thomtg

I believe Roger and I stipulated what it means for something to be "undefined" earlier. (See Post #138 and Post #178.)

Here are 2 sets (groups) of numbers: {1, 3, 5} {2, 4, 6, 8} How many (a number) groups contain the number 7? Merlin, The question asked can be unpacked procedurally as, 1. Is 7 an element of the first set {1, 3, 5}? False 2. Is 7 an element of the second set {2, 4, 6, 8}? False 3. How many times was the operation "an element of" performed? 2 4. How many times did it fail to yield the result True? 2 5. How many times did it succeed? 2 - 2 = 0 Would you not agree that it is epistemology that establishes the criteria for postulating anything in any science, including mathematics? If at one time it was thought that concepts could in reality be formed without referentce or linkage to reality, and then at a later time it was rethought otherwise; wouldn't you say that that epistemological change in the standard of the unit would cause a tectonic change in every science that depended on it? Merlin, I believe we are getting close to an agreement about the nature of mathematics as a science of measurement, for you have agreed that in order to discover any mathematical fact at all, you have to engage in some mental operations (e.g., counting). It is on this basis that I have to disagree with you that you did not have to unpack procedurally the way I did and that you just had to count. Count what in reality? What you counted was not something you perceived in reality. You were counting your mental operations! Introspect, Sir, and see. On the other question, the "unit" I had in mind is the one Ayn Rand defined in the second chapter of ITOE. With Rand, we have a new standard for this unit. Since, for example, the base of set-theory mathematics is built historically on mapping "set" onto this unit, Rand's new standard necessitates foundational changes to everything related to sets.

Michael, Welcome to the ontology of the zero. You pose a legitimate question concerning the nature of 0. To what facts of reality does 0 refer? This is a philosophical question. And the answer must be philosophical, not mathematical. Any mathematician who tries to answer it must answer it in his capacity not as a professional mathematician but as an amateur philosopher. You are the first person to counterpropose philosophically another view of 0 to Roger's. (See Post #105.) If I understand you, you are saying that 0 identifies a relation to any identity-bearing something, in relation to that something's absence. In which case, I do not see any incompatibility whatsoever with what you express and what Roger has proposed. Where Roger's proposal identifies the role of 0 in math operations, yours identifies its role in the math quantities being operated. Since a quantity as a relational existent presupposes other existents (entities, attributes, etc.), it follows that some math operations require some presumed quantity on the understanding and operational context that a relation to some existents must exist but that it may exist (thereafter) in any quantity. So 0 in this strict sense is not a quantity per se but denotes a placeholder (and/or a result) in some math operations for the absence of a presumed, existing quantity. Thus, like "i", which was discovered much later in history, the concept "0" is a methodological concept. (For the full context of my analysis, see ITOE Ch. 4 on introspection and the Appendix on numbers.) Ontologically speaking, as nothing is not another something, so zero is not another quantity. To think so is to commit the fallacy of Reification of the Zero. (ITOE 60) Welcome to this "side" of the proposal, Michael. :flowers:

Michelle, I know you must sense a difference between what I mean when I say I am an Objectivist and what someone from a more orthodox bent means, so I want to make it clear. You actually put your finger on it with the word "group." One approach (the one I do not do) is to identify with a group of people who are making an "Objectivist movement" to save the world from an orgy of this or that. Another approach (which is the one I do) is simply to use the label as a point of reference in terms of a body of thought. It's like calling a university professor a Kantian or an Aristotelian. This designation does not mean that the Kantian professor is trying to band together with others to save the world in the name of Kant. All it means is that the professor studied Kant's works, focuses substantial intellectual effort on his thought, and agrees with a portion of it. Calling such a person a Kantian merely helps others properly identify when they are presented in public with a vast array of different professors. [...] Michelle, I am in agreement with MSK on this. (See this thread for my condition for being an Objectivist.) When I identify a body of thought, I credit the person who originated it. When Ayn Rand called herself an Aristotelian, she identified and credited Aristotle for having originated a body of thought for establishing the foundation for all true thoughts and for identifying reason, as opposed to mysticism or skepticism, as the means for knowledge. (ARA 148d) So for me, crediting a body of thought to its originator is a matter of civility. In Rand's case, she gave hers a name, "Objectivism," in order to depersonalize it for a very practical reason. She was both a novelist and a philosopher. While I am both a Randian (or a Rand fan)--because I enjoy her novels, and an Objectivist--because I understand her philosophy; others need not be.

Here are 2 sets (groups) of numbers: {1, 3, 5} {2, 4, 6, 8} How many (a number) groups contain the number 7? Merlin, The question asked can be unpacked procedurally as, 1. Is 7 an element of the first set {1, 3, 5}? False 2. Is 7 an element of the second set {2, 4, 6, 8}? False 3. How many times was the operation "an element of" performed? 2 4. How many times did it fail to yield the result True? 2 5. How many times did it succeed? 2 - 2 = 0 Would you not agree that it is epistemology that establishes the criteria for postulating anything in any science, including mathematics? If at one time it was thought that concepts could in reality be formed without referentce or linkage to reality, and then at a later time it was rethought otherwise; wouldn't you say that that epistemological change in the standard of the unit would cause a tectonic change in every science that depended on it?

[...] Want an example? Ask and ya shall receive: Rand verbatim calls Peter Keating "a perfect example of a selfless man". Now let's look at Rand's definition of "selfessness" [altruism] Atlas Shrugged, p. 323: Ivy Starnes to Dagny. "That was our plan. It was based on the principle of selflessness [i. e. "altruism"] . It required men to be motivated not by personal gain, but by love for their brothers." (end quote) Now with Keating being identified as "selfless" [i e. an "altruist"] , it logically follows that (again, according to Rand) he is motivated not by personal gain, but by love for his brothers." Right? Seriously, Brant, do you really believe Keating was motivated by love of his "brother" (= fellow human being) Howard Roark and not by personal gain, when he asked him to do his work for him? He was motivated by personal gain, wasn't he, Brant? It sticks out a mile. [...] Xray, You have found a great definition of "selflesness" from Atlas Shrugged, as defined by the character Ivy Starnes. However, Ivy Starnes did not speak for Ayn Rand in the novel. Only through the characters John Galt and other heroes did Rand speak to her readers directly. Ivy Starnes, by contrast, represented the commonly accepted philosophy of the time period. And her definition of "selflessness," as Rand reported to us in the story, accurately reflected the commonly accepted meaning of the term, "to be motivated not by personal gain, but by love for their brothers." As you have surmised, this is utterly impossible--a contradiction in the very essence of not only human action but any animal action. (See my latest reformulation of the classification of "self-interest" in Post #61.) But Ayn Rand did not endorse this definition; she merely told the readers about it through the voice of the Starnes heiress. Though you have found a contradiction, the contradiction was not in Ayn Rand's Objectivist ethics. In fact it was she who first identified the very contradiction you are now attributing to her system. It was she who identified the contradiction inherent in any ethical system that disregards the facts of reality, including the reality of human nature, such as self-interest, volition, reason. If anything is accurate in your assessment, I would say you have identified a big flaw in a great number of moral codes, but the flaw is definitely 100-percent not in egoism. (See the definitions here.) You are of course within your right to be irate at seasoned Objectivists (and non-Objectivists) who are sloppy in their thinking. However, I continue to recommend the principle of charity when reading the writings of Ayn Rand, whose thinking is anything but sloppy. --- Great questions! Really great and penetrating. But I cannot answer your questions in the current context because I have not gotten permission from you to use the term "egoism" (or "egotism," or "egoist," or "egotist," or "egoistic," or "egotistic") in the precise meaning I have delineated. I am not asking that you grant me that "egoism" as I or Rand have defined it, is true. I am asking whether I may be permitted to use "egoism" in the new meaning unequivocally. That is, in order for me to continue the discussion, I need permission from you that you will interpret me as never using the word "egois___" in the conventionally accepted meaning of the word--that it will always mean what I have defined in the root post and Post #12--that while human action is totally motivated by self-interest, there are distinctions within "self-interest"--that there are "rational self-interest," "irrational self-interest," and volitionless "nonrational self-interest"--that "selfishness" is defined as "rational self-interest." [...]Until you grant me this permission, I am unable to continue. You need not ask my permission to use those terms, Thom, but jmpo, using them in the discussion poses certain problems. [...] So my suggestion would be: why not drop the whole terminological ballast by the wayside for the time being and go ahead without it? We don't need it because we have agreed on one fundamental point: Peter Keating was moved by self-interest. His self-interest just happend to be different from Roark's. [...] But I do need your assent in order to continue. They are your questions, not other viewers', not passerbys', not the chance onlookers'. Precisely because using them in the discussion poses certain problems, which I elaborated earlier (in Post #26), I need your assent that you can and will interpret the words exactly as I have painstakingly defined them. This is a simple matter of justice. And that is why I need your permission to continue.

