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PostPosted: Sun Nov 07, 2004 2:44 am 
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Let's go deeper. We are using many different ideas of truth; I'll give you one that might surprise you. It's from set theory, of all things.

On the face of it, any declarative statement is either true or false, but we are very familiar with such statements which have some degree of truth and falsehood -- or which might completely divorced from being determinably either true or false. Examples of such might be "Emy is very cool" and "Tamayo knows what she is talking about", respectively.

However, there is a class of statements which must be either true or false, and those are the analytic statements. They are the statements built up from atomic statements whose truth or falsity are given by assumption, from the conjunction, disjunction and negation of analytic statements, and from the universal and existential quantification of analytic statements. In short, they're the very boring sentences of logic that no-one save perhaps a computer programmer might want to consider.

Now, everyone must at times make decisions about what to do on the basis of the truth or falsehood of some statement. For example, if I come to a traffic light at an intersection, I will proceed through the intersection if the light is green but I will stop otherwise. I can express this as a function:

action(traffic light colour) ::= if traffic light colour = green then proceed else stop

The if ... then ... else construction itself is itself a function from truth-values, being the stuff after the if, and the choice between the stuff after the then and the stuff after the else. Consider what we might find when we try an if-then-else with constant truth values:

perform ::= if true then sing else dance

The value of "perform" is thus always "sing". Conversely,

president ::= if false then Kerry else Bush

the value of "president" is "Bush".

In a very real, very fundamental sense, truth is the selection of the first of a pair of two things, and falsehood is the selection of the second of the two things. That is all they are. Giving them greater meaning than that is error. Indeed, if it is impossible to judge for any given decision whether or not the truth-value of the predicate on which one is deciding is meaningful, then the decision itself must be adjudged meaningless.

air quality(sunset colour) ::= if sunset colour = pinkish-gold then smoggy else clear

The above decision must be decried "silly" -- but not only because it's not even necessarily a good way to make that decision, but because the test "sunset colour = pinkish-gold" is not falsifiable. What I see as "pinkish-gold" you may describe as "russet", and neither of us will ever be able to tell what precisely it means to be pinkish-gold (or russet, for that matter).

Given this perspective, the search for Truth with a capital T, or for "truth" with quotation marks, is just plain misguided. Stop it.


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PostPosted: Sun Nov 07, 2004 6:58 am 
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Truth: The state of being the case.

Effective: Producing a decided, decisive, or desired effect.

As one can see by simply opening a dictionary, truth does not in fact have anything to do with effectiveness.

I have more to go with this somewhere, but I just woke up.


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PostPosted: Sun Nov 07, 2004 1:54 pm 
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When discussing truth and set logic, one must include Empty Set logic.

Empty Set Logic is a dog of a different animal. Since the statement can't be proven false, it must be true, right? WRONG!

Consider this: Last time I went to Mars, I had a hotdog.

Techinically speaking, you can't disprove that. You can't show me a single instance where I went to Mars and didn't have a hotdog. Therefore, it must be true.

Of course, you can't prove it either. You can't show me a single instance where I went to Mars and had a hotdog, either. Therefore it must be false.

-------

Wait a second... a statement can't be both true and false at the same time, right? At this point, we must look at the assumptions: I went to Mars.

Now we determine that the statement is false, because the assumption is false. But if we can't determine if the assumptions are false, then we have no meaningful method of determining the truth or falsehood of a statement.

And thus all religions that believe in god(s) are neither true nor false, because we can't test the assumptions. We can't even look at two entirely contradictory religions and say "One of them has to be false," because we still can't test the assumptions.

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PostPosted: Sun Nov 07, 2004 2:32 pm 
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And thus all religions that believe in god(s) are neither true nor false, because we can't test the assumptions. We can't even look at two entirely contradictory religions and say "One of them has to be false," because we still can't test the assumptions.

How's that work?

If you have 2 propositions:
if A = X then "A$" is true
if B = X then "B$" is true
given A <> B

if you start from the assumption that EITHER A = X OR B = X
you can prove that EITHER A$ is true OR B$ is true.

I'm pretty sure i didn't totally miss the boat in logic.

