Strangely enough, when I read your idea last night I was thinking that God and the devil is the most fundamental paradox. It is the whole issue of opposition, like good and evil, male and female, light and dark, heaven and hell.

Nevertheless, I do believe that your consideration of paradoxes involves more than the matter of opposites. Perhaps you are asking whether they exist a priori or if they are mere aspects of the divided, binary consciousness of our thinking? — Jack Cummins

You're right in saying that God and the Devil are opposites - yin and yang in a manner of speaking. However, the will to unify is a divine directive and the need to divide is a demonic desire. Give the thought just a moment or so and it'll all sink in. Contradictions are what stops in our tracks, at least for me. When someone thinks/speaks/acts in ways that fit the description of an antinomy, we immediately descend into darkness, our minds struggling to make sense of what is before it viz. a contradiction. A good piece of advice that I was fortunate to chance upon is that whenever one is faced with a contradiction, it's time to draw a distinction as a means of resolving the contradiction and then, when the one splits into the two, the conflict resolves, and we comprehend the thought/speech/act. Every time, we're faced with what appears to us as doublethink we'll use this principle and divide the world up into smaller but more numerous parts. This is, in every sense of the word "opposite", going in the direction opposite to where we want to go - our destination is to unify our experience of reality in, if possible, one word, if not, in one sentence.

Given that's the case, the only option that makes sense and does not too is bring the two halves that are in opposition together and thus the contradiction X & ~X. Every possible truth will flow out of it as naturally as the waters of the rivers in my country, yes I seem to have one, flow from the glaciers high atop the mountains. What's curious is this - we live in a world rife with paradoxes and yet our minds seem to be more familiar with a lack/absence of them. I need to add this to my growing list of paradoxes. Thanks for leading me to it. By the way, does the world make sense to you or is the general suspicion that we haven't yet figured out what the truth is a false intuition?

I'm sure the details are insignificant, so proceed with your investigation of reality! Bully show — jgill

The Devil, as they say, is in the details. Thus, it seems, god must be in the rought outline/general overview and that's when contradictions crawl out of the woodwork. The Devil's supposed to be comprehensible because whenever there's a contradiction the Devil draws a distinction. To divide, perhaps with the nefarious intent to rule, is the Devil's modus operandi. God, on the other hand, unites and thus, for that reason, must be a contradiction and being that God's incomprehensible. A bit of religious detour there but you can be a Deist about it and the argument still makes sense.

To me a contradiction worse than an unproved assumption. — Rotorblade

This, I believe, is incorrect. When we have an unproved or shaky assumption, the antithesis of the thesis using that assumption issues forth. Look at all the philosophies that are around - there's a certain claim and then there's what I like to call the anti-claim. For instance, theism has atheism, realism conflicts with anti-realism, physicalism is pitted against non-physicalism, and so on. Such a state of affairs occurs precisely because some of the assumptions, premises, in the arguments involved haven't been established beyond doubt. In a sense, we could say that believing in a contradiction that proves both sides of a debate is the same as being uncertain about key premises that participate in that debate. This should, if one adheres to the principles of rationality, render everyone an agnostic on the issue at hand.

Coincidentally, according to Wikipedia, String Theory - the most promising candidate for a TOE - is the legacy of S-Matrix Theory, a project undertaken by Werner Heisenberg (1901 - 1976) of the uncertainty principle fame and it just dawned on me that uncertainty is an innate and fundamental aspect of reality - nothing we do, whether we use better instruments, better labs, or better experimenters, can remove the uncertainty.

Thank you for your suggestions. Will give it a look. I think I read his (Fritjof Capra's) book, The Tao Of Physics, as a teenager. It was a very interesting read although much above my pay grade then and now.

To Those Interested And You Two

I'm, as of now, trying to read up on paraconsistent logic and dialetheism but both these theories don't quite cut it. The former has rules that preclude the principle of explosion and the latter's negation isn't exactly the negation I'm looking for.

Furthermore, I would like to draw your attention to the existence of paradoxes, the kind that's not about being counter-intuitive or surprising or unexpected but about contradictions. There are contradictions in the universe right? For instance, a theory that proves there are good people can be expressed in logical terms as below:

If Theory T then there are good people

Now, if Theory T also entails there are bad people then the following would be true.

If Theory T then there are bad people (not-good people)

That would mean,

If Theory T then (there are good people AND there are not-good people)

There are good people AND there are not-good people is a contradiction and the only way to prove contradictions is if you start with one - we have to, in this case, assume both that Theory T is true and that Theory T is false.

There are some issues with this line of thinking and I'm willing to discuss it if you want to.

Too many metaphors broh! — Noble Dust

Really? All this while I've been thinking of myself as incapable of figurative discourse. G'day!

Never heard of David Lynch though his name has a familiar ring to it. Anyway, I have a theory regarding this business about reality being an illusion. Since you mentioned Hinduism perhaps you're referring to Maya and I'll run with that for the moment.

Maya and its other Eastern and Western counterparts render reality into an hierarchy, one level of which is Maya/illusion itself and the other, allegedly deeper, level is true reality. It's not too much of a stretch, in fact it's patently clear, that with this attitude, it's turtles all the way down - one level of reality under another ad infinitum. One could even say, for that matter, that it's all illusion from start to finish assuming there's an end.

