Empty Set doesn't exist

If you cant sense it, then it doesnt exist.

You cant see emptiness, therefore emptiness doesnt exist.

>>159
fuck off, jewish girl

>>161 you must think you're so kodak right now ^^

>>162
fuck off, jewish girl

***161

 >>162 hory shit it's a brain teaser that one =)

>>163 no stop i didn't get the first one yet =D

>>etc etc ^^

>>164
fuck off, jewish girl

***165 trying desperately to cover

---that it Is kodak ^^

Oh it's ice kodak, that's how kodak it is....

***165 "argh it burns it's so kodak" ^^

>>156
One way to look at infinity is just to look at a non-terminating process. ``God'' I could give one definition which fits in a very small program (such as Schmidhuber's conception of the Universal Dovetailer, which is a trivial scheduler + interpreter (such as an universal turing machine)), but unfortunately for you the program is also non-terminating and increases in its (always unbounded but finite) size each internal time step, so you obviously won't like it as you don't like anything which grows in size unboundedly, even if finite at each step (actually our universe seems to do just that as well). I could also give another definition which is non-computational, but mathematically well-understood, but yet still partially accessible to senses, but I'm not going to go into that definition for that discussion could stretch for a long time. I cannot give you any popular religions ``God'''s implementation for they either have impossible properties (showing they are false concepts that can never exist in any possible world and still retain all the claimed properties) or they are far too complex (surely we have yet to digitize a human mind or create an artificial general intelligence, you can't expect me to be able to do that for now). So stop asking someone to implement something on which nobody can even agree on a definition.
>>157
Which is what the rest of the post does. It just shows that there was a specification showing a programmer's expectations, there was an implementation that didn't do exactly what the programmer wanted, but still mostly fit the specification, and there was a reverse engineer who could create a specification which describes exactly what the program does, as opposed to what the programmer intended the program to do.

*maps arbitrary to kodak... kodak enkodak kodak ^^
**kodak that kodaktail kodak, kodak probably so conkodaked right kodak

kookokkoookoko ^^

So stop asking someone to implement something on which nobody can even agree on a definition.

That's no excuse! Hell, computer programmer's can agree on '=', yet they still implement it!

>>170
One way to look at infinity is just to look at a non-terminating process.
Don't know of such process. Any known process either terminates or repeats itself.

there was a specification showing a programmer's expectations, there was an implementation that didn't do exactly what the programmer wanted
What if specification had error, and implementation was right? It is common to have outdate comments or mismatched interfaces.

>>172
That's no excuse! Hell, computer programmer's can agree on '=', yet they still implement it!
They first implement it, then trying to agree, creating some junk theories about it in the process. Haskell would be a good example of language based on junk theory.

>>173
And Haskell is the cure.

>>173
Don't know of such process. Any known process either terminates or repeats itself.
Only because you're looking at finite state machines which could technically repeat themselves given enough time (if sometimes much longer than the expected lifetime of the universe).
In my example, the UD is simple, imagine you have a scheduler which each time step creates a new process, the initial program that it runs is defined by index 0, the next process will be the previous number + 1, and so on. Thus at t=0, you have process 0 running, t=1, you have process 0 running for 1 time step, and process 1 being started, at t=2, you have process 0 running for 2 time steps, process 1 running for 1 time step, and process 2 just started, and so on. If you can't think of abstract machines which have unbounded memory (which can grow as it sees fit), just consider that your machine is constantly upgraded with more and more memory. You will obviously say that the machine "terminates" along with the universe, but then you have to define the universe and other things which will require such unbounded concepts which you're trying so hard to avoid.
What if specification had error, and implementation was right? It is common to have outdate comments or mismatched interfaces.
It's possible. It just shows that there was a standard that promises something and a program written by the standard writter which wasn't quite compliant to that standard, even though 'it worked'.

Oh, and when I said "process x", where x is some index value, that x is to be interpreted as the program's code in some Turing-equivalent language/encoding (even if most programs will be invalid, all valid programs will run in this "infinite"/non-halting run).

>>173
A continous measurement of time doesn't repeat itself.

>>176
sometimes much longer than the expected lifetime of the universe
How do you know the "lifetime of the universe" wont itself repeat, when the universe exhausts all uniq state?

>>178
how do you know the time wont make a loop, when the universe exhausts all uniq state?