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 Post subject: Heh, and Icy's back in his usual form. Flee, or he will destroy us all!! (Or at least our pathetic human ontological contructs)
PostPosted: Sun Nov 07, 2004 2:41 pm 
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Just noticed this:
Tamayo wrote:
I could say, "the gravity equations work as they do because mass concentrations bend the spatial manifold through time", but I am begging the question. I can't tell you why that occurs.

I’m sure you know this (and I’m not being facetious), but to clarify for others on the board: All mass has gravity and bends spacetime, it’s just that only in large concentrations does the effect become pronounced enough to be easily observed. [/Pedant]

To give a concrete example of what I was talking about earlier, let’s say I accept your above Einsteinian description of how gravity works by curving spacetime, and then ask how that works, and so we postulate and discover that it has a messenger particle, so I ask how the graviton works, and some string theorist (or M-theorist, or whatever they’re calling themselves these days) says that it can be mathematically modeled as a closed string that vibrates in such-and-such a manner, etc., etc. We may never get the complete answer, as I said, but we can at least try to gain a deeper and more useful understanding.

Just to reiterate, I never use “why” in connection with scientific questions, and if I did, it would be in a manner synonymous with “how” above.


Emy wrote:
Either Tam hit the wrong button, or she thought it didn't belong in a political debate.

Nonsense! Threads going wildly off-topic is a hallowed Kyhm tradition :P


IcyMonkey wrote:
Just because something works doesn't mean that it's true. The connection between effectiveness and truth is an entirely human-created one.

I thought your position was that they were one and the same?


IcyMonkey wrote:
Honestly, and I know I'm going to get a lot of shit for saying this, the idea of "objective reality" is pretty stupid. What matters in science is that the equations work. Asking what is "really" happening is mistakenly believing science can give us "truth". "Truth" simply does not exist. There are methods of acting or predicting events that are more effective than other methods, but this has nothing to do with "truth".

Tsk. Icy, I thought you had given up trying this Semantic-Fu nonsense on me. You know perfectly well that I have limited definitions of “truth” and “reality”, and use those words essentially as convenient placeholders, because otherwise communication would be pretty much impossible (or at least massively annoying). What you’re talking about is Absolute Truth™, which isn’t something that’s really feasible to even think about pursuing right now, if ever.

If it helps you, anytime I say something like “how the universe works”, mentally replace it with “how the universe seems to work, in accordance with the repeatable aspects of our experiential observations, which cannot ultimately be proven to actually conform to any sort of “external universe”, if indeed such a thing can be said to exist, although as they seem to be all we have to go on at the moment I personally favor trying to explore these experiential constructs to the greatest extent possible, because hey, why not?”

See, if I tried to talk like that all the time, I would be deservingly lynched by the board. So in your words, suck it up, and realize that some of us are willing to use words like “truth” in a limited context while still understanding the fundamental weakness of the concept.


IcyMonkey wrote:
BTW, I'm honjestly a bigger fan of the Copenhagen interpretation -- in the end, it's a less complicated model than Everett-DeWitt.

Must... wait until... post for other thread... is finished. Grar!


Also, as I’ve said before, I don’t really like your designation of “useful” as the ultimate arbiter of what we consider true. I would prefer something like the term “repeatable”, since there are plenty of things we believe to be true that aren’t technically “useful” in any traditional sense of the word.


"David Hume, the greatest skeptic of them all, once remarked that after a gathering of skeptics met to proclaim the veracity of skepticism as a philosophy, all of the members of the gathering nonetheless left by the door rather than the window."

(Although it was actually a character in one of his books that pointed this out, I still found it amusing. This came to mind because I just heard Hume quoted in the surprisingly-entertaining-despite-the-sloppy-programming Enter the Matrix, which I played for the first time the other day)


Tamayo wrote:
Wandering Idiot wrote:
Tamayo wrote:
We have to adjust to Clarke's Law: The universe is not only stranger than we know, but stranger than we can understand.

I always thought Clarke's Law was "any sufficiently advanced technology is indistinguishable from magic"?'

That's Clarke's Second Law.

Wikipedia disagrees with you. Actually, there seems to be some confusion over the origin of that quote. Clarke claims in an interview that he paraphrased it from J.B.S. Haldane, but I’ve also found it attributed to the astrophysicist Sir Arthur Eddington.

Ah well, I like it either way. But I hardly consider pithy quotes to be the ultimate form of Truth™ (shut up, Icy).