Hi Michelle, There are two aspects of this question that are generally ignored. First, children are not objects that can be owned. Therefore, they should be treated differently under the law. Generally, it would be correct to assume that if there was no good reason for the state to prevent a person from owning something, then he should have the right to own it. The default is always that the person has the right to do something unless there is some compelling reason why he doesn't have that right. For example, a person arguably has the right to own a stereo or a car or a house if he paid for it. He also has the right to drive the car, but not in a reckless manner. Driving it in a reckless manner would put other people's lives at risk and therefore there is a compelling reason for not considering reckless driving a right. So, you would be right in asking the question the way you did if it were only inert objects that were at stake. But that is not the case here. A parent and child exist in a relationship involving the use of force as a natural consequence of the nature of parents and children. A child is a dependent on the parent and the parent must sometimes control the child for his/her own good. The child, at a young age at least, is unable to care for himself/herself and therefore does not enjoy all of the rights that accrue to adults. Therefore, it is proper for the adult to force the child to do certain things and forcibly prevent him from doing others. For example, the parent may forcibly prevent a small child from running out into the street into traffic. Given the above considerations, it is just as proper to ask, why should the state allow gay couples to adopt children as it is to ask why the state should disallow gay couples from adopting children. In allowing a gay couple to adopt a child, the state is assigning to the gay couple the power to control the child in a forcible manner. So, it is proper for the representatives of the state to ask whether the couple would be suitable stewards of the rights and responsibilities of parenthood. Now, it may be the case that some gay couples would be fine parents and that some non-gay couples would not, but --- and this is the second aspect that is usually ignored --- it is not always possible for whomever is working for the state to make an accurate determination of who would or would not make a good parent. It is therefore sometimes necessary to observe general characteristics of groups rather than individual characteristics. At first, this may seem antithetical to the notion of individuality, but consider age-of-consent laws. It may be that some individuals are ready to enter into sexual relationships at the age of 14 while others are not ready until they are 20. However, without age-of-consent laws, it is very difficult to prevent children from being exploited by sexual predators. Therefore, we arbitrarily draw a line and say that an adult (over 22, say) cannot have sex with anyone younger than a certain age (17, for example) and that no person 22 or younger can have sex with a person more than five years younger. The law may not fairly treat everyone, but laws must be based on realistic considerations. The same is true for adoption. The media like to trot out really nice looking homosexual couples when discussing adoption and you may know a very nice couple, but if, on average, homosexual couples are significantly worse potential parents, and if it is difficult to determine that by looking at other factors such as income and criminal history, then it might make sense to restrict homosexual couples from adopting, even though that might be unfair to some such couples. I am not an expert on the issue, so I don't know what the statistics are or if anyone has even bothered to collect them, but my experiences, just looking at personals for gay and straight relationships, is that people seeking heterosexual relationships tend to be much more responsible than those seeking gay relationships. The ads by women seeking men, for example, tend to be much more responsible than other kinds of ads. Also, I happen to know that married men tend to earn more money than single men. Therefore, since women are typically the primary child care providers in heterosexual relationships and men tend to earn most of the money, I would make an educated guess that heterosexual couples would, on average, make better parents then homosexuals. At least, I think it is a legitimate consideration. Darrell Very well put. One implication I think Objectivists must assent to is that the state must regulate adoption of minors in order to protect their rights. Another implication on this view is that the state cannot regulate adoption of adults among adults, because an adult-to-adult reltionship is not a depend-to-independent relationship, not a child-to-parent relationship.

A judgment that is not a subjective value judgment is a contradiction. All judgments are necessarily subjective. But do not confuse subjectivity with relativism. Even though I am not convinced of several aspects of Rand's ethical objectivism. For instance, the statement that survival is the ultimate telos of all life is blatantly false - survival is only a means to an end, which is reproduction - thus, survival is only the telos of all life in the sense that it leads to the survival of the species ... this need not have the otherwise devastating effect on Objectivist ethics that it would seem to imply when you consider that, unlike any other known lifeform, the human is a creature capable of self-created telos. Survival still factors heavily into the equation, but even though strong instincts draw us toward reproduction, it is not a necessity for a person to a live a full life. Survival, however, is. Michelle, Your comment has led me to re-evaluate my own formulation of what it means to act self-interestedly. You have stated elsewhere that you take responsibility for yourself to discover and correct mistakes in your worldview and in your set of values in order to go through life. I interpret it then that you value your mind and respect its fragility, its potential for making errors. And to value one's mind in this sense translates to wanting to discover one's errors of knowledge and acting to correct them. If this is correct, I agree completely. With that as a presupposition taken in the spirit of benevolence, I am bringing to your attention two potential errors in your Post #27 above that "[T]he statement that 'survival is the ultimate telos of all life' is blatantly false--that survival is only a means to an end, which is reproduction." Although I disagree with your assessment of the statement, which is the first error, I am more interested in alerting you to the second, more serious error of viewing values as intrinsic. Reproduction is valuable, for sure, but is it the ultimate end? There is a fine line between taking values as subjective (relativism) and taking values as intrinsic. The Objectivist ethics stands on that fine line, balancing as if on a tensioned highwire, taking values to be objective. In your dismissal of the theory that values are subjective, I am afraid that you are counterbalancing too much toward the other side, potentially falling toward treating values as totally apart from individual valuation. It is the error that could lead to disastrous results on the personal level, as it had led countless times at the social level. See, for example, Xray's identifying from history the intrinsic valuation of "racial superiority" and of "virginity". (Of course, her mischaracterizing them as "objective" is a case of the opposite counterbalancing error.) Is reproduction an end in itself, a value in itself? If, as you state (in Post #47), that no value exists by itself and that valuing is a subjective, individual act; then I believe that your view about reproduction is a misintegration--an error. Dr. Leonard Peikoff has two podcasts that I am aware of that address the present issue. Podcast 17 at 13:16 answers "Is reproduction a value in its own right?" Podcast 27 at 01:19 answers "Is part of Ayn Rand's validation of the Objectivist ethics in conflict with modern biology--in conflict with the consensus of biologists who claim that the ultimate goal is the reproduction of the organism?" For my own take of the distinction between values being objective versus nonobjective (subjective and intrinsic), see this blog entry here. For a critique of intrinsic valuing in a recent event, see here. And now, to my own error, thanks to you. It is not actually an error; to be more precise, it it more of a refinement to the formulation on the basis of more knowledge. I have stated earlier (in the root post and Post #12) that while human action is totally motivated by self-interest, there are distinctions within the notion of "self-interest"--that there are "rational self-interest," "irrational self-interest," and volitionless "nonrational self-interest"--and that "selfishness" is defined as "rational self-interest." What about a human action from an error of knowledge? Where does that fit? Here now is my reformulation of self-interested human actions that takes this fact into consideration. 1. Every animal action is motivated 100 percent by self-interest. 2. The "self" is an animal's consciousness, the faculty that distinguishes animals from plants. 3. An animal action is a conscious action (as opposed to a reflex) for the self-interest of the animal. 4. "Human action" is a species of "animal action"--as bird actions and fish actions are also animal actions. 5. Human action is volitional. 6. Because of volition, only human action, as opposed to bird action and fish action, must be guided by ethics. 7. Human action is conscious action but requires in addition the volitional consent of the human self--the mind. 8. The "self" of a human is that portion of consciousness that must be activated volitionally by choice. 9. "Reason" is the faculty of consciousness that a human must choose volitionally to activate. 10. A man acting under coercion is not acting humanly and is merely acting animalistically; and 3 applies. 11. A man acting without freedom acts toward his volitionless nonrational self-interest. 12. A man acting with freedom is acting toward his volitional self-interest. 13. A man acting with freedom through reason is acting toward his volitional rational self-interest. 14. A man acting with freedom bypassing reason is acting toward his volitional irrational self-interest. 15. Ethics pertains to human actions motivated completely by volitional self-interest. 16. "Egoism" is the moral code that a man's existence is his to live and enjoy, and rationality is his highest virtue. 17. "Egoist" is one who values his mind and respects its judgments. (See root post for other definitions.) 18. "Selfishness," before the discovery of egoism, is a concern for one's volitional self-interest. 19. "Selflessness," before the discovery of egoism, is a concern for others' volitional self-interest. (Contradiction) 20. "Selfishness," in the new conception of egoism, is a concern for one's volitional rational self-interest. 21. "Selflessness," in the new conception of egoism, is a concern for one's volitional irrational self-interest. 22. A rational man (by 13) acts selfishly (pro self). 23. An irrational man (by 14) act selflessly or unselfishly (against the self). 24. A coerced man (by 11) acts nonselfishly (without the self (by 8)). 25. Refining 22 (the Michelle Amendment): Through errors of judgment, a rational man's action may turn out to be selfless. 26. Refining 17: "Egoist" is one who values his mind, respects its judgments, and respects its fragility. 27. "Second-hander" (by 14) is one who does not value his mind and disrespects its nature by abusing its development, denigrating its evidence, evading its judgments, bypassing it for his emotions, and deferring it to the minds of others. P.S. You have also stated elsewhere that you don't take much credence in evolutionary psychology (which I agree with you) and for that reason you believe we are not born tabula rasa but with inherited instincts--which I disagree, but which is another error for another time.

