I think that such confusion over whether certain experiences really happened or not does exist in certain states of delirium, such as those involved in alcohol intoxication, psychosis and dementia — Jack Cummins

Unfortunately, possible. Nevertheless, the brain, as a precautionary measure, might want to forget dreams so that we don't confuse them with the real. If it didn't do that, I foresee, even with my myopia, a great many problems that can be avoided by simply failing to remember dreams. Why risk it? Are dreams really that important?

I did a Google search of the most common dream people have and it's falling from heights. Of course, there might be a deep meaning to this particular dream theme but we all.get scared of heights to varying extents. If dreams are about our fears then a much easier way to work out the comtents of dreams is to work backwards from what makes us afraid and extrapolate the findings to dreams instead of interviewing people about their dreams. You get the idea, right?

Please do but only if you feel like it though. TonesInDeepFreeze seems intelligent and well-read but his playing style is more brute force like the Deep Blue supercomputer which, I have to admit, defeated the world chess champion, Garry Kasparov despite...everything I guess.

I did start this thread, and I do think Tones asks a reasonable question. You’re continually entering these long sequences of symbolic code as if they mean something. So he’s saying, based on what? You’re claiming this is something Godel says, so, like, provide the citation. — Wayfarer

Well, good advice Wayfarer. Truth be told, the contents of my post is drawn in full from the video in your OP. It's all in the video.

If you think there is anything wrong in my rebuttal, then you should be able to point to it exactly. — TonesInDeepFreeze

For the nth time, your post isn't a rebuttal.

Sure, if "captures the essence" means grossly mischaracterizes with ignorant confusions. — TonesInDeepFreeze

You seem to be contradicting yourself. First set your own house in order is advice that I've been given and have heeded. I suggest a similar course of action for your good self. Have a g'day.

Thank you for your time. G'day.

I noticed in one of your comments, you say that 'Perhaps dreams aren't really dreams.' and you go on to say that would mean that our waking experience isn't real. If that were the case it could be the basis for the Eastern idea of maya, or the idea of reality as an illusion. Or, alternatively it could even be the basis for the soliptist point of view. Do you have any further thoughts on the matter? — Jack Cummins

Thanks for asking this question. It just popped into my head why we can't remember our dreams. There's a very good reason for that. First some context. I know a person, an acquaintance only. We engage in the occasional chit-chat and a constant feature in these rare conversations we have is the one where he can't seem to tell whether one of his experiences actually happened or whether it was only a dream. As you might've already guessed, there's nothing about the mental images of dreams and waking states that could aid us in distinguishing whether a particular memory was the real deal or a dream. He seemed confused and troubled by it and I feel he still hasn't figured out the truth.

Anyway, to get right to the point, if one recalls one's dreams perfectly, there's a small chance that you might confuse reality, believed to be the waking state and the unreal, the dreams. Just imagine if a woman had a nightmare in which she's raped by a certain Mr. X, she recalls it and what if she can't tell whether it was when she was dreaming or when she was awake? Frightening! Just thinking of it gives me the chills!

Perhaps, this answers your question!

That is is nothing like Godel's proof. On so many levels it is nonsensical.

What actual version of a Godel's proof have you read in a paper or book? — TonesInDeepFreeze

Well, let's you tell us how Gödel's argument works. C'mon. Out with it!

Sorry sir/madam, as the case may be but I just remembered that I wanted to start a thread in a similar vein centered around the quote below,

If there is no God, everything is permitted. — Fyodor Doestevsky (Brothers Karamazov)

Doestevsky's words seem to square with the title of the OP which is "Belief in god is necessary for being good".

As far as I can tell, Doestevesky is spot on. A thorough survey of the philosophy of ethics reveals a stark and disturbing truth viz. no existent moral theory that's made a clean break from theism manages to draw a clear boundary between that which is moral (good, mandatory) and immoral (bad, prohibited). Instead what they give us is only rough guidelines in ethics which land up making nothing compulsory (good) or forbidden (bad) and everything is, more or less, permitted (amoral from a certain perspective) depending on the situation of course. A case in point is killing. For argument's sake let's contextualize killing in utilitarianism (most happiness for the most people). As per utilitarianism, I shouldn't kill a defenseless child but I can off a man who tries to detonate a bomb in a crowded mall. See? Not killing isn't mandatory, nor is killing prohibited, and that makes killing permissible, exactly what Doestevsky is asserting in the quote above.