Tamayo wrote:
Wandering Idiot wrote:
Anyway, it's an assumption. You can't know for sure that we (or our non-human descendants) will never be able to understand the universe.

Well, yes, actually, I can. The volume of the sum of the human species' knowledge (of all sorts) is currently expanding exponentially with time, and shows no sign of slowing down, ever. There just isn't time for anyone to learn everything there is to know.

And what if we eventually find a way to essentially transcend time, allowing for an infinite amount of knowledge to be collected in a finite amount of “time”? (Just as an example, I’ve seen one rather wild proposed method that involved making use of the energy of the collapsing universe. I’m not sure the math would come out right, but it’s at least interesting) Given what you undoubtedly are aware of regarding the fluidity of the concepts of space and time in General Relativity, and how it changed our previous conceptions of them, are you really willing to make categorical statements based on nothing more than the fact that a rough graph of our current progress/time relationship doesn't have a vertical asymptote, even taking into account the possibility of potential future revolutions of our understanding of the universe just as profound as that of GR? And what’s with this “human species” nonsense when I specifically mentioned non-human descended intelligences? If anything were able to gain a complete understanding of the universe, I seriously doubt it would be anything remotely resembling human. To put it another way, how would you go about trying to explain quantum mechanics to an ant? You can’t, at least not in any way that would be both accurate and comprehensible to it. Similarly, if there were some hypothetical intelligence that is to ours as ours is to an ant, or even more so, don’t you think it might be able to come up with solutions we never could in response to questions we couldn’t even comprehend?

Quite frankly, I don’t think we even know enough at present to even have any semblance of an idea of how much we don’t know. It seems entirely too early to be setting rigid limits on the ultimate extent of our knowledge.

So no, you can’t, not without being speculative to the point of uselessness.


Tamayo wrote:
You want "truth" with the quotes; I can't give it to you. I even think that looking for the kind of truth that comes with quotes is something better left to religion than to philosophy. Metaphysics is (almost) pointless.

See, I’d put it the other way, and say that Truth without the quotes is the domain of religion et al ;)

But of course I normally leave the quotes off, for the same reason I don’t go around talking like I do in my “expanded” phrasing to Icy, above. I do think it’s a good thing to always try and keep in the back of your mind, though. (Icy seems to keep it in the front of his... Although I’m sure he still exits through the primary opening of a room)


Thinman wrote:
Incidentally, I understood that light was a particle who's existence was a function of a wave of probability, not a wavicle. Can someone confirm/deny this?

Probably.


Seriously though, the interpretation swings around a bit. There was some big controversy involving duality last August that I’ve been meaning to look into further, so I wouldn’t want to give a “generally accepted definition” that no longer holds. But last time I checked, I believe it was more common to think of photons as “particles” that exhibit wave-like properties, if only for the sake of convenience. I haven’t heard the term “wavicle” used in a while.


Emy wrote:
Off topic: WI, you were right, a tesseract is just another name for a 4 dimensional hypercube. Also, go read And he build a crooked house by (who else) Heinlein.

Wow, that’s wayyy off topic :) (That reminds me, I never made my last reply in that thread)

Very well, you’re not the first person to recommend it to me, so I shall acquiesce to your massive Heinlein-whoredom and go read the book already. (Then I’ll retaliate by finally making a post in your book-recommendation thread. [Overabundance of Hard Sci-fi Recommendation Power, GO!!] )

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PostPosted: Sun Nov 07, 2004 3:12 pm 
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WI wrote:
I specifically mentioned non-human descended intelligences?

Actually, no.
WI wrote:
You can't know for sure that we (or our non-human descendants) will never be able to understand the universe.

What you mentioned were non-human intelligences derived from human beings, otherwise, they wouldn't be our descendants (unless you know something about our fellow forumites that i don't. . .). I interpretted your meaning to be "beings descended from us who have evolved or mutated beyond (or at least outside of) the classification of humanity."

