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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
The equanimity of the initial states of concentration is equanimity with respect to the senses: ... equanimity in face of multiformity, connected with multiformity⊠[which is] equanimity among material shapes, among sounds, smells, flavours, touches. (MN III 220, Pali Text Society Vol III p 268) I swear there is a simple and direct quote somewhere in the sermons, where he cites the things that cease in each of the four initial states of concentration, but I'm not coming up with it. Next best thing: By getting rid of joy, by getting rid of anguish, by the going down of [oneâs] former pleasures and sorrows, [one enters] into and [abides] in the fourth meditation which has neither anguish nor joy, and which is entirely purified by equanimity and mindfulness. (MN 1 22, Vol I pg 28) ... by abandoning both ease and discomfort, by the ending of both happiness and unhappiness felt before, (one) attains and abides in the fourth trance, a state of neither ease nor discomfort, an equanimity of utter purity. (SN V 215, Pali Text Society vol V p 190) Whoever, Ananda, should speak thus⊠And what, Ananda is the other happiness more excellent and exquisite than that happiness? Here, Ananda, [an individual], by getting rid of happiness and by getting rid of anguish, by the going down of [their] former pleasures and sorrows, enters and abides in the fourth meditation which has neither anguish nor happiness, and which is entirely purified by equanimity and mindfulness. This, Ananda, is the other happiness that is more excellent and exquisite than that happiness (the happiness of the third "meditation", or concentration). (MN I 398-399, Vol II pg 67; material in parenthesis added) That last, not the best translation by Horner in my opinion, because of her pairing of "which has neither anguish nor happiness" with "this... is the other happiness...". However, if we piece it together from the translations above, there's a happiness that ceases in the fourth concentration (what was felt before), and a happiness that is felt, in connection with the equanimity and mindfulness of the concentration. For me, there comes a moment where necessity in the movement of breath can place attention anywhere in the body "with no particle left out", and there's an openness to the senses that's required in that. The activity of the body follows from the location of awareness at that time, I guess there's a sense of well-being. Is that happiness? It's a draw, anyway. "You know, sometimes zazen gets up and walks around."--Kobun Chino Otogawa at the S.F. Zen Center It's like a hypnosis, where the hypnotist makes a suggestion that you get up and walk around (and you do so without willing your body to move), but the hypnotist is on the other side of the wall. Maybe--do you have the experience of "being breathed", then? âŠI say that determinate thought is action. When one determines, one acts by deed, word, or thought. (AN III 415, Pali Text Society Vol III p 294) And what are the activities? These are the three activities:âthose of deed, speech and mind. These are activities. (SN II 3, Pali Text Society vol II p 4) âŠI have seen that the ceasing of the activities is gradual. When one has attained the first trance, ("determinate thought" in) speech has ceased. When one has attained the second trance, thought initial and sustained has ceased. When one has attained the third trance, zest has ceased. When one has attained the fourth trance, ("determinate thought" in) inbreathing and outbreathing have ceased⊠Both ("determinate thought" in) perception and ("determinate thought" in) feeling have ceased when one has attained the cessation of ("determinate thought" in) perception and feeling. (SN IV 217, Pali Text Society vol IV p 146, material in parenthesis added) Gautama claimed there was a happiness in each of the states of concentration. As with the fourth concentration I discussed above, it's not the kind of happiness that is the opposite of sorrow, that is experienced in day-to-day living. More like a well-being. Thin, compared to the happiness that's the opposite of sorrow, that's what I mean. The "cessation of ('determinate thought' in) feeling and perceiving" is the attainment associated with Gautama's insight into dependent causation, an example of which would be: exercise of will --> persistence of (location of) consciousness-->stationing of consciousness-->recurrence of consciousness-->grasping after self (suffering). There's a happiness, according to Gautama, in the "cessation of feeling and perceiving", but again it's likely to be more like a subtle well-being, and a happiness that is only present while the concentration is ongoing. Shunryu Suzuki said: So, when you practice zazen, your mind should be concentrated in your breathing and this kind of activity is the fundamental activity of the universal being. If so, how you should use your mind is quite clear. Without this experience, or this practice, it is impossible to attain the absolute freedom. (âThursday Morning Lecturesâ, November 4th 1965, Los Altos; emphasis added) Gautama said: And what⊠is the ceasing of action? That ceasing of action by body, speech, and mind, by which one contacts freedom,âthat is called âthe ceasing of actionâ. (SN IV 145, Pali Text Society Vol IV p 85) Maybe more about that, than happiness.- 568 replies
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https://zenmudra.com/230919-Pirates-very-interesting.mp4 I wonder why anyone would sign up to be a member of the forum, and not post or comment--they can always view the discussion without signing up! Maybe because of the summary emails? The view count is only forum member views, right?
