thomtg

Hi YD, You have posed some interesting questions, which, in order for me to discuss in depth, I will first need to define some terms. altruism: the moral code that a man's existence is to serve other men and that sacrifice is his highest virtue. sacrifice: the giving up of a higher value for the sake of a lower value. egoism: the moral code that a man's existence is his to live and enjoy and rationality is his highest virtue. rationality: the use of reason as the only means for acquiring knowledge and guiding one's actions. moral code: [or in TVOS, code of values:] a set of abstract principles [serving as] a system of teleological measurement which grades the choices and actions open to man, according to the degree to which they achieve or frustrate the code's standard of value. benevolence: the principle that, because other men are potential traders (material and spiritual), in order to make voluntarily trades with them, one should treat them with courtesy, generosity, and respect. trade: the <strike>giving up</strike> exchange of a value voluntarily for the sake of an equal value, to mutual benefit. The act of buying a drink for a friend is a consequence of a long chain of reasoning. So the act by itself, as a situation, as an event, can come from many motives. An altruist or an egoist could both end up buying a drink for someone else--the former, because he feels it is his duty to serve; the latter, because he esteems his friend and cares for his well-being. A person's motive depends on what he values, and values are determined by one's accepted moral code. If you want to evaluate the morality of an action, you have to know the actor and his moral code. Your friend's reporting of the act, it seems to me, is his way of using it as evidence for the notion of "karma." The act happened, then "karma" happened--so he claims. Your attributing some action as altruistic (or otherwise) should not depend on the fact of the subsequent reporting of that action. The reporting is a separate act, and is determined by some other motive. Now, concerning the argument your friend makes, this to me is a logical fallacy called post hoc (or, post hoc ergo propter hoc). Just because something happens and then another thing happens, does not make the first to be the cause of the second. Objectivism does not denigrating doing "good" deeds. There is the virtue of benevolence, which is very much integrated with the basic virtues in the Objectivist ethics. An egoist values himself for the long term. If he were obnoxious and thinking of himself only in the short term, then, while he might gain something in the moment, he would lose out in the long run because other people would not want to deal continually with him. If reason had been his guide, he would have seen that his momentary gain came at a high cost in the long run, thereby that "gain" was not a good trade but was actually a sacrifice. There is nothing wrong with feeling gratified. In fact, it is natural to experience gratification for gaining a value. What is at issue however is not the experience of gratification but the nature of that which one values. A person's set of values, his hierarchy of values--those things he commits his life to gain and keep--are they in fact objective to his nature as a rational being? What is the standard of values from which that hierarchy was evaluated? So, if someone chooses fame for a value, and he works and eventually gets praise, celebrity, fame; then it is natural for him to feel gratified. But is "fame" an objective value? Peter Keating went for fame and praise from others, and look where he ended up.

