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dream_weaver

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  1. Who owns those Objectivist websites?

    There are tools like https://whois.icann.org/en that might be able to shed some insight by digging into the details provided. Mark Da Cunha comes up for several while http://www.whoisguard.com/ is returned for the others in the list provided.
  2. Here’s What’s Wrong with Ayn Rand’s Philosophy By Craig Biddle. Posted at The Objective Standard Many articles have been written about what’s wrong with Ayn Rand’s philosophy. But, to my knowledge, none of them presents her ideas accurately. So I thought it would be helpful to write one that does. Here’s what’s wrong with Rand’s ideas: A nice, brief1, satirical article. 1. Less than 3000 words.
  3. Biologists Replicate Key Evolutionary Step

    Meteroites' mechanical energy might have created building blocks of life on Earth Researchers in Germany are now arguing that a meteorite impact could have created the molecules that gave life its big break. Their experiments are the first to show that the mechanical energy released during an impact could have transformed simple chemicals into amino acids.1 ‘I was standing in front of the Coliseum. Everybody was taking pictures but I was looking at the floor and saw these very round stones,’ he recounts. He took a few of them back to Germany and found that they could replace metal milling balls in his mechanochemical experiments.2
  4. Yeast not only gives rise to bread, it gave rise to an answer to a question that has eluded evolutionary biologists. "To understand why the world is full of plants and animals, including humans, we need to know how one-celled organisms made the switch to living as a group, as multicelled organisms," said Sam Scheiner, program director in the National Science Foundation (NSF)'s Division of Environmental Biology. "This study is the first to experimentally observe that transition, providing a look at an event that took place hundreds of millions of years ago."
  5. Confucius Institute

    This was featured on the Drudge Report starting at 8:30 last night until 10:30 this morning. How China Infiltrated U.S. Classrooms Given the role of education in shaping young minds, and the notion that education is far too important to leave in the hands of the state, this adds a level of concern of allowing a foreign state to cast their lot into the fray. Confucius Institute: Hanban has been shrewd in compelling universities to host Confucius Institutes. Marshall Sahlins, a retired University of Chicago anthropologist and author of the 2014 pamphlet Confucius Institutes: Academic Malware, reports that each Confucius Institute comes with “$100,000 … in start up costs provided by Hanban, with annual payments of the like over a five-year period, and instruction subsidized as well, including the air fares and salaries of the teachers provided from China. … Hanban also agrees to send textbooks, videos, and other classroom materials for these courses—materials that are often welcome in institutions without an important China studies program of their own.” And each Confucius Institute typically partners with a Chinese university. They’re kind of like restaurant franchises: Open the kit, and you’re in business. American universities can continue to collect full tuition from their students while essentially outsourcing instruction in Chinese. In other words, it’s free money for the schools. At many (though not all) Confucius-hosting campuses, students can receive course credit for classes completed at the institute. But the institutes go to some length to obscure their political purpose. There’s the name, for example: Most Americans associate Confucius with wisdom, or cutesy aphorisms. It’s likely the centers would be less successful were they called Mao Institutes. The Institutes also offer a plethora of “fun” classes—not for academic credit, and often open to members of the general public—in subjects like dumpling making and tai chi. Compelling, in a free market, would be an odd enough term. In this case agenda is being packaged and sold to a clientele that has been inured by decades of government encouragement. Is it really that big a step to extend egalitarianism at a governmental level? A tip of the hat to McMaster University in Canada: Meanwhile, if Hanban’s instructors are not adequately vetted back home, there can be trouble. Consider the case of Sonia Zhao. Zhao, a Chinese national, was dispatched by Hanban to McMaster University in Hamilton, Ontario, in 2011 to teach Chinese language. She’s also a practitioner of Falun Gong, the Buddhist-tinged spiritual movement that Beijing despises as a threat to its authority. Zhao quit a year into her tenure, arguing that McMaster University was “giving legitimization to discrimination.” That’s because, in order to secure her employment with Hanban, Zhao said she was forced to disguise her fealty to Falun Gong. Her employment contract with Hanban explicitly stated that she was “not allowed to join illegal organizations such as Falun Gong,” she said. This kind of open religious discrimination is illegal in Canada, as it would be in the United States. McMaster University, in light of this disclosure, subsequently shuttered its Confucius Institute in 2013, citing the institute’s “hiring practices.” Starting in 2004 in South Korea, Confucius Institute has spread and now 40% of their export is being consumed stateside, a subsidized wolf with an authentic looking sheepskin.
  6. Confucius Institute