My take on reality is slightly different. I look at the world as if it's a cut diamond, sparkling in all its glory, something that happens as light enters it through its many facets. Each facet is real as real can be. As you can see, such a point of view, results in the dissolution of the notion of Maya as there's no illusion we have to dispel in order to get to the truth, just different sides to reality.

David Lynch's movies if they do "...shows us illusions and then shows us how these illusions are manifestations of something real." seem to be precisely what I'm talking about.

There's more that can be said but I'll leave you with that to chew on.

You sound envious! — Noble Dust

Headshot! Sniper! I'm now sprawled on the ground with a gaping hole in my skull, bits and pieces of brain matter everywhere, a halo of blood circles my noggin. Confirmed kill, soldier! You're one step closer to the medal.

If it is just drawing from things that already exist? Wouldn't that just be copying things then and not being original or creative? — Darkneos

Perhaps the creative aspect of realistic art is in the method and not in the result. Too, there's the matter of not everybody being able to draw and paint - it takes talent or loads of practice or both - and this makes art, even if it's only copying an object onto a canvas, a rare ability and thus art becomes, if only in a limited sense, an object of admiration and perhaps even a cause for envy for those of us not thus gifted.

My two cents...

Suppose the maximum potential energy of dominoes is 10 joules and when standing upright lengthwise they're in metastable state of 6 joules. If the kinetic energy required to topple the next domino in the sequence is 6 joules then, we have the makings of a domino effect. As the metastable 6 joules of energy in one domino gets converted to kinetic energy and the potential energy falls to zero, the next domino will fall and we have our domino effect.

Since N is an element of A, it is something: an element of A. :worry: — jgill

That's the mistake we make.

I'm so glad you have proven this to your satisfaction. It shows that something is nothing to worry about. Thank you. :up: — jgill

It all depends on how you interpret the meaning of not-x where x = anything (individuals to categories).

In fact, it looks like a set-theoretic paradox.

I'm confused at this point. There's the notion of out-of-our-control proclivities/tendencies/preferences that has everything to do with free will, specifically its absence and then there are habits which have to be, from the way people treat them, under our control. Presumably, habits are manifestations of out-of-our-control proclivities/tendencies/preferences. Why in Heaven's name do habits have a bad rep?

I just read Gnomon's post about how the so-called laws of nature are considered habits. It smacks of determinism and you know the rest...habits and free will form an odd couple and the received wisdom, if one can call it that, is that we can change our habits.

The empty set is not nothing. But it contains nothing. At least in naive set theory. :nerd: — jgill

Suppose the univeraal set U = A u B

Well, suppose A = {x, y} and B = {v, w}

Suppose N = Nothing. So, { } = {N}

{x} is a subset of A and x is an element of A

{ } is a subset of A, { } has N as an element. So A = {x, y, N}

Similarly,

{v} is a subset of B and v is an element of B

{ } is a subset of B, { } has N as an element. So B = {v, w, N}

Not A = A' = {v, w}

Not B = B' = {x, y}

Nothing = N = Not A and Not B = A' n B' = { }

A' n B' = (A u B)' = {x, y, v, w, N}' = { } = {N} ???

A complement of a set can't contain an element of that set. Contradiction!

Ergo,

1. { } can't be a subset of every set

and/or

2. We can't say that Nothing is not <insert anything>. The best philsophical concept for what I'm getting at is category error.

For Nothing to be, Nothing must be neither something nor not-something but that's a contradiction. Ergo, Nothing is impossible. That's why there's something.

So, ironically, in order to be egotistical, I must also at times be altruistic. — Pinprick

That's not just ironic, it's a contradiction.

Let's be pragmatic here, shall we? The human condition either already is or is on the verge of becoming the way I'll describe it below:

Humanity is like a spaceship leaking precious air, there are 4 astronauts, and only 1 oxygen tank available containing just enough of the precious gas for 1 person.

If you're altruistic and share the oxygen tank all of you will die and, unfortunately, sacrificing, another act of altruism, will require 3 astronauts to give up their lives. Only 1 astronaut will make it.

If you're egoistic, you'll take the oxygen tank and live to see another day. The result, 1 astronaut will survive.

As you can see, it doesn't matter whether you're egoistic or altruistic, only 1 person will get out of this harrowing situation with their life still intact.

As far as I can tell, nothing is, as is generally understood, not a thing. Suppose, now that there's a world with only two objects viz. X and Y and they're different from each other in the sense X is not Y and Y is not X.

Nothing = The empty set = { }

[D n E = The intersections of sets D and E..........D u E = The union of sets D and E]

In this world, let set A = {X} and set B = {Y} and nothing would be neither X nor Y or both not X and not Y.

The set Not A or A' = {Y, { }} because nothing is not X.

Similarly, the set Not B or B' = {X, { }}

Nothing is Not A and Not B (neither X nor Y) = A' n B' = {X, { }} n {Y, { }} = {{ }}, Also note that according to set theory the empty set [{ }] is a subset of every set i.e. it can be said to be an element of all sets.

But A' n B' = (A u B)' by DeMorgan's law and A u B = {X, { }} u {Y, { }} = (X, Y, { }}. Again, the empty set [{ }] is a subset of every set and so can be considered an element of all sets. So A' n B' = (A u B)' = {X, Y, { }}'

That means Nothing = A' n B' = {{ }} = (A u B)' = {X, Y, { }}'. This is a contradiction! A complement of a set [(A u B)'] can't contain an element that's in that set [{ }].