This really does make a lot of sense from a process-model perspective. Drawing from Chapter 8 of ITOE "Consciousness and Identity," I would add that in identifying facts of reality, including the ontology of numbers, we must take cognizant of not only the existents but also the nature of how the mind works. Your explanation respects both aspects. Another example is the notion of something being "undefined" in mathematics. Does it mean, as Laure suggests in Post #110, that anything that is computed variously and produced incompatible results should be considered undefined? No, that simply means that something is being defined incompatibly. And in a contradictorily incompatible relationship, both relata cannot be true; at least one is false. It leaves the possibility that one or the other may be true. So, I would say that "undefined" is not as defined, and that it should be interpreted as "not operable or calculable by any process." In the case of 0^0/0^0, it surely is calculable to 1. :thumbsup: Laure, Let me try to channel Roger's spirit and answer your questions. [Channeling Roger:] If we accept the proposal and interpret the number zero ontologically to stand for a mental blocker of mathematical operations (from Post #105), then indeed: 1. Any number multiplied by 0 must mean that that number is not multiplied [period]. The operation is blocked. The operation is not processed. It is in this sense that the product is "undefined." (See above.) So, 0*0 is undefined, as 44*0 is undefined. 2. Now, for the power operation x^y, the explicit form of the operation is 1 * x^y, meaning 1 times y groups of things taken x at a time. Thus, 0^n becomes 1 * n groups of things taken 0 at a time. But because the latter is an operation blocker, 1 is not multiplied [period]. So, the result remains 1. Thus 0^n = 1. 3. The transformation of 0*0 == 0^2 is invalid. The former had no base number to begin; it's stopped before it's started. The latter has the identity element for multiplication 1 at the start; and it ends there. 4. For the grade-school example (1-1) * (1-1), each parenthetical group (1-1) does proceed operationally, and the result for each is nothing, as represented by 0. When looked at by a mental processor, 0 * 0 is a non-operation, for there is nothing to process. Mentally, nothing is multiplied [period]. [Channelling done] Now, Roger, I have a question for you. On this proposal, 1*0 is different from 0*1. The former is blocked; the latter is zero. Is this correct? Other than what we have covered so far, I think we can content ourselves that all financial spreadsheets continue to be perfectly sound. We just have to remember what the numbers stand for ontologically. There is no escape from metaphysics.

Laure, Thanks for the vote of confidence that we may at some point come to a meeting of minds, one way or the other. I do believe you are beginning to see a discrepancy of some sort. If so, this calls for extra effort at introspection to determine the cause. An imperative statement (e.g., Kant's categorical imperative) is a statement issuing a command. For example, "(You) turn off the TV and do your homework." It is an order for action. If it is carried out, the action becomes a man-made fact; if not, its absence becomes a fact. An if-then statement is not an imperative statement. It is a hypothetical statement potentially conveying a hypothetical proposition, one that is either true or false. It is a statement asserting a relationship between two subthoughts, i.e., the relationship that the truth of the antecedent is sufficient to guarantee the truth of the consequent. A principle of good shopkeeping is, "If you break it, you buy it." This is a hypothetical statement. It asserts a relation of dependence of the presence of one fact on another. It is not a command. All Objectivist moral principles (unlike those in a command ethics, such as Kant's Golden rule, or Christian morality) are principles in the form of a hypothetical statement. One pratical principle, for example, is "If you want to succeed in a career, (you) work hard at your job." It is never, "Work hard at your job." The relationship here is one of ends to means. A moral principle has a reason; and if the reason is true, it is sufficient to guarantee the truth of the moral consequence. Here is a more abstract principle: "If reason is your sole means of acquiring knowledge, then you should refrain from deluding and corrupting reason by faking reality" (the virtue of honesty). The relationship here is one of value to virtue. (See DK "Ruled--Or Principled".) MI1 or "(You) add a dollar now, if HP1 is true" is surely a hypothetical statement. It asserts the thought that there is a relationship between the fact of HP1 and the fact of another dollar on the table, i.e., the relationship that the truth of the antecedent ("HP1 is true") is sufficient to guarantee the truth of the consequent ("Add a dollar now (is true)"). It presumes from the start the implicit moral principle (A2) that "If you are honorable, you will do as you promised." So, MIx (1 through 6) are thoroughly and legitimately hypothetical statements. But notice what I haven't said. I have not mentioned "material implication." Mathematical logic prescribes that hypothetical propositions be mapped to and computed by the "material implication" connective/operation, which is based on the truth table for a compound "disjunction" with a nested "negation" operation. My claim is that technologists, so long as they are still unaffected at root by this prescription, continue to treat hypothetical statements as hypothetical, not as truth functional, which makes possible all the technological wonders of the world. The reason is that "material implication," if it were put into actual practice, would not work at all due to an inherent paradox. If logic tells us to question our premises if we find problems, why aren't we doing the same to material implications if we find them paradoxical? If you agree that there is a paradox with material implication, then I ask that you introspect to see whether in your inferential and programmatical processes do you actually evaluate an "if" as an "if" and not as a "material implication." I believe that a three-pass introspection should yield some interesting results. It should be apparent to both of us from your coded program that you are employing material implication to evaluate HPx. So, I recommend you continue that mode of evaluation in your first pass of introspection. Then when you switch perspective to the person holding the money, determine how it is that he is acting on his principles. (Rational and honorable people think and act on their judgments.) Use this method in the second pass to evaluate everything again. Then in the final pass, confirm what you the technologist actually did when you coded the program. If all goes well, you should see a discrepancy.

I am beginning to see your point of view, Ted.

