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A possible world makes sense if and only if it refers to a future state of the one real world. Other ways I've seen it used are gibberish.

Thanks. Does employer-employer mean or include customer-supplier, e.g. when a supplier fulfills specs previously given by the customer? Does employee-employee mean or include teamwork, e.g. each one doing different things with the same end goal?

The title of your Chapter 4, collaboration, intrigued me. Using Amazon's "Look Inside" feature, I can see collaboration types 1, 2, and 8. Will you tell us what 3-7 are, at least the labels?

My perspective was whether or not a number was the ratio of two integers, or is equivalent to such a ratio. It either is or isn't. The lengths of the sides of the two are not different in kind in that they are both real numbers, if that's what you mean. And, of course, we can't measure lengths with unlimited precision. Any measurement we express in digits is equivalent to a rational number, e.g. the diagonal of a 1-inch square is 1.41421356237 with 12-digit precision. 1.41421356237 = 141421356237/100000000000

Decimal expansions in base 7 would still include finite, infinite non-recurring, and infinite recurring instances. If by "actual quantities in reality" you mean the result of a measurement, then the result is a matter of precision, i.e. how many significant digits. I doubt there is any mathematician who would say that rational and irrational numbers designate are not different in kind.

The Wright Brothers #1 The Wright Brothers #2 The Wright Brothers #3

Hi Russell, If and when you do move, you might contact Anu Seppala at ARI. She gave me contacts for two couples in the Cleveland area who registered for OCON 2019.

P.S. That should be finite and recurring. That should be non-finite and non-recurring.

Thanks for the reference to Kitcher. I read that book many years ago, but not recently and before I wrote the blog posts. On page 211 Kitcher says: “By contrast, because he cleaves to the intuitive idea that a set must be bigger than any of its proper subsets, Bolzano is unable to define even an order relation between infinite sets. The root of the problem is that, since he is forced to give up the thesis that the existence of one-to-one correspondence suffices for identity of cardinality, Bolzano has no way to compare infinite sets with different members. Second, Cantor’s work yields a new perspective on an old subject: we have recognized the importance of one-to-one correspondence to cardinality; we have appreciated the difference between cardinal and ordinal numbers; we have recognized the special features of the ordering of natural numbers. But we do not even need to go so far into transfinite arithmetic to receive explanatory dividends. Cantor’s initial results on the denumerability of the rationals and algebraic numbers, and the nondenumerability of the reals, provide us with a new understanding of the difference between the real numbers and the algebraic numbers.” In my view Kitcher’s view is rather one-sided, favoring Cantor’s ideas over Bolzano’s. “Bolzano is unable to define even an order relation between infinite sets.” Why not? While the proper subset method is unable to give an order relation between all infinite sets, it is able to give an order relation between some infinite sets. An example of the former is the rationals in the interval [0,2] and the reals in the interval [0,1]. An example of the latter is the integers and reals. It seems Kitcher values the denumerability/nondenumerability criteria much more than I do. According to Cantor, the rationals are denumerable, but the reals are not. On the other hand, comparing the rational numbers to the reals can also be done on the criteria of decimal expansions. We know that rational numbers have finite or recurring decimals expansions and irrational numbers have non-finite or non-recurring decimals. Stephen, I’m sure you know this, but I will give examples for other readers who might not. Rational number examples: 2/7 = 0.2857142857142857….. infinite, recurring 3/10 = 0.3 finite 77238/100000 = 0.77238 finite Irrational number examples: sqrt(2) =1.414213562373095….. infinite, nonrecurring pi = 3.1415926535897932384…. infinite, nonrecurring Starting with any rational number with a finite decimal expansion, one could generate an unlimited number of partly irrational numbers by appending digits randomly (nonrecurring) on the right side. I believe that is as sound or more sound than Cantor’s diagonal argument for real numbers (link).

Infinity contra-Cantor #1Infinity contra-Cantor #2Approaching Infinity

Producers. There are traders who only buy and sell, for example, on a commodities exchange. They may buy and sell pork bellies, corn, wheat, etc. without ever producing those things. If farmers didn't produce those things, the traders couldn't buy and sell them.