How did we arrive at this contradiction?

We ended up with this contradiction because we assumed that the nothing can be put in a negated category such as Not A, Not B, or, in our world, in categories such as Not red, Not solid, Not good, etc and this is in agreement with my intuition regarding the issue viz. we can't assert that nothing doesn't possess a property over and above the fact that we can't claim that nothing possesses a property. So, it's incorrect to say that nothing is not <insert property>.

If so, I present the following argument that nothing is an impossibility,

1. If nothing is possible then, nothing is neither a this nor a not this [this stands for a property/quality]
2. Impossible that neither a this nor a not this [It's a contradiction]
Ergo,
3. Nothing is impossible
4. If nothing is impossible then something must be
Ergo,
5. Something must be and is

This is why there's something rather than nothing.

:chin:

Thank you for engaging. I've been shut down for maintenance. Check back later!

very beautiful definition of beauty, — Thinking

This statement has the seeds of a paradox. I can't quite put my finger on it though. The topic is beauty. You not only have something truthful to say about it but also it's beautiful. That means, beauty is some kind of extra feature to things. It must be added on - things just can't be whatever they are but need to be beautified but that sentiment is at loggerheads with those who, in fits of deep emotion, say things like, "the sense of awe and wonder evoked by the beauty of the universe". Is "beauty" just an excuse for humans to impose their own sense of symmetry onto the universe, assuming as some have that our beauty-meter is symmetry-sensitive?

So, running with that simple assumption - the assumption that beauty is symmetry or its close cousins - what's so symmetrical about your "beautiful definition of beauty"? In what sense can a definition be symmetric? Anyone care to address this question?

In a very simple, geometric sense, one half of the definition should mirror the other half. Is your definition a palindrome? I've got it! Eureka. Beauty is "OOH HOO"

OOH = an expression of delight
HOO = she (I believe Scottish) = an expression of triumph

Beauty delights. Women are the quintessential objects of beauty [survey the mythology of all cultures]. And one is triumphant when one acquires a thing beautiful.

:rofl:

infinite does compute — f64

So, what's infinity + 1? How does your answer, which must be infinity, square with the answer to 2 + 1?

Infinity DOES NOT COMPUTE!

What's 1 ÷ infinity? If it's 0 then infinity × 0 = 1??

Infinity DOES NOT COMPUTE!

What does infinity even mean? — f64

Let's not get our knickers in a twist. Take a simple instance of infinity, Whole numbers = {0, 1, 2,...}

Then take a part of it, a subset, Even numbers = {0, 2, 4,...}

We know, from the great Cantor's work, the cardinality of the set of Even numbers = cardinality of the set of Whole numbers. A part = The whole.

Infinity DOES NOT COMPUTE! [ :joke: ]

finally get that magical rational number that finally squares to 2 — f64

I tried. The precision, as per my calculations, can be infinite.

x = sqrt(2) = 1.4142135624...

Assume, x = 1.414...

1000x = 1414.414414...

999x = 1413

x = 1413/999 = sqrt(2) correct to 3 decimal places

y = 1.4142135...

10000000y = 14142135.4142135...

9999999y = 14142134

y = 14142134/9999999 = sqrt(2) correct to 7 decimal places.

In this way we can achieve arbitrary precision (infinite) on the value of the sqrt(2). Just saying. My relationship eith math is love-hate. I love math but I think she hates me!

computer checkable proof — f64

A proof of the existence of noncomputables is not the same as an algorithm that can generate noncomputables.

Chaitin gently suggesting that maybe real numbers aren't real — f64

Insofar as the universe being a simulation is the issue, the distinction real-unreal is irrelevant. The real numbers can be accessed through our minds and that means they have to be encoded in the simulation unless the universe is a partial simulation like a cyborg or thereabouts.

understand infinity — f64

DOES NOT COMPUTE!

Thanks for the stimulating discussion. I'm out of my depth here so thanks for indulging me and my bizarre ideas.

I think I have it figured out. Emotivism leads to relativism, relativism leads to nihilism, nihilism leads to pragmatism, pragmatism leads to egoism, and, last but not the least, egoism leads to hedonism.

The fact that morality is by and large an emotional entity implies that it'll vary more than agree. That being the case, we come face to face with being unable to justify morality in any universally acceptable sense. Ergo, we must be practical and the only person we can actually take care of is ourselves. So, let's make ourselves happy.

:lol:

delete :lol:

What about pi and e? I've made the distinction computable irrationals and noncomputable irrationals thinking that the former could be reduced to an algorithm and the latter not. That seems to be the received mathematical opinion as per my "research" for what it's worth.

That there are noncomputable irrational numbers is certain: [url=http://Chaitin's constant is an example (actually a family of examples) of a non-computable number. It represents the probability that a randomly-generated program (in a certain model) will halt. It can be calculated approximately, but there is (provably) no algorithm for calculating it with arbitrary precision.Aug]Chaitin's constant[/url]

If there's no algorithm that can compute a number, each digit will, if the universe is a simulation, require a separate line in the code and that means such a program will be infinite, can't be finished, ergo, can't be run, hence, the universe can't be a simulation because of the existence of such numbers (noncomputable irrational numbers).