I am not here to debate altruism in this thread, which is why it was specifically spun out from the others. Here I am mainly interested in discussing the difference between being self-interested and being egoistic. (I will be happy to discuss altruism in another thread if it is to my self-interest.) Going by this definition, every thief, and robber and murderer would be unselfish too. But I suppose not even their defense lawyer would refer to them as unselfish, even if the lawyer were a Randist. The problem with Rand is that she created her own linguistic universe, often using terms in complete contradiction to the accepted common language code. For example, she ar... [...] Precisely. Going by this definition, every thief, robber, and murderer would be considered unselfish. Observe the complete inversion of this conception of selfishness in contrast to the conventional view--as you say, it is "in complete contradiction to the accepted" meaning of the word. By the conventional view, one often hears that it is the thief or robber or murderer who was selfish and who did not think of anyone else but him. Not if one understands Ayn Rand's alternate conception. You have identifed a major problem in discussing philosophy in general. This is not a problem specific to Rand, but it does happen that Rand brought into the world many new ideas about the nature of reality--much more than other philosophers--such that in order to discuss the Objectivist philosophy, we have to discern the conventional meaning of a word versus its Objectivist meaning. This does not presume that we, you or me in particular, have to accept the Objectivist meaning of a word to be true. Nor does it presume that Ayn Rand has to accept the conventional meaning of a word to be true. Of course, if a word does have two meanings that are complete inversions of each other, then the two meanings cannot both be true. That is, at least one must be false. But so long as an individual is aware of the existence of two or more distinct, subtly different meanings to a word, he must pay special respect toward himself and his audience to specify and contextualize which meaning he means whenever he uses such an equivocal word in discourse. To this last, I find Rand's usage of equivocal words to be very respectful toward her reader--if the reader grants her the principle of charity. Nevertheless, while not presuming acceptance of the truth of a particular meaning, each individual does have a responsibility to himself to know which meaning he is using. Otherwise, it would be a form of bad faith. To use words equivocally--to equivocate--to himself is fallacious, i.e., an error of reasoning; and to equivocate deliberately to others is to mislead. Observe how careful Ayn Rand was and how respectful she was to herself when she wrote in her journal about the character Peter Keating prior to the writing of Second-Hand Lives. Even to herself, and knowing that she was writing in the journal strictly for her eyes only, Rand was careful to say that Peter was an egoist "in the accepted meaning of the word." She was acknowledging the term to herself that there existed a meaning to the word that was accepted widely at the time. But she was not endorsing it to be true, to be correct, in her own mind. She merely recorded the fact of the existence of this meaning. In publishing the novel The Fountainhead, Rand developed a brand new conception of an "egoist," a man who values his mind and who considers reason as his sole means of knowledge, as his sole guide to action. This was her projection of the ideal man. Howard Roark was this ideal man in this fictional world, not Peter Keating. Roark was the egoist. And in the writing of the novel, the reader is left no doubt which meaning Rand was using. Roark's courtroom speech and all the background facts about him leave no doubt to the discriminating reader about Rand's unequivocal meaning to "egoist." And even to forestall the possibility of a contextual error, Rand noted her usage of the word in the Introduction to the 25th anniversary edition, to make sure the reader to pay attention to her specific use and meaning of the word, and not to be mistaken ever that she was referring to the "accepted meaning of the word." Thus the problem that you have identified is surmountable. When a word has multiple meanings, or when a word is discovered to have a new meaning (true or false), the author is responsible and must be careful to establish which meaning he is using. Likewise, the reader is equally responsible and must be discriminating to discern from the context of the writing which meaning was intended. Whether that meaning is true or false is a subsequent matter. The preliminaries must be this if the problem is to be avoided. Good catch, Xray! You found something I did not notice before. [...] Prior to the existence of the novel, there was on earth no such idea of "selfishness" (rational self-interest), no such idea of "egoist" (one who values his mind, with reason as his sole means of guidance), no such idea of "second-hander" (one who denies the self and acts on the opinions of others), etc. The annex reflects this and simply records a historical fact. The "ego(t)ist" conception at the time before the novel is probably the Nietzschean "individualist" who would trample on anybody and everybody to get what he desired--e.g., pushing out an old architect in the firm, selling one's wife for a contract, etc. What about Roark blowing up the building, potentially endangering other people's lives? Isn't that an act of ruthless egotism too? How can he, from a breach of contract, feel entilted to such an act of destruction? What does this say about the psychological make-up of this "hero" whom Rand created "as man should be"? And how does this act of violence gel with the Randian dogma of non-initiation of violence? [...] Great questions! Really great and penetrating. But I cannot answer your questions in the current context because I have not gotten permission from you to use the term "egoism" (or "egotism," or "egoist," or "egotist," or "egoistic," or "egotistic") in the precise meaning I have delineated. I am not asking that you grant me that "egoism" as I or Rand have defined it, is true. I am asking whether I may be permitted to use "egoism" in the new meaning unequivocally. That is, in order for me to continue the discussion, I need permission from you that you will interpret me as never using the word "egois___" in the conventionally accepted meaning of the word--that it will always mean what I have defined in the root post and Post #12--that while human action is totally motivated by self-interest, there are distinctions within "self-interest"--that there are "rational self-interest," "irrational self-interest," and volitionless "nonrational self-interest"--that "selfishness" is defined as "rational self-interest." Will you permit me to have this privilege? With privilege, there is also responsibility. If I have your permission, I promise not to equivocate to mislead you in discussing these great questions, and I also promise that if I need to refer to another meaning of the term, that I will regiment its context. Until you grant me this permission, I am unable to continue.

I agree that axioms need to be grounded. True sentences (axioms, theorems, etc.) are true by virtue of some standard of truth. Objectivists take a version of the correspondence theory of truth to be that standard. And by this standard, axioms in science (including math, philosophy, chemistry, etc.) cannot be arbitrarily defined. They must have a basis in facts of reality. Mathematics in particular is a science of measurement. On this conception, the philosophy of mathematics needs to take cognizant both of man the measurer and of that which can be measured, in establishing criteria for determining truths in mathematics. Hence, I agree that "mathematics is an ~abstraction from~ the real world, and that, to be valid, every rule and procedure must be based on or ultimately derivable from a concrete mental operation directed toward real objects and their attributes, actions, and relations." On the ontology of the number zero. I would like for us to remember the basic philosophical question: what in reality is the nature of the number zero? Now, in agreement with the topic of this thread, Roger is proposing the number zero to be a blocker of mathematical operations. (See Post #14.) As I see it, there are three legitimate ways to falsify this proposal: Find a counterexample, reject an implicit premise, or propose an alternate more informative proposal. The zeroth power is one example being discussed. Let it be the test case for the proposal. Since the proposal is an attempt to answer a philosophical question, any rebuttal, in my view, is necessarily philosophical. Anyone who counterproposes does so therefore in his capacity as a philosopher, and not as anything else, be he mundanely a mathematician, politician, lawyer, botanist, businessman, chemist, teacher, housewife, or trombonist.

Well, yes, but what is Objectivism, really. --Brant If you want a core set of integrated ideas of what Objectivism is, I would refer you to a short summary excerpted here in Dec. 23, 2006 by MSK. If my understanding of "understanding" is correct (see top Post #1 and Post #32), understanding this core will enable anyone to become an Objectivist.

Ah, yes, but I have mentioned elsewhere that Russell's theory of definite descriptions is faulty (here and here). And if it is faulty, Gödel's slingshot argument comes to the fore, which since the 1970s, the latter has indeed come to take up the field in mathematical logic. I don't think anyone (else) here presumes he is smarter than anyone else, dead or alive. The issue is not smartness or intelligence. By the way, I don't think I am that smart. I know there are others whose native intelligence is greater than mine, as I know there are people who are physically stronger, faster, etc. But I can spot an error, even if it comes from one smarter than me. Have you read Roger's discussion on the ontology of the zero (Post #14)? Have you read his refutation of the slingshot argument (Post #88)? Can you spot an error therein?

