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Tristan L

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  1. Thank you all for your interesting and information-giving answers! @zapatos Of course no planning is involved, that's correct. It's just easier to say the short and onefold/simple "Feature A evolved so as to do function F" than the cumbersome "By random chance, some individuals had A and others didn't, and since A does the bootful/advantageous function F, individuals with A-giving genes spawned more successfully/spowfully than individuals without them, and so A-giving genes became commoner in the population over time". I'm asking why we didn't evolve to give birth earlier. Of course it could be accidental, but since the fit of the baby's head size to the mother's birth canal size is a tight one, there's a good chance that there's a reason for this. Is it that smarter brains don't simply go through stages that correspond to less smart ones? That is, might it pehaps be the case that the human brain never is at a chimpanzee brain's level - when the human brain is as functional as the chimpanzee's, it's already smarter, and when it's as smart as the chimpanzee's, it's not yet functional enough?
  2. That ambiguity in meaning of words can indeed be very hindering. A much better word imho is German/Theech "Zerlegung", which unmistakably means that which is meant by English "partitioning" (should we use that word from now on for the mathematical concept?) or "sectioning" or something like that. This brings us to the minor side-issue of speech: I don't mean to mock or anything; I just have a side-hobby of bringing back English's true potential, and that includes brooking/using truly English words, for byspel "byspel", which is the proper English word for "example" and cognate/orbeteed to German "Beispiel". I brook this proper English on purpose/ettling where it's not the object but only the tool of talking; after all, that's the ord/point of speech. But again, that's just a hobby of mine. This is a very intrysting problem indeed 🤔. I'd say that it evolves as follows: If the pressure/thrutch is the same on both sides of the resting piston, nothing will happen. Otherwise, 1. the piston will start to go from the high-thrutch side to the low-thrutch side. 2. As it goes in that direction, internal energy of the high-pressure gas is transferred to kinetic energy of both gases and internal energy of the low-pressure gas. 3. When both thruthes become equal, the piston goes on shrithing/moving thanks to the inertia of the gases. 4. Now, the kinetic energy of the gases and internal energy of the former high-thrutch gas (now the low-pressure gas) are transferred to internal energy of the former low-thrutch gas (now the high-pressure one), slowing down the piston, until 5. the piston is at rest again. Now, the whole ongoings repeat in the other righting/direction. Entropy doesn't change/wrixle during the whole process, so the Second Law of Thermodynamics is of no brook/use. But of course, we have another Second Law, namely that of Newton, and this one helps us further here. Actually, I believe that we shouldn't find this too surprising 🤔, for there are other systems which wrixle/change although their entropy stays the same, e.g. a frictionless pendulum swinging. Mark that the system doesn't have to be periodic, I think; for instance, two bodies shrithing/moving at not-zero relative speed forever in space (forget about gravitational waves) make up such a system.
  3. Not at all, you quite misunderstood; I would never dare to lay down the law for anything and never will; I only repeat 8th-grade mathematical definitions and knowledge. In truth, this statement of yours is simply incorrect. Could you please enlighten me as to the sinn/sense of what you've written there? Set theory does indeed not need every set to only contain sets (though ZFC does actually rule out ur-elements for convenience), but a *partition* does indeed only contain sets as elements, namely disjoint subsets of the ground-set. I brook/use the words "element" and "member" in exactly one and the same meaning. Oh, I thank you for the info, but my friend's 13 year old cousin already told me today morning. 😉 {1} is not a partition of S; it's a member/element e.g. of {{1}, {2, 3, 4}} and of {{1}, {2, 3}, {4}}, which in turn are partitions of S; accordingly, it's an underset of S. It's funny that you borrowed my lines which I was about to write to you 🤣:
  4. I think you misunderstand the meaning of disjoint in set theory. This should be cleared up prior to any other consideration. We should indeed clear up any misunderstandings before we go on, so we'll do that right now: For any sets S, T, "S is disjoint with T" means that S and T share no elements in common. For any sets P, S, "P is a partition of S" means that all members of P are subsets of S and any two members T, B of P are disjoint, th.i. share no elements of S in common, and the union of all members of P is S. Now to my above quote, which I'll sweetle/explain with the help of a byspel/example: {1, 2, 3, 4} is our groundset. All three of the following are partitions of {1, 2, 3, 4}: {{1, 2}, {3, 4}} {{1, 3}, {2, 4}} {{1}, {2}, {3, 4}} The first and the second are disjoint since they have no elements in common, but the first and the third one are not, for they have the member {3, 4} in common.