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
I think the notation is "set x where x is not an element of itself" (but I could be wrong!). The set of all sets that are not elements of themselves, the paradox. "The theory of everything" was Hawking's. He gave up on it, in 2002: Godel and the End of Physics So, yes, I guess it never ends, per the lecture.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
Can't be pickling anymore. The heart is tattooed, and the doc says just the one thing would undo that beautiful work.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
I'll admit that I am following the barest thread of the arguments. I still regard Godel's proofs as the greatest work in mathematics, ever, for showing that there is no consistent set of axioms that can encompass all that is known in mathematics. That is philosophy, I agree! The deal with Cantor's diagonal proof, as I understand it: he assumes a completed infinity, in both the counting numbers and the real numbers. That's the assumption that gives rise to the contradictions. He's clearly making a constructed set, and that's real, until he considers it completed and draws his conclusion about the sizes of the two infinities. That's the way I understand it. From Wikipedia, "actual infinity": During the Renaissance and by early modern times the voices in favor of actual infinity were rather rare. The continuum actually consists of infinitely many indivisibles (G. Galilei [9, p. 97]) I am so in favour of actual infinity. (G.W. Leibniz [9, p. 97]) However, the majority of pre-modern thinkers[citation needed] agreed with the well-known quote of Gauss: I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction.[9] (C.F. Gauss [in a letter to Schumacher, 12 July 1831]) Actual infinity is now commonly accepted. The drastic change was initialized by Bolzano and Cantor in the 19th century. Bernard Bolzano, who introduced the notion of set (in German: Menge), and Georg Cantor, who introduced set theory, opposed the general attitude. Cantor distinguished three realms of infinity: (1) the infinity of God (which he called the "absolutum"), (2) the infinity of reality (which he called "nature") and (3) the transfinite numbers and sets of mathematics. ... One proof is based on the notion of God. First, from the highest perfection of God, we infer the possibility of the creation of the transfinite, then, from his all-grace and splendor, we infer the necessity that the creation of the transfinite in fact has happened. (G. Cantor [3, p. 400]) ... One of the most vigorous and fruitful branches of mathematics [...] a paradise created by Cantor from which nobody shall ever expel us [...] the most admirable blossom of the mathematical mind and altogether one of the outstanding achievements of man's purely intellectual activity. (D. Hilbert on set theory) Aw, too bad, Hilbert--Godel threw you out of paradise! More from Wikipedia: There are at least two different ways of looking at the numbers: as a completed infinity and as an incomplete infinity... regarding the numbers as an incomplete infinity offers a viable and interesting alternative to regarding the numbers as a completed infinity, one that leads to great simplifications in some areas of mathematics and that has strong connections with problems of computational complexity. (E. Nelson) During the renaissance, particularly with Bruno, actual infinity transfers from God to the world. The finite world models of contemporary science clearly show how this power of the idea of actual infinity has ceased with classical (modern) physics. Under this aspect, the inclusion of actual infinity into mathematics, which explicitly started with G. Cantor only towards the end of the last century, seems displeasing. Within the intellectual overall picture of our century ... actual infinity brings about an impression of anachronism. (P. Lorenzen) There is also a paragraph in the Wikipedia article titled "Current Mathematical Practice", seemingly at odds with the drift of the rest of the article, that says: ... The ability to define ordinal numbers in a consistent, meaningful way, renders much of the debate moot; whatever personal opinion one may hold about infinity or constructability, the existence of a rich theory for working with infinities using the tools of algebra and logic is clearly in hand. This section of the page shows no references, in contrast to the rest of the page (I've removed the references from my other quotes, for the sake of simplicity). On the spectrum--not saying that there are gaps in the spectrum. I don't see where that says anything about there being different sizes of infinity--?- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