Indeed he was. Just as everyone else in the book was driven by self-interest. It can't be otherwise because it is biologically hardwired. Would you agree that self-interest is the driving force behind all our actions? I'm not talking about what the self-interest is (Roark's self-interest obviously differed from Keating's), only try to establish a common epistemological denominator in the discussion so that we can take it from there. Yes, I do agree that self-interest is the driving force behind all human actions. Moreover, I state in my root post: "This is nothing new to ethics. To this extent, [Peter Keating] was a regular, typical human being. Indeed he typified a conscious animal. All animal actions, apart from reflexes, are motivated. ... An action and its motivation is inseparable. An animal action without a motive is a contradiction in terms." I then go on to subclass "self-interest" into "rational self-interest," "irrational self-interest," and volitionless "nonrational self-interest." So per Rand, Keating asking Roark to do his work for him was an "unselfish" act? [...] Two points: 1. Since ideas are thought by human beings, and while an idea may have been taught down through the ages, there must have been an individual who independently discovered it the first time. (This is not to say that many individuals could not have independently arrived at the same idea.) "2+2=4" as an idea had to be discovered, but since everybody knows it and uses it nowadays, no one remembers who first discovered it. I am crediting Ayn Rand for being the first to discover the cited ideas. But now that I have independently assessed them for myself that they are true, I have adopted them, integrated them, used them, and made them my own--as I have made "2+2=4" mine. 2. So, yes, I think that Keating's asking Roark to design the Cortlandt homes for him was an unselfish act. Why? Because Keating well knew that a man's achievement is his own, and that any fame that follows is always derivative of that which one has achieved. Keating knew he could not achieve, but he wanted the fame. He desired a consequence contra to its cause. It was a desire for unreality that motivated him--the knowledge of the facts be damned. Since the act was motivated by this irrational desire, against the consent of his mind's rational judgments of causality; therefore, his asking Roark to do the work was an unselfish act. How is it that Rand called Keating an egoist then? [ETA It's actually egotist with a 't' in between but I don't think the English language makes a real distinction betwen egoist and egotist - they're mere spelling variations.] Good catch, Xray! You found something I did not notice before. The "self" in "selfishness" is man's mind, particularly, that faculty of conscious ness that thinks, i.e., the ego. When that which thinks is set aside in favor of emotion or desire (apart from rationally derived desires) or in favor of the opinions of others, the self is set aside. Any volitional action motivated by such set-asides are unselfish, selfless acts. Read page 696 again and ask yourself if anyone would call Peter Keating an egoist in the exact sense defined here and in the root post. The cited quotation in the annex is Ayn Rand's sketch of the character Peter Keating before she wrote the novel. I interpret Rand in this specific context to be adopting the popular vernacular of the period, hence the phrase "in the accepted meaning of the word." Prior to the existence of the novel, there was on earth no such idea of "selfishness" (rational self-interest), no such idea of "egoist" (one who values his mind, with reason as his sole means of guidance), no such idea of "second-hander" (one who denies the self and acts on the opinions of others), etc. The annex reflects this and simply records a historical fact. The "ego(t)ist" conception at the time before the novel is probably the Nietzschean "individualist" who would trample on anybody and everybody to get what he desired--e.g., pushing out an old architect in the firm, selling one's wife for a contract, etc. Indeed, in the "Introduction" to the 25th annniversary edition, p. viii, Rand mentions the spelling to this word. But throughout the novel itself, she never uses the word to attribute to Peter Keating. Beginning with Ayn Rand, we have a new conception of egoism. ("A New Concept of Egoism" is also the subtitle of her book The Virtue of Selfishness.) Rand discovered the idea. She found it true. She used it. Now, thanks to her, anyone else on earth can take it-- or leave it. Since I find it true, I adopt it and use it.

I think that a very grotesque and (potentially) destructive obfuscation and equivocation by Goedel is his "slingshot" argument, which purports to prove that all true sentences stand for the same thing. Check out the wikipedia entry on "slingshot argument" for background on this kind of argument. I took part in a discussion on the Analytic list on the Enlightenment website back in September of 2000, and I deconstructed the Modern Logic approach to dealing with the slingshot by using plain language instead. It seemed clear to me where the equivocation and obfuscation was, and that you didn't need special symbolic machinery to uncover it, just a sharp eye and a refusal to be taken in by thimbleriggery. Perhaps some of the readers on this list can see it, too, as I lay it out. I'm sorry that the link to the Analytic list no longer works, or I could point you toward the initial heavily-symbolized essay by Bryan Register and the reply by Thomas Radcliffe, both of which motivated the following essay and followup comments. REB Goedel’s “Slingshot” Error: Begging the Question—or Equivocation? by Roger E. Bissell The following material was originally written for and posted on the Analytic list on 9/22/00 and 9/25/00. Comments are welcome. [...] C4: Therefore, Fact A1 is the same fact as Fact B1. (Nut the cat's having two eyes is the same fact as Bolt the cat's having one eye.) FALSE!!!!!!!! Now, C4 is precisely the kind of conclusion -- wiping out the distinction between different facts -- that the slingshot wants us to accept, and thereby to jettison the fundamental idea that propositions are true if and when they correctly refer to facts. Having shown that the slingshot arrives at a palpable contradiction, and having exposed the equivocations that cause it, I rest my case -- and renew my insistence that we keep our logical analyses anchored to the real world (assuming that Nut and Bolt are real cats :-), especially when analyzing sophistical arguments such as Goedel's slingshot! Roger, I just read both versions of your refutation of the slingshot argument, which was first suggested by Kurt Gödel (1944). If both versions are correct, and I think they are, then a whole field of mathematical logic needs to be mowed down! All of our knowledge--all of our true sentences together--is alleged to be about one single "Fact"? Preposterous! Yet this conclusion has been taken seriously since 1944. Even now, from Google search, ivory-tower intellectuals continue to take it seriously. Here is a fascinating book review in Notre Dame Philosophical Review on the slingshot argument (Neale, Stephen, Facing Facts, Oxford University Press, 2001). More current is this 2007 sidebar article in Stanford Encyclopedia of Philosophy "The Slingshot Argument," claiming, "There is a famous argument of Davidson's to the effect that if true statements correspond to facts, then they all correspond to the same Great Fact." Mortimer Adler's little book Ten Philosophical Mistakes (1985) comes to mind. What began as a kernel of error grew and seeded a whole field. Your presentation, Roger, really highlights the value of learning how to read and write plain prose instead of relying on the abstractness of symbols. There is a bias toward symbolic representation of truths--supposedly to remove misinterpretation--that I think is completely unwarranted. This slingshot error could have and should have been snipped long ago. We get back again to the source of the error: Misunderstanding through misreading. The slingshot argument misreads what facts are, in relation to truths. Here on this forum thread, history is repeating itself: a misreading "that 'add nothing' is the equivalent of 'do not add anything' " (Post #82). There seems to be a vested interest in maintaining misunderstanding. Why? I don't know. But I for one wish to see a proposed new idea being treated and debated more seriously among self-professed rational individuals.