  5. I was hoping that you'd actually read and try to understand what I've written, at least the last post of mine, where I sweetle very clearly that I'm not talking about partitioning physical 3D space, but rather PHASE-ROOM. All I'm saying about disjointness is that macro-states are eachotherly disjoint sets of microstates; can we agree/forewyrd on that? Also, what exactly do you have in mind when you talk of disjointness?
  6. @studiot, could you please at least try to understand what I'm saying 🙂 before you behaving as if you know everything about the matter? It's just like with my entropy-thread, where you appear to know the matter at hand very well and seek to graciously sweetle/explain it to me, but in fact understand very little what I'm even talking about.
  7. Of course the human baby's brain needs to have some basic ability at birth, but for that basic functionality, such a huge baby brain is a total overkill, isn't it? A chimpanzee baby's brain is also up to the job, so why don't human mothers give birth once their babies have chimpanzee-level intelligence, and then the babies' brains grow to grown-up human proportions as the child grows ip? Indeed, a reptilian brain is enough to perform all the bodily functions, so what would be wrong with giving birth while the human baby still has reptilian-level intelligence? All the higher functions, e.g. bonding, can come later on, can't they?
  8. Human mothers have a hard time giving birth to babies compared to other mothers in the animal kingdom because human babies' heads are so big. One often reads that this is so because we humans have such big brains. But what does grown-up brain size have to do with baby brain size? After all, the huge human brain ultimately comes from one single cell, the zygote, so why don't human mothers simply give birth earlier? The brain can grow as much as it wants after birth, so why does it have to be already so big at birth?
  9. Alice: "As much as it hurts me to admit it - for I have the strongest stance against him -, I must say none of you have managed to tackle Bob. [sigh]" Come on, Alice, how can that be so hard?! Ok, so let me say a bit more about the goal of this thread and clarify what it's truly about. First off: It's not - Bob: "... and therefore it is 😉 ..." - about Bob the sophist, but rather about Bob the monist. Orspringlily/Originally, I didn't have a weird interlocutor like Bob in mind at all; rather, I was wondering how to define logical operators, in particular NOT. The first thing to characterize this operator than sprang to my mind was Doube-Negation: NOT(NOT(A)) = A for every proposition A, but then I immediately realized that YES (affirmation) also fulfills this bethinging/condition: YES(YES(A)) = A for every proposition A. I thought a bit more about the matter and came to the conclusion that to define NOT, I need NOT in the first place; even worse: To set NOT apart from YES, I already need the setting asunder of NO from YES, but even if I can take that as a given starting-ord/point, it would still fit with YES and NOT being the same, for if YES is indeed the same as NOT, difference is the same as sameness. Please think carefully about the following as a start:- Bob: "YES2(NOT1 =2 YES1)" Alice: "No Bob, in truth NOT2(NOT1 =2 YES1)." Bob: "True, and since YES3(NOT2 =3 YES2), we have NOT2(NOT1 =2 YES1) =3 YES2(NOT1 =2 YES1), so you forewyrd/agree with me that YES2(NOT1 =2 YES1)." Alice: "No, in truth NOT3(NOT2 =3 YES2)." ... For every proper natural rimetale/number (i.e. every positive whole rimetale) n, the exchange runs like so: Alice: "No Bob, in truth NOTn+1(NOTn =n+1 YESn)." Bob: "Yes Alice, and since YESn+2(NOTn+1 =n+2 YESn+1), we have NOTn+1(NOTn =n+1 YESn) =n+2 YESn+1(NOTn =n+1 YESn), so you forewyrd/agree with me that YESn+1(NOTn =n+1 YESn)." ... Alice: "No Bob, in sooth/reality we have NOTω0(YESn+1(NOTn =n+1 YESn) for any proper natural n) and NOTω0(YESn+1(NOTn =n+1 YESn) for every proper natural n)", where "ω0" means the first not-endly ordinal / fade-rimetale. Bob: "Yes Alice, and since YESω0+1(NOTω0 =ω0+1 YESω0), we have (NOTω0(YESn+1(NOTn =n+1 YESn) for any proper natural n)) =ω0+1 (YESω0(YESn+1(NOTn =n+1 YESn) for some proper natural n)) and (NOTω0(YESn+1(NOTn =n+1 YESn) for every proper natural n)) =ω0+1 (YESω0(YESn+1(NOTn =n+1 YESn) for every proper natural n)), so you forewyrd with me that YESω0(YESn+1(NOTn =n+1 YESn) for every proper natural n). ... Then it goes on like this with all the ordinals. Let me tell you beforehand that Bob appears to agree with all of you and to affirm everything that you've said or will say or could say (and even what you could not say). Bob comes over as a sophist, but the true Bob is a truly radical/rootly monist. Bob the sophist can easily be beaten by Alice's ruse: "Bob, since you don't want me to hit you and wanting is the same as not wanting, I'll fulfill your wish and hit you 😁", but what about Bob the monist? The challenge of this thread, then, is this: How can we escape radical monism? Oh no, Bob has to say something again: "Even if you do manage to escape, which you easily can, you can't excape, for to can escape is the same as to not can escape." Alice: "Bob's soothly/really a pain in the neck, but he does show us something deep yet so onefold/simple that it seems to have been overlooked over the ages: that fornoing/negation is most magnificently rounful/mysterious and rouny/mystical." I'm obviously not merely concered with first-order flitecraft, but with all-order-flitecraft and beyond. No, Excluded Middle actually has little to do with my point. Can you give me one example/byspel where Excluded Middle fails?
  10. 🤣👍 Bob: "Why, of course it's wrong, that is, right! Thus, it has no errors, i.e. loads of them, and it's indeed worth it to spot them." It's not alone there; Latin also doesn't have exact equivalents of "yes" and "no" afaik. Bob: "You're right on every single point. (Indeed, you're always right, for you're always right or wrong by the Excluded Middle Law, and since both are the same, you're always right or right, th.i. right by Idempotence of OR.) Of course assertion isn't flite, and of course things aren't true just because I say so. In other words, and these are your exact - and as always impeccably true - words: 'assertion is flite, and things are true just because Bob says so'." Although the following is only a part of Bob's fishy whatever, it's an important one for understanding him: He draws object-yes=object-no from meta-yes=meta-no. But again, this is just the beginning. Yes, but just as Alice's threat to hit him, this is throughly unphilosophical. What's that? Alice says: "But on Bob's account, being unphilosophical is the same as being philosophical, so showing him the door, or giving him one of my karate-kicks 😁, is fair philosophical debating." Bob: 😰 So Bob's own weapons can be brooked/used against him. Alice: "I fully forewyrd/agree with you ..." Bob: "... as do I." On the point! Unluckily, that's just what Bob claims: That what he does is not arguing (but something far better) and that there's no informational content ever since all is supposedly one, though we have to bear in mind that for him, arguing = not arguing and meaningfulness=meaninglessness and ability to communicate = inability to communicate and info-content = no info-content (1 bit = 0 bit). Alice: "From my POV, which I share with you guys, he can tell us stuff, and what he says is meaningful but trivially false; but from his POV, he can and can't tell us anything and what he says is meaningful and meaningless and true and false." Bob: "How often do I have to say this again: I'm utterly wrong." *** Alice: "I've made the following metaphor: We see ourselves on one side of a chessboard-paper and Bob on the opposite side, and on the rectangular paper we fight him. But the true Bob is the one who tries to join our side and his side of the paper and makes an open cylinder out of the rectangle."