An interesting reply on StackExchange to the question, Does Cantor's Theorem require Russell's paradox? (reply #2): In the latter 19th century when Set Theory as an area of general study was beginning, it was often assumed that we could assume the existence of the set of all and only those things that had any specific property P. This is known as the Axiom Schema of Abstraction. (A "schema" because it it an infinite list of axioms, one for each property P that you can state.) Russell showed this was illogical because the assumption that {x:xâx} exists is paradoxical.(Note: It does not depend on any definition of what â means. Russell offered the Barber Paradox to illustrate this: A barber shaves all those and only those who don't shave themselves. Does the barber shave the barber? For barber, read "set". For shaves, read "contains as a member".) One remedy was to eliminate Abstraction and replace it with the schema of Comprehension (Specification): Informally it says that if X is a set then there exists a set Y whose members are all, and only, those members of X that have some specified property. The crucial difference is that, although we can say that if a set X exists then Y={xâX:xâx} exists, we cannot prove from Comprehension that {x:xâx} exists. Comprehension also implies, by contradiction, there is no set V of all sets. Otherwise we would have the set {xâV:xâx}, which would be {x:xâx} and we'd have Russell's Paradox again. As already stated in other responses to your Q, Cantor's theorem does employ an instance of Comprehension. BTW. The original names for some (most?) of the axioms of modern set theory were not English and different writers have at times used different English names for them. "Extensionality" (Informally, sets X and Y are equal iff they have the same members) is also called Regularity... And some textbooks combine the Comprehension schema and the Separation schema into a single schema, which they also call Separation. (Aug 19, 2018; DanielWainfleet; emphasis added) Plus, 'way down in the comments: Without Comprehension (Specification) we cannot guarantee, in proving Cantor's theorem, that R={xâS:xâf(x)} will always exist. We need a few more axioms too, in order to give a set-theoretic definition of "function" â DanielWainfleet Aug 22, 2018 If I'm reading all this correctly (and it's mostly over my head), Cantor's paradise requires some fancy footwork around Russell's paradox. And from the Stanford excerpt I posted, would seem that the situation is really not resolved: "Cantor's paradise", can you get there at all.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
Beat me, whip me, make me quote my own material (again): Dogen emphasized the practice of zazen, literally âseated Zenâ. Wikipedia describes the derivation of the word âZenâ as follows: The term Zen is derived from the Japanese pronunciation of the Middle Chinese word chĂĄn, an abbreviation of chĂĄnnĂ , which is a Chinese transliteration of the Sanskrit word dhyÄna (âmeditationâ). Yogapedia provides a definition of âdhyanaâ based on the Sanskrit roots of the word: Dhyana is a Sanskrit word meaning âmeditation.â It is derived from the root words, dhi, meaning âreceptacleâ or âthe mindâ; and yana, meaning âmovingâ or âgoing.â (dhyana, dec. 9 2017, âYogapediaâ, authorship not ascribed; https://www.yogapedia.com/definition/5284/dhyana) Dhyana could therefore be said to translate literally as âmind movingâ. The sixth patriarch of Zen in China pointed directly to the mind moving, in a case from the âGateless Gateâ collection: Not the Wind, Not the Flag Two monks were arguing about a flag. One said: âThe flag is moving.â The other said: âThe wind is moving.â The sixth patriarch happened to be passing by. He told them: âNot the wind, not the flag; mind is moving.â Mumonâs comment: The sixth patriarch said: âThe wind is not moving, the flag is not moving. Mind is moving.â What did he mean? If you understand this intimately, you will see the two monks there trying to buy iron and gaining gold. The sixth patriarch could not bear to see those two dull heads, so he made such a bargain. Wind, flag, mind moves, The same understanding. When the mouth opens All are wrong. (The Gateless Gate, by Ekai (called Mu-mon), tr. Nyogen Senzaki and Paul Reps [1934], at sacred-texts.com) ... Ekai claims that the sixth patriarch said: âthe flag is not moving, the wind is not movingâ. Heâs putting words in the mouth of the Sixth Patriarch, there. To me, what the sixth patriarch said was, pay attention to the singularity of self-awareness that moves, not to the flag or the wind. Ekai says, âif you understand this intimatelyâ. To understand intimately is to experience movement in the location of self-awareness, of mind, for oneself. To understand in words without experience falls short (âwhen the mouth opens, all are wrongâ). For me, itâs a lot like falling asleep. I have to let myself breatheârelax, calm down, let go of thoughts, and realize some presence of mind. As the senses locate the presence of mind, particularly the senses concerned with balance, the location of mind may move. (Not the Wind, Not the Flag) The necessity that places attention in the movement of breath, that's hard to lay hold of. That to me is the nature that Shunryu Suzuki referred to, that we all have. As I wrote before, I believe on this thread: Thereâs a frailty in the structure of the lower spine, and the movement of breath can place the point of awareness in such a fashion as to engage a mechanism of support for the spine, often in stages. Gautama was able to say something about those stages, both in terms of their delineation, and also in terms of the feeling associated with each. Dogen really only specified two stages, plus something that happens sometimes in connection with those two stages: When you find your place where you are, practice occurs, actualizing the fundamental point. When you find your way at this moment, practice occurs, actualizing the fundamental point⊠Although actualized immediately, the inconceivable may not be apparent. ("Genjo Koan", tr Tanahashi) For me, I look increasingly to Gautama's descriptions. I think a case could be made that most of the principals in Ch'an and Zen were familiar with at least some of the Pali sermons, so to that extent, there are some teachings in common. The emphasis on "mind to mind transmission outside of scripture", I think that came later in Ch'an--I don't see evidence of it in the teachings of Yuanwu in "Letters" or "The Blue Cliff Record", but maybe with the disciple of his who attempted to destroy all copies of "The ... Record". WIth "mind to mind transmission outside of scripture", the lineage becomes the thing, even though passing down the robe and bowl was discontinued in the 6th century C. E.. My take.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