Laure, Thank you very much for the two replies. Your diligence in following this topic, on the nature of hypothetical statements, reminds me of an original Star Trek episode, Episode 305 "Is There in Truth no Beauty?," in which a telepathic doctor, Doctor Miranda Jones, said to Spock before the mind-meld: "Now, Spock, this is to the death, ...!" Let me address your beginning and ending first. Gosh, I guess I'm not human. [...] You may want to withdraw that judgment, Laure, when we are done with our introspective journey. The hypothetico-propositional form "if p then q" is a legitimate propositional structure that is distinct from other propositional forms for factual identification in human cognition. That it has been claimed by modern logic to be equivalent truth-functionally to the alternate-propositional form "q or not p" is the issue under dispute. I am disputing it. (And you will too if our journey is successful.) The fact to be demonstrated is, technologists, and everyone else for that matter, treat them distinctly. Treating if's as if they were material implications gives rise to paradoxes, making them impractical. I have stated nothing here that I haven't already stated in my original post. Your program works great and concretizes perfectly the discrepancy in modern logic between theory and practice. But we are getting ahead of ourselves. I recommend you use and annotate the program as you introspect in the next three iterations. To your answer, I agree that "5" is the answer modern logic would prescribe. The truths of hypothetical statements are to be computed truth functionally, in accordance with the truth table of "material implication." I included the same answer as yours in the original post in the form of a hidden spoiler tag. I also included therein the truth table of "material implication" and its mapping from a compound "disjunction." Yes, I do mean that you introspect to determine their truth values. You agree, do you not, that MIx (1 through 6) are instructions in the form of hypothetical statements? These are statements addressed to someone with honor and integrity. Rational human beings think and act on their judgments. These are hypothetical statements to be thought of and acted on. Therefore, these hypothetical statements can be evaluated logically in the same and exact way as the hypothetical statements HPx (1 through 6). You thought and acted per instruction A3 [a typo] to yield your answers, did you not? How did you do it? Introspect what you did. Laure1. If HP1 then I say "true." Laure2. If HP2 then I say "true." Laure3. If HP3 then I say "true." Laure4. If HP4 then I say "true." Laure5. If HP5 then I say "true." Laure6. If HP6 then I say "true." Laure7. If MI1 then I say "true." Laure8. If MI2 then I say "true." Laure9. If MI3 then I say "true." LaureA. If MI4 then I say "true." LaureB. If MI5 then I say "true." LaureC. If MI6 then I say "true." Secondly, considering the MIx instructions again, would you agree that in comprehending them cognitively as hypothetical statements, they are the same as: "Adding a dollar now is true if HPx is true"? The other person, too, thought and acted per instruction A3. I am asking you now to introspect what he did. Other1. If MI1 then I say "true." Other2. If MI2 then I say "true." Other3. If MI3 then I say "true." Other4. If MI4 then I say "true." Other5. If MI5 then I say "true." Other6. If MI6 then I say "true." Other7. If HP1 then I say "true." Other8. If HP2 then I say "true." Other9. If HP3 then I say "true." OtherA. If HP4 then I say "true." OtherB. If HP5 then I say "true." OtherC. If HP6 then I say "true." Finally, consider the technological wonders of computer programs, yours in particular. Evaluate your hypothetical statements CS_x (1 through 6). #include <stdio.h> void main() { int Table[7] = {1,0,0,0,0,0,0}; // Table starts with 1 dollar int Hand[7] = {4,0,0,0,0,0,0}; // Hand starts with 4 dollars if (Table[0]!=1 || &Table) // Note" "||" means OR // CS_1. "If HP1 then {..., I say 'true'}." { Table[1] = Table[0] + 1; Hand[1] = Hand[0] - 1; printf("Step 1 TRUE, Table=%d, Hand=%d\n", Table[1], Hand[1]); } else // CSn1. "If not HP1 then {...}." { Table[1] = Table[0]; Hand[1] = Hand[0]; printf("Step 1 FALSE, Table=%d, Hand=%d\n", Table[1], Hand[1]); } if (Table[1]!=2 || Table[1] == Table[0] + 1) // CS_2. "If HP2 then {..., I say 'true'}." { Table[2] = Table[1] + 1; Hand[2] = Hand[1] - 1; printf("Step 2 TRUE, Table=%d, Hand=%d\n", Table[2], Hand[2]); } else // CSn2. "If not HP2 then {...}." { Table[2] = Table[1]; Hand[2] = Hand[1]; printf("Step 2 FALSE, Table=%d, Hand=%d\n", Table[2], Hand[2]); } if (Table[2] != 3 || Hand[2] == 3) // CS_3. "If HP3 then {..., I say 'true'}." { Table[3] = Table[2] + 1; Hand[3] = Hand[2] - 1; printf("Step 3 TRUE, Table=%d, Hand=%d\n", Table[3], Hand[3]); } else // CSn3. "If not HP3 then {...}." { Table[3] = Table[2]; Hand[3] = Hand[2]; printf("Step 3 FALSE, Table=%d, Hand=%d\n", Table[3], Hand[3]); } if (Table[3]!=2 ||Table[3] == Table[2] + 1) // CS_4. "If HP4 then {..., I say 'true'}." { Table[4] = Table[3] + 1; Hand[4] = Hand[3] - 1; printf("Step 4 TRUE, Table=%d, Hand=%d\n", Table[4], Hand[4]); } else // CS_n4. "If not HP4 then {...}." { Table[4] = Table[3]; Hand[4] = Hand[3]; printf("Step 4 FALSE, Table=%d, Hand=%d\n", Table[4], Hand[4]); } if (Table[4] != 3 || Hand[4] == 0) // CS_5. "If HP5 then {..., I say 'true'}." { Table[5] = Table[4] + 1; Hand[5] = Hand[4] - 1; printf("Step 5 TRUE, Table=%d, Hand=%d\n", Table[5], Hand[5]); } else // CSn5. "If not HP5 then {...}." { Table[5] = Table[4]; Hand[5] = Hand[4]; printf("Step 5 FALSE, Table=%d, Hand=%d\n", Table[5], Hand[5]); } if (Table[5] <= 0 || Hand[5] > 0) // CS_6. "If HP6 then {..., I say 'true'}." { Table[6] = Table[5] + 1; Hand[6] = Hand[5] - 1; printf("Step 6 TRUE, Table=%d, Hand=%d\n", Table[6], Hand[6]); } else // CSn6. "If not HP6 then {...}." { Table[6] = Table[5]; Hand[6] = Hand[5]; printf("Step 6 FALSE, Table=%d, Hand=%d\n", Table[6], Hand[6]); } }

An introductory thread evoked a side question , which I would like to discuss here. Would you agree that Peter Keating was motivated by 100 per cent self-interest in his search for fame and praise from others? Yes, Peter Keating was motivated 100 percent by self-interest in his pursuit of fame in The Fountainhead. He was driven by what he thought was best for him, which is the praise and approval of others. Every decision he made was motivated and calculated by what was to be in it for him. Every action he took served his purpose, his personal goal, his desire, his value, his interest. Keating was motivated by self-interest. But so what? This is nothing new to ethics. To this extent, he was a regular, typical human being. Indeed he typified a conscious animal. All animal actions, apart from reflexes, are motivated. (Plants have vegetative actions, too, but let us delimit the topic and set that issue aside.) An action and its motivation is inseparable. An animal action without a motive is a contradiction in terms. Keating's actions, his pursuits, were no different. Human actions, distinguished as a subset of animal actions, is a little more complicated by the fact of volition. Although still motivated, human actions in addition can be chosen freely from among alternatives. The distinction is this: Confronted by a robber wielding a knife, a victim's every action is still motivated, motivated in the interest of the victim's life, but such an action in the presence of physical force is not volitionally chosen. Human actions are thus dependent on the absence of coercion from other men. There is thus a distinction between merely motivated actions--actions of animals and of coerced individuals--and freely chosen actions. This distinction makes all the difference. Chosen actions need the consent of the actor's own mind. With a knife on his back, the victim's motivated actions bypass whatever judgments he had. In freedom, a man's own judgment guides his actions. The action of a man who thinks "2+2=4" but who is coerced to write down "2+2=5," is completely, 100-percent, motivated action, but the action is not to his interest in a new and fundamental sense. In the one sense, there is the animal, moment-by-moment, non-rational interest; in the other, there is the human, long-term, rational interest. In the presence of freedom, however, human actions require an active use of the mind. Not only are there the multitude of existential alternatives to choose from, but there are the mental alternatives to choose from as well; and the most fundamental of which is the choice to think. Man has the capacity to make this choice (in freedom) to think or not. This is volition. The alternatives to think or not, to be guided by reason or not, in choosing the multitude of alternatives and actions, have great, inescapable consequences. Volition in the presence of freedom bestows a great responsibility to a human being. If he thinks "2+2=4," he has the free will to act on that knowledge in his everyday action, or not. He can choose to write down "4" as a result, or he can choose to write down "5"; and he can carry out actions subsequent to it. He is free to act, but he cannot escape the consequence of his motivated actions. That is, he can choose to act rationally on the basis of his judgment, or he can discard his judgment and act without its guidance, i.e., he can act irrationally. Thus the broad concept "self-interest," the one that applies not only to men but also to animals, must be intensified, according to Ayn Rand, to distinguish that self-interest that is generated by human volitional judgments. Thus, Rand defines "selfishness" as rational self-interest. Human actions that are guided by the individual's judgments are actions motivated by rational self-interest. A man acting on motives other than the free-will judgment of his mind, whether by coercion from others or by his own emotional whim, is not acting toward his rational self-interest. That is, to act by coercion is to be motivated by non-rational interest--an interest not of his own choosing. And to act by emotion, unaided by his rational judgment, is to be motivated by irrational self-interest. On Rand's conception, a rational man acts selfishly. An irrational man acts unselfishly. A coerced man acts robotically, animalistically, non-mindedly. Herein lies one of Rand's great insights in ethics. She identifies the source of man's greatness: his mind, the ego. When a person chooses to value his mind and respects its volitional nature, he is an egoist. When he doesn't place much value to it and disrespects its nature by abusing its development, denigrating its evidence, evading its judgments, deferring it to his emotions and desires of the moment, deferring it to the minds of others, he is a second-hander. And this last is concretized in the character Peter Keating. In the fictional world, Keating was a second-hander, and every one of his actions was motivated by his self-interest toward fame and praise of others. But he was not acting toward his rational self-interest. He never thought whether becoming an architect to please his mother was really to his self-interest. Even if he did, he deferred whatever thought he had to hers and to her emotions. Every decision and action was motivated for himself, for what's best for him. But was it motivated selfishly, if that self was denied of its judgments? He never knew himself, that budding artist that never was. Motivated, yes, by definition, but second-handedly, without a self, he acted selflessly. He was not acting selfishly.