>>179
How do you know the "lifetime of the universe" wont itself repeat, when the universe exhausts all uniq state?
Sure it could. That could be true if the universe's structure happens to be a bounded/finite one. Evidence for this is lacking, but it's not an impossibility - there is more evidence for the unbounded (but still locally finite) view.
Here's something for you, the subjective idealist to wonder about: It may be that the notion of time and even the notion physical law is directly connected (I'm not going to use the term 'caused', because it's not that simple) to the nature of consciousness. For consciousness (or forming memories or having experiences), you require an arrow of time. For computation, you require an arrow of time. Without an arrow of time, the "universe" is just a static mathematical or computational structure. What about physical sturctures? You can only observe those that fit your particular inner mental/'physical' structure: you will never observe an universe where (the arrow of) time doesn't exist, as tht is required for your subjective time to exist, you will never observe an universe where various laws of entropy don't apply (although this can be relaxed greatly), and if computationalism is to be taken seriously, you will never observe an universe where some form of quantum indeterminism doesn't apply.

>>180
you will never observe...
Why would you care about the things you'll never observe? They are just your fantasy anyway. Now I'm sure you're a potential schizo, who sees things.

I'm a 16 y/o male and for years I've been paranoid that someones always watching me and that they'll try to kill me. I have tried keeping the windows in my room shut. I check the closet every night. I even check under my bed at night. I sleep with the bedroom door shut and locked and I find it hard if not impossible to sleep at other peoples houses. I also can't sleep in the same room as anyone or i can't sleep at all. Then recently I've started to hear a voice which reminds me of one of those horror movies like saw telling me to hurt myself and other people. Its cause me to get into physical altercations with my mother, father, and older brother. It has also caused me to call Children and Youth Services and report my parents for neglect and abuse. It's caused me to lie to the people I care about and hurt them emotionally. I'm starting to fear that if it keeps telling me to do it I'll hurt or even possible kill myself or someone I care about. I have even had some strange hallucinations that I wasn't really worried about because I thought they were just day dreams but they've started to turn violent and I'm getting worried. I don't drink, smoke, do any drugs, or Self Injure and there isn't any other possible cause that i can think of. So if there is any sort of advice you have I really would like to know before I go marching into a doctors and claim I have Schizophrenia.

>>181
Why would you care about the things you'll never observe? They are just your fantasy anyway.
Why does a scientist care about what his theory predicts and what it doesn't predict?
Now I'm sure you're a potential schizo, who sees things.
My observations so far have been of a most stable lawful physical world.

>>183

Why does a scientist care about what his theory predicts and what it doesn't predict?
Why does a scientist care why his theory doesn't predict the existence of God?

My observations so far have been of a most stable lawful physical world.
Yep! You observe "evidence for the unbounded view", but fail to present such evidence to the humble goyim.

Why does a scientist care why his theory doesn't predict the existence of God?
Limitative results are just as important, if not more important, science usually can show theories wrong, but it cannot show them right - at best they are just confirmed by experiment. If you can show that certain things are impossible, that is progress forward.
Yep! You observe "evidence for the unbounded view", but fail to present such evidence to the humble goyim.
Depends on which unbounded view you mean - there are quite a few. In cosmology you have the concept of "eternal inflation". In some multiverse theories, you almost always end up with some unbounded parameters. In multiverse theories which even vary the laws themselves, you again end up with the infinity of structures or possible computations - this infinity is almost always at the meta-level, not at the local level which you experience, however this is important, if the "everything" was limited in entities, it would be a (mathematical) miracle (highly improbable event) if anything like you or me would ever have any chance of existing at all. In the computational theory of mind, one yet again ends up with this globally unbounded, but locally finite ontology which predicts that the shape of physical law will always have certain properties (mostly confirmed by quantum mechanics so far). Terms to google for each case:
1) "eternal inflation" ( http://arxiv.org/abs/astro-ph/0101507 )
2) "Ultimate Ensemble" ( http://arxiv.org/abs/0704.0646 http://arxiv.org/abs/1008.1066 http://arxiv.org/abs/gr-qc/9704009 ), "Algorithmic theories of everything" ( http://arxiv.org/abs/quant-ph/0011122 ), "Universal Dovetailer Argument"/"Movie Graph Argument" ( http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html http://iridia.ulb.ac.be/~marchal/publications/CC&Q.pdf ) or if you want an easier to grasp understanding of this concept, read the novel "Permutation City", you might even like it as it takes a partially ultrafinitist view near the end.

Note that I intentionally avoided the cases where scientists put real numbers in their physical theories - you would reject such theories out of hand, however the problem is that in almost all cases where you take reality seriously, you end up with at least the countable infinity - this is not easily avoidable, even if it can be locally avoided, just never globally.