Now that I think of it, humans have struggled greatly with the concept of infinity. Basically, infinity DOESN'T COMPUTE! for humans. Last I checked, it all "started making sense" in the 1870's with Georg Cantor's work. This, at some level, suggests that the universe doesn't contain actual infinities and that our brains can't handle what is essentially infinite information. The universe could be a simulation for that reason - no algorithm can manage infinity: infinity + 1 = infinity; infinity + infinity = infinity; and so on. We hit a wall and things stop making sense: IT DOESN'T COMPUTE!

The other side of this story is that non-computable irrationals (Chaitin's constant for example) exist. In other words, the universe does contain instances of infinite randomness and these can't be reduced to finite algorithms. Ergo, the universe isn't a simulation.

Fine, name one. All you have is an existence proof; and an existence proof is a weaker class of metaphysical existence than a constructive proof like showing that 2/3 or pi exists. — fishfry

What do you mean? Any point on the well-known number line exist in the same metaphysical sense as another point. There's e and there's pi and there's a non-computable irrational number between them which is a point on the number line. Are you saying some points on the number line are different from other points on the number line? If yes, never heard that before but that's probably just me. Care to clarify your metaphysical objection?

I'm afraid I didn't follow your algorithm at all — fishfry

The algorithm I posted is just something that popped into my mind and isn't one that's ready for prime time as they say. What's the problem with it though? It's got only 4 instructions.

Let's go over it together.

Assume that a substitition-cipher-like process is involved and 0 is substitited with 9, 1 with 8, 2 with 7, 3 with 6 , and 4 with 5

1. The first step is to print a number n [e.g. 29]

2. The second step is to find how many digits n has, say it has d digits [d = 2]

3. The third step is to create a d digit number with all digits substituted/changed from n and assign it to n [n = 70 as 2 is replaced with 7, 0 is swapped with 9]

4. Go to 1

The first iteration of this algorithm using the examples I gave will print 2970

The second iteration would look like this: 29707029

The third iteration would look like this: 2970702970292970

The fourth iteration would like this :29707029702929707029297029707029

Is there are repetition in the sequence of digits? No. So, no pattern

Is the sequence random?

This is a difficult question for me to answer but here's what I think:

(i). If only four digits (0, 2, 7, 9) are being considered, the sequence is random as each digit appears the same number of times as the other digits, making their appearance in the sequence equiprobable (that's randomness right)

However,

(ii). If we consider all 10 digits available to us (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), the digits are not random; only 0, 2, 7, 9 make an appearance

As I admitted at the outset, I'm neither a coder nor a mathematician so kindly cut me some slack.

But if you are generating a number from an algorithm, you haven't generated a noncomputable. — fishfry

If you notice the algorithm isn't mathematical. It's more like a cipher but I don't know whether that, in itself, suffices to make the output of the algorithm non-computable. It is irrational thought as the digits are infinite and don't repeat.

There is an enumeration of the computable numbers; but there is no computable enumeration of the computable numbers! — fishfry

I found this on wikipedia:

While the set of real numbers is uncountable, the set of computable numbers is classically countable and thus almost all real numbers are not computable — wikipedia

:chin:

And either way, mathematical existence is not physical existence, A computer could put in our minds the idea of a flying horse, Captain Ahab, Captain Kirk, and noncomputable numbers. But since those things don't exist in the physical world, they are not evidence that the world is not a computer. — fishfry

I don't know to whom I said this to but I'll say it again for your benefit: E-V-E-R-Y-T-H-I-N-G is a simulation if reality is a simulation and that non-computable irrational numbers exist in some space (mental/platonic/mathematical, you decide), it must be accounted for in the code that creates the simulation.

Penrose's bad ideas are better than most people's good ones. — fishfry

:rofl: I'm voting for you if you ever contest elections! You should be president.

All that out of the way, I'd like to run something by you. I have this notion of infinite randomness in my mind. To me it means the existence of an infinity that is completely devoid of all patterns. If such infinite randomness were discovered to exist (I don't care as to where) can we infer the impossibility of reality being an illusion based on the premise that to code infinite randomness would require an infinite set of instructions, a task that can't be completed, and if so, such a code can't ever be actually executed?

I find this interesting. A massive 2-ton boulder perched atop a hill may need only the strength of a child to push it over and produce an incredible amount of energy.

If a small domino is able to topple a slightly larger domino (and so on and so on), doesn't the energy increase (not from nothing simply the potential energy stored [by whatever placed it there]) or, I suppose it doesn't "increase" the potential energy was simply there all along, rather, doesn't the kinetic energy amplify? — Outlander

I took a look at the wikipedia page on the domino effect. The entire phenomenon is based on what they call meta-stable states and my hunch is, as the dominoes get larger the less meta-stable they'll be and the more kinetic energy that'll be needed to knock them off balance and, if my reasoning is correct, there's going to a cap on how large the kinetic energy of a falling domino can become. :chin:

However, you can get amplification if you have a row of dominoes of increasing size — Jacob-B

It gets harder to topple the next domino if the dominos increase in size until one doesn't fall over and the causal chain breaks.

A chain reaction will become stronger with every reaction in the chain and will continue to get stronger until every reactant is consumed.

it would have an effect on you — Jacob-B

Yes, but no effect on the fully-loaded truck, right? I guess I should've been more specific - my pushing wouldn't have the intended effect.