Shane, You and MSK (in his Post #4) have found me out. In crafting my query for a show of hands about Objectivists' interpretations of truth and reading comprehension, I deliberately used a term not found in any dictionary but had to end with the letter 's' to simulate the plural form of a noun. And because I couldn't think of any quick or random way to generate the term, I honed in on the physical layout of the keyboard and typed a progression of keys with my right hand on the home row. Well done! But the question remains. If this were in a real situation (and there's no answer you can peek from the back of the Textbook), what judgment are you to make on reading T2? This is what I am interested in. I am interested in the introspective, psycho-epistemological evaluation of reading T2. As I mentioned before, the scenario I am describing is not that uncommon, which is why I would like to understand how people deal with it. For example, take your case and MSK's. Now, MSK has already given his answer (even though he didn't vote). He evaluates T2 as meaningless because "gfd" is meaningless. Contrast this evaluation against another vote that the principle of bivalence holds: that a statement is either true or false. Which is the correct view? It doesn't matter to me in the present context. I am merely trying to document the various processes and reasons for evaluating T2. What is your answer? Some people often say, if it is either true or false, then it is not meaningless; you say if it is both true and false, it is meaningless. What is the order of precedence for you? Meaning and then truth? Or Truth and then meaning? So, disregard what others have voted or opined. I am requesting your independent evaluation of the status of T2. The more detailed your opinion, the better. Take a stand.

Laure, Thank you for your interest in following my train of thought. But I will disagree with you from the outset. I have shown the discrepancy in two modes. What I have asked of the interested reader has been to follow this train of thought to see for himself. One side has paradoxes. The other does not. There is considerable amount of introspection involved in this task. After all, we are dealing with the iffiness of hypotheticals. Isn't it paradoxical that logic teaches that whenever there is a seeming problem, one should go back and question the premises, and yet when logic itself has paradoxes (as interpreted by the state model logic) few want to examine its premises? This is all I am trying to suggest. So, if you wish to engage in debugging the problem, either with my train of thought or with logic itself, I welcome the open dialog, provided you grant me the principle of charity. I have presented my case the best I could, given the constraints. If you are willing to start afresh, may I ask, without looking at the spoilers, how many dollars do you find there on the table after reading HP1 through HP6? I then ask that you introspect the process of how you arrive at that total. Is HP1 true or false, ..., HP6 true or false? I then ask that you use the exact evaluative method just introspected to evaluate the instructions MI1 through MI6. What do you find?

Peter, Though short, your post summarizes a structural point of my article. I also take your parenthetical comment about "effete, hatred-eaten mystics" exactly for what it is in the context: an attempt at humor. Thanks for your understanding.

I'd say that philosophy is fundamentally correct (on the Aristotelian-Objectivist basis), while mathematics is "operationally" valid, but its principles (some of them) have been misinterpreted ontologically. For instance, when you write out the equation 1 + 0 = 1, does that represent the ~addition~ of 0 to 1? That is the standard interpretation. But how can you add nothing to something? Actually, what you are doing is ~not~ adding ~anything~ to something. In other words, the notation ~really~ symbolizes that you ~are not~ adding anything to 1, not that you ~are~ adding 0 to it. The zero means the operation of adding IS NOT PERFORMED. This can also be seen for "multiplication by zero." Typically, we are taught that any number multiplied by 0 is 0. This is another misinterpretation of what is going on. In 5 x 3 = 15, you are multiplying 5 by 3, but in the expression "5 x 0," you are not ~multiplying~ 5 by ~zero~; you are ~not multiplying~ 5 by ~anything~. You are specifying that there ~zero~ multiples of 5. Considering that multiplication is just compressed addition, you can see this easily: 5 x 3 is 5 + 5 + 5, 3 multiples of 5. The number 5 must appear 3 times as the only addends, and the sum of those three multiples of 5 is 15. However, 5 x 0 is ~no~ multiplies of 5. The number 5 must appear 0 times, and there are no other addends, which means no addition (and hence no multiplication) is being performed. 0 is expressed as the product of 5 and 0, but this is not the expression of a multiplication operation, but what must be the situation when no such operation is performed! A similar thing happens in regard to the "zero power," which is always 1 for any real number (except 0?). E.g., 5 to the zero power is 1, 100 to the zero power is 1, etc. Some people are mystified by this, wondering what it means ontologically. Well, its meaning is in the operation that ~is not~ being performed. (In that respect, a zero power is like a zero addend, as above.) See, the key to grasping what is going on with powers is to realize that the factor 1 is always the base to which the power multiplication is applied or not. E.g., 5 squared (i.e., to the second power) ~actually~ means the number one multiplied by the number 5 two times. 5 to the 3rd power means 1 multiplied by the number 5 3 times. 5 to the 0th power means 1 ~not~ multiplied by the number 5 ~any~ times. The zero means the operation of power multiplication on the factor 1 IS NOT PERFORMED. That is why any number to the zero power is always 1. Not because 5 is ~taken~ times ~itself~ zero times, but because 1 is ~not taken~ times 5 ~any~ times. This reminds me of the old saw about evidence and justification: absence of evidence is NOT evidence of absence. Nothing is not something. In other words, I think Thom is onto something -- and it's not nothing! The complement of a set is always understood in regard to some larger set, of which they both are subsets and together in relation to which they non-overlappingly comprise the total membership of the larger set. For instance, in regard to a set of six apples, the set comprised by two of those apples is the complement of the set comprised by the the other four of those apples. There is no problem understanding the meaning of "complement" here, nor of the union of a set and its complement in relation to a larger whole. But it is the fact a set and its complement are both subsets of a ~larger~ whole that rules out considering the "empty" set as the complement of the larger whole. To complement means to add to something in order to make a whole. But the six apples ~already~ are a whole six apples, and you cannot meaningfully add ~zero~ apples in order to make the six apples a whole, because they already ~are~ a whole. Zero apples is (are?) NO PART of six apples, and thus NO SUBSET of six apples. You cannot speak of the ~union~ of something and nothing, so you cannot speak of the union of zero apples and six apples, any more than you can speak of adding 0 and 6. What you are doing is ~not~ adding ~anything~ to 6, because the 6 is already 6. You are ~not~ finding the union of ~anything~ with the set of six apples, because the set of six apples is already a set of six apples. The notation expressing a union of the null set with another set simply means that the operation of set union IS NOT PERFORMED. That, IMHO, is the ontological meaning of operations conventionally taken to involve zero or null sets. The operations are actually being specified as not having been performed! In this way, a number of mathematical and logical expressions conventionally regarded as arbitrary premises in order to build a system of inference can instead be seen as specifying that zero and null sets are operation-blockers. In the same way, the concept of "nothing" is also an operation-blocker. Nothing does not exist. You can't get inside it, outside of it, around it, underneath it, period. All that exists is Existence, and Existence is ~all~ that exists. It is a complete sum total. It cannot have a complement, because there isn't anything you can add to it. And you especially can't add Nothing to it, because Nothing isn't anything. So, Existence as the set or sum total of everything that exists cannot have a complement. Existence as a sum total ~must~ exist. It cannot go out of existence, so it has no "opposite" either--no whatever-it-is that there would be if Existence stopped existing (because it can't). "Nothing" or "non-existence" only has meaning in relation to some specific thing that might or might not exist, but even then, it's an operation-blocker. If you look into a room that contains a table and chair, and someone asks you what you see, your perceptual mechanism finds the two objects to lock onto, and you report, "I see a table and chair." But if you look into an empty room, and someone asks you what you see, how do you reply? Do you say, "I see nothing there"? Perhaps, but what you are really saying is, "I ~don't see~ ~anything~ there." You are not ~seeing~ ~nothing~. You are ~not seeing~ ~anything~ (except a room). The absence of anything in the room is an operation-blocker. There isn't anything for your perceptual mechanism to lock onto (except for the room itself), so your entity-perceiving function is blocked. So, Thom, I guess I'm on your side on this one. (I know I'm on ~my~ side, anyway. I hope this helps. REB I am sorry I missed this the first time around, very interesting. Thank you, Ted, for seeing the import of this perspective.