Congruent with my other thread : Not bad for an amateur, huh. I'm glad you see the merit in my perspective, Thom, and I appreciate your additional comments, linking mathematics, logic, and epistemology (viz., concept-formation). I first came up with this angle a little over 12 years ago in David Kelley's cyberseminar on propositions. They were wondering what was the ontological interpretation of x to the zero power. I told them it had to do with an operation that was not performed on the unit 1. (If Ba'al agreed with this, he'd still probably want to say: "an operation that performed no times on the unit 1." I have a couple of essays on my web site about zero powers and such, but I won't bother with links at this time. Those interested can prowl around on www.rogerbissell.com and find it easily enough. Anyway, I'm grateful for this particular discussion, because it has crystallized my thinking more generally about zero as not an operator, but a blocker of operations. [Emphasis added, Thom.] I agree with you that in order to properly orient mathematics (back) to the real world, a lot of re-interpretation is necessary. Some of that re-interpretation has to do with getting clear about exactly what operations we are or are not performing. So, it's not all metaphysical/ontological, but the fact that the operations of mathematics can be performed on things in the real world means that such homely little examples I used such as the empty room vs. the room with 5 chairs can actually shed light on what operations can and cannot be performed mentally, mathematically or logically or otherwise. REB Roger, I think we are on to something. For quite a while now, I have been studying about the discrepancy between what most mathematical logicians say about logic and what computer programmers do when they write software applications--or what chip designers do when laying out logic circuits. What I have noticed is that the former have a state model of logic while the latter have a process model. I mean by this, that logicians are concerned with truth tables, mappings, and all possible contingent states of affairs, as if from an omniscient bird's-eye view; while on the other hand, that programmers are concerned mainly with processing logical operations to reach some goal state. The discrepancy lies in the fact that programmers and designers do not follow what logicians have claimed about the nature of logic. Now the issue isn't whether without the sciences of logic, mathematical logic, and other subsequent sciences, there would not exist modern products of technology; all of which is true and readily conceded. The issue is whether logicians have interpreted modern logic in such a way that make inferences in the real world practical. And plainly, the fact is that programmers and designers (henceforth, technologists) do not take the former's interpretation into consideration when making their programming or designing decisions to do their work. In a sense, the practical technologists are doing logic without epistemological guidance from modern logicians as to how it is that their jobs turn out to be productive and conforming to reality. They know that logic works wondrously, but they don't know why. They are perplexed because that which is often claimed to be the explanation doesn't match with what they are doing. The mathematical logicians' theory doesn't match with the technologists' practice. There is the disconnect. I think this is exactly where Objectivist epistemology can enter to help correct centuries-old mistakes in the various sciences, most crucially, the modern science of logic. To begin, "logic" itself, as a fundamental concept of method, must be redefined on an Aristotelian-Objectivist foundation. (ITOE 36) It is as if we are repeating history: Logic is neither subjective (psychologism) nor intrinsic (logicism) but objective. For the rest of this article, I'm going to show the consequence of an aspect of the state model of logic. I will contrast this model with how technologists actually do logic. And by modus tollens, I falsify the state model and outline indirectly a theory of the process model of logic. To illustrate what I mean about the discrepancy, consider the well-known paradox of entailment in modern logic. If whenever you have two contradictory premises in an argument, your conclusion validly can be deuces wild. For example, since the dog is on the mat, and it isn't (at the same time in the same respect); therefore, the U.S. economy negotiates one trillion decisions per microsecond. Since the argument is valid, so say modern logicians, therefore "the U.S. economy negotiates one trillion decisions per microsecond" is proven by virtue of the argument. In fact, on this basis, you can insert anything for the conclusion-part of the argument, and it will come out as perfectly validated. If you did not independently know the truth or falsity of a statement, and you plug that statement as the conclusion part of the argument, and the whole argument delivers the verdict of, yes, valid; what then do you conclude of its conclusion? Whenever you hear a "therefore" before a statement, and the argument is a valid one, what do you usually conclude? That the conlusion is false? No, if the point of valid reasoning is to have a way of inferring new truths from prior truths, then naturally whenever you hear that an argument is valid, then you would have to conclude naturally that that which you didn't know to be true or false before is now known to be true. Not so fast, according to the state model of logic. Modern logicians caution that in reason, don't trust your reason. The inserted statement into the conclusion could have been known by some other means to be false. And the whole argument could still come out clean (laundered?) as valid. Not only that, there is also this truism concerning your premises: Who can say honestly that he doesn't have one or two falsehoods floating in his head? If so, whenever he makes an argument to infer new truths, might he not have contradictory premises? Therefore, might he not have valid reasoning whose conclusion he cannot trust to be true? So, in other words, you can't trust whatever you knew prior, to be true. This double injunction--don't trust reason, and don't trust knowledge--follows from the paradox of entailment. It comes straight out of bedrock logic in modern times. Technologists, and the man on the street with his common sense, don't buy any of that. I won't try to "prove" it just yet, but the evidence is everywhere--counterevidence, that is. All the modern gadgets and conveniences of life attest to this. The state model of logic is littered with paradoxes. Many of them, if not most, have their origins in a conception of truth as being functional. The entailment paradox is no different and is merely the simplest and nearest to the theoretical foundation of the theory. A cornerstone of this theory is a particular conception of the hypothetical proposition, which in mathematical logic is allegedly mapped to a logical operation called the "material implication." The consequence of this mapping, if followed, would make practical technology unworkable. Indeed, it is not followed, because this "material implication" is itself paradoxical. A hypothetical proposition is nothing more than an everyday English "if" statement. It is a statement asserting a relationship of dependence between two thoughts, between the antecedent and the consequent, to identify some dependency among facts, events, or possibilities. We say something is a fact because of its relationship to another fact. There is no mystery about it. We assert these relations all the time. But in modern logic, there is a paradox in the way its truth is derived. The grammatical form of the hypothetical proposition in the state-model view is treated as a truth function. This truth function maps "if" to "either the consequent or not the antecedent," reducing the "if" to an "either-or" statement with a nested "not." And this reduction is called "material implication." (The "either-or" itself is mapped primitively to a logical operation called the "disjunction.") If this sounds complicated to understand, requiring a college education or higher, that's so because it is. Modern logic is a logic not suited for human thinking. Man-made electronic machines only seem to follow this modern logic, but they actually do not--a point that I will show presently. Put yourself in the place of the first-person pronoun in this situation below and follow HP1 through HP6: A1. I see a dollar on the table right now. A2. You have four dollars in your hands, and you honor what you promise. A2. You will add another dollar on the table for each time I evaluate an "if" statement to be true. HP1. "If the table has a dollar on it, then the table is serving its function as a table." MI1. Add dollar now if HP1. HP2. "If the table has 2 dollars now, then I have gained a dollar." MI2. Add dollar now if HP2. HP3. "If the table has 3 dollars now, then you have 3 dollars left in your hands." MI3. Add dollar now if HP3. HP4. "If the table has 2 dollars now, then I have gained another dollar." MI4. Add dollar now if HP4. HP5. "If the table has 3 now dollars now, then you have no money left." MI5. Add dollar now if HP5. HP6. "If the table has any money at all now, then you have some money in your hands." MI6. Add dollar now if HP6. Before you read on, how many dollars should there be on the table? Common sense says . According to modern logic, there should be on the table. It has to be so because of the way modern logic prescribes how truth is to be computed. Truth function for entailment: f((P1+P2+...+Pn), C) = V Premises Conclusion F() Validity T T = T T F = F F T = T F F = T Truth function for material implication: f(A, C) = MI Antecedent Consequent F()= Implication T T = T T F = F F T = T F F = T Truth function for MI-reduced: f.either-or(C, f.not(A)) = "either C OR not A" Ante. Conse. Not(Antedent) F() OR(C,not(A)) T T F = T T F F = F F T T = T F F T = T With these truth functions, the following items are supposed to be hypothetical propositions, the paradoxes of the "if" are in PMI3 and PMI4: PMI1. "If 2+2=4, then 4-2=2." true PMI2. "If 2+2=4, then 4-2=3." false PMI3. "If 2+2=5, then 2+2=4." true PMI4. "If 2+2=5, then 2+2=6." true The paradox summarizes conventionally as follows: The "if" statement is true both whenever the consequent is evaluated true, no matter the antecedent; and whenever the antecedent is evaluated false, no matter the consequent. This is why HP4 and HP5 above, by modern prescription, are evaluated true. The states of affairs of both the antecedent and the consequent are evaluated simultaneously and independently to compute the truth of the compound statement. At the primitive level, it matters not which clause gets evaluated first, consequent or antecedent, so long as both are evaluated. This is by virtue of the so-called commutativity property of the disjunction operation, e.g., PMI1 being translated and evaluated as equivalent to: either "4-2=2" is true or "2+2=4" is not true. In fact (1), ordinary people, and practical technologists among them, never follow this state model of logic, not because it is inefficient, but because it doesn't work in reality. To see how this is so, follow the statements MI1 through MI6. If you followed the state-model logic, you would have to add 6 dollars to the table (2 dollars of which you don't have) since the clause "Add dollar now" is evaluated simultaneously and independently of any other clause, and is evaluated true since you are an honorable person. In fact (2), the consequent "Add dollar now" comes into effect, and to be evaluated, only when the antecedent is true. And when the consequent is evaluated, by your putting a dollar on the table, then the whole compound statement, e.g., MI1, is true. Only if (and I emphasize "only"), and to repeat, only if you fail in that instance to put a dollar on the table can the whole compound statement be false. "Add dollar now" is always carried out, true, whenever it comes into effect for evaluation; your integrity ensured it. Thus, it should be apparent that there are two different conceptions of logic: a state model in accordance with truth functions and tables, and a process model in accordance with practical life. On the one hand, you are told to evaluate both antecedents and consequents to compute truth. On the other, you think and act otherwise. Logicians would evaluate MI1 through MI6 as true. From the commonsensical point of view, the standard by which people and technological machines operate, MI1, MI2, and MI6 are true. Those are the "if" statements that actually do add another dollar on the table. Being human, in order to evaluate the iffiness of "if" statements, one has to have accepted some particular standard or another for their evaluations. But how is one to evaluate which "if"-model has the better "if" without resorting to some ontological interpretation about the nature of hypothetical relations, or without resorting to some epistemological conception of a human consciousness that must grasp such relations. The irony is that the state model of logic presupposes a God-like consciousness contemplating eternal relations. If only we were so. Humans don't argue from contradictions if we can help it, and we don't evaluate "if" from disjunctions. Why don't technologists and the common man buy into modern logic? Because they implicitly hold on to a this-worldly view of logic, which has up until now been left undefended. It is the implicit view that logic must be a practical art, an instrumental means for discovering the facts of reality. And to the extent that this view is in the minds of technologists and that it hasn't been corroded or corrupted or replaced outright by the opposite view; to that extent has modernity been hobbling along. This quotation from Ayn Rand neatly summarizes what has happened in the science of logic. Today's frantic development in the field of technology has a quality reminiscent of the days preceding the economic crash of 1929: riding on the momentum of the past, on the unacknowledged remnants of an Aristotelian epistemology, it is a hectic, feverish expansion, heedless of the fact that its theoretical account is long since overdrawn--that in the field of scientific theory, unable to integrate or interpret their own data, scientists are abetting the resurgence of a primitive mysticism. [AR CTUI 11]

