way from their standard usa, or invent a large number of neologisms. Normally a combination of the 2 approaches is used, but Ayn Rand went almost exclusively for the former (I cant think of a single neologism in Objectivism). The problem with using words in a different way from normal is that, as you pointed out, it can cause communication problems. Ayn Rand, to her credit, defined all the technical terms she used and, more importantly, gave the reasons why she was using her definitions rather than the standard ones (an excellent example of this is her discussion of selfishness at the beginning of VoS). But not everyone has read Ayn Rand's work, and using a term in the Objectivist way when talking to someone who hasnt studied the philosophy can communication to break down entirely. I've noticed that people (not just Objectivists) tend to assume that others are using words using words to mean the same thing they are, and this is often not the case. The essay by Peikoff in IOE, "The Analytic-Synthetic Dichotomy" struck me as a particularly extreme example of this. In many places , Peikoff bases his argument on the claim that truths cannot be split into two categories, 'logical' and 'non-logical'. But what he ignores is that the people who advocate this distinction are not using the word 'logic' to mean the same thing that Ayn Rand and Peikoff use it to mean - the Objectivist definition of logic is fairly technical to the philosophy, and is not what others generally mean when they use the term (in this case, 'logical truths' normally refers to truths which are established via deductive logic alone). I think the lesson is that there is nothing wrong with redefining ordinary words, but it is vital to bear in mind that not everyone is going to know what your definition is unless you explicitly tell them.

Why would fraud be distinct from any other case of lying (what is the definition of fraud here?). A seller who lies to a buyer is guilty of obtaining their property under false pretences, but a husband who lies to his wife is guilting of obtaining her time, and indeed her life, under false pretences. Also, why do you believe people have a right not to be lied to? Unless I'm mistaken, all other rights within Objectivism involve restrictions on force, so an exception is certainly being made here.

While fraud is morally wrong for the reasons given, it is not a form of force, either directly or indirectly. There is no contact with a person's body, or property involved in fraud. I think that supporting laws which criminalize lying is a very dangerous path to take - if a man has an affair and then denies it to his wife, why wouldnt be an initiation of force, for the same reasons you give? Would this action be morally wrong? Perhaps, depending on circumstances. Would it warrant state intervention? Certainly not. While this is certainly annoying, it does not mean the spammer has initiated force against you any more than if someone pinned your mailing address to a public lamppost. The problem of spamming will disappear when/if some kind of pay-per-email scheme is implemented (meaning that people will have to pay a trivially small fee of around $0.01 to email you) - regulation is not the answer.

The PD is an interpretation of a payoff matrix where a nash equilibrium (the state which occurs when both parties make the best move possible, taking their opponents possibilites into account) results in an outcome which isnt pareto optimal (the best outcome for either party). You're perfectly free to invent your own interpretation if you like. There's hundreds of examples you can choose from which have more application to real life, including these: 1) In a busy city, the amount of traffic on the road generally means it takes a long time to get to work in the morning. If everyone 'cooperated' took public transport instead of driving then most people would get to work quicker, since the roads would no longer be congested. But, then it would be in people's advantage to drive because there wouldnt be much traffic. So everyone would 'cheat' and go back to driving, meaning the congestion would return and it would take ages to get into work again. Driving is always the best option for each individal (using a minimax analysis), but because of this, you will end up with a worse result than if everyone collectively picked the inferior option of driving to work. 2) Two companies are competiting in the same market. If one lowers its price on an item then it gets more customers. But then the other company will also lower its price, meaning that they both end up selling the item for a lower price than they would have if they both 'cooperated' and maintained the original price, hence they make less profit. It is also especially relevant to most "free rider" problems, and it will come up in any debate involving a society which funds the military/police through voluntary financing rather than taxation. Here, the 'best result' for any individual person would be if everyone else paid while he doesnt, since then he will then receive the benefits of the services in question for free. But if everyone thinks this way and makes this choice, there will not be enough money for the police/army to exist, and everyone ends up worse off. There are obvious counter arguments (social stigma etc), but the PD idea is certainly relevant.

There is an excellent article on capmag regarding gambling which you might want to check out: http://www.capmag.com/article.asp?id=2811

I like the Pound poetry which i have read (although admittedly that hasnt been much). As far as I know, he expressed regret later in life over his anti-semiticism (not that this, or any other aspects of his life, matter when it comes to evaluating his work). It's a fairly broad term which names a historical period which spanned the first half of the twentieth century. Pound is a considered a leading (artistic) modernist, as is Joyce, Eliot and Picasso, although the term is often applied to fields other than just art. See wikipedia for a brief summary.

There's probably a danger of getting Objectivism lumped in with religion if you present it badly, but it certainly sounds like an interesting topic, and one I would like to read. I would imagine that most people who are seriously committed to an ideology, be it religion, Objectivism or Marxism, would be happier than the average person due to the sense of meaning and purpose which can be derived from having an overarching set of principles which integrate your life. But even with that caveat, I think Objectivists would be happier than most, due to the overwhelmingly positive aspects of the philosophy.

Could someone explain why they think that fraud constitutes an initiation of force? I can sort of see the logic in the case of someone obtaining something through fraudulent means (althogh that seems like a fairly ad hoc definition of 'force' - almost as if the word were being stretched to make it cover all the things that are considered wrong, rather than being used objectively), but you cant really include faking an email address in that category, regardless of how irritating it might be.