Consider now a theistic morality grounded in an all-powerful, all-knowing, all-good God. Such a morality would, by token of such wisdom, goodness and power, make a clear distinction beween good (mandatory) and bad (prohibited). There wouldn't, rather shouldn't, be special cases that would require us to relax, or make some concessions in re, the moral laws that (we believe) God decreed. Killing, for example, would always be evil and not killing, similarly, would be good in all situations.

Thus, If God doesn't exist, everything is permitted [amoral or fuzzy boundary between good and bad]. The proof is right under our noses in the form of moral paradoxes e.g. murderer asking for your friend's whereabouts (Kantian ethics), hanging an innocent man to prevent a bloody riot (Utilitarianism).

This then leads us to the gist of Doestoevsky's quote. There's another situation in which everything is permitted, morally speaking, and that's when the axioms/postulates of our moral theory (those that have distanced from theism) are mutually inconsistent or if together they constitute a contradiction. By ex falso quodlibet, everything is permitted. To cut to the chase, Doestoevsky is saying the absence of God is logically equivalent to an inconsistent moral theory that's atheistic and, from the preceding paragraphs, he's hit the nail on the head, right? And if one really wants to push the envelope, Doestoevsky is claiming that atheism is a contradiction!

Yes, it's possible he might get a chuckle at your hapless ignorance. — TonesInDeepFreeze

Now, hold on a minute. The post I made is clear and to the point and captures the essence of Cantor's views on infinity.

It wasn't just that Kronecker criticized the work. But it does seems reasonable to think that his professional difficulties vis-a-vis Kronecker might have contributed to his poor mental condition, but I don't think we know for sure. — TonesInDeepFreeze

Indeed, any ideas why Kroenecker was so dead against Cantor? Was there anything more going on then just an academic disagreement on infinity? You know, like a personal grudge, anti-Russian sentiments? Your guess is as good as mine.

I pretty much figured that you didn't know what you were writing when you said that there is a 1-1 correspondence. — TonesInDeepFreeze

And now I know you don't know what an analogy is.

I pointed out that you have failed to address my rebuttal. And your reply to that is to again fail to address my rebuttal. — TonesInDeepFreeze

You're assuming things. Whatever you said doesn't qualify as a rebuttal and thus I had to restate my argument.

The key statement in Gödel's argument is: This sentence is unprovable.

The "argument" A (Adele) proceeds as follows,

1. If this sentence is provable then this sentence is unprovable [Gödel's key premise]
2. This sentence is provable [assume for reductio ad absurdum]
3. This sentence is unprovable [1, 2 MP]
4. This sentence is provable and this sentence is unprovable [2, 3 Conj]
5. This sentence is unprovable [2 - 4 reductio ad absurdum]

However...

Gödel's key premise is problematic,

2. If this sentence is provable then this sentence is unprovable [Gödel's key premise]
7. This sentence is unprovable or this sentence is unprovable [2 Imp]
8. This sentence is unprovable [7 Taut]

I've used only equivalence rules of natural deduction which means that Gödel's key premise, 2. If this sentence is provable then this sentence is unprovable is logically equivalent to 8. This sentence is unprovable.

If so, "argument" A becomes,

1. Thus sentence is unprovable [Gödel's key premise via substitution of "if this sentence is provable then this sentence is unprovable" = " this sentence is unprovable"]
2. This sentence is provable [assume for reductio ad absurdum]
3. This sentence is provable and this sentence is unprovable [1, 2 Conj]
4. This sentence is unprovable [2 - 3 reductio ad absurdum]

Notice, the conclusion, line 5 appears in the premises, line 1 [Gödel's key premise]. In other words, Gödel's argument begs the question, is circular and therefore, fallacious.

I don't know how he reads in the original German, but the above is not how the set theory that came from Cantor works. — TonesInDeepFreeze

I admit it's possible that there's more of me in my post about infinity than Cantor. Nevertheless, I'm fairly confident that what I wrote would've brought a smile to his face. He was a deeply troubled man I believe, in no small measure due to Leopold Kroenecker's scathing criticisms of his life's work.