    According to a Wikipedia entree on Confucius Institute, in 2014 the University of Chicago and Pennsylvania State University cut ties with the Confucius Institute. So yes, academic standards do have some sway still. In The Establishing of An Establishment the critique was levied as follows: Nothing could be as dangerous a threat to our institutions as a proposal to establish a government committee to deal with "antidemocratic thoughts" or B.F. Skinner's thoughts or anyone's thoughts. The liberal New Republic was quick to sense the danger and to protest (January 28, 1972). But, not questioning the propriety of government grants, it merely expounded the other side of the same contradiction: it objected to the notion of the government determining which ideas are right or acceptable and thus establishing a kind of intellectual orthodoxy. In the same Wikipedia article: On 4 December 2014, the United States House Foreign Affairs Subcommittee on Africa, Global Health, Global Human Rights and International Organizations held a hearing entitled "Is Academic Freedom Threatened by China's Influence on U.S. Universities?". Chairman Chris Smith said, "U.S. colleges and universities should not be outsourcing academic control, faculty and student oversight or curriculum to a foreign government", and called for a GAO study into agreements between American universities and China. In The Establishing of An Establishment, a distinction is drawn between private monies of a rich individual (I'll extend that to a private organization) and monies extorted by force from unwilling victims. Tara Smith at the behest of BB&T is private monies. Confucius Institute is paid for by the Chinese government along with the host university. U.S. taxpayer subsidies for grants was excerpted as follows: The fundamental evil of government grants is the fact that men are forced to pay for the support of ideas diametrically opposed to their own. This is a profound violation of an individual's integrity and conscience. It is viciously wrong to take the money of rational men for the support of B.F. Skinner—or vice versa. With a little liberty, from early in her article, transform: Governmental encouragement does not order men to believe that the false is true: it merely makes them indifferent to the issue of truth or falsehood. into: Governmental encouragement does not order men to believe that wrong is right: it merely makes them indifferent to the issue of right and wrong. I would clarify that the indifference isn't across the board, encompassing what is undeniably right and wrong, but in the areas that are not as clear cut and easy to identify. Or put in a different way, did the earlier grants and subsidies picked from the pockets of the American taxpayer help pave the way to blurring the academic standards or objectivity resting on the universities?
  7. Re-blogged post: I, Pencil: The Movie

    The New York Times Magazine Inside One of America’s Last Pencil Factories A photographer captures a colorful world of craft and complexity. Photographs by CHRISTOPHER PAYNE Text by SAM ANDERSON JAN. 12, 2018 Closing paragraph: Photographs like these do something similar. They preserve the secret origins of objects we tend to take for granted. They show us the pride and connection of the humans who make those objects, as well as a mode of manufacturing that is itself disappearing in favor of automation. Like a pencil, these photos trace motions that may someday be gone. Some of these pictures capture a high degree of automation all ready in place.
  8. A pig under an oak tree