Thom, This is not correct. Without going into Rand's idea that all concept formation is volitional (which is an overreach), integrating percepts from sensations is an epistemological issue and volition is not at all involved in that. Epistemology deals with the manner we obtain information and the validity of it and consciousness in general. Not all consciousness is volitional either. We have innate mental processes. We have an overlap where innate processes and volition both work. And we have volition. We can guide our concept formation with volition. We can't turn concept formation off, though, and start living on the mental level of a dog. That part is not volitional. This fact means many concepts get integrated automatically. Michael Michael, I don't deny there are inborn capacities. What I deny is that conceptual activities employing such capacities are automatic. So although distractions do have some automatic, neurological basis, they can be managed volitionally. Isn't that why we can say that some people have better concentration level than others. If distractions are beyond our volitional control, why are there so many books about time management and so on? Now consider your view that many concepts get integrated automatically. I don't think that can work efficiently. Focused awareness has many levels. At the dazed level, as in turning on the TV in the room without paying attention to it, you are not going to get anything meaningful from it. And if you do get something out of it, your integration will not be high quality abstractions; you'll get the osmotic version, the second-hand version, the distracted version. In a way, a focused awareness at a higher level is the key to managing distractions. If let's say your awareness level is at 2, then when a distraction comes in, it may wipe away your first-level activities and may direct you to another. But since your awareness level is at 2, you are able to catch yourself, to notice your being distracted, and to redirect your faculties to your original activities or your original topics or your original purposes. So a higher-level focus mitigate a lower-level distraction. On this basis, for example, the number of mutations that happens on a thread is an indication of the level of focused attention OL readers and posters on that thread put into maintaining the topic.

Michael (MSK), You are asking questions I would ask to make a determination of the status of T2. What are your answers from the context given and why? By the way, the scenario I am describing is not that uncommon, which is why I would like to understand how people deal with it.

I went for meaningless because I am open-minded and allowing of ambiguity. Strictly, the statement is false, but I accept that "gfds" might have some contextual meaning that would allow a vernacular understanding, though, if so, that is not explained. Therefore, I chose "meaningless." Logically, it is false. [...] Michael (MEM), I don't follow. You think T2 is logically false, but you voted meaningless?

Roger, the week has gone by, and its weekend is nearly over. I assume then that my Part 1 in Post #66 has proven insuperable to overcome in your conception of existential import. Let me finish it off with some comments to your two rejoinders to my Parts 3 and 2, respectively, in Post #67 and Post #70. Your rejoinder to Part 3 (Post #67): On universals of emptiness: I apologize for inadvertently ascribing ill intention on your exposition. I meant to highlight only the actual switch in the direction of analysis. My identification of the particular fallacy was erroneous. (There is still a fallacy, but now I don't know what to call it.) I thinly induced your principles, Roger, from only the limited jumble of "god-awful" examples and distortions I was able to generate in Post #31 earlier in our discussion. I did not fully realize that I should have been much more outlandish with the examples in order to capture the full Rube Golberg. :angel: Nevertheless, I see your point of view, and I am perfectly content to substitute in REB6 and REB7 to the list of principles that characterize your theory of existential import: R1-R8, P1, which I enumerated at the beginning of Post #66. Here they are, in my own words (from your second version in Post #70): REB6: An affirmation whose designation of the subject is empty must be false, except when the predicate is either identical to the subject or an empty superclass thereof; which then makes it vacuously true. REB7: A denial whose designation of the subject is empty must be true, except when the predicate is either identical to the subject or an empty superclass thereof; which then makes it vacuously false. The problem with the reply to my Part 3, Roger, is that it re-affirms my very point that there is a switch in meaning. What used to be a triple set of presumed equivalences is now a quadruple set. The guidelines even when emended prescribe equivocations for three sets. Here are your answers, first in Post #32: With the above, I reorganized them in Post #66 as: Then in your rejoinder, you merely affirm that the set {C7, C8} is equivalent to {11, 12}, which I agree. However, you haven't denied that your Post #32 asserts {11, 12} equivalently to {C9, C10}, and yonder {C5, C6}. Now I grant you that the odd Cs (C5, C7, C9) are all false, and the even Cs (C6, C8, C10) are all true; but I draw a triple line against the respective triplets being equivalent in meaning as you claimed. I drew the scratchpad to make that clear. My essential point from Post #66 is still unchallenged: In fact, it would seem that you have transgressed your guidelines to move from one order of existence to another, from the realm of impossible objects (circle that is square) to the realm of real objects (circle). This is the direct effect of R8, which you indirectly affirm in the reformulated REB6-7 rules. And speaking of REB6-7 and R8, I want to be clear that I take the word "identical" precisely to mean having two separate things be similar to the highest degree. (See Merlin Jetton's Objectivity article "Pursuing Similarity", p. 42.) If we are on the same page with this meaning, then as I said before in Post #31, we are moving the issue beyond merely the theory of existential import, to the theory of propositions. Your rejoinder to Part 2 (Post #70): On singulars described to emptiness: Okay, I see two typos in my presentation in this part in Post #66. While I first recapitulated your interpretation correctly (from your Post #32), I then made the typos in its expansion. Though typographically incorrect, I correctly attributed your R6-7 (or REB6-7) for each expansion. My point about the expansions was not so much on the truth and falsity of the statements, which I had already highlighted in the recapitulations, as on the expansions themselves being required. I wanted to draw attention to your reliance on R5, which goes beyond R2. It is the need to transmogrify one assertion into three. And you affirmed the same approach again in Post #70. Why must you make singular statements of the descriptive kind special? Notice that R5 is orthogonal to REB6-7. R5 is the real issue here while REB6-7 are merely tangential, which is why I even used "The current President of France" ("TcPoF") to illustrate the same fallacy in using R5. It is what I mentioned in Post #31 as your translation of Bertrand Russell's theory of descriptions. --- To conclude: Although you may have saved REB6-7 in the Part 3 by adding an exception clause, that does not change the fact that you make exceptions to empty designations, as opposed to designations of different orders of existence. REB6-7 is orthogonal to R4, which I agreed from the start. So, in a sense, your first rejoinder has not landed on the real targets, which in Part 3 are my comments against R8. And in Part 2, the comments against your R5 are the targets, which are independent of your defense of REB6-7, and they have not been sunk.

Buddhists are a-theists in that they don't have a personal god. But the "cycle of rebirths" with Nirvana as the ultimative stage of ending the cycle of suffering is clearly a valuing concept. Which begs the question: "Who judges people to be reborn? What is the "valuing" instance? Xray, you have uncovered the "stolen concept" fallacy inherent in the claim that Buddhism is atheistic.