A couple of things regarding the wisdom-ignorance duo in relation to god

1. Socratic Paradox

I know that I know nothing — Socrates

Socrates is the wisest — Delphic Oracle

2. God Of The Gaps

God of the gaps is a theological perspective in which gaps in scientific knowledge are taken to be evidence or proof of God's existence. — Wikipedia

It's a pet theory of mine and maybe completely off the mark but I'd like to bounce it off you. I believe that all religions have as their ultimate foundation the Socratic Paradox - wisdom is recognizing one's ignorance - and thus God is, even if other things, essentially the embodiment of our ignorance - the God of the gaps. In short, when we worship god, we're confessing, even if unknowingly, our ignorance and that's wisdom.

What's the greatest form of ignorance? Not knowing anything, right?

Not knowing anything = An Ignoramus (the greatest ignorance) = God

Therefore Anselm's argument becomes,

[Anselm]1. God = An Ignoramus (the greatest ignorance)

2. If x = An Ignoramus then x exists [to be an ignoramus, one has to exist]

[Anselm]3. If God = An Ignoramus then God exists [from 2]

Ergo,

[Anselm]4. God exists [An Ignoramus exists]

I finally have an argument that supports Anselm's premise viz. If greatest then exists which appears as 3. If God = An Ignoramus then God exists.

methodical doubt. — AaslaanArawii

:up: I like that. It's as if there's some certainty to, regarding how to handle, uncertainty.

But the body would rather shut down its ability to move externally and potentially lose an arm or leg than to shut down the conciousness and lose out on the ability to process data. — AaslaanArawii

Postpandrial Somnolence

We spend about one-third of our life sleeping or attempting to do so

Hedonism

VS

As the body attempts to preserve oxygen delivery to the brain and heart, blood is shunted away from extremities and nonvital organs.

I've been giving this idea of the all vs the individual some thought and since you've given it a mathematical flavor, I'll just continue along the same trajectory.

You've talked about "...the primordial unit, the one..." and it resonates with my thoughts - how exactly did the all/the many come to be? By way of an answer in concordance with the OP's thesis, I suggest contextualizing the matter within reproduction. A human body is a community of cells that has been accorded the status of a unit, a one, an individual but that's not the end of the story for this community of cells also began as a unit, a one, the zygote - the "...primordial unit..." - formed when sperm and egg fuse. It's as if the all/the many is an illusion and science has, by digging up the hidden unity, on multiple occasions, dispelled this illusion. :chin:

This is a puzzle I've been grappling with for the past week or so. A single cell divides but the net effect is multiplication into a population of cells and when you divide this population, you get back to a single cell. The one divides into the many and the many divides into the one.

Presuppositions and premises not the same thing — tim wood

There are two parts to an argument - premises and conclusion. In which of these two will presuppositions make an appearance? :chin:

if in starting with God, you end with God — tim wood

Whatever the ontological argument is, it's not a circulus in probando. It begins with a definition dealing exclusively with god's greatness. The other, more important, premise establishes the critical link between greatness and existence.

P(X is lying | X gives testimony) = [P(X gives testimony | X is lying)] * P(X is lying)]/P(X gives testimony]

If X's testimony is guaranteed, P(X gives testimony) = 100% = 1

P(X is lying | X gives testimony) = [1 * P(X is lying)]/1

P(X is lying | X gives testimony) = P(X is lying)

Makes sense because X can't lie until and unless X gives faer testimony.

Firstly, a domino effect isn't exactly a chain reaction. Yes, there's a causal sequence in the domino effect but what's missing is an amplification of the cause-effect involved, a feature of chain reactions.

Also, what do you make of the slippery slope fallacy? I don't know how to explain this but I like to look at it as a causal web and one causal strand in this web may either assist or, more to the point, inhibit another causal strand thereby preventing all causation from being domino effects.

A puzzle I'm working on, when I have the time of course, is whether everything has an effect or not. The principle of sufficient reason is quite clear regarding how everything has a cause but nobody seems too worried about the flip side of this coin i.e. does everything have an effect?

In terms of physical strength I'm well below average and I'm sure if I tried to push a fully-loaded truck, I wouldn't be able to. So, in a sense, the causal chain, insofar as the fully-loaded truck and me are concerned, leads to a dead end. In other words, I'm not, can't be, a cause with respect to the fully-loaded truck's motion.

@f64

If you claim noncomputatlble numbers exist, name one. — fishfry

Suppose the following is the complete list of computable irrational numbers between e and pi

2.71828...[e]
2.71829...
2.71832...
.
.
.
3.14158...
3.14159...[pi]

Using Cantor's diagonal argument I can show that there's a number not on this list x such that e < x < pi. In other words there exists a non-computable irrational number between e and pi, existing in the same sense as e or pi.

Now that I think about it, I believe an infinite random sequence of numbers can be generated using a simple algorithm:

1. Display v [a number, any number]
2. Calculate character length of display = c
3. Change one/all digits in the display of character length c and assign it to v
4. Go to 1

Note: After the first display operation for v, subsequent v's are attached to the previous v. So if the first v = 2, the second v = 23, the third v = 2345 or 2325, the fourth v = 23451267 or v = 23251246, ad infinitum.

And that's as far as I managed to get...comments?!