    The Ayn Rand Letter Vol. III, No. 9 January 28, 1974 Philosophical Detection There is an old fable which I read in Russian (I do not know whether it exists in English). A pig comes upon an oak tree, devours the acorns strewn on the ground and, when his belly is full, starts digging the soil to undercut the oak tree's roots. A bird perched on a high branch upbraids him, saying: "If you could lift your snoot, you would discover that the acorns grow on this tree." Fable writer Ivan Krylov monument in Saint Petersburg A Poem: The Sow Under The Oak Tree A poem by Ivan Andreyevich Krylov, translated by Yana Kane Beneath an oak a sow pigged out on acorns, Then napped under the shady canopy, At last, refreshed, she set her snout to digging, Baring the roots that fed the ancient tree. “Stop! Stop!” called out a raven from the branches. “The oak tree’s roots are damaged when you dig.” “What do I care if this useless stump does wither? Acorns are all I’m after,” said the pig. The oak tree’s voice then joined the conversation. “Ingrate!” said to the swine the mighty tree, “If you could lift your snout up from your grubbing, You’d see that all the acorns come from me.” ------- An ignoramus mocking education, Scoffing at science, is blind just like that sow, Failing to see that on the tree of knowledge Ripened the comforts he’s enjoying now. A Hog under an Oak Ivan Krylov A Hog under a mighty Oak Had glutted tons of tasty acorns, then, supine, Napped in its shade; but when awoke, He, with persistence and the snoot of real swine, The giant's roots began to undermine. "The tree is hurt when they're exposed," A Raven on a branch arose. "It may dry up and perish - don't you care?" "Not in the least!" The Hog raised up its head. "Why would the prospect make me scared? The tree is useless; be it dead Two hundred fifty years, I won't regret a second. Nutritious acorns - only that's what's reckoned!" - "Ungrateful pig!" The tree exclaimed with scorn. "Had you been fit to turn your mug around You'd have a chance to figure out Where your beloved fruit is born." A paragraph from Alexander Volokh: Twenty-Five Years Of Environmental Regulation: What Americans Have Learned Even in the absence of the legal system to settle disputes, the very existence of private property was often an effective conservation device. For example (or rather, for a counterexample), many of you may remember the fable by Ivan Andreyevich Krylov about the pig beneath the oak, who ate its fill of acorns and started to dig up the roots of oak. "But this will harm the tree, you know," from the oak's branches said the crow. "Without its roots, the tree may dry." "Oh, let it!" was the pig's reply. "What do I care? The roots don't matter. I just want acorns -- for they make me fatter." In America, we call this the story of killing the goose that laid the golden eggs. Economists call this problem "The Tragedy of the Commons" -- when a resource is collectively owned, no one has an incentive to invest in the improvement of that resource. Instead, they have an incentive to chop down the tree and take the acorns before they are ripe, because if they don't, someone else will. This is why Americans have dirty public parks. On the other hand, private ownership of the resource encourages responsible stewardship. This is why Americans have clean private lawns. If the pig had been a shrewd businessman who owned the oak and had secure property rights, he would have waited until all the acorns were ripe, and probably would have planted more trees and sold the excess acorns. Click for additional illustration of the Krylov's fable "Pig under the oak" by aleks-klepnev found at Diviantart.
  9. Universals

    Once again, from ITOE2's Appendix—The Role of Words (pg. 273): AR: And more than that; the fact that Aristotle is right and not Plato is very relevant here: abstractions [universals], as such, do not exist. Only concretes exist. We could not deal with a sum of concrete objects constantly without losing our grasp of them. But what do we do conceptually? We substitute a concrete—a visual or auditory concrete—for the unlimited, open-ended number of concretes which that new concrete subsumes. Ask yourself about the physical concretes referred to by cats, dogs, cows, chickens, tigers, bears, etc., relationship to the concept of animal. Or the physical concretes referred to by grass, trees, bushes, ferns, rushes, etc., relationship to the concept of vegetation. Or the physical concretes referred to by bacteria, amoeba, etc., relationship to the concept of prokaryotes. Are animal, vegetable, prokaryotes, etc., concrete and physical enough in nature to be integrated into the concept of living organism? Do the conceptual chains required to arrive at length, color, weight, consciousness, time, space, speed, acceleration, etc., constitute concrete enough substitutions to qualify as non-physical things? What about the symbols referred to as letters, selectively organized into words, and ultimately comprised into sentences? Are these "concretes" or "non-physical things"? If these are further crafted into paragraphs, does such activity gain greater concreteness or wane deeper into a non-physical status by further structuring? What, specifically, do you take as a concrete being physical in nature?
  10. Universals

    That was stated with a particular context.
  11. Universals

    It is not a matter of what I believe. Isolate what the attribute of length is, understand how it is not metaphysically separable from the concretes that possess it. The aspects of "a thought", "an emotion" or even "a memory" follow similar lines of reasoning. Incidentally, concrete is being used here as: existing in a material or physical form; real or solid; not abstract.
  12. Universals