I bid 5011.00. Reserve not met. I will not increase my bid. Look at the hands. The weakest part of this composition. If they had displayed just a little more artistic competence this painting would be worth much more. --Brant Well, Brant, you bade the highest bid on eBay (on the 7th of May), and you were the higher bidder against one other collector interested in purchasing The Mandarin. This bidder's highest was $3,601.00. It is too bad no bid met the reserve when the auction expired yesterday.

Happy birthday, Barbara! I think you are a super senior. Here's to your work on POET v2.0.

"Rand defined what she meant", you wrote. Where is that specific definition of hers in terms of "benevolent" in connection to "universe"? Here. About source: A, B Stephen, I would like to learn from you exactly how you did what you did: to recall ideas you had heard or studied and to locate precisely from where they were communicated or learned. But back to the point, you have two parenthetical snippets: To which I would add the principle of charity. And before anyone jumps in and imputes the literal meaning and thus to claim outlandishly some conclusion about me or about Ayn Rand, Leonard Peikoff, etc., or about Objectivism and its movements--whew, this is tiresome!--I mean by this principle, that in order to gain objectivity, whenever I read something from someone, that I should give him the assumption that he is writing logically, that I should grant him the benefit of the doubt--barring evidence otherwise. Thus, if I read a sentence from a text and I don't understand it, then it is my responsibility to find everything possible from the text and the related texts (e.g., earlier texts, dictionaries, lexicons, etc.) to make that sentence intelligible. Bill's root post gives a short summary from the author herself of the emotional leitmotif of her 1000-page book. In my view, before anyone has the right to criticize the summary as to whether it accurately summarizes the book or not, he must have read the book. To criticize the summary, and worse yet, to summarize the summary--condensing the entire book into a one-line quip--and to impute a meaning to the author's words contrary to the intended; that's being uncharitable. To be uncharitable in this sense is not to be objective. By the way, Bill, thanks for opening the book, finding this letter from Ayn Rand, and typing it manually to post it to this forum thread--all for the enlightenment and reading pleasure of all who apply themselves. You, the writer/typist, clearly hold the principle of respect--that you respect your readers' intelligence and diligence to grasp objective meaning and understanding from what you offered.

I'm a little late replying to this because I didn't see it earlier, but I disagree. Firstly, see post #23. Secondly, defining a set requires some criteria for membership, e.g. people in a room less than 6 feet tall. But suppose the criteria were people in a room greater than 10 feet tall. It is a set in the sense of having a criteria for membership. It's simply that none of the people qualify as a member. It's an empty set. Merlin, though I saw your Post #23, and had assumed your endorsement of the quoted passages, I did not include it in the discussion on Post #25 which you excerpted above. But since you now bring it up explicitly, I have to ask you whether you are endorsing the dropping of context in the definition of "empty set" in that cited article. My context for claiming the absence of an "empty" set is grounded in the relational aspect of a concept and its referents from the perspective of the human consciousness that isolates the latter to form the former. Tell me if there can be a concept without the units from which their integration results into a concept with an affixed word. If you appeal to the fact that there are plenty of people who use legitimate, everyday words without knowing their meanings, or referents, I will grant you that. But then those words as they use them are not concepts for them. They are uttering sounds and writing scribbles, not words, and not concepts. The relation between a concept and its referents cannot be severed. The identities of the relata depend on the existence of the relation. We are here discussing the ontology of the primacy of entities with respect to relations and their attributes. Don't you tell me that it doesn't apply to math, if it is the math needed for living on earth. One can no more say that one is a parent without having had at least one child, and one can no more claim to be a straight husband without the correlative existence of a wife, than one can somehow claim the existence of a set without the correlative existence of its elements. A correction to mathematics from the Aristotelian-Objectivist perspective is exactly what is desperately needed today to clear up the widespread errors in all the sciences that depend on standards of measurement. Invalidating the "empty" set is only the beginning. Now, to address your second point, [Whoops, gotta go. I'll finish this later.] [ --- --- resumption -- I'll have you know that I'm missing American Idol (live) for this. (But this is worth it.) --- --- ] Now, to address your second point, you are wondering whether it is possible to form a set with criteria so strict that no element qualifies for membership. Let me translate this problem into epistemological terms. what is the cognitive problem to be solved here for a volitional consciousness? It is the problem of identifying a qualified instance of a concept. "Qualified instance" of a concept, as defined by Ayn Rand (ITOE 23) is a category of existents identified by means of integrating known concepts with more intensive knowledge. It is a subdivision of a concept on the basis of a fixed range of variations within the measurements specified that distinguishes the units to be integrated from other existents. If it is the volitional goal of a person to isolate and integrate many concretes (mental or existential) into one unit for further integrations and identifications, i.e., the goal of unit economy, then an ad hoc qualified instance is the perfect unit to identify some aspects of reality, and a descriptive phrase from known words, specifying the criteria, is the perfect linguistic vehicle to convey this ad hoc unit to consciousness for thought and speech. But notice that, with any unit of integration, whether it be an ad hoc qualified instance or a permanent concept, the epistemological requirement for its identification is still axiomatically operant; namely, for every action of consciousness there must be a content. For a qualified instance to be valid, therefore, the units must exist for abstraction. Said another way, the qualified instance must be reducible down to perceptual reality, if it is to be valid and not a floating abstraction. Of course, a volitional consciousness doesn't have to choose to do this. And even if it does so choose, unlike automatic perception, the process of forming a qualified instance from intensive knowledge can still be error prone. These are the reasons why a rational being needs to have objectivity in the cognitive process. And this is summarized earlier in Post #25 in a one-line principle: So, yes, a set does require criteria for membership, but the process of forming it requires actual contents and more intensive knowledge. And crucially, the product of cognition, the qualified instance, i.e., the set, cannot be dissociated from the objectivity of the cognitive action. If what you want is a valid unit for further integrations and identifications, you can't be subjective; you can't make it up by whim. Now, let's take a look at your counterexample: Suppose you are standing at the door looking into a room full of people. You want to make several integrations and identifications, and you want to do them objectively. These are your cognitive goals. Let's now activate your consciousness and put it in focus: QI1. "People in a room less than 6 feet tall." QI2. "People in a room greater than 10 feet tall." PI1. "QI1 are stylish dressers." PI2. "QI2 are drinkers of frobscottle." I would say that QI1 qualifies as a valid unit. QI2 is not a unit. It is not that QI2 is empty, but that there can be no QI2 qua unit/set/QI. Linguistically, we can still say it, but saying so doesn't make it so, a floating abstraction. And analogous to the invention of the zero, we can likewise invent a symbol, say, "{}", for the sake of further processing, i.e., of further integrations and identifications, to denote that QI2 is not at all a unit. Thus, PI1 qualifies as a propositional identification, subject to further verification. But PI2 is not a unit of identification, not because it isn't grammatical or meaningful in some context (see The BFG, by Roald Dahl), but because there is now the fact that QI2 is {} and is not a unit and cannot qualify as the subject in the propositional structure. This judgment, i.e., this identification, i.e., a conscious action, requires a subject, i.e., a content. Therefore, upon encountering QI2 during your cognitive processing of PI2, I would hope that you, the cognitive processor, will adhere to objectivity and halt its processing. And if you can't process it, you can't verify subsequently whether it is true or false. Of course, on encountering any absence of a unit, you the volitional consciousness, can choose to halt processing--as dictated by the principle of action+content--or: you can choose to proceed with the misintegration and misidentification--as dictated by whim.