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PostPosted: Sun Nov 07, 2004 4:36 pm 
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WI: I realize I'm pretty much beating a dead horse in terms of this "truth does not exist" thing, but you have to keep in mind that our newer boardies still seem to believe in silly ideas like "truth" and "objective reality" as something more than convenient constructs. :)

And yes, my ramblings were totally off topic, but haven't you silly n00bs seen any old skool Debate Club threads? That's like a hallowed tradition here. I remember back in the day, when every single debate thread morphed into a discussion of metaphysics. And no one complained! And every time someone wanted to make a new topic, we couldn't just hit a button! WE HAD TO MAKE THAT TOPIC FROM SCRATCH OUT OF BEARSKIN AND BEAVER FAT! We had to kill those critters with our BARE HANDS too! You young people today have it too easy!

Now where did I leave my Ensure?

*icy hobbles off with his walker*

Oh, and if any of you kids still think truth exists and want to debate it, I've revived this thread for that purpose, so read my responses to your points and post any thoughts you have about what I've said. AND GET ME SOME PUDDING WHILE YOU'RE AT IT! It builds character.


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PostPosted: Sun Nov 07, 2004 4:59 pm 
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You reallize the "n00bs" you're talking about are also no fewer than 5 years older than you, right?

I don't think anyone said that truth or objective reality are anything more than convenient concepts. What we have said, againa and again, is that you have to accept a common defintion of these convenient concepts in order to work with this debate from where it started.

You jumped into the middle of a discussion to question the basic assumptions everyone else had accepted. While this can prove scientifically useful in some cases, it was merely a distraction here. Particularly since you offered neither better terms, nor beter basic assumptions. In essence, you were trolling, though in a slightly less offensive and more intellectual manner than the average troll.

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PostPosted: Sun Nov 07, 2004 5:28 pm 
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Emy wrote:
You reallize the "n00bs" you're talking about are also no fewer than 5 years older than you, right?


<3

Quote:
I don't think anyone said that truth or objective reality are anything more than convenient concepts. What we have said, againa and again, is that you have to accept a common defintion of these convenient concepts in order to work with this debate from where it started.

You jumped into the middle of a discussion to question the basic assumptions everyone else had accepted. While this can prove scientifically useful in some cases, it was merely a distraction here. Particularly since you offered neither better terms, nor beter basic assumptions. In essence, you were trolling, though in a slightly less offensive and more intellectual manner than the average troll.


Ouch. If I was trolling, I apologize. I think I might have had some misconceptions regarding the nature of this discussion. I had essentially assumed that this debate was about the role of science vs. metaphysics/philosophy in explaining different aspects of the universe. I had stopped reading the thread that this thread branched off of, and Tamayo's first post seemed to imply (to me) that what I was talking about had at least something to do with the topic up for discussion.

Admittedly, the nature of truth is one of my favorite topics to rant about, and I was hoping to provoke, with my posts, some old-skool philosophical discussion, what with the return of WI and all. However, if indeed this was an inappropriate thread to try that in, I'm sorry for distracting you all from the topic at hand.

Also, looking back upon my posts to this thread, I realize that I was a bit snarky with some of my replies in a way that could be misinterpreted as asshole-ish. This was simply my (apparently failed) attempt to inject a little bit of levity into the discussion in (once again) an attempt to revive old-skool pedantic-absurdist-style debate-fu.

So, er... Carry on!


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PostPosted: Sun Nov 07, 2004 6:47 pm 
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I say, what is "true" is what can be repeatably proven effective and conducive to the continued sanity of the particular human being in question. That being said, there seems to be some sort of common ground among men (in the Asimovian sense, Tamayo) on what is actualyl happening. We generally all consider the brake to be to the left of the gas pedal, that sort of thing.

There. We have general, pragmatic truth(lowercase). What science, and this thread, seems to aim for is specific, experimental Truth(uppercase). IMHO, science is little more than a religion based on logic.

And logic is one of the concepts I hate the most in life. See this post for a more detailed explanation of why. (Static concept vs. dynamic existence.)

Not that I dislike science. I love science. I just get sick of people thinking science is somehow better than, say Christianity or Islam, considering that adherents of all three in their least sensible forms (pseudoscience and fundamentalism) have advocated the genocide of other branches of humanity at one point in time.

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PostPosted: Sun Nov 07, 2004 8:44 pm 
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Icy, I think that it's been repeatedly proven that you aren't, in fact, the smartest one here. No need to be a pretentious ass and try to compensate for it.