China From Above Information and Investment #1 Information and Investment #2 Information and Investment #3 Information and Investment #4

Modern Austrian Economics #3 Modern Austrian Economics #4 Modern Austrian Economics #5 Maximum size of animals Few, several, many, and some The Organization of Industry #1 The Organization of Industry #2 Perfect Competition #1 Perfect Competition #2 Perfect Competition #3 Amazon HQ2 & HQ3 #1 Amazon HQ2 & HQ3 #2 Amazon HQ2 & HQ3 #3 Bohemian Rhapsody Mass shootings

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Two Kinds of AprioriAccountable Capitalism ActRothbard on Economic Paradigms

Yes, Book IV, Chapter XX.5 http://enlightenment.supersaturated.com/johnlocke/longcontents.html

I didn't see a forum where I thought this post fits well. If the moderators want to move it to another forum , that's okay. Anyway, I've been posting to this blog for a while, and believe some would find an interest in a couple recent ones. LeBron, Trump, Altruism Marconi #6 This is one of a series of 11 that I wrote while reading a biography of Guglielmo Marconi, the inventor of wireless technology and often credited with inventing the radio. The post refers to John Galt.

Relatedly, there is an article "Conceptualism in Abelard and Rand" by Peter Saint-Andre in The Journal of Ayn Rand Studies V4N1. It can be read online for free with free registration at www.jstor.org (link). The abstract for it is: The author provides textual evidence that calls into question Ayn Rand's characterization of conceptualism as simply a kind of nominalism, as well as her claim that her theory of knowledge is a sui generis "Objectivism" rather than a form of conceptualism. Here is a webpage I found searching for Saint-Andre's article. I had not seen it and only scanned it, so I won't comment on it.

One dictionary definition is "a question raised for inquiry, consideration, or solution" (link). Many times problem is used to mean something to be explained more than solved.

The first sentence of the second paragraph in the opening post expresses a centuries old view about universals. Wikipedia's summary of the problem of universals is here. It refers to conceptualism, for which Wikipedia has a link to another summary. It arose later and now is generally considered a major alternative to realism and nominalism. The quote in the opening post is from Objectivism and the Corruption of Rationality. On Amazon there are several reviews, most of which are 1-star or 5-stars. One of the 1-star reviews is by me. If you haven't already read the book, maybe the reviews will help you to decide whether or not the book is worth reading.

More exactly, Roderick T. Long wrote an article referencing Browne's work in JARS V7N1, and Browne responded to Long's article in JARS V8N1. Both can be read online with a free subscription to www.jstor.org.

Thank you for your post, Stephen B. I will comment on one part of it. I think that interpretation is consistent with most, but not all, of what Ayn Rand wrote. I think my clause "but not all" can be based on a number of things she wrote, but I will limit myself to two. One is the passage in VoS quoted in the third post of this thread. Two is from Atlas Shrugged, p. 29, as follows. Taggart Transcontinental has lost a shipping contract with Ellis Wyatt to a competitor. Dagny Taggart: "We've lost the Wyatt oil fields" (p. 16). Dagny Taggart: "Ellis Wyatt is not asking anybody to give him a chance. And I'm not in business to give chances. I'm running a railroad." James Taggart: "That's an extremely narrow view, it seems to me. I don't see why we should want to help one man instead of a whole nation." Dagny Taggart: "I'm not interested in helping anybody. I want to make money." How is it that Dagny is not interested in helping Ellis Wyatt? She wishes that Taggart Transcontinental still had Ellis Wyatt as a customer. If that were still the case, her making money is helping herself, and she would be helping Ellis Wyatt achieve his goals. Returning to your passage I quoted, I like a little different wording, indicated by brackets: "an egoism in which some right actions are not [solely] for the actor’s [benefit], only [partly] so. [Partly], they could be for the [benefit] of one not oneself, nonetheless count as egoistic." While X can help Y when X and Y are trading partners, X rationally helping Y is not limited to trading. For example, X and Y could be co-workers for the same firm Z. X and Y each have the same goal of Z's goal/success. Similarly, in basketball player X could assist his/her teammate Y to achieve their mutual goal of their team winning the game.

Spelling corrected.

Your minding reading skills are poor.

I asked a simple question: "Also, why couldn't a breach be voluntary or forced by a non-altruist thug?" You refused to answer it. Bye.