And that is exactly what mathematics is. Ontology has nothing to do with mathematics. But you are jettisoning commutativity of the identity element, which is fatal and makes nonsense of mathematics! Dragonfly, If I understand Roger correctly, it is the fact that "zero" is the absence of any quantity, not that it is the identity element for the addition operation, that blocks the commutativity of the addition operation. So, I do not think Roger is arguing for jettisoning commutativity of the identity element, say, in multiplication. On the other hand, given Roger's interpretation, I think he would conclude "0 x X = 0" as a valid statement--but not "X x 0 = 0".

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, [...] [...] 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, [...] [...] 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 [aka to make math complete (per Merlin's)] 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 Roger, this is a major philosophical insight about arithmetic and set theory! There is no humility here, no "IMHO" about it, kudos for having the courage to express it! I think you are right. Your presentation of the misinterpretations of the philosophy behind mathematics in this context deserves serious study. If we take the Aristotelian-Objectivist approach as the correct line of sight, then Objectivists have much work ahead of us to turn the ship of Math toward the right direction. Let me distill three of your points that are directly pertinent to the topic. From the excerpt, I think you are saying : That (1) the conventional interpretation of the set operator "complement" is mistaken in applying this operation to a content that is either the "empty" set or the set of everything. Other set operators--"union," "intersection," "product," "difference," etc.--may be similarly misinterpreted with respect to {} and U, but this is irrelevant in the current scope. That (2) the proper context for performing the "complement" operation is on a set within U (absolute complement) or within a "larger" set (relative complement), and the result of which must be within the larger set, complementing that which is being complemented. That (3) the processor must take account of both the action and the content for the result to be valid. To all of these, I agree. Why? Your first and second points translate "complement" from the cognitive process of isolation and classification. I can isolate something in a field of perception and make that the focus, and I can leave the rest, its complement, in the background. At the conceptual level, if I classify drinking cups into cup-sizes small, medium, and large; and if I prefer the mediums, then I will have opposed them against the sizes small and large as one aggregate subclass. Now, with cups, as an entire class, I can always oppose it within a larger classification of objects, such as drinking vessels, from which an opposite aggregate subclass of noncups would include glasses, cans, and bottles. I can do the same cognitive operation with drinking vessels at the next level of classification, and so on, until I come to that axiomatic class of everything. But here, the context of a "larger" class for my cognitive operation has reached its maximum. Therefore, I'm done. I have no context to try to isolate, to subclass, i.e., to oppose, the class of everything. At this level, there can be no valid result from the operation. The context "blocks" this action. It is not that the opposite of everything is nothing, but that there can be no opposite of everything. At the fundamental level, the nature of consciousness is such that every conscious state entails some content independent of it. Without a content, there is no conscious awareness. To be conscious is to be conscious of something. A conscious awareness of nothing is a contradiction in terms. (And a self-conscious awareness of nothing but itself is a contradiction in terms.) That said, a perception without that which is perceived is a contradiction; an isolation or classification without that which is be isolated or classified is inconceivable. Thus, your third point applies here. A "complement" of nothing cannot get off the ground. It is not that the opposite of nothing is anything or even everything, but that there can be no opposite of nothing. --- The same fact implies two further points. (1) Three distinct sets, all nonempty, are involved in the complement operation: the set to be operated on, the context-set for the operation, and the result-set from the operation. And (2) the to-be-operated-on set is always smaller--not smaller or equal to, but smaller--than the context-set. Adding your above, (3) the to-be-operated-on set cannot be the "empty" set. If mathematics and epistemology ever need to concur, a point of concurrence must be here. Since epistemology sets criteria of investigation and criteria of determining truth for all branches of knowledge, with math being one such branch, it is epistemology that arbitrates among branches of knowledge whenever conflicts arise. Thus, just as you don't form a more abstract concept (the larger-scale integration) from a less abstract one plus an alleged other that is vacuous in meaning or referent, so you don't form a new set by taking an old set and a "set" that is empty. A concept is always an integration of at least two or more units which are isolated from other units commensurably measured. This applies to concepts per se. So should it apply to sets per se. --- If you were asked to find the intersection of {1, 3, 5} and {2, 4, 6}, would you: (1) perform and answer nothing, i.e. the null set, and then insist you didn't do anything, or (2) say you can't answer because answering would imply some bizarre metaphysical interpretations? I would answer Merlin's particular objection about the handling of a set intersection, when based on the presented interpretation, as follows: There can be no such thing as an "empty" set. A "set" with no element is not a set. Stipulating by definition or by axiom that it be so does not make it so. In what sense then does the notation "{}" or the phrase "the empty set" denote? It denotes nothing more than the absence of everything in whatever context-set one operates on. All sets denote their elements, i.e., their units. When a "set" fails in denotation, it fails to be a set. So, "{}" is not a set. It denotes not a presence of elements but an absence of elements. (See ITOE for the full context.) Now, to the intersection question specifically, the answer is exactly to be expected: {}. But the interpretation is that "{}" is not some set to be plugged into another operation. In effect, "{}" denotes the absence of any set. It denotes that the intersection operation produces an undefined result, requiring the cessation of any subsequent operation.

A proper government protecting individual rights, when properly defined and understood, will neither restrict the freedom of movement nor issue travel papers. (It may have to to help people travel to unfree countries, but not for anyone entering the country. That is not say there cannot be some border security.) I think the "privileges" of citizenship in relation to a government should be enumerated constitutionally. In the scheme of checks and balances, citizens are privileged to vote for or recall their representatives and to run for offices. Thus, individual rights and citizens' privileges are independent of each other.

Bill, here below are my integrations. The meaning of the latter will be obscured unless you go to the pages cited in ITOE. From the branch of mathematics, the opposite of nothing is everything, and the opposite of everything is nothing. From the branch of philosophy, neither can there be an opposite of nothing, nor can there be an opposite of everything.

Good rebuttal, Bill. Now consider another thing I have also said. If you accept the normative premise that your knowledge of reality must be an integrated whole, then my intent becomes apparent. I am not denying that ideas in respective systems of thought are already self-consistent (I am not asserting it either), but I deny that systems of thought can be separately free floating. Does the notion of "complement" in set theory have any use to the task of living on earth? What are its links to the rest of our knowledge? What are its links to reality? We can and should apply these same questions to our notions in philosophy. I invite you to proceed if you accept the normative premise. And if you then don't see a contradiction, I definitely want to know about it.

I'm in agreement with Bill. Whenever one reports something, there is a cognitive responsibility to pass judgment on it. (This responsibility is something modern journalism has shirked in the name of "neutrality." See DK's "Can Reporters Handle the Truth?") If someone posts a link and simply says "Oh, have a look at this"; this act is akin to uttering a sentence fragment "Raisin."