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 Post subject: This may be my shortest Debate Club post *ever*...
PostPosted: Mon Nov 08, 2004 7:57 pm 
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Emy-chan wrote:
WI wrote:
[...] when I specifically mentioned non-human descended intelligences?

Actually, no.
WI wrote:
You can't know for sure that we (or our non-human descendants) will never be able to understand the universe.

What you mentioned were non-human intelligences derived from human beings, otherwise, they wouldn't be our descendants (unless you know something about our fellow forumites that I don't. . .). I interpreted your meaning to be "beings descended from us who have evolved or mutated beyond (or at least outside of) the classification of humanity."

Ah, I see. No, I was using the futurist’s definition of “descendance” which includes any intelligence created through artificial means (a sentient AI, for instance), as well as any subsequent intelligences created by that intelligence, etc., not just actual genetic descendants. Sorry, I probably should have been more clear about that :)

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PostPosted: Tue Nov 09, 2004 8:05 am 
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Emy wrote:
You reallize the "n00bs" you're talking about are also no fewer than 5 years older than you, right?


Age is not a good measure of inteligence, knowledge or seniority, but icy, please keep on topic... not that I really have any real understanding of exactly what the topic is. Also, butt out Baron, your post contributed nothing to this discussion.

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PostPosted: Tue Nov 09, 2004 11:27 am 
Icy wrote:
Long-winded rant about his firm disbelief in truth


I find it rather amusing that a person can be so adament about something being wrong, yet create it at the same time.

Follow with me if you will:

- Icy creates theory that there is no such thing as the truth.
- Icy proceeds to attempt to prove this theory.
- Icy succeeds in proving this theory, at least to himself, thus creating....dun dun dun...a new truth, or since that word seems to be taboo in your eyes, a new way that things in reality function and exist. (Unless of course you weren't trying to propaganda us who use the word truth as a definition of function with rhetoric about how reality really functions. )

Now, of course I have to take a side in this debate and I'll side with WI. We accept what is observed within our universe to be the truth, but rather it's absolute or not is beyond our grasp until a time when travel between realities is possible. So until we discover a way to uncover the absolute truth, we have to accept that which science shows us through experimentation and observation as being universal law, aka truth.


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 Post subject: As I understand things . . .
PostPosted: Tue Nov 09, 2004 4:11 pm 
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Kakashi wrote:
Icy wrote:
Long-winded rant about his firm disbelief in truth


I find it rather amusing that a person can be so adament about something being wrong, yet create it at the same time.

Follow with me if you will:

- Icy creates theory that there is no such thing as the truth.
- Icy proceeds to attempt to prove this theory.
- Icy succeeds in proving this theory, at least to himself, thus creating....dun dun dun...a new truth, or since that word seems to be taboo in your eyes, a new way that things in reality function and exist. (Unless of course you weren't trying to propaganda us who use the word truth as a definition of function with rhetoric about how reality really functions. )


You misunderstand Icy, Kakashi - what he's arguing about is that one cannot use the difference between objective and subjective reality to determine which is TRUER because neither one is truer than the other - they're the same thing.

And I question your statement on grounds that you define "truth" by "reality," and one cannot define a word by its synonym.

Simple, general, pragmatic "truth" was never in question - what was in question was the conception of WHAT, precisely, such "truth" consisted of.

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ptlis wrote:
Emy wrote:
You reallize the "n00bs" you're talking about are also no fewer than 5 years older than you, right?


Age is not a good measure of inteligence, knowledge or seniority, but icy, please keep on topic... not that I really have any real understanding of exactly what the topic is. Also, butt out Baron, your post contributed nothing to this discussion.

ptlis
With the age comment i was responding to character of his post:
Quote:
[...]You young people today have it too easy![...]
I thought it was obvious, directly following his facetious post, that my comment was also facetious. Apparently not.

Ghost wrote:
You misunderstand Icy, Kakashi - what he's arguing about is that one cannot use the difference between objective and subjective reality to determine which is TRUER because neither one is truer than the other - they're the same thing.
I must have missed something then, because he specifically stated that neither objective nor subjective reality exists.
Ghost wrote:
Simple, general, pragmatic "truth" was never in question - what was in question was the conception of WHAT, precisely, such "truth" consisted of.
Actually, the original topic, before Icy unleashed his theory on metaphysics into the thread, was the question of what the limits of science might be, and possibly a scientific (as opposed to intelectual) discussion of whether we can answer 'why' questions, or merely 'how' questions through scientific processes.