  11. Well, I like philosophizing a lot, but a good amount of self-criticism isn't bad, so the curious case of Bob the Monist reminds us to ask whether philosophy is just a waste of time. Bob: "Why, of couse it is! After all, it's the usefullest thing you can do with your time, and usefulness is identical with uselessness." Alice: "Of course he's wrong." Bob: "Yes, I'm definitely wrong. Heck, what I say is ridiculous and blatantly incorrect, going against the most basic laws of logic/flitecraft... and since wrongness=rightness, I'm utterly right in every way, and I'm the wisest of all." Alice: "I had a huge flite/argument about it with him, but all flites were of little use. He himself triumphantly claimed that what he does outdoes all fliting in smartness. He immediately admits that his premise/forestep is false, and then uses false=true to draw the conclusion that his premise is true. While my fliting/arguing was useless, I could have gotten him by threatening violence." Also heed the short flite in the opening post. No, of course not; I'm on Alice's side. Alice: "The problem is just that he's as slippery as a fish; if we use a philosophical flite against him, he won't go against us, but instead take the flite as being for him, since for=against after him. Therefore, we can't meaningfully flite against him from his POV; not because he's too strong for us, but because going against him is the same as going with him according to him. We simply can't grip him in a talk." Bob: "True, and that means that I am too strong for the lot of you and that my claim is true in the strongest possible way. 😁" Alice: "😠. But there is a point: We can't define negation without using negation. We can't even negate the identity of yes and no without making use of negation in the first place." Yeah, that's the problem: Bob threatens to collapse logic, and the very tool with which to halt that collapse, negation, is itself under attack by the collapse. Well, I am being humorous, but the funniest thing of all is that the flitecraftio/logician who hears the tale of Alice and Bob and truly gives it thought goes like this: "Hahahaha! 🤣 Hahaha! Haha! Ha! Um... What if everything truly is one and the same, including oneness and not-oneness?"
  12. Again, I ask the same question as before: Is affirmation the same as negation? This time, I'll add a bit of clarification to help certain individuals with their strained understanding 😉: Bob flites/argues that yes = no on all meta-levels, th.i. over-levels, and so makes in particular the following flite: 0. Meta-NOT(object-yes = object-no) (obviously true premise/forestep) 1. Meta-YES(object-yes = object-no) (from (1.) by the law that meta-no = meta-yes) 2. object-yes = object-no after all (a reformulation of (1.) Alice now says: "No, meta-yes ≠ meta-no", to which Bob replies: "True, and since over-meta-yes = over-meta-no, you're saying that meta-yes = meta-no after all"; that is, Bob does the same thing as before one level higher. Alice says that Bob's flites/arguments are fully unflitecrafty/illogical, but Bob dryly answers that flitecraftiness is one and the same as unflitecraftiness. Coming back to the above-mentioned certain individuals, accusing Bob of lacking understanding only shows that they themselves lack what they falsely assert Bob lacks. Ironically, Bob could actually come to their rescue if he wants to, namely by claiming that not understanding is the same understanding. But even though cursing and not cursing are one and the same after Bob, I, having a normal, Alice-like mindset, ask those individuals to nevertheless keep to the rules of courteous philosophical talk. 😀
  13. Let me quote Bob's response to statements of that kind from my book Is Yes the Same as No? A Bewildering Tale about Agreement and Disagreement: To this, Bob would answer: "True, and since yes=no, we have (it can't be that both are true) = (it can be that both are true). Moreover, both options are one and the same: (yes = no) = (yes ≠ no)." Bob would say: "Yes, and that means that I do want do that, for wanting to is the same as wanting not to. Furthermore, to stop saying 'no' ist the same as to go on saying it, so of course I want to do that." How do you answer Bob?
  14. The question is already in the title: Is affirmation the same as negation?
  15. Goodstein's Theorem cannot be proven in first-order Peano-arithmetic, but it can be shown in the system of the second-order Dedekind-Peano-axioms (called "DP" in this thread), and this system is what I'm interested in.
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