You're too quick, Daniel! I added a bunch of material to that post, on account of a very interesting article from someone at Stanford, which I quote from.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
Where do you stand on the law of the excluded middle? ok, never mind, I see that in the rarified air of the attempts to get around the Russell paradox, the approach of the Intuitionists is not necessarily any better. But lo and behold: It is also worth noting that Russellâs paradox was not the only paradox that troubled Russell and, hence, not the only motivation for the type restrictions one finds in Principia Mathematica. In his earlier work, The Principles of Mathematics, Russell devotes a chapter to âthe Contradictionâ (Russellâs paradox), presenting it in several forms and dismissing several non-starter responses. He then signals that he will âshortlyâ discuss the doctrine of types. This doesnât happen for several hundred pages, until we reach the very end of the book, in Appendix B! There Russell presents an incipient, simple theory of types, not the theory of types we find in Principia Mathematica. Why was the later theory needed? The reason is that in Appendix B Russell also presents another paradox which he thinks cannot be resolved by means of the simple theory of types. This new paradox concerns propositions, not classes, and it, together with the semantic paradoxes, led Russell to formulate his ramified version of the theory of types. The new, propositional version of the paradox has not figured prominently in the subsequent development of logic and set theory, but it sorely puzzled Russell. For one thing, it seems to contradict Cantorâs theorem. Russell writes: âWe cannot admit that there are more ranges [classes of propositions] than propositionsâ (1903, 527). The reason is that there seem to be easy, one to one correlations between classes of propositions and propositions. For example, the class m of propositions can be correlated with the proposition that every proposition in m is true. This, together with a fine-grained principle of individuation for propositions (asserting, for one thing, that if the classes m and n of propositions differ, then any proposition about m will differ from any proposition about n) leads to contradiction. There has been relatively little discussion of this paradox, although it played a key role in the development of Churchâs logic of sense and denotation. While we have several set theories to choose from, we do not have anything like a well-developed theory of Russellian propositions, although such propositions are central to the views of Millians and direct-reference theorists. One would think that such a theory would be required for the foundations of semantics, if not for the foundations of mathematics. Thus, while one of Russellâs paradoxes has led to the fruitful development of the foundations of mathematics, his âotherâ paradox has yet to lead to anything remotely similar in the foundations of semantics. To be sure, Church (1974a) and Anderson (1989) have attempted to develop a Russellian intensional logic based on the ramified theory of types, but an argument can be made that the ramified theory is too restrictive to serve as a foundation for the semantics of natural language. ... Russellâs paradox has never been passĂ©, but recently there has been an explosion of interest in it by scholars involved in research in mathematical logic and in philosophical and historical studies of modern logic. A glance at the contents of the 2004 volume One Hundred Years of Russellâs Paradox shows prominent mathematical and philosophical logicians and historians of logic poring over the paradox, proposing new ways back into Cantorâs paradise, or other ways of resolving the issue. Their investigations include radically new ways out of the dilemma posed by the paradox, new studies of the theories of types (simple and ramified, and extensions thereof), new interpretations of Russellâs paradox and constructive theories, of Russellâs paradox of propositions and of his own attempt at an untyped theory (the substitution theory), and so forth. All of this reminds us that fruitful work can arise from the most unlikely of observations. As Dana Scott has put it, âIt is to be understood from the start that Russellâs paradox is not to be regarded as a disaster. It and the related paradoxes show that the naĂŻve notion of all-inclusive collections is untenable. That is an interesting result, no doubt about it." (https://plato.stanford.edu/entries/russell-paradox/#ERP) Note "... new ways back into Cantor's paradise". I take that to mean, transcendental numbers are still questionable, in spite of the theory of types. That being so, I still respect the approach of the Intuitionists, in only accepting constructed infinity, and not something that is here, there, and everywhere.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