    This is along the lines of the right question. The concepts "concrete", "universal", "abstraction", "entity" could easily be factored into the following excerpt from the Appendix—Concepts as Mental Existents <ITOE2, pg. 153-154> : Prof. F: If you and I have the same concept [of X], does that mean that the same entity is in both of our minds? AR: If we are both careful and rational thinkers, yes. Or rather, put it this way: the same entity should be in both of our minds [of X] mine. This is immediately followed up with an example that illustrates the complexity of what serves as the concrete for the basis of the entity: Prof. F: Okay, taking concepts, therefore, as entities: they do not have spatial location, do they? AR: No, I have said they are mental entities. Prof. A: When you say a concept is a mental entity, you don't mean "entity" in the sense that a man is an entity, do you? AR: I mean it in the same sense in which I mean a thought, an emotion, or a memory is an entity, a mental entity—or put it this way: a phenomenon of consciousness. And for an addition addendum on the thought: Prof. A: Wouldn't you say that consciousness is itself an attribute of man? AR: Right. A faculty of man. And of animals, or at least the middle and higher animals. Also relevant would be the opening exchange from Appendix—Entities and Their Makeup, Attributes as Metaphysical <ITOE2, pg. 277-278>: Prof. A: In regard to the concept of an attribute—for example, "length"—since the attribute is something which does not exist separate in reality, is the referent of the concept of an attribute in the category of the epistemological rather than the metaphysical? AR: Oh no, why? Prof. A: Because length doesn't exist per se in reality. Length is a human form of breaking up the identities of things. AR: Wait a moment, that's a very, very dangerous statement. Length does exist in reality, only it doesn't exist by itself. It is not separable from an entity, but it certainly exists in reality. If it didn't, what would we be doing with our concepts of attributes? They would be pure fantasy then. The only thing that is epistemological and not metaphysical in the concept of "length" is the act of mental separation, of considering this attribute separately as if it were a separate thing. How would you project a physical object which had no length? You couldn't. And therefore if to say it is epistemological rather than metaphysical is to say it exists only in relation to your grasp of it, or it requires your grasp of it in order to acquire existence—it doesn't. Surely, if anything is metaphysical, attributes are. To rephrase the question of "what is a concrete?" slightly, is it legitimate to ask what the concrete of "thought", "an emotion", or "a memory" is, either as a mental entity or even as a phenomenon of consciousness? Does the fact that they are attributes of an attribute banish them, or make them anything less metaphysical (while this is not your question specifically, it does tie back into the thread.) <tongue in cheek> Perhaps Prof. A can just be written off as a rabble rouser! Still, Miss Rand's response, as rendered by Harry Binswanger, suggests the ability of an act of mental separation: of considering an attribute separately as if it were a separate thing, without actually divorcing the considered attribute of its metaphysical stature.. Does it make a difference if it is simply length from the object that possesses it, or the "concrete" object of thought from the entity which performs it? <Once again, tongue in cheek> The fate of the Objectivist Movement depends on your response.
  13. Universals

    Appendix—The Role of Words And more than that; the fact that Aristotle is right and not Plato is very relevant here: abstractions, as such, do not exist. Only concretes exist. We could not deal with a sum of concrete objects constantly without losing our grasp of them. But what do we do conceptually? We substitute a concrete—a visual or auditory concrete—for the unlimited, open-ended number of concretes which that new concrete subsumes. This is followed by an example going from "a visual or auditory concrete" to a tactile case involving Helen Keller. Abstractions from abstractions via visual/auditory/tactile/(open ended?) concretes. This is why "{t]he process of forming a concept is not complete until its constituent units have been integrated into a single mental unit by means of a specific word." The word serves as the concrete that enables us to retain the product of the process of abstraction.
  14. Universals

    It would save searching for it, if you have it readily assessable.
  15. Universals

    Prof. D: Then a mental entity is a concrete? AR: As a mental entity, yes. It is a concrete in relation to the wider abstraction which is the concept of "concept." It appears that there is some agreement with a question which postures a mental entity as a concrete. In the chapter Abstractions from Abstractions, the beginning of the eighth paragraph: The first stages of integrating concepts into wider concepts are fairly simple, because they still refer to perceptual concretes. This appears after what she had written in the next to the last sentence of the fifth paragraph of the same chapter: Up to that time, he is able to retain the referents of his concepts by perceptual, predominantly visual means; as his conceptual chain moves farther and farther away from perceptual concretes, the issue of verbal definitions becomes crucial. In the Appendix—Abstraction as Measurement Omission there is this: You didn't start by looking at reality from scratch so to speak, and as a first-level concept form the concept "mental entity" as distinguished from "physical entity." That would not be possible. They would be incommensurable. The concept "entity" is delineated by "mental" or "physical", refining the particular context of its extended application. Is the choice to delineate "concretes" in the next to the last sentence of the fifth paragraph lessened by entertaining the potentiality of "mental concretes"? Or to ask somewhat differently: as his conceptual chain moves farther and father away from perceptual concretes . . . or moves closer and closer toward what? non-perceptual concretes?
  16. Grames response comes off as a more plausible dismissal of a conspiracy. Harder to dismiss is the notion of groups actively distributing propaganda to effect change. The obvious way not to fall for propaganda is to understand in what ways it is propaganda. It is not difficult to imagine how frustrating it might be if the participants understood the magnitude of their task at hand. Spies and counterspies are usually extensions of governmental activity. Even to say "semi-private organizations" rings of governmental orchestration and/or support. After reviewing The Establishing of an Establishment, a couple of things leap out. Nine paragraphs before the end of the article, in parenthesis: And the issue of grants is only one of the countless ways in which the same arbitrary power intrudes into men's lives. Talk of behind the scenes influences does not come across as an arbitrary power. Couched as such, it comes across as intentional. The other thing, ten paragraphs into this essay contained a question that has lurked in the background of my mind, but never clearly articulated: what makes men indifferent to the issue of truth or falsehood. Governmental encouragement does not order men to believe that the false is true: it merely makes them indifferent to the issue of truth or falsehood. One way to think of it is the propaganda machines churn it out relentlessly. Sure it is just one errant line in this article, or a couple of cliche's in that article. It adds up, like a "torrent from the broken dam of the sewer of centuries". But, when the cool-aide doesn't have you drop dead right away, the fact that the witch-doctor poisoned the pitcher is much harder to detect. The shelves in the marketplace of ideas are filled with paste jewelry copied from paste jewelry by artisans who have never seen the original gems. The exclusivity of the original gems ensure that only the artisans that demand them actually seek out the boutiques that carry them.
  17. Universals