Actually, the original notion from ancient philosophy, was that being is a good and that non-being was, therefore, an imperfection. I suppose you could argue against the idea that 'being is good', but if you're not inclined to find that intuition resonant, then probably there is no point in arguing it. — Wayfarer

Interesting! When you put it that way, it kinda rings a bell. Since you mentioned that "...being is good..." I'd like to explore the moral dimension of Anselm's argument. The aspect of morality that's germane to the ontological argument is morality's ultimate vision viz. the world, people, ought to be a certain way and not how it is. If so, then the existence of morality is evidence for either the nonexistence or imperfect nature of the good. If that's the case, how does Anselm reconcile his belief that the perfect good must exist with morality which is, at the end of the day, an admission that the good either doesn't instantiate or if it does, it's imperfect? Ethics, predicated on the reality of an imperfect world and Anselm's assertion that the perfect exists strike a discordant note. It's like someone who believes there are no elves but that there's an elf god. :chin:

Refute what? And where do you imagine "ontological" came from or what it refers to? And it is not possible to get out of bed in the morning, nor into it at night, without presuppositions of various types and qualities. — tim wood

Yes, this is an attempt at refutation. Can you be more specific about Anselm's presuppositions? The ontological argument has only two premises:

1. If greatest then exists
2. God is the greatest
Ergo,
3. God exists

What are the presuppositions?

By the way the mathematician Kurt Godel had his own version of the ontological argument which is much longer I presume but that's another story.

And perhaps the question would never arise if instead of the one word "existence," we had several for the several different kinds of existence. — tim wood

I suppose so. Existence in the imagination can be distinguished from existence in reality. This is what I touched upon in my earlier post, that there's an illegal move from a priori existence (imagination) to a posteriori existence (reality).

However, what do you make of theoretical physics? Mathematical models of the universe seem to predict the existence of certain physical objects and mathematical models are, to my knowledge, a priori in that they don't rely on actual observations but thus predicted objects like neutrinos and the Higgs-Boson have been confirmed to exist in reality in experiments a posteriori. I consider such instances of amazing predictions made by theoretical physicists to be ones in which existence in reality can be proved by existence in imagination.

This leads us to the interesting question, is there a mathematical model of the universe that requires god to exist? Anselm, it seems, had anticipated/prefigured theoretical physics as a legitimate discipline. Of course reducing god to math is going to be a tough nut to crack but that there's a possibility of proving god using a branch of science (theoretical physics) that has a good track record is an opportunity we must seize with both hands. Mind you, I'm not a scientist so some or all of this may sound bizarre, crazy, or worse, stupid.

Nope. The crux, as you call it, lies in recognizing that the existence of God is presupposed in all the thinking that Christians do. And each of the religions in each its own way. Which of course is a way of saying that God certainly exists - just not, at all, in the way some people understand it. — tim wood

The ontological "argument". No presuppositions. If you have issues with it, refute it. I'd like to see it done.

Interesting, so the boy will associate his senses with the thoughts he is thinking about in that experience. So what if he is thinking of something of something like a "black hole" in which you can only perceive visually. I think in that case all he is left is to think of the image of a black hole. In other words the boy will associate certain thoughts with which he was able to perceive them with his senses or feelings, and at the base level you might only be left with images. — Thinking

I'm just curious about how language, the so-called sophisticated version we use in ordinary and also specialized discourse an example of which is your posts, has, in a way, failed at capturing the complete experience - the whole enchilda of the accompanying sense-data naturally associated with words - of words. I've enjoyed chocolate, too much to be honest, but when I encounter the word "chocoloate", I don't, nobody does, experience the sweetness, the crunchiness, the aroma, etc. which I do when I'm actually munching on a chocolate bar.

It's as if "chocolate" refers to something other than the sensations I described of biting down on one and, at some level, these very sensations are what chocolate means to us and that's what I find odd.

Truth be told, there are many times when people can access the complete experience of words albeit in a fragmented manner. However, these occasions are few and far between and what usually happens is words are stripped of their associations (sensory or otherwise), associations that are part of their natural environment and also are essential features that go into their definitions. The aftermath of such processing, done automatically probably due to neurological constraints, is words whose meanings are, for this reason, incomplete. That's what I suspect is the downside. The upside is we'll be spared sensory overload and confusion - our senses have other more important chores and what happens if you see a bar of chocolate floating around with poop in your toilet?

My hunch is that it all boils down to patterns. Words, if you look at what they really are - their definitions - are basically patterns extracted from the world and its contents. Patterns are abstractions and while sensory patterns do exist, what our minds are really interested in are the motifs that go towards creating categories, a necessary step for words to have meaning. Patterns/motifs don't have smells/colors/sounds/flavors/texture.

Sure they have. To "refute" it you have to understand it, and most folks who try, don't. The right way is to breathe, relax, and then read it somewhat closely, It is an argument that says if you think a certain way and believe certain things, then certain conclusions follow (according to Anselm). Or, if you think and believe the moon is made of green cheese, then very likely mice would like it there. There is no refuting this kind of argument. And in his reply to his critic Gaunilo, Anselm made it clear he understood exactly the nature and kind of his argument - and better than almost all of his critics to date. — tim wood

The crux of the argument is in treating existence as greater or as having something to do with greatness. Expressed logically, the key premise of the ontological argument is:

1. If great then exists.

There's an active thread on antinatalism on the forum titled "everything wrong with antinatalism" and the essence of antinatalism is nonexistence is better than existence. How would you reconcile the antinatalist viewpoint with statement 1 above? Antintalism is premised on the claim that,

2. If not exists then great.

It only takes a moment to realize that Anselm's central premise directly contradicts Antinatalism's.