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Note to self: When WI, Tamayo, and Icy talk together, stop listening for a while, you'll feel better.

Yes, I am aware this does not contribute meaningfully, I still refuse to do that. I'm just saying, is all...


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Responses, tipsy depressed Tamayo style.

Herbal Enema wrote:
Consider this: Last time I went to Mars, I had a hotdog.


Yes, that's true. It's something everyone here is forgetting: that, presuming a contradiction, anything at all can be deduced. Here's another one: six equals nine, therefore I am the Queen of England.

Six equals nine, therefore two equals three, therefore one equals two.

The Queen and I are two, therefore the Queen and I are one.

Contradictions = bad.

IcyMonkey wrote:
"knowledge of the universe" is ultimately fictional


That's interesting. I'll comment a few quotes from now ....

Quote:
the relationship between representation and represented is tenuous at best


No, it is not. A model of a computer is an abstract computer. A language in which it is possible to make a formal description of the most general concept of a computer -- even that is a computer. You may say to me, "I've never played Counterstrike on the English language", but there's nothing stopping you from doing so, if you want to wait several years between screen frames as some poor shmuck calculates out each picture by hand. What, you say? There's a person involved? Yes, just as there's a power source for your home PC. Without the dinosaurs (okay, okay, ancient flora) who died to make your local coal power plant go, you wouldn't play Counterstrike on your PC either.

There exist software emulators with which you on your Pentium IV can run ancient Atari 2600 games better than the 2600 ever could. You may say to me, "a person who uses the English language to make a formal description of a computer is like my Pentium IV PC running an Atari 2600 emulator in order to play a 2600 game." You're exactly right. It is even the case that your computer can't run the game unless you have the 2600 emulator program running also.

An emulator program, by the way, is a formal description of a computer -- and that is all it is, no more and no less.

Quote:
We define 2 as "1+1", and we define 4 as "1+1+1+1". Thus, "2+2=4" is "(1+1)+(1+1)=1+1+1+1 ---> 1+1+1+1 = 1+1+1+1", which is essentially the same as saying "A is A".


You still haven't addressed the truth, validity or what-not of analytic statements. I had a whole clever rant about that subject going. ;-) As a specialist in a mathematical discipline, I am emotionally very attached to analytic statements, so much so that anyone who says that they are somehow assailable had better have his or her ducks in an entire phalanx, let alone a row.

Quote:
If anyone can actually tell me why we should assume reality is as simple as possible, and is governed by a single rule-set, then please do so.


Okay. Firstly, let us presume that two sets of axioms A and B are both sufficient for constructing models for describing and predicting the observable universe, and that the models constructed by A and B are both entirely successful for those purposes. That is, if the model built from A correctly describes an event X or accurately predicts another event Y, then the model built from B will describe X and predict Y in the same way for any possible X or Y.

Now, I contend that, unless either A or B is inconsistent, the union of A and B is not inconsistent. That is, given all the axioms of A and of B together, I cannot derive the statement "P and not P", because if that were the case, then there would be some event Z that models built on A and on B would describe differently. (Okay, I'm hand-waving, here. I'm less tipsy than I was, but I had more wine that I'm used to, and I'm tired. Excuses, excuses.)

So, if there is some subset C of the intersection of the axiom sets A and B from which a model can be built which describes and predicts the observable universe in the same way that both A and B do, then those axioms in A and B which are not also in C are irrelevant. It is rather similar to the statement "The circumflex accent over a vowel denotes a consonant, and usually the consonant `s', that used to precede that vowel but has in modern writing been elided" in the context of English grammar. Yes, it's true -- but it's true for French. In English, we do not use circumflex accents at all, so the statement is still true, but only vacuously. It's true in in a similar way that Herbal ate hot dogs on Mars.

Wandering Idiot wrote:
And what if we eventually find a way to essentially transcend time, allowing for an infinite amount of knowledge to be collected in a finite amount of “time”? (Just as an example, I’ve seen one rather wild proposed method that involved making use of the energy of the collapsing universe. I’m not sure the math would come out right, but it’s at least interesting) Given what you undoubtedly are aware of regarding the fluidity of the concepts of space and time in General Relativity, and how it changed our previous conceptions of them, are you really willing to make categorical statements based on nothing more than the fact that a rough graph of our current progress/time relationship doesn't have a vertical asymptote, even taking into account the possibility of potential future revolutions of our understanding of the universe just as profound as that of GR?