I was thinking more like: In my school, there are only two kinds of sickness. One is to go looking for a donkey riding on the donkey. The other is to be unwilling to dismount once having mounted the donkey. ⊠Once you have recognized the donkey, to mount it and be unwilling to dismount is the sickness that is most difficult to treat. I tell you that you need not mount the donkey; you are the donkey! (âInstant Zen: Waking Up in the Presentâ, tr T. Cleary, Shambala p 4)- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
Not the version in the Pali Text Society translation of Samyutta Nikaya volume V. Let's see if I can copy that version in, from the PDF available here. (ix) Vesali. Thus have I heard * On a certain occasion the Exalted One was staying near Vesali, in Great Wood, at the House with the peaked gable. Now on that occasion the Exalted One was talking to the monks in divers ways on the subject of the unlovely, was speaking in praise of the unlovely, was speaking m praise of meditation on the unlovely. After that the Exalted One addressed the monks, saying: Monks, I wish to dwell in solitude for the half-month. I am not to be visited by anyone save by the single one who brings my food. So be it, lord/ replied the monks to the Exalted One. Thus no one visited the Exalted One save only the single one who brought his food. So those monks, saying, â The Exalted One has in divers ways spoken on the subject of the unlovely, he has spoken in praise of the unlovely, he has spoken in praise of meditation on the unlovely, spent their time given to meditation on the unlovely in all its varied applications. As to this body, they worried about it, felt shame and loathing for it, and sought for a weapon to slay themselves. Nay, as many as ten monks did so in a single day; even twenty, thirty of them slew themselves in a single day. Now at the end of that half-month the Exalted One, on returning from his solitary life, said to the venerable Ananda â How is it, Ananda ? The order of monks seems diminished. â As to that, lord, the Exalted One spoke to the monks in divers ways on the subject of the unlovely, spoke in praise of the unlovely, spoke in praise of meditation on the unlovely. Then the monks, saying, â The Exalted One has (thus spoken) . . . spent their time given to meditation on the unlovely in all its varied applications. As to this body, they worried about it, felt shame and loathing for it, and sought for a weapon to slay themselves. Nay, as many as ten monks did so in a single day; even twenty, thirty of them slew themselves in a single day. It were a good thing, lord, if the Exalted One would teach some other method, so that the order of monks might be established in gnosis. â Very well then, Ananda. Summon the monks who dwell in the neighbourhood of Vesali to the service-hall. 'Very good, lord, replied the venerable Ananda to the Exalted One, and, after summoning all the monks who dwelt in the neighbourhood of Vesali to the service-hall, he came to the Exalted One and said: â Lord, the order of monks is assembled. Now let the Exalted One do as he deems fit. Then the Exalted One went to the service-hall, and on arriving there sat down on a seat made ready. As he thus sat the Exalted One addressed the monks, saying: 'Monks, this intent concentration on in-breathing and outbreathing, if cultivated and made much of, is something peaceful and choice, something perfect in itself,2 and a pleasant way of living too. Moreover it allays evil, unprofitable states that have arisen and makes them vanish in a moment. Just as, monks, in the last month of the hot season the dust and dirt fly up, and then out of due season a great rain-cloud lays them and makes them vanish in a moment,âeven so intent concentration on in-breathing and out-breathing, if cultivated and made much of, is something peaceful and choice, something perfect in itself, and a pleasant way of living too. Moreover it allays evil, unprofitable states that have arisen, and makes them vanish in a moment. And how cultivated, monks, how made much of, does intent concentration on in-breathing and out-breathing (have this effect) ? In this method a monk who has gone to the forest or the root of a tree or a lonely place, sits down cross-legged . . . holding the body straight. Setting mindfulness in front of him, he breathes in mindfully and mindfully breathes out. As he draws in a long breath he knows: A long breath I draw in. As he draws in a short breath he knows: A short breath I draw in. As he breathes out a short breath he knows: I breathe out a short breath. Thus he makes up his mind (repeating): I shall breathe in, feeling it go through the whole body. Feeling it go through the whole body I shall breathe out. Calming down the bodily aggregate I shall breathe in. Calming down the bodily aggregate I shall breathe out.â Thus he makes up his mind (repeating): â Feeling the thrill of zest I shall breathe in. Feeling the thrill of zest I shall breathe out. Feeling the sense of ease I shall breathe in. Feeling the sense of ease I shall breathe out.â He makes up his mind (repeating): â Aware of all mental factors I shall breathe in. Aware of all mental factors I shall breathe out. Calming down the mental factors I shall breathe in. Calming down the mental factors I shall breathe out. Aware of mind I shall breathe in. Aware of mind I shall breathe out.â He makes up his mind (repeating): Gladdening my mind I shall breathe in. Gladdening my mind I shall breathe out. Composing my mind I shall breathe in. Composing my mind I shall breathe out. Detaching my mind I shall breathe in. Detaching my mind I shall breathe out.