    Contrast Wikipedia's neutral presentation of the issue (the problem of universals) with the Introduction to Objectivist Epistemology Forward to the First Edition. Here's the first paragraph from the Forward directed toward presenting the issue: The issue of concepts (known as "the problem of universals") is philosophy's central issue. Since man's knowledge is gained and held in conceptual form, the validity of man's knowledge depends on the validity of concepts. But concepts are abstractions or universals, and everything that man perceives is particular, concrete. What is the relationship between abstractions and concretes? To what precisely do concepts refer in reality? Do they refer to something real, something that exists—or are they merely inventions of man's mind, arbitrary constructs or loose approximations that cannot claim to represent knowledge? Bypassing the quotation, she raises one example To exemplify the issue as it is usually presented: When we refer to three persons as "men," what do we designate by that term? The three persons are three individuals who differ in every particular respect and may not possess a single identical characteristic (not even their fingerprints). If you list all their particular characteristics, you will not find one representing "manness." Where is the "manness" in men? What, in reality, corresponds to the concept "man" in our mind? Note the immediate identification of "the problem of universals" as the issue of concepts and planting it squarely as philosophy's central issue. This is followed by the recognition that man's knowledge is conceptual in nature, the validity of man's knowledge rests on the validity of concepts. Knowledge and concepts have logical element to them. Concepts are abstractions or universals. This reiterates that it is the issue of concepts., which subsumes abstractions or universals. This is contrasted with everything that man perceives as particulars, concretes. So far, I don't think Miss Rand has offered either a theory or an attempt at solving "the problem of universals." She is framing the questions and setting her stage, if you will, for the introductory acts yet to unfold.
  18. The Witch-Doctors of the past have by and large been replaced by the Which-Doctors of the present.

    Instead of the reliance of one's own mind as the final arbiter, encouragement to seek out the Which-Doctors is almost ubiquitous. Which career should I seek? Which house should I buy? Which foods should I be eating? Which set of answers should I be seeking to implement.

    When the Patients are ready, the Doctors will appear.

  19. What Sonic The Hedgehog Shows Us About Evil

    Sonic the Hedgehog's full name is actually Ogilvie Maurice Hedgehog. (Not validated. From 100 Strange But True Facts.) —my guess is that you've already been there, seen that . . . but in the unlikely event that you haven't . . .
  20. BitCoin

    I wasn't thinking in such terms. I'm thinking of it in terms of being rational about everything . . . 'cept this one thing. "If I can keep this one arbitrary setter of value, I'll be a rational valuer in all other things." It cedes permission to the mind that being a rational valuer in all things is not required. Exception one is eventually followed by exception two . . .
  21. The Royal Family of Nominalism

    In reality, who is becoming the slave? The servant-slave mentality, or the "nominalist" attempting to gain a stable of servant-slaves by deceiving their minds, in essence, raising the stableboys to a position higher than reality, where the "nominalist" becomes a pawn of their blindness, a slave of their non-thinking and their evasions?
  22. BitCoin