Incorrect.

2 = {0 1} and has cardinality 2.

K = {K} and has cardinality 1. — TonesInDeepFreeze

You're barking up the wrong tree. The choice of number 2 is irrelevant to my argument.

The analogy is perfect.
— TheMadFool

You still have not addressed my rebuttal. — TonesInDeepFreeze

The analogy is perfect for describing the silliness/inanity/vacuousness of the notion of a set that contains itself.

Since it's a restatement, I don't need to address it again, — TonesInDeepFreeze

You haven't addressed it and that's why I'm restating it.

I gave you specific detail why the analogy doesn't work for you. — TonesInDeepFreeze

The analogy is perfect. There's a precise 1-to-1 correspondence between 2 and K, creating the set that contains itself and multiplying by 1, and last but not the least, making K a member of itself matches perfectly with 2 × 1 = 2.

My best guess is that the controversy regarding the existence/nonexistence of infinities, their categorization as potential and actual, the former being thought of as existing while the not, is an unfortunate relic of the past, specifically how infinity was first defined.

How infinity was defined (from ancient Greeks and Indians till just before Georg Cantor) operationally and thus its conceptualization as an endless process. As is obvious to me now, this idea of the infinite as a task that can't be completed immediately and violently conflicts with infinity as actual defined as ended/completed, leaving only potential infinity as a conceivable mathematical object.

Enter Georg Cantor and he discards, perhaps because he intuits the complication I refer to above, the traditional idea of infinity as an endless task in favor of, surprisingly, an even older understanding of numbers viz. 1-to-1 correspondence. Thus, he defines infinity as a set whose members can be put in a 1-to-1 correspondence with the set of natural numbers. As you can see, defining infinity as such sidesteps the vexing issue of endlessness; that infinity can't be completed is a non issue because all that matters is whether or not we can uniquely match one element of a given set with another element of the set of natural numbers {1, 2, 3,...}.

It's exactly how the first mathematicians, by that I mean to refer to prehistoric times when tally marks were first invented/discovered, solved counting problems. Prehistoric people didn't know how to count, some say, beyond 2 and 3 and more were, for them uncountable which comes very, very close to what infinity is to the modern man. The way they got around this problem was by matching what they wanted to count, their population, livestock, etc. the relevant individuals with counters (tally marks). As you can see, we don't have to know the actual size of what's being counted, all that's required is a unique tally for each member of the set of objects that's being counted. Completing/ending/finishing the counting process of infinity is now a non issue.

To cut to the chase, infinity under this interpretation (1-to-1 correspondence between a set and the set of natural numbers), very ingeniously I must say, avoids the endless nature of infinity and the controversy over actual and potential infinities fails to gain the traction it needs to wreak havoc in set theory that was designed to deal with infinity.

Coming to the matter of an actual infinity in set theory, it becomes patently clear that there are sets whose elements can be put in a 1-to-1 correspondence with the elements of the set of natural numbers which includes itself and hence, in that sense, there are actual infinities.

No, it was as "planned", and consistent (without reguarity). — TonesInDeepFreeze

Sorry, I beg to differ. K =/= {K}.

I gave you a very good reason. Please address the proof. I'll restate it here for your viewing pleasure.

1. There's a set N that can't be a member of another set. Either the attempt to make N an element of another set won't make sense or it will.

If it's the former, case closed. Like trying to multiply 2 with $. It's nonsense.


If it's the latter, all attempts to make N a member of another set will result in N, the set itself. Like multiplying 2 with 1: 2 × 1 = 2; 2 × 1× 1 = 2. Multiplying by 1 does nothing to 2.

2. You claim there's a set K = {K}. Let's try and make K a member of another set like so {K}. However, {K} = K. Let's try something different like so {{K}}. However {{K}} = {K} = K. Basically, this is analogous to multiplying 2 with 1 (see vide infra): just as "× 1" does nothing to the number 2, if K = {K}, making K a member of another set literally does nothing too.

...{...{...{...{K}...}...}...}... = K. The curly braces, an infinity of them return the same value K. Just like 2 × 1 × 1 × 1 x... = 2 in which case, multiplying by 1 changes nothing about the number 2.