â He makes up his mind (repeating): â Contemplating impermanence I shall breathe in. Contemplating impermanence I shall breathe out. Contemplating dispassion I shall breathe in. Contemplating dispassion I shall breathe out. Contemplating cessation I shall breathe in. Contemplating cessation I shall breathe out. Contemplating renunciation I shall breathe in. Contemplating renunciation I shall breathe out.â Thus cultivated, monks, thus made much of, intent concentration on in-breathing and out-breathing . . . allays evil, unprofitable states that have arisen, and makes them vanish in a moment. " How is it, Ananda ? The order of monks seems diminished."--priceless. "It were a good thing, lord, if the Exalted One would teach some other method, so that the order of monks might be established in gnosis."--ya think? Sermons that begin with "Thus have I heard" are thought to have been the recollections of Ananda, Gautama's attendant, who apparently had a photographic memory for sound.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
By the power never invested in me, I hereby baptise and empower thee Sir Daniel! Rise, and shed thy pearls!- 568 replies
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Mark Foote replied to galen_burnett's topic in General Discussion
The acceptance of "actual infinity" allows for the proof that there are no gaps in the real number line, true. That's one of the proofs that the Intuitionists haven't been able to come up with, if I understand correctly, and of course calculus depends on it. Am I getting that right? a. : a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true. b. : a self-contradictory statement that at first seems true. Paradox Definition & Meaning - Merriam-Webster Not familiar with category theory. Somehow it seems to me that Godel's theorems resolve the issue of paradoxes derived from axioms in mathematics by saying that only a limited set of axioms can be used, and the whole of what is known to be true in mathematics can never be derived from a limited set of axioms. So what does that say about "actual infinity". I guess that it's there and we're here, and never the twain shall meet.- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
Shikantaza is "just sitting", sitting minus any "doing something". I never put forward the idea of bliss. I did say that Gautama said there was a happiness in all the states of concentration, including the final "cessation of ('determinate thought' in) feeling and perceiving". It's not the happiness that's the draw, though, IMHO. I did not say that the â[permanent] cessation of determinate thoughtâ may be attained. Here's the teaching, from the Pali sermons with some commentary on my part: Gautamaâs teaching revolved around action, around one specific kind of action: âŠI say that determinate thought is action. When one determines, one acts by deed, word, or thought. (AN III 415, Pali Text Society Vol III p 294) âWhen one determinesââwhen a person exercises volition, or choice, action of âdeed, word, or thoughtâ follows. Gautama also spoke of âthe activitiesâ. The activities are the actions that take place as a consequence of the exercise of volition: And what are the activities? These are the three activities:âthose of deed, speech and mind. These are activities. (SN II 3, Pali Text Society vol II p 4) Gautama claimed that a ceasing of âactionâ is possible: And what⊠is the ceasing of action? That ceasing of action by body, speech, and mind, by which one contacts freedom,âthat is called âthe ceasing of actionâ. (SN IV 145, Pali Text Society Vol IV p 85) He spoke in detail about how âthe activitiesâ come to cease: âŠI have seen that the ceasing of the activities is gradual. When one has attained the first trance, speech has ceased. When one has attained the second trance, thought initial and sustained has ceased. When one has attained the third trance, zest has ceased. When one has attained the fourth trance, inbreathing and outbreathing have ceased⊠Both perception and feeling have ceased when one has attained the cessation of perception and feeling. (SN IV 217, Pali Text Society vol IV p 146) (A Way of Living) The "trances" or states of concentration are not permanent. Gautama spent most of his time in the first concentration, with thought applied and sustained--that, he said was his way of living, "especially in the rainy season". However, there is this: Gautama described his way of living as a mindfulness composed of sixteen thoughts applied and sustained, each thought applied or sustained in the course of an inhalation or an exhalation. The fifteenth of the thoughts that he applied and sustained was: Contemplating cessation I shall breathe in. Contemplating cessation I shall breathe out. (SN V 312, Pali Text Society Vol V pg 275-276; tr. F. L. Woodward) From the descriptions Gautama made of concentration, he apparently attained the fourth concentration regularly. He then took an overview of the body (which he termed âthe survey-signâ of the concentration, or âthe fifth limb of concentrationâ). The overview enabled him to re-enter the fourth concentration, as required in his mindfulness. (From my next post, hopefully) I'll try to answer the rest of your questions at some point, but I think maybe this answers your central concern. You're right, I don't expect to experience the cessation of ("determinate thought" in) feeling and perceiving, with the accompanying insight into dependent causation (and suffering)--Gautama's enlightenment. I'm only looking for the