Firstly, I must confess, I am an adherent of the strong AI tenet: that brains and the minds they host are computers. Certainly, any artificial intelligence (as you suggest) must be a computer. If you wish to disagree with me on that, please find another topic; this is not the topic where that proposition ought to be discussed.

Then, based on that idea, therefore, I tell you: only the smallest of the infinite sets, being those sets with size aleph-zero, are computable. Any larger set, and especially operations on any larger sets, can only be approximated by a computer. In that nearly all physical quantities of interest can only be measured by complex numbers, and given my postulate that thinking beings are Turing-complete but no more than that (as no more than that is necessary or perhaps even possible), perfect knowledge of the universe is actually impossible. Don't even suggest that approximate knowledge is good enough. If you are a physicist, you know enough chaos theory to be annoyed.

Ghost wrote:
And logic is one of the concepts I hate the most in life.


I followed the link. I went and read your rant. You might want to read beyond first-year logic; there are, in fact, several very-well-defined logical constructions to deal with dynamic systems. An author you might wish to look up is Brian Chellas.

Logic is a game with symbols, rather like (say) a crossword puzzle. It would be silly to say you hate the concept of crossword puzzles. It is even sillier to say you hate logic.


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PostPosted: Thu Nov 11, 2004 4:18 pm 
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I less than three you so much Tam.

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 Post subject: I’m not even going to bring up Cantor’s Absolute Infinite*, because I’ve only seen it in passing and don’t understand it fully. (*Or am I?)
PostPosted: Fri Nov 12, 2004 3:09 am 
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Tamayo wrote:
Responses, tipsy depressed Tamayo style.

Aw, I like drunken depressed Tamayo. Especially if she’s always going to force me to go refresh my understanding of set theory :)


I’ve recreated parts of the whole conversation-thread here for conveniencnessism. If anyone wants the full thing, go read the previous posts, you lazy bastard :
Tamayo wrote:
Wandering Idiot wrote:
Tamayo wrote:
Wandering Idiot wrote:
Anyway, it's an assumption. You can't know for sure that we (or our non-human descendants) will never be able to understand the universe.

Well, yes, actually, I can. The volume of the sum of the human species' knowledge (of all sorts) is currently expanding exponentially with time, and shows no sign of slowing down, ever. There just isn't time for anyone to learn everything there is to know.

And what if we eventually find a way to essentially transcend time, allowing for an infinite amount of knowledge to be collected in a finite amount of “time”? [...]

Firstly, I must confess, I am an adherent of the strong AI tenet: that brains and the minds they host are computers.

By “computers” I assume you mean Turing machines. Fair enough. Penrose might argue the point, but I’ve never found his arguments particularly convincing. And of course I’m a pretty staunch cognitive reductionist (not as much as I would be if we actually had a working neurological model of cognition, but about as sure as I am of anything that isn’t provable as yet), until I see any good evidence otherwise.

Besides, we unromantic rational types have to stick together against the Evil Fuzzy-Minded Soulists™ ;) They’re everywhere... <.< >.> Aha! I see you over there, quoting Descartes! *Flings his copy of GEB at EF-MS™. If nothing else, the force of impact alone should slow him down.*


Tamayo wrote:
Then, based on that idea, therefore, I tell you: only the smallest of the infinite sets, being those sets with size aleph-zero, are computable. Any larger set, and especially operations on any larger sets, can only be approximated by a computer. In that nearly all physical quantities of interest can only be measured by complex numbers, and given my postulate that thinking beings are Turing-complete but no more than that (as no more than that is necessary or perhaps even possible), perfect knowledge of the universe is actually impossible.