In essence, there's no difference between set N, a set that can't be a member of any set (thus can't contain itself) and set K [K = {K}] defined as a set that contains itself. It's a paradox! The set K = {K} cannot exist. Period!

That is argument by analogy, which is not valid for deduction such as mathematics. And the analogy even works against your claim. — TonesInDeepFreeze

The analogy was meant for you and is definitely not something I would submit for publication although I just might if given the opportunity - it makes so much sense.

Perhaps dreams aren't really dreams, a statement that makes complete sense since some have voiced the opinion that reality, our waking experience, isn't really real.

A set can't contain itself. Period!

Suppose K can't be contained in another set like so {K}, any attempt to do so will result in K.

The set that allegedly contains itself is K = {K}. Take K and make it an element of a set thus, {K} and what happens? It's, according to how it's defined, K again. That didn't quite go as planned, did it? Let's work with {K} then; making {K} a member of another set like this {{K}} and what happens? {{K}} = {K} = K which in plain English means K can't be made a member of another set.

The whole exercise involving K = {K} is akin to claiming that b × 1 =/= b. Multiplying by 1 doesn't change b into some other number.

Banno In other words, your claim is

To be good -> To believe in God
— TheMadFool

That' s exactly wrong. — Banno

:ok:

Of course, of course, there are many possibilities, all of which could be true either alone or in some intriguing combination. Until the truth is discovered, we may speculate all we want without being right/wrong about what dreaming is all about.

The first step in counting symbols is to fix the alphabet and inference rules. What you've done is use two different symbolic systems. — fishfry

Indeed, you're correct. We must reduce the symbol set's size to a minimum. Ambiguity must be eliminated at all cost I suppose and that's gonna affect the symbol count, increasing it. We would also have to look into the smallest unit of thought which I reckon is a single concept, each assigned an exclusive symbol of its own. What else? I'm out of my elements I'm afraid.

What strikes me as odd is if we go by the number of symbols in judging proof length then, it becomes more a linguistic issue than a logical one.

In other words, your claim is

To be good -> To believe in God

Sorry to disappoint you but it looks like you're wrong because the contrapositive, To not believe in God -> To be bad, is false.

What is of greater concern, what is a bigger problem, is the converse, To believe in God -> To be good, is false.

If hell - the worst possible situation one can possibly imagine and multiply it by infinity - is no deterrent and if heaven - best-case scenario again times infinity - is no incentive, I'm at a loss as to what can keep us on the straight and narrow.

Also,

With or without religion, good people can behave well and bad people can do evil; but for good people to do evil - that takes religion. — Steven Weinberg

Go back to read the posts. — TonesInDeepFreeze

I hear you, I hear you, old chap (I really hope "old chap" is appropriate) :lol:

Ok. I present below an argument in two symbolic versions, one in plain English and the other using logical notation, of the same argument.

In English (Argument A)
1. If x is greater than two then x is greater than one
2. x is greater than two
Ergo,
3. x is greater than one [1, 2 modus ponens]

In logical notation (argument B)
1. (x > 2) -> (x > 1)
2. x > 2
Ergo,
3. x > 1 [1, 2 DS]

If we go by symbol count, argument B is much, much shorter than argument A i.e. symbol count judges argument A and B as different. However, logically, these two arguments are identical, their premises are identical, their conclusions are too.

:chin:

The scientists don't seem to be able to formulate one single coherent thought — hwyl

I had this strange thought a coupla days ago. I'm myopic, both literally and figuratively, and without my glasses, I only see extremely blurred images. Quite indubitably the fact that the images I see when I don my spectacles become clear is conclusive proof that the problem or fault lies with my eyes, me.

However, it occurred to me that if reality itself were fuzzy, no matter how much I improve my vision, the image will forever remain grainy like old photographs or, in this digital age, pixelated.

To cut to the chase, that "scientists don't seem to be able to formulate one single coherent thought" maybe an indication of the inherent haziness of reality. Just saying...

... yet left like a bride waiting at the altar.