natural way to incorporate "the cessation of ('determinate thought' in) inbreathing and outbreathing", cessation with regard to the activity of the body, into my daily life. Not for the happiness--more like, just to live a natural life, in light of the experience. Gautama said that for an enlightened individual, the asavas or "poisons" of sensual desire, becoming, and ignorance were cut off, like a palm tree at the stump, never to grow again. I can't verify that. That would be the difference between an enlightened individual and anyone else, but if you ask me, most of the folks that have been and are regarded as enlightened have mastered the fourth of the initial concentrations, and maybe something of the further concentrations but not the cessation of feeling and perceiving. They get really good at dropping volition in action of the body, particularly in the movement of breath, and the presence that accompanies "one-pointedness of mind". That's a good thing, but the asavas don't seem to have been cut off at the root, for many of them.- 568 replies
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elders and betters amongst the lake waterfowl eye suspiciously
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
Cantor distinguished two types of actual infinity, the transfinite and the absolute, about which he affirmed: These concepts are to be strictly differentiated, insofar the former is, to be sure, infinite, yet capable of increase, whereas the latter is incapable of increase and is therefore indeterminable as a mathematical concept. This mistake we find, for example, in Pantheism. (G. Cantor, Ăber verschiedene Standpunkte in bezug auf das aktuelle Unendliche, in Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, pp. 375, 378) ... For intuitionists, infinity is described as potential; terms synonymous with this notion are becoming or constructive.[12] For example, Stephen Kleene describes the notion of a Turing machine tape as "a linear 'tape', (potentially) infinite in both directions." To access memory on the tape, a Turing machine moves a read head along it in finitely many steps: the tape is therefore only "potentially" infinite, sinceâââwhile there is always the ability to take another stepâââinfinity itself is never actually reached. Mathematicians generally accept actual infinities. Georg Cantor is the most significant mathematician who defended actual infinities. He decided that it is possible for natural and real numbers to be definite sets, and that if one rejects the axiom of Euclidean finiteness (that states that actualities, singly and in aggregates, are necessarily finite), then one is not involved in any contradiction. (Wikipedia, "Actual Infinity") The reason the intuitionists disavow "actual infinity" is because of the contradictions it allows. That's mathematics, but I look at mathematics as the most reliable means we have for modeling the universe in a predictive manner. Consequently, I expect that the assumption of an actual infinity in the physical or spiritual realm will in the end yield contradictions, and make whatever model is assumed based on the actual infinity subject to predictive failure. Whaddya say, wantah give us a prediction, based on the omnipotence and transcendence of your actual infinity?- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
"Seeking" is not what I'm doing. "Returning to", is more like what I'm doing, except I'm "not doing". My post yesterday at 09:51 AM: " I find relief in that, satisfaction in that, amazement in that."- 568 replies
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How would you counter this hypothesis to the âEnlightenmentâ idea?
Mark Foote replied to galen_burnett's topic in General Discussion
Could you explain this a bit further please? I believe I know both what a Rational Number isâanything that can be divided to give a non-infinite Quotientâand a Real Number isâany non-Imaginary Number. Between any two rational numbers, there's another rational number (just find a common denominator large enough to make the numerators differ by more than 2, then add one to the lowest numerator: 1/4 and 1/2, use the common denominator 8, so 2/8 and 4/8, the fraction 3/8 lies between them). That actually means you have an infinite number of rationals between any two rationals, right, because this process can be repeated between one of the original numbers and the new number forever). You would think all those rationals would fill the number line. But no, then there are the irrationals. Here's a swift proof from stack exchange that between any two rationals, there's an irrational: ... there is a slightly more elementary way of doing this: â2 is irrational. A rational times an irrational is irrational, and the sum of a rational with an irrational is irrational. It's then easy to check that s=a+ â2(bâa)/2 is an irrational number between a and b. The real clincher is Cantor's proof that the infinity of the real numbers is bigger than the infinity of the rationals. Cantor said (essentially), suppose we have a table that maps the integers to the real numbers, 1 to 1: The number one is mapped to pi in the table, and similarly each counting number is mapped to an irrational number, and we suppose that our mapping is one-to-one. That would mean the infinity of the counting numbers is the same as the infinity of the irrational numbers. Now we add one to a single digit of each of the irrational numbers, along the diagonal: The new number is not in the table. We know that, because it differs