EDIT2: [A brief note about aleph numbers, by WI: Although it might seem like all infinities are equal, there are actually some that are "larger" than others. The size of a set of numbers is called its cardinality. The cardinality of infinite sets is designated by an aleph number. Common examples of sets with cardinality aleph-0, the "smallest" type of infinity, would be the integers and the counting numbers (i.e. naturals). Examples of aleph-1 sets, the next largest, are the reals (which include all decimals, not just whole numbers), and the complex numbers (reals plus imaginary components). If you're still confused, you could think of it this way- if you pick an arbitrary number in an infinite aleph-0 set (the integers, for instance), you can name a definite next number in the sequence in either direction, which you can't with a number in an aleph-1 set, as there are an infinite amount of potential "next numbers". Alternately, you could note that there are only a finite amount of numbers between any two members of an aleph-0 set, but an infinite amount between any two members of an aleph-1 set. Infinite sets of aleph-1 or higher are generally considered uncomputable, even by a Turing machine that runs for an infinite amount of time (and this is something Turing himself said, which is where I saw it before). If you have any other questions, direct them towards Tamayo, as I'm seriously near the edges of my mathematical knowledge here.

Later Note: The above is partially incorrect, as it isn't provable within the current mathmatical framework that the reals are actually aleph-1. (I don't remember set theory as well as I thought, apparently ^^) See Tamayo's post on the next page for more. I'll leave this note up as is since she responded to some specific things I said (I should note that the central point of the below remains unchanged)
]

<3 @ Tipsy Tamayo. I had to think about this for a while.

I’m pretty sure I’ve seen that before, except I think it used the reals as an example, not the complex numbers. But you’re right- the latter are used in, off the top of my head, electrical engineering, general relativity, and quantum mechanics, and probably various other things. The question is, even if we need complex numbers (or reals, for that matter) to understand the universe, do we really need the explicit infinite set of them, if the universe turns out to be finite and completely quantized? I guess you could argue that the explicit set is, conceptually, a part of the universe, but you could also argue that it’s a Platonic ideal that doesn’t actually exist (for the reasons you pointed out).

Now that being said, I'm actually inclined to agree with you that we‘ll probably never be able to understand the universe completely. If you look at the post that I linked in response to Icy earlier, I say pretty much the same thing (albeit in less technical terms). After all, even assuming the universe is completely finite and quantized, it would still require infinite computing power to get around the Gödel-esque limitations of self-consciousness, without which any being or computational device would fall short of complete understanding. In other words, the universe would have to be “bigger” (in the sense of computational potential) than itself, which seems like an obvious contradiction. And that’s without even mentioning the inherent quantum uncertainty of the universe, which even the Everett interpretation doesn’t get you around from a practical point of view (although I suppose one could argue for having a complete probabilistic understanding of the universe rather than a determinist one, but that just runs you up against the Gödel problem again, even more forcefully). Of course, those are both subject to circumvention by speculative hypercomputing methods, like the example I gave earlier, or the traditional one of a Turing machine that somehow runs for an infinite amount of time, which your explanation is not.


To me, gaining a complete understanding of the universe is a bit like disproving the existence of God (in fact, a case could be made for them being one and the same). It’s something I think there’s a good chance we’ll never be able to do, but I’m open to the possibility of some manner of transcendent post-human intelligence being able to, although it would certainly require fundamental rewriting of our current understanding of the universe.

My problem with your post was that you treated it as an absolute certainty rather than an informed guess, which I still don't think we know nearly enough to say at present.


Quote:
If you are a physicist, you know enough chaos theory to be annoyed.

Just for the record*, I’m no physicist, I just find the subject interesting. (Although if I go back to finish college, I probably will double-major in Physics, since CS alone didn’t hold my interest as well as I would have hoped :P [But yet I’d rather not end up on the street with a sign reading “will calculate quantum probability distributions for food” or something, hence the CS.] )

* What record, you ask? You know, the one the NSA keeps of all online communications. <.< >.> [/tinfoil hat]


EDIT: I just realized this post could use a few explanatory notes for some of the other posters about aleph numbers and whatnot (I had to go look those up myself to make sure I was remembering them right). But since it’s now... dear Eris, 4:15 AM, I’ll have to leave it for the morning. Luckily for me I’m off Fridays. [Later: Added, obviously :) ]

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Belief is the death of intelligence. As soon as one believes a doctrine of any sort, or assumes certitude, one stops thinking about that aspect of existence.
- Robert Anton Wilson


Last edited by Wandering Idiot on Sun Nov 28, 2004 8:23 pm, edited 4 times in total.

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