And sure, JC is the original "rabbi zombie on a stick". :halo: — 180 Proof

You crack me up! I have very few reasons to laugh. Thanks for giving me one and that too free of charge. I guess as Po says in Kungfu Panda, "there is no charge for awesomeness." :rofl:

Food for thought: REM sleep (dreams) if not interrupted results in total failure to recollect one's dreams. Why is that? Dreams are about familiar objects like one's lover (wet dreams) or other everyday objects, implying that the brain in REM sleep has access to long-term memory. However the dream itself isn't stored into long-term memory and thus our inability to remember them later, say in the morning when you wake up after a night's sleep. It appears that the brain wants to ensure that sleep and awake states don't communicate with each other. It almost feels like a conspiracy masterminded by the brain; you know, like keeping two criminals (bad analogy but bear with me) in separate cells to prevent them from cooperating and breaking out of prison. That said, dreams seem to be held in short-term memory as we can recall them if woken up in REM sleep. To make the long story short, dreaming accesses long-term memory but the hypotheticals it deals with exist for a very brief moment in short-term memory.

An interesting corollary follows: quite possibly those who complain of poor memory are dreaming (sleep walking).

There seems to be a wide variety of hypotheses, confirmed or tentative, about dreams.

Speaking for myself, drawing from personal experience, dreams tend to be more visual than anything else i.e. the primary sensory modality in dreams is vision; not surprising because we're supposed to sleep at night when sunlight is absent and dreams are somnological phenomena.

Why would our visual system be activated intermittently during episodes of REM (rapid eye movement)?

The contents of our dreams tend to be random in most cases bearing no relationship to immediate and even remote experiences while awake. Yes we do see people we know and objects we're familiar (not necessarily though) with in our dreams but the contexts in which they occur are completely novel and lie outside of our, how shall I put it?, history. I guess what I mean is that despite the fact that we seem people/objects that we're acquainted in our waking states, that they appear to be in completely new contexts suggests that our minds project their thoughts into the visual cortex of our brains. In other words, dreams are a combination of visual cortex activation and thought projection, whichever part of the brain that does that. That's why we see objects we're aware of (visual cortex switched on) but in entirely strange settings (thought projection...prefrontal cortex?).

Mayhaps, the brain is generating possible worlds, different scenarios, contemplating hypotheticals i.e. imagining "what if?" To what end though is a mystery to me. What's the purpose of thinking hypothetically?

Last but not the least, this is going to make you laugh, it's quite possible that dreams are screensavers

A maximum speed in a given medium. And "instantaneous" requires at the least what it means to be instantaneous, and for what observer. — tim wood

:ok:

The only way out of it is through it' ~ some dude. — Wayfarer

:up:

Two points, possibly irrelevant.

1) Following Bell's theorem, something strange is happening, and the more likely account just is FTL transmission.

2) Much that is blue in nature isn't. It's just the way the surface structure reflects light. — tim wood

I went through the Wikipedia page on teleportation and it says that teleportation would violate Newton's laws but I don't know how and it really doesn't matter because so long as claims about teleportation are concerned, if it doesn't break the light speed barrier, it fails to impress, right? After all, the object may have simply transformed into energy (sound? light?) and though it might appear to have teleported, it in fact traversed the distance in some form.

Given things that travel through space seem to have a fixed speed (sound: 330 m/s; light: 300,000 km/s), we might even be able to identify what the object that teleports transforms into. All this assuming teleportation isn't instantaneous.

I don't quite comprehend what culture means but if it includes religious elements such as rituals, festivals, ceremonies, etc. and anything that can be affected by the ongoing digitilization mania e.g. book culture then yes there's been changes, a lot I suppose, but I wouldn't characterize it as a decline, it feels more like how novels are adapted to films, there's a change that's technology-driven but the story is still the same. Of course, there'll be major differences between the before and after pictures of culture as I understand it, caused largely by tech industries and science, but the old should be recognizable in the new. Televangelists, online prayer groups, e-book reading groups, etc. I should stop now because I'm just about certain that I'm talking out of my hat!

The bottom line, old wine in a new bottle.

Hey don’t take it personally. I think you’re writing and analytical skills are OK, but just be mindful on the subject in this case. There are some writers who work on the relationship of Buddhist doctrine and modern philosophy, I’ll try and find some references. — Wayfarer

:up: :ok:

In what way, gentlemen, is the 'Mu' mind-state distinguishable from the prefrontal lobotomized mind-state? How does Nagaruna's purported soteriology differ from psychosurgical zombification? And isn't latter much easier to attain, and therefore more worth the trouble, than the former?