    The most obvious question to me is: Can a proper government be responsible for developing a body of law regarding "collisions' and dealings between people in accordance with correct principles while at the same time invoking (dictating) a fiat monetary system?
  23. BitCoin

    This summary is out of OPAR: (Money itself must be a freely chosen material value, a commodity such as gold, which is an objective equivalent of wealth. Under capitalism, money is not worthless paper arbitrarily decreed to be legal tender by men in positions of political power.) In The Ayn Rand Letter, Vol III, No. 12 Moral Inflation: Today, people are beginning to understand that the government's account is overdrawn, that a piece of paper is not the equivalent of a gold coin, or an automobile, or a loaf of bread—and that if you attempt to falsify monetary values, you do not achieve abundance, you merely debase the currency and go bankrupt. or in Vol III, No. 19 Egalitarianism and Inflation: Now project what would happen to your community of a hundred hard-working, prosperous, forward-moving people, if one man were allowed to trade on your market, not by means of gold, but by means of paper—i.e., if he paid you, not with a material commodity, not with goods he had actually produced, but merely with a promissory note on his future production. There is also the passage from Francisco's The Meaning of Money about 3/4 of the way through The Aristocracy of Pull. Miss Rand tended to tender the term gold. She exchanged it with "a material commodity" in the latter cited reference.
  24. The Snowflake Conjecture

    I hadn't thought of the snowflake's journey that way. Between influence a snowflake's unique journey has (different journeys, different results), and the lab produced snowflakes (same journey, essentially same result), I have what I need to be satisfied that the two propositions are indeed true.
  25. The Snowflake Conjecture

    It snowed last night. It snowed last night. The sky bears had a pillow fight. They tore up every cloud in sight, and tossed down all the feathers white. Oh, it snowed last night. It snowed last night… Every snowflake is different. No two snowflakes are alike. Looking out over snow covered fields, there are a lot of snowflakes. They melt. More snow falls. They don't melt. More snow falls, increasing the depth of coverage. That's a lot of snowflakes. Isolate a snowflake. Catch one falling from the sky. Look at its intricate detail. Catch another one. Compare it. Every snowflake is different. No two snowflakes are alike. There are too many to compare. There are too many winters from which the snowflakes are no longer available for such a comparison. Their icy, crystalline structure have a clear prism appearance to them. Yet the field of snow appears white. The crystalline structure has an appearance of symmetry, often across multiple planes of symmetry. Still, with such a vast number of snowflakes that fall . . . how many snowflakes have fallen? Break the problem down into smaller, soluble considerations. How wide is one snowflake? How long is it? How thick is it? Measure a few more. Identify a range for each axis of measurement. Wait. These snowflakes are not thin square prisms. They are more like thin hexagons. Hexagons can be nested, except . . . they don't all fall laying flat. And there are more than can be seen from one geographic location. And then there's this snowfall, and snow has fallen before. How can it be that every snowflake is different and that no two snowflakes are alike? Snow falls in both the northern and southern hemispheres. Is the planet Earth the only place the in the universe that snow forms? Look at the shape of those snowflakes again. How many permutations can there possibly be. Can there be more permutations than there are snowflakes? Is this the axis down which every snowflake is different and that no two snowflakes are alike? All S is P. All snowflakes are different. Wherein lies the logical leap? In the finiteness of quantity? In the finiteness of permutations? Should a variation in the specific temperature of the particular snowflakes be tossed into the mix to augment the permutation angle? In the grand scheme of things, this may be a trivial inquiry. But is it? Does this challenge the notion for the basis of accepting the truth or falsehood of a proposition? Another consideration may be a case of two snowflakes found to which no measurable difference of any kind can be found. (I would consider this a hypothetical scenario.) In one of Pat Corvini's talks, she approaches this angle using Achilles and the Tortoise. The short of her conclusion, with which I agree, is that if two lengths or distances are indiscernible by available measurement means . . . they are the same. The onus of proof lay with the asserter of the positive. If mom or dad said that all snowflakes are different, being challenged, could invoke the response "Look for yourself, and see." Does the limited sampling of comparisons justify the logical leap? From my examination of Collatz Conjecture, I would have to conclude that the truth or falsehood of "Every snowflake is different" and "No two snowflakes are alike" can be reached. In the examination of Collatz Conjecture, all sorts of patterns emerge that can be identified which repeat themselves, yet each pattern is distinctly different. Permutations manifest that repeat in a similar manner without being the same, other than in their form. I'm not so sure I can do the same with this snowflake conjecture . . . before they melt.
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