Thom - Complement and opposite are not the same thing. [...] Bill, thank you for highlighting my semantic bridge from mathematics to everyday philosophy. Yes, my equating of "complement" to "opposite" was deliberate. I wanted to emphasize the connection that mathematics has a role to play in philosophy, and vice versa, for the purpose of living in the world. While I do realize that the term "opposite" is equivocal in the realm of logic to mean either of two incompatible relationships, namely, contrariety and contradiction; I did not want to admix all these terms without the proper context. Rather, I would like for interested readers to understand the issue from the view of mathematics and then to be able to relate it to philosophy. So, the issue here purports to be a contradiction between two branches of knowledge concerning the opposite of some notion to be some other notion. On the math side, "opposite" means "complement." On the philosophy side, I cited page references for readers to follow up to see which meaning of "opposite" Ayn Rand discusses in the present context. Ian, "Nothing," and "nonexistence" are synonymous English words denoting a legitimate concept, which Christopher can also notate in Chinese. What that concept is, is central to the present issue, namely, the issue of the opposite of nothing. That is, while the concept does exist, the issue I am curious about is the nature of its opposite. The predicate "does not exist" is straightforwardly the denial of existence. What is the opposite of "existence"? This is also central to the issue.

This is a show of hands of sort, not a pragmatic test of truth, to discover a statistic, a quantity about a population of a class, namely, the class of Objectivists on OL who ever thought about the implications of logic for any learning through reading. Suppose you are reading a serious scientific article in a research journal from a credible scientist in the field. You are reading along, paragraph by paragraph, sentence by sentence, and then you chance upon this: T2: "Some gfds are gfds." Knowing from the context that "gfds" is not a symbol standing for any other variable, and finding that it is not referenced thereafter in the refereed article, how are you to interpret T2, given your integrated knowledge of science, logic, and Objectivist epistemology? Would you say that T2 is true? Why? False? Why? Or meaningless? Why?

Ayn Rand in ITOE has a special place for mathematics, a science which she holds in high esteem. Mathematics in her view discovers and defines standards of measurement for all conceptual cognition. Since every formation of any concept depends on grasping similarities on the basis of measurements, since every piece of knowledge one has ever thought or communicated depends on such concepts, therefore by AAA-1, all of man's knowledge of reality depends on mathematics, the science of measurement. (ITOE 7) Now, knowledge, if it is knowledge of reality, has to be integrated without contradictions. Mathematics, biology, history, and philosophy, if they purport to be knowledge, must integrate coherently together, not free floating unencumbered. So, when one branch of knowledge makes a claim contradictory to another branch, something is really wrong: Both cannot be true, and both cannot be false. Suppose one branch makes a claim that does contradict another branch, how is one to resolve it? Rand answers in ITOE, "It is not the special sciences that teach man to think; it is philosophy that lays down the epistemological criteria of all special sciences." (For the full context of this statement, see ITOE 78.) Does this mean that philosophy trumps other branches? No. I take it to mean that each branch has its own set of criteria for investigating and determining truth in accord with the particular aspect of reality under study and in accord with the nature of man's consciousness. But it does mean that epistemology has to discover and define the nature of knowledge and then to define the criteria for all branches of knowledge. So, here then is a modern problem: mathematics makes a claim that contradicts philosophy. More specifically, a branch of math, set theory--which is the basis of mathematical logic and many other offshoots dependent on it--this branch has an axiom stating that the complement of the empty set is the universal set. That is, the opposite of nothing is everything. Its corollary is that the complement of everything is nothing. Now this mathematical axiom contradicts philosophy, namely, the Objectivist philosophy. In particular, it contradicts a basic philosophical axiom, the axiom of existence: that existence exists--and its corollary: that only existence exists. (For the full context, see 58-60.) It suffices to say informally, the opposite of existence is not nonexistence. By the nature of the problem, both branches cannot stand apart in epistemological détente, if they purport to be knowledge. Being axioms, the repudiation of either one has fundamental ramifications for its respective branch, if not its destruction. One side must be true, but which one?

Michael, we were on the same page from the start, even when you disagreed. Notice: But that is precisely my point: [...] And now, to this other remaining bit about my attributing distraction to a lack of mental purpose. Check your Post #19 above. You stated that distraction is an epistemological problem. Anything epistemological is a volitional issue. Distraction may have some neurological basis, but it is ultimately in the volitional agent's power to control. Yet, in your immediately above post, Post #21, you imply that being distracted is akin to the growling of the stomach--akin to an automatic, deterministic process, uncontrolled by volitional means. So now which is it? Is distraction a volitional issue or not? I would go with your Post #19. If so, then by the rest of Post #21, we are in complete agreement. Inefficiency in thinking does become habitual, if one does not consciously correct it. And as BB in POET points out, that takes constancy of purpose, which, by the way, is another reason why Ayn Rand identifies Purpose a cardinal value. (TVOS 25)

This question recurred yesterday evening after my gang of friends, we went out to watch the latest Star Trek movie. What about the status of Star Trekkers? Well, anyone who has read books and watched enough Star Trek TV episodes, cartoons, and movies; and who really understands Gene Roddenbery's fictional universe and assents to its imaginative truth, is a Star Trekker. Of course, the whole saga is plain fantasy; so he should not confuse the imaginative order with the real order of things. Nevertheless, the principle of understanding X'ism and being an X'ist, operates just the same in either order. So in a sense the answer to your question, Chris, has a loophole. Being a Star Trekker is perfectly fine. Wearing Star Fleet uniforms and greeting each others in alien languages in everyday life, on the other hand,... that's not cool, ... but that's a separate (psychological) issue.

I agree with all your three quick observations, Bill. My original post was inspired by a tangential comment elsewhere, which claimed that Ayn Rand attacked the professions of logic, mathematics, and physics. I could not reconcile that charge with what I had remembered about FTNI, where she made a clear distinction between the professions and their best professionals on the one side, and their worst on the other. So, I would add to your Point 1, to suggest to others also a careful reading of FTNI and/or my original post. An injustice was done against Rand in that other thread and now here again in this thread. It is a curious thing to bear responsibility for one's judgments. I find in Ayn Rand an exemplar unsurpassed. When she denounces a professional, say, a politican, it is devastatingly personal. But when she praises one, such as the founder of the science of logic, it is equally passionate from the heart. She judges from her convictions of truth--the pressures to fake reality be damned. So I get goose bumps either way when a judgment is found, against the worst or for the best. So too I get in her dedication to the future: "The Intellectuals are dead—long live the intellectuals!"