Then there's the so-called experience machine argument made by Robert Nozick which, all said and done, proves that people prefer the real over the faux which, when rephrased as a conditional which it is, becomes,

3. If great then real

Statement 3 is a just a variation on Anselm's premise, statement 1

My personal take on the issue is that existence is an empirical claim and being so requires empirical data/evidence as proof. Anselm's key premise, statement 1. If greater then exists makes what looks like an illegal move from the a priori to the a posteriori, from the ideal to the empirical (I hope I got that right). This is clear and apparent in Anselm's original sentence which is "god is that than which nothing greater can be conceived". Conceiving is an a priori activity and existence is an a posteriori claim. I guess the point I'm trying to make is that there's a yawning chasm, unbridgeable to my reckoning, between conceived greatness in our imagination and existence in the reality.

Having said that there's the small matter of theoretical physics. Wolfgang Pauli was supposed to have predicted, purely by a priori reasoning, the existence of neutrinos, later confirmed a posteriori. Odd!

There's a lot to process and I just don't have the energy. I'll leave it at that.

Christopher Hitchens — Jack Cummins

A handy tool in your toolkit should be Hitchens' Razor: What can be asserted without evidence can be dismissed without evidence. It seems to have attracted some criticism but, to me, it's a burden of proof issue and assuredly, the one who makes the claim must furnish the proof for that claim whatever it is. I believe the Latin equivalent is: quod grātīs asseritur, grātīs negātur (what is asserted gratuitously can be negated gratuitously).

Coincidentally, Hitchens' razor is a good example of an old idea that has been adapted to the modern audience by a prominent social figure who's, among other things surely, a strident opponent of religion.

one writer leads onto another — Jack Cummins

I suppose ideas that are mutually compatible or mutually supporting clump, to use a biological term, together and a synergy develops among them that, on occasion, becomes the breeding ground for other, newer, ideas. At other times, conflicting ideas experience attrition as they vie for people's attention and adherence and even here too new ideas, either by way of a compromise or a rejection of the inconsistency, emerge from what is essentially the carnage of ideological wars.

You might want to give this (Multiple Discovery) a look.

and this:

Carl Wilhelm Scheele (9 December 1742 – 21 May 1786) was a German and Swedish Pomeranian pharmaceutical chemist. Isaac Asimov called him "hard-luck Scheele" because he made a number of chemical discoveries before others who are generally given the credit. — Wikipedia

and this:
Heroic Theory of Invention And Scientific Development

and this:

[The profound significance of Mendel's work was not recognized until the turn of the 20th century (more than three decades later) with the rediscovery of his laws. Erich von Tschermak, Hugo de Vries and Carl Correns independently verified several of Mendel's experimental findings in 1900, ushering in the modern age of genetics] Rediscovery Of Gregor Mendel's Work — Wikipedia

and this:

Leibniz-Newton Calculus Controversy

It appears that the invention/discovery of new ideas has a Jekyll and Hyde personality. Sometimes, rediscovering/reinventing an idea/invention brings the original discoverer/inventor to public awareness and this becomes the occasion for receiving recognition in their respective fields e.g Gregor Mendel's case. Other times, multiple discoveries result in no-holds-barred fights among the discoverers/inventors, all of whom want to claim primacy in the discovery/invention e.g. the Leibniz-Newton debate.

Speaking for myself, I suppose it's a good idea to do adequate research before one claims that one's idea is a novel one. Two thousand years have passed since the earliest thinkers graced the world and even if one makes a conservative estimate of the rate at which new ideas/inventions are born there should be enough ideas/inventions out there to make the odds of duplication quite high.

A very interesting question and I suspect we should, in the spirit of exploration if not because we have a good grasp of the matter, discuss it. After a very superficial survey of linguistics, that's all I have the time for, I'm left with the impression that no one has any idea how humans learned to speak. A well-tested, proven, theory on language acquisition would've come in handy. Anyway, no point ruing over a missing theory, instead let's take this opportunity to explore, what is as far as I can tell, uncharted waters.

The first name to pop into my head is Ivan Pavlov and his dog experiment in which he trained dogs to expect food when a bell was rung and the evidence that his training was successful was the dogs' oral response - salivation/drooling. It's clear or at least it's highly likely that Pavlov's dogs had learned to associate the bell's ring with food but what's intriguing is what is, quite obviously, the gut-reaction or visceral response of the dogs. Dogs salivating under normal circumstances occurs when they're actually feeding but Pavlov's experiment food was offered only after a certain amount of time had elapsed after the bell was rung. Is it beyond the limits of reasonableness to come to the conclusion that the dogs had, for lack of a better word, internalized the ringing of the bell and associated it with not only a picture of the food but also the smell, and taste of it? In short, Pavlov's dogs had linked the bell's sound to the complete experience - all senses are a go - of feeding on dog treats. For the dogs, the bell's sound = eating dog treats.

Coming to the boy without word, he too may be able to, provided there's some level of consistency in his experiences, associate certain sights/sounds/tastes/touches/smells with other events/objects in his life just like Pavlov's dogs. These associations once firmly established could become a means of communication between the boy and an interested second party.