from the first number in the table at the first digit, it differs from the second number at the second digit, and so forth through the whole table. Conclusion: the natural numbers cannot be mapped one-to-one to the irrational numbers, the infinity of the irrational numbers is bigger than the infinity of the rationals. Source for these tables is here. So when Daniel is talking about an omnipresent infinity--which one? The assumption that makes Cantor's proof possible is the assumption that we can talk about infinity as though it were a completed thing, an "actual infinity". Doing so allows certain contradictions, for example, the set of all sets that don't contain themselves--does that set contain itself, or not? The mathematician Poincare sums it up nicely for me (from Wikipedia, actual infinity): There is no actual infinity, that the Cantorians have forgotten and have been trapped by contradictions. (H. Poincare [Les mathematiques et la logique III, Rev. metaphys. morale (1906) p. 316]) (About Completed Infinities) There's an entire school of mathematics that doesn't accept the notion of a completed, or "actual", infinity: the Intuitionists. The difficulty is, without completed infinities, some of the critical proofs of higher mathematics can't be made. It all comes back to the use of the excluded middle, which Intuitionists reject. However: In his lecture in 1941 at Yale and the subsequent paper, Gödel proposed a solution: "that the negation of a universal proposition was to be understood as asserting the existence ⊠of a counterexample" (Dawson, p. 157). ...The debate seemed to weaken: mathematicians, logicians and engineers continue to use the law of excluded middle (and double negation) in their daily work. (WIkipedia, Law of Excluded Middle) When Daniel proposes that the infinite is everywhere--well, we know there are holes in the infinity of the rational numbers... what makes him think there's only one infinity, and it's everywhere? Devil's advocate, you know.- 568 replies
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ik de zenmeester I have that big stick, you know for just such as you
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Why study martial arts if you'd never fight back?
Mark Foote replied to Franky's topic in General Discussion
Thanks for that. My memory is that he was standing in a dojo, fairly well let, and spinning at shoulder height and overhead. I'm thinking I must have seen this in the brief period of time when I was taking Aikido, very brief period of time, at the dojo. Not the age of the internet. Looked at a lot of video of Ueshiba doing stick form just now, maybe I'm mis-remembering--the pointed stick routine is impressive. What got me about the video I saw was how much he enjoyed just spinning the stick. That's what stuck with me. I see that the form of jiu-jitsu that gave rise to Aikido was daito-ryu, but jiu-jitsu was around for centuries, as I'm sure you would agree. I took six months of jiu-jitsu at a local YMCA, concurrent with judo, when I was in high school. Like this Britannica entry: jujitsu, Japanese jĆ«jitsu (âgentle artâ), also spelled jujutsu, also called yawara, form of martial art and method of fighting that makes use of few or no weapons and employs holds, throws, and paralyzing blows to subdue an opponent. It evolved among the warrior class (bushi, or samurai) in Japan from about the 17th century. Designed to complement a warriorâs swordsmanship in combat, it was a necessarily ruthless style, with the usual object of warfare: crippling or killing an antagonist. Jujitsu was a general name for many systems of fighting involving techniques of hitting, kicking, kneeing, throwing, choking, immobilizing holds, and use of certain weapons. Central to these systems was the concept jĆ«, from a Chinese character commonly interpreted as âgentleââgentle, however, in the sense of bending or yielding to an opponentâs direction of attack while attempting to control it. Also involved was the use of hard or tough parts of the body (e.g., knuckles, fists, elbows, and knees) against an enemyâs vulnerable points. Jujitsu declined after the Satsuma Rebellion of 1877, but it has enjoyed renewed popularity since the 1990s. Don't know where I got the extra "i", I guess I stand corrected!- 66 replies
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Sit down unnoticed amongest the orchard flowers look around, take stock
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Yup. Exciting and spooky pulls me into the present, into my body. Doubt is a whole 'nother bag, at least to me.
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Why study martial arts if you'd never fight back?
Mark Foote replied to Franky's topic in General Discussion
My understanding is that jiu-jitsu was the original grappling art. Certainly judo was drawn from jiu-jitsu, but I think Aikido as well. God, Mark Hammel is bad! At least Driver is making no attempt. I"ve been pleasantly surprised at Rosario Dawson's fight scenes, as Ashoka Tano in Star Wars. At least she has basic stances!- 66 replies
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Why study martial arts if you'd never fight back?
Mark Foote replied to Franky's topic in General Discussion
My favorite footage of Ueshiba showed him spinning a staff. I know they practice staff moves in Aikido, but I've never seen anyone just spin a staff and move the way Ueshiba did. Haven't been able to find the video online.- 66 replies
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