... The above examples ~terribly~ jumble up my view, if that is what they purport to illustrate (for purposes of reductio ad absurdum?). Let me run through them and give ~my~ interpretations and evaluations of them: ... Thom, these examples are god-awful distortions of what I advocate, but I'll address them anyway. ... Thom, I have steeped in this stuff for DECADES. It makes perfect sense to me, and I think that all the major logicians and their texts are out to lunch on this issue! You have done nothing to shake my grasp of this or my confidence that I am correct, not one iota. ... ... Roger, Thank you for responding. I wish to acknowledge immediately my admiration of you for the evident fact that after nearly 20 years of steeped study you are still open to fresh engagement with relative newcomers like me, and, perhaps, to be corrected by new evidence and reasoning. That last post of mine (linked above) was partly an effort at fact finding, to find out what you actually claim about existential import. Now I do believe I understand you. Let me first summarize in my own words your view before giving my interpretation of it. First, by integrating and reorganizing your pained interpretations we can discern the following ideas: R1: If a string of real words is grammatical and declarative, it is a sentence conveying a proposition that is either true or false. R2: You accept the idea of elliptical statements. E.g., the statement "John Smith is a lottery winner" is ambiguous, because there are many men with such a name. When a newspaper reports him as a winner, the statement is really elliptical to mean "John Aaron Smith of 123 Main Street, Sometown, Somestate, Someday, month, year, etc., is a lottery winner." It is still one simple assertion, asserting one individual having won the lottery. R3: Whenever the subject term has no referents in the present, the verb tense is elliptical for a compound noun, which must be made explicit. In other words, whenever you see the copula in the present tense, you want to make explicit that the designation of the subject term encompasses only those existents presently existing. And whenever the copula is in the past tense, you want to make explicit that the designation of the subject term encompasses the existents existing only in some past date. R4: Elliptical modes of existence (a.k.a. domains of discourse) include the real order, the imaginative order, and their subdomains. R5: Singular statements (of the descriptive kind) must be transmogrified into compound statements. R6: An affirmation whose designation of the subject is empty must be false. R7: A denial whose designation of the subject is empty must be true. R8: Compound-noun statements must be transformed associatively by treating subject terms and predicate terms identically. Thus, 1. "All dinosaurs are scaly" is R3 elliptical for "All dinosaurs are presently existing scaly creatures"; and since none exists presently (R4), 1 is false. 2. "No dinosaur is scaly" is R3 elliptical for "No dinosaur is a presently existing scaly creature"; and by R6, 2 is true. 3. "All unicorns are horned horses" is elliptical for either 3a. "All unicorns are imaginary horned horses"; and by R4, 3a is true (in the imaginative order). 3b. "All unicorns are real horned horses"; and by R4 and R6 and EAE-1 arg, 3b is false (in the real order). 4. "No unicorn is a horned horse" is elliptical for either 4a. "No unicorn is an imaginary horned horse"; 4a is false (in the imaginative order). 4b. "No unicorn is a real horned horse"; by R7 in the real order, 4b is true (in the real order. 5. "TpKoF is bald" is reinterpreted by R5 to "TpKoF is a presently existing person, AND he is presently bald"; and since the first conjunct is false by R6, the compound statement is false; hence, 5 is false. 6. "TpKoF isn't bald" is reinterpreted by R5 to "TpKoF is a presently existing person, AND he isn't presently bald"; and since the first conjunct is false by R6, the compound statement is false, even though the second conjunct is true by R7; hence 6 is false. 7. "All dinosaurs were scaly" is R3 elliptical for "All dinosaurs were past-existing scaly creatures"; 7 is true. 8. "No dinosaur was scaly" is R3 elliptical for "No dinosaur was a past-existing scaly creature"; 8 is false. 9. "TpKoF was bald" is reinterpreted by R5 to "TpKoF was a past-existing person, AND he was bald"; by R3 and R6, the first conjunct is false, rendering the compound false; hence, 9 is false. 10. "TpKoF wasn't bald" is reinterpreted by R5 to "TpKoF was a past-existing person, AND he wasn't bald"; again, while the second conjunct is true by R3 and R7, since the first conjunct is false, the compound is false; hence, 10 is false. 11. "All squared-circles are triangular"; by R1, R6, R8, and C9 (see scratchpad), 11 is false. 12. "No squared-circle is triangular"; by R1, R7, R8, and C10 (see scratchpad), 11 is true. --------------- Here now is my interpretation: Except for R2 and R4, I disagree with R1, partial R3, R5, R6, R7, and R8. Since I agree with your interpretation of those statements of the imaginative order, we'll skip them. The rest will be discussed in three parts: universals of the real that no longer exist, singulars described to emptiness, universals of emptiness. Part 1: Among universals of the real that used to exist but exist no longer: R3 implies that the elliptical phrases "presently existing" and "past-existing" applies to and restricts the subjects that used to exist but exist no longer. If it had been applied simply, I would have no problem with that. What is problematic is its presumption: P1. The restrictive phrase is confused with the verb tense, which forces the restriction not on the subject but on the predicate. This forced restriction implies R8 being at work. P1 is seen in the dinosaur statements 1, 2, 7, and 8. [Given the supposition that dinosaurs had scales,] 1. "All dinosaurs are scaly" becomes by R2 "All dinosaurs (open-ended past, present, and future) are scaly creatures (open-ended past, present, and future)." It becomes by R3 "All presently existing dinosaurs (open-ended present) are scaly creatures (open-ended past, present, and future)." BUT the P1 presumption now enters: "All dinosaurs (open-ended past, present, and future) are presently existing scaly creatures (open-ended present)." The entire transformation changes the predicate--a fallacy of equivocation. What started out and could have been assessed true, is now deemed false. 2. "No dinosaur is scaly" becomes by R2 "No dinosaur (o-eppf) is a scaly creature (o-eppf)." It becomes by R3 "No presently existing dinosaur (open-ended present) is a scaly creature (o-eppf)." BUT the P1 presumption now enters: "No dinosaur (o-eppf) is a presently existing scaly creature (open-ended present)." Again, the entire transformation changes the predicate--another fallacy of equivocation. What started out and could have been assessed false, is now deemed true. The P1 presumption is also at work in statements 7 and 8, only that it is obscured by the already explicit verb tense. 7. "All dinosaurs were scaly" becomes by R2 "All dinosaurs (o-eppf) were scaly creatures (o-eppf)." It becomes by R3 "All past-existing dinosaurs (open-ended past) were scaly creatures (o-eppf)." But with P1, it becomes "All dinosaurs (o-eppf) were past-existing scaly creatures (open-ended past)." But for the equivocation, everything is true at every stage. 