(Asking for a karma-challenged and depressive realist / absurdist friend.) — 180 Proof

Excellent question. If you remember our discussion about Mind No-Mind Equivalency Paradox and the more recent...er...engagement in the Knowledge Is Good OR Knowledge Is Not Good (Ethics & Epistemology), you'll get a feel of what Mu vs Zombie is all about and before I forget, Jesus Christ was an authentic zombie.

[...]Because something is happening here and you don't know what it is, do you, Mr. Jones? — Bob Dylan (Ballad Of A Thin Man)

‘Technique’ is too narrow a term for what Nāgārjuna’s philosophy conveys. Techne is craft or skill or know-how in achieving an outcome. You might then say, well, isn’t enlightenment an outcome that Nāgārjuna wishes to achieve? That’s a deep question in its own right. But your analysis of ‘useless machines’ and logical puzzles is about as far from Nāgārjuna’s intent as it is possible to be. Nāgārjuna’s intent is soteriological, I think he would have no interest in so-called philosophical analysis, if that’s what it is, for its own sake. — Wayfarer

How right you are, it takes a great deal of ignorance to reduce Nagarjuna's philosophy to a technique - the odds are great that there's a lot more to it than just that. I concede your point wholeheartedly. If you found my analysis inappropriate or worse, inimical to the gist of Nagarjuna's ideas, treat it as an idiosyncratic interpretation that though different is not all that truthful.

Symbol length is just one way to measure the length of a proof. It's the one the OP is interested in but it's not the only one. — fishfry

:sweat: So, I wasn't talking nonsense.

There's no preferred way, there are just different ways to measure things. — fishfry

That's news to me. The way it seems to me, there's no point in talking about a book - the book being a message of some kind - in terms of how many words are in it. Similarly, proofs - logical entities - shouldn't be viewed as symbols.

I think there’s something deeply mistaken in that phrase. — Wayfarer

Possible but care to clarify. I respect your intuition if it's one but if you have good reasons, I'm all ears.

Without wanting to sound dismissive, that's why I posted that snippet from Harold Stewart. — Wayfarer

I guess the idea is to stop people, practitioners mainly, from cogitating in any sense of that word (Mu) by, in a way, distracting the mind with physical activity. I'm just guessing though, could be completely off the mark. I've done my share of manual labor - not the kind those who have menial jobs perform but close - and I've noticed that when physically engaged, especially when its strenuous, one stops thinking or even if one is thinking, one can't recall it (this seems a topic in itself but outside the scope of this conversation). Perhaps Nagarjuna's technique was exclusively intellectual in character, something that didn't go down well with his fans in the far east. Plus, the physical approach used in Zen gives the body the respect that's due to it - body & mind together will probably go much further than either of them alone.

everything you want — Benj96

is different from you want everything.

Seen thus, your question seems rather uninteresting. No offense intended.

Thanks for the encouraging words and I like the joke about how Blaise Pascal woul've written a shorter letter had he had the time :smile:

What I find problematic with defining proof length in terms of numbers of symbols in one is that it seems to miss the point. Proofs are, if you really look at it, logical entities and symbols are not, at least not in the numerical sense.

In my humble opinion, proof "lengths" must be measured, if possible, in terms of how many logical steps are taken from the start (premises) to the end (conclusion). To illustrate,

1. p v q [premise]
2. ~p [premise]
Ergo,
3. q [conclusion]

The proof "length" in the above argument, a disjunctive syllogism, is 3 since 3 logical steps were taken. If we use symbol count then the same proof has a proof length of 6 symbols. I'm not sure but it might be that there's a correlation between symbol sets for a particular logical system and the number of logical steps necessary for a proof in that system.

Also, natural deduction seems to employ a classical method which consists of 3 propositions, 2 premises and 1 conclusion. What this means is, if we take into account logical steps instead of symbol count, proof lengths should be multiples of 3. This immediately gives us an easy technique for finding put if a given proof is the shortest available or not. If a proof has logical steps that aren't multiples of 3, something's wrong. [Warning! I might've overlooked other factors that might affect the number of logical steps in a proof].