This leads us to what is, for me, a fascinating phenomenon, synesthesia. A little off-topic but I'm sure there'll be some useful conclusions pertinent to the OP we can draw. Synesthesia describes the experience of activation of our sensory system (smell/taste/sight/touch/hearing), either in part or as a whole, with recall (of memories). We could say, in some sense, that Pavlov's dogs were experiencing synesthesia (activation of their digestive responses) when they heard the bell, the sound of the bell triggering a memory of a previous happy encounter with food.

If you notice, ordinary language, though capable of inducing visceral reactions e.g. I recall my mouth watering in anticipation when someone offered me a helping of my favorite dish, usually fails to evoke such responses. For instance the word "theory" or the word "language" only elicit thoughts - no drooling, no sweet odors, no bright colors, no tastes, absolutely nothing in terms of sensory stimulation takes place.

To sum up, the boy without words, because he lacks sophisticated language, will experience "language" in a more immediate, direct, visceral sense. Each association that forms in his mind, like the one in Pavlov's dogs, will, when accessed, evoke a complete experience. So, for example, if he's learned to associate a certain pretty waitress with food, seeing her will make his mouth water, he'll begin to smell his favorite meal, he'll hear the sound it makes when the food is in his mouth, he'll feel the food's texture in his mouth, he'll smell the aroma, and so on - like Pavolv's dogs

When people acquire language skills of the kind we're employing in this discussion, we lose out on what I've described as the complete experience of communication. Yes, we might flush and our hearts might beat faster when we hear the word "sex" but nobody, to my knowledge, ever has had an orgasm just hearing/reading the word "sex".

But what your post is completely missing, is that this has a meta-cognitive and meta-ethical dimension — Wayfarer

what truly is — Wayfarer

Interesting take on the reality as a simulation theory. Though thematically The Matrix movies and the, as you mentioned, philosophical notion of reality as an illusion are more or less identical, there's a subtle difference between Plato's allegory of the cave, the Buddhist Maya and The Matrix movies. In the case of the former, the illusion is the bad guy and we're advised to move away from it towards the light so to speak as if to say that knowing true reality will be a panacea for all our misery. In the case of the latter - The Matrix movies - this, what is a Platonic ideal, is turned on its head and the illusion of living normal lives in a simulated world's good, nay, far better than reality as living batteries for AI overlords.


Read f64's response below and you'll get an idea of how people might, after catching a glimpse of the real world chockablock with what most people know as "the hard facts of life" or what my father calls "bitter truths", come scurrying back to their AI masters begging to be plugged back into The Matrix.

The first is Cipher's response. To me it doesn't much matter if my everyday reality is called a simulation or not. Pleasure and pain as I know them, the things I value, 'real' or not, just are what they are. I'm not offended by the idea that it's a simulation, but the question (as always?) is what does that really mean? — f64

Here's what I suppose will be what most people will opt for in descending order of preference:

1. Real + happiness
2. Simulated + happiness
3. Simulated + suffering
4. Real + suffering

If given a full-option offer, people will chose the real over a simulation provided that in both cases the same level of happiness is guaranteed. If the first choice is taken away, people will happily choose a simulated reality [this is what I suspect Cypher/Cipher is going through]. Neo, Morpheus, and the rest of the human underground resistance chose 4 only because their victory is a gateway to 1. Had, option 1 been precluded for whatever reason, almost everyone would go for option 2 and ask to be reconnected to The Matrix.

The second response is more technical. The so-called 'existence' of non-computable numbers seems to be a kind of fictional/conventional existence within a particular domain. What do we mean by 'existence' and 'infinite'? Within the game the players know well enough to keep the game going, but what are we to make of these tokens removed from that semi-controlled original context? — f64

If say x, an non-computable irrational number, exists, I mean, limiting myself to the current domain of discourse, that it has the same ontolological status as, say, the number 2 or the square root of 2 or pi or e. If reality is a simulation, there should be some lines in the code that describe these numbers, these lines being executed to render the number to us in full detail.

The problem is numbers like x are patternless random infinities insofar as their digits matter. There's no pattern so the lines in the simulation code can't be a short, compact formula. The digits are infinite and so, in light of the preceding observation, there has to be infinite lines in the code, each line for each random digit. Thus, randomness and infinity, properties of numbers like x, will need a program of infinite length, length being a function of the number of instruction lines in the program. Being infinite, such a program can't be completed and if it can't be completed, it can't be run. Since numbers like x exist in our world, at least in the mathematical universe, reality can't be a simulation.

Why? You seem to assume that whatever meta-reality "programs" our reality is subject to the same laws and processes that occur in our world. Perhaps our notion of time does not exist there, nor the physical laws of our universe. In that case your argument concerning the irrationals is meaningless. Just a thought. — jgill

Yes, but a code that simulates reality has to be finite. It's not just a spatio-temporal matter, it has to do with the nature of infinite randomness as something that can't be contained within a finite number of steps, and programs will consist of step-by-step rendering of the simulation.

I remember 2 arguments I made not so long ago and here they are for you to peruse through.


Argument 1
1. God is omnipotent
2. If God can't know all things, including the future, without nullifying our free will then God isn't omnipotent
Ergo,
3. God can know all things, including the future, without nullifying our free will [1, 2 Modus Tollens]

Argument 2
1. God is omnipotent
2. If god is omnipotent then god can do anything
3. If god can do anything then god can see the future and still ensure that we have free will
Ergo,
4 God can do anything [1, 2 modus ponens]
Ergo,
5. God can see the future and still ensure that we have free will [3, 4 modus ponens]