8. "No dinosaur was scaly" becomes by R2 "No dinosaur (o-eppf) was a scaly creature (o-eppf)." It becomes by R3 "No past-existing dinosaur (open-ended past) was a scaly creature (o-eppf)." But with P1, it becomes "No dinosaur (o-eppf) was a past-existing scaly creature (open-ended past)." But for the equivocation, everything is false at every stage. All of these show that the R3 rule is innocuous by itself and in fact unnecessary even for extinct subjects. They show that verb tense has a separate function (i.e., temporalizing identification) that is independent of referential qualification. What is noxious is P1. If I grant you that "scaly creatures" and "presently existing creatures" aren't synonyms, then you must grant me that "dinosaurs" and "past-existing dinosaurs" aren't synonyms as well. Part 2: For singulars described to emptiness: The glaring treatment of singulars is in transmogrifying them from a simple assertion into a compound assertion, by use of R5. (Singular statements make use of R3 as well and presumes P1. While this defect has already been described in Part 1, one thing to note about it here is that P1 now distributes across the conjunction.) Contrast a simple proper name designating rigidly some individual, say, Nicolas Sarkozy. He is the current President of France in 2009 (TcPoF). D1. "Nicolas Sarkozy is remarried"; this is true. D2. "Nicolas Sarkozy isn't remarried; this is false. D3. "Nicolas Sarkozy was divorced"; this is true. D4. "Nicolas Sarkozy wasn't divorced"; this is false. D5. "TcPoF is remarried"; this is true. D6. "TcPoF isn't remarried; this is false. D7. "TcPoF was divorced"; this is true. D8. "TcPoF wasn't divorced"; this is false. A proper name denotes an individual. Without the concrete individual, the name is just a visual-auditory scribble. So, when it is used in a sentence in the attempt to assert a truth, there is no question that the name and the individual have already been linked--linked not inferentially but causally, through causal acts of perception, etc. With that being already done, the assertion is the first and only act needed to identify the fact. On the other hand, a definite description (i.e., a descriptive phrase uniquely identifying an individual among a population), does require a conceptual act of isolation to locate the individual. An individual concrete must be isolated conceptually before any assertion can be made about him/it. Otherwise, the phrase reverts to just another visual-auditory scribble and there is no subject to be said about anything. This process must eventually reach a causal basis for the linkage between the description to the individual concrete. But however long or tedious this process is, it is prior to an assertion. So, again, the assertion with a singular denoting phrase for a subject stands on its own as a lone act of identification. The underlying principle from the above is what I will dub in the present context -R1b. -R1b. A singular statement requires the prior isolation of an individual concrete; otherwise, it isn't a statement. What happens instead by means of R5, R6, and R7 is the requirement to turn a simple statement into a compound statement, asserting three or more propositions. It goes beyond the mere use of R2. It requires D5. "TcPoF is remarried" to become: D5a. "TcPoF is a real organism" and D5b. "TcPoF is a remarried person" and D5c. "D5a AND D5b"; so that the whole thing is true. Similarly, you want D6. "TcPoF isn't remarried" to become: D6a. "TcPoF is a real organism" and D6b. "TcPoF isn't a remarried person" and D6c. "D6a AND D6b"; so that the whole thing is false. Note that R5 requires that we add D5a and D5c for D5, and D6a and D6c for D6. Note especially that the predicate for D5a and D6a by the nature of the setup is completely arbitrary. This new middle term didn't have to be "organism"; it could have been "animal" or "human" or "person" or even "president." The point is, it was not in the original sentence. Rule R5 simply and arbitrarily requires an extra identification and an extra conjunction. What should have been but one, now becomes three or more (by means of R5), and they require independent processes of verification. AND then, rather than taking -R1b as a principle, the present theory chooses R1, in additional to the already mentioned theses, to interpret singulars described to emptiness. 5. "TpKoF is bald" becomes: 5a. "TpKoF is a real person" and 5b. "TpKoF is a bald person" and 5c. "5a AND 5b"; which happens to be true. And 6. "TpKoF isn't bald" becomes: 6a. "TpKoF is a real person" and 6b. "TpKoF isn't a bald person" and 6c. "6a AND 6b"; which is false true. If one had accepted the R5 explosion rule as a given, and had one taken -R1b instead of R1, the verification process would have halted on the first recognition--that TpKoF is a mere audio-visual scribble--and every one of the substatements would have yielded neither true nor false. But because the present theory accepts R5(R1), R6 and R7 become its corollaries. Part 3: On universals of emptiness: ... The concept of "squared-circle" has "no place in any assertion"??? It "doesn't mean anything"??? Come on! A squared-circle is just a specific kind of contradictory idea, a "real circle that has an impossible attribute"--and we Randians are comfortable asserting (with Rand) that "contradictions don't exist," aren't we? So why can't we say "contradictions are real things with contradictory attributes"? Surely that is meaningful and false! ... Okay, you got me. I was hasty and vague. I should have said that "... it has no place in an affirmative assertion. ... the statements asserting squared-circles are neither true nor false..." Recall the two statements and your interpretation: 11. "All squared-circles are triangular"; by R1, R6, R8, and C9 (see scratchpad), 11 is false. 12. "No squared-circle is triangular"; by R1, R7, R8, and C10 (see scratchpad), 11 is true. Scratchpad table to transform statements 11 and 12: C1. "Every circle is a square"; C1 is false. C2. "Every circle isn't a square"; C2 is true. C3. "Every circle is a triangle"; C3 is false. C4. "Every circle isn't a triangle"; C4 is true. C5. "Every circle is both a square and a triangle"; C5 is false. C6. "Every circle isn't both a square and a triangle"; C6 is true. C7. "Every circle that is square is a triangle"; C7 is not considered. C8. "Every circle that is square isn't a triangle"; C8 is not considered. C9. "Every circle that is square is a (real) circle that is both square and triangular"; C9 is equivalent to C5. C10. "Every circle that is square isn't a (real) circle that is both square and triangular"; C10 is equivalent to C6. (Note: I am taking the liberty of regimenting O-form statements "No S is P" to the more literal version "Every S isn't P" in order to better separate and discern S and P.) According to your post (linked above), first, 11 is transformed to C9, and 12 to C10. Then from the results, you explicitly equate C9 with C5, and C10 with C6. This is from the assumption of rule R8. Parts of nouns shift from subject to predicate interchangeably. What is noteworthy is that C7 and C8, the actual original statements, are not identified and acknowledged even as candidates for consideration. Here therefore is the fallacy of diversion, the bait-and-switch fallacy. While the scratchpad table does show correctly that C5 is false and C6 true, they however are not equivalent respectively to C7 and C8. Since 11 is actually C7, and 12 actually C8, we have to evaluate the subject as a compound noun. But this is precisely what the present theory neglects to do. But suppose we proceed to follow through with the theory as summarized. Since the repugnant concept is without referents in the real order, the subject is empty in designation. Thus, by R6, C7 is false; by R7, C8 is true. And this leads to an internal absurdity when the axiom of identity is regimented in the propositional forms: C7p: "Every squared-circle is a squared-circle"; by R6 is false. C8p: "Every squared-circle isn't a squared-circle"; by R7 is true. --------- In Parts 1, 2, and 3, I have analyzed your view of existential import, showing its dependence on R1-R8 and P1. I agree with R2 and R4. I have shown that R3 is innocuous and superfluous by itself but is untenable with P1. R5 and R8 are shown to be fallacious, and R6 and R7 lead to absurdities. Only one remains, R1. I have partially refuted it with -R1b. The more general refutation to R1 fortunately is already discussed elsewhere on OL (with/by Robert Campbell) and ITOE 19-23 passim. Without R1, R3(P1), R5-R8, this theory of existential import falls apart.

This is serious scholarship. I can't wait for the books to come out.