Michael, Let's concretize what distractions primarily are. I identify the physiological process of perception to be automatic and biological and requiring replenishment and rest (sleep). It is perception that can be distracting because its field is so wide. If the base of man's conceptual knowledge of reality is perception, then that fact alone shows how vast and rich and detailed a single "glance" can be. This is where volition is required to enable the individual to focus conceptually on the particular aspect of reality of his interest to be aware of. Therefore, it is the very nature of a conceptual being to need to choose to focus his conceptual apparatus on some particular area. If he doesn't choose, perception continues to flood in, but he won't get much conceptually out of it. And all of this is natural and an uneliminatable aspect of nature. Now if you can isolate a particular area of perception to focus on conceptually, surely you can use the same capacity to manage interruptions from people, phone calls, e-mails, etc. If you can block out the nagging pain from a freshly scratched knee to continue your intellectual work, surely you can push out lower-level emotional distractions from your higher-level purpose. The key is to have a purpose and to commit to it at a sufficiently high level. Is it not in NB's TPOSE that he says the source of self-efficacy is the will to understand? This is the controlling purpose: to want to understand and to commit to it, come what may. So I reject your compromise that it is possible to have genuine focus and yet still be distracted in some other form. You cite the counterexample of someone who is focused on paying bills but can't transfer the focus level to reading forum posts. This example doesn't apply. I maintain that volitional focus is always purpose related. The primary one is the will to understand or know. Ayn Rand's definition of "thinking" as a volitional activity has an integrated component of purpose. The basic choice is to think or not. Why think? Rand defines "thinking" as a mental identification or classification of what exists. (ARA 158, BB POET L01 S03); and she defines "thought" as a purposefully directed process of cognition. (ITOE 32a). Using your example, I can explain it this way: What is the purpose in that situation? It is to pay bills. Now, because he is insufficiently focused, he loses track of his purpose and thus spends time reading OL forum posts. It is not poor cognition that I am attributing. It is the purpose that he has lost that leads him not to have any strong purpose subsequently when he spends time reading and writing forum posts. When one doesn't have a purpose, what is there to will? At the adult level, however, everything that is conceptual is volitional, hence the need for epistemology. Granted that conceptual capacities can't be turned off, they have to be activated explicitly, volitionally. After all, thinking is a choice. Now, at the baby level, I find Rand's explanation much more plausible than Nyquist's. In ITOE 150-152, Rand talks about this very topic in answer to a question about how the baby abstracts for the first time when he doesn't know what abstraction is. "No, you do something else volitionally. That is, you abstract volitionally, but you don't will it directly the first time. Do you know what you will? You will to observe. You use your senses, you look around, and your will is to grasp to understand. And you observe similarities. Now, you don't know yet that this is the process of abstraction, and a great many people never grasp consciously that that's what the process is. But you are engaged in it once you begin to observe similarities." Thus, while our automatic capacities cannot be turned off, they don't get activated and run by themselves either unless we choose to engage them. Purpose is truly a cardinal value to jumpstart every action, psychological and existential. In fact, willing qua action of consciousness requires an objective content, which is purpose. (ITOE 29-30) I would say, therefore, that much of the mutations on OL threads stem from inefficiency in maintaining purpose at a sufficiently high level. This is a habit people can acquire, a habit of not caring where their minds wander. It is, as you said, the same character profile that finds Twitter appealing.

Considering the many comments lately about theism on OL, I thought it might be interesting to use the idea to exemplify and contrast further my analysis of understanding X'ism versus being an X'ist. To begin, let's quote Barbara Branden in a recent post elsewhere, where she asserts a logical link between assenting to the truth of a belief and being its believer: "... one cannot ... claim to be a Christian while denying the existence of God..." I interpret this to mean, if you deny the belief of God's existence, then you cannot be a Christian. The contrapositive of this hypothetical proposition is, if you are a Christian, then you believe that God exists. More generally, Barbara's statement becomes, if you are a theist, then you assent theism to be true. From the general statement, we can infer logically that if you take theism to be false, you are therefore an atheist. By this logic, if you are an Objectivist, then you assent Objectivism (or some stipulated core part) to be true. And if you deny Objectivism to be true, then you are not an Objectivist. The hypothetical relationship which Barbara asserts is much stronger than the one I have been discussing in the present thread. Where she asserts "If you are an X'ist/ian, then you believe/understand X'ism," the converse position I have argued is weaker, "If you believe/understand X'ism, then you are an X'ist/ian." What is the difference? Setting aside the obvious but tangential difference of "mere belief" versus "understanding," the difference of interest in the present context is that Barbara's formulation completely removes fake Christians or fake theists. If you don't have the belief (and think it true), then you are not its believer. In my formulation, I admit the possibility of fake Objectivists. I make no claim about the status of those who don't understand Objectivism but who nevertheless claim to be Objectivists. So, it would seem that my formulation aims at the cognitive condition of understanding. If you understand X'ism, being an X'ist automatically follows as a consequence. Barbara's formulation, on the other hand, aims at self-identifying. If you don't understand X'ism, you cannot be an X'ist. The two converses complement and strengthen each other. And while I happen to agree to the truths of both, I have only defended, "If you understand X'ism, you are an X'ist." If this hypothetical relationship is true, which I have earlier argued to be true, one can see the impossibility of the combination of someone simultaneously understanding Objectivism but not being an Objectivist. This is tantamount to claiming impossibly for somone to understand atheism to be true but not being an atheist. With this formulation, I remove fake or mis- understanding; I deny the existence of the non-Objectivists who understand X'ism. On my formulation, I think it is more honest cognitively for someone to say he is not an Objectivist than for him to say that he understands Objectivism but is not an Objectivist. Conversely, in Barbara's formulation, it is more honest for someone to misconclude and say that Objectivism is false than for him to say that he is an Objectivist but believes the core of Objectivism to be false.