However, don't dispair - if you do show arithmetic inconsistent, everyone will be forced to completly rethink their theories, but for now, almost no-one doubts that arithmetic or computation leads to inconsistencies. If I ever saw an inconsistency proof of arithmetic, I would be shocked and it would shake my world-view, but then I would read it and understand it, and if it was correct, I would accept it and continue to move on from there as now our knowledge is more complete and we can form better theories. However, for now, I'll continue my religious bet in the consistency of arithmetic (the same as almost any scientist or mathematician) and reason from there.

>>185
Limitative results are just as important, if not more important, science usually can show theories wrong,
So, for an average scientist God is important? Nice. That explains why I hate modern science, which is full of hypocrisy.

In cosmology you have the concept...
In some multiverse theories...
You mean some religious cosmologists made up a "concept", then built crazy theories on top of it, and now we have to accept it as an evidence?

in almost all cases where you take reality seriously
"Reality" is just what I see.

it would be a (mathematical) miracle (highly improbable event) if anything like you or me would ever have any chance of existing at all.
What is "probability"? What is a "chance"? Please, care to avoid buzzwords. I maybe a goy, but such blatant bullshit is offensive even for me.

you end up with at least the countable infinity
"Cantor's obsession with mathematical infinity and God's transcendence eventually landed him in an insane asylum."

http://arxiv.org
A site full of crazy theories and unconfirmed data! What could be better?...

read the novel "Permutation City"
A shiny sci-fi novel! Even better than arxiv.org! Thank you, honorable rabbi, I'll study it like Torah.

So, for an average scientist God is important? Nice. That explains why I hate modern science, which is full of hypocrisy.
What? What does this have to do with God, unless you're afraid that some kid will be able to show your concept of deity impossible because it features some trivial contradictions.
You don't seem to understand what science is - it's a methodology which allows one to define, test, falsify theories.
"Reality" is just what I see.
That's a limited point of view. For me, reality is what I obtain by deduction and induction through senses and thought. If my inductive beliefs tell me that a star exists some million light years from home, I don't have a problem assuming that, but if you only went by your senses, it would just be a tiny blip of light and nothing more.
"Cantor's obsession with mathematical infinity and God's transcendence eventually landed him in an insane asylum."
Just understand someone's work by itself and judge it with your own mind. You cannot take others beliefs as your own - that's dumb - you have to understand what they are and you can only take them once you understood them. Cantor did pioneer an important mathematical technique - diagonalization and whatever his personal problems and beliefs is irrelevant to the validity of his mathematical work, even if motivated by non-mathematical goals.
A site full of crazy theories and unconfirmed data! What could be better?...
Nobody is going to chew the food for you. Believing in science because by authoritarian argument is wrong, instead you should read and understand something by yourself and then judge if it's true or not. However, if you do insist on the authoritarian argument, it's not like the people that wrote that work are unknown and you cannot check their credentials and reputations: almost all are professors and have Ph. d's., and more than half are even well-known within their fields.
A shiny sci-fi novel! Even better than arxiv.org! Thank you, honorable rabbi, I'll study it like Torah.
I figured that if you're not educated enough to understand some of those papers (even though some are not hard at all to understand), a novel from a good hard sci-fi author on the subject would at least make it easier for you to understand certain concepts. The author is so serious about his work being as accurate as possible that he even wrote a manual on general realitivy and quantum mechanics to supplement some of his novels. He's also known to have written some Loop Quantum Gravity papers - this isn't your average fiction writer, but an actual scientist with good physics and mathematics background.
And I will repeat it again - even if some author was some bum living under a bridge, that would not diminish the validity or invalidity of some work - the work must always be judged on its own merit.

>>186
What is "probability"? What is a "chance"? Please, care to avoid buzzwords. I maybe a goy, but such blatant bullshit is offensive even for me.
Consider that you have a particular memory limit for everything that can possibly exist. No number greater than that and so on.
Now consider all the possible Turing-equivalent programs that define some laws of physics, up to your favorite upper bound. Given that you claimed some such limit, you can now decide very exactly which of them will result in our own laws of physics. Some such program may represent the laws of physics of our world, but you see, there's a memory limit, so it will only run a finite number of steps (or will loop). There is also another problem: the first-person indeterimism and the quantum laws that would follow would become severly limited (given the UDA view) and would be likely to contradict our current observations (of course, you try to rise the limit just high enough to prevent that, but you see, you will have to keep rising the limit as time progresses to keep the laws agreeing - you end up with the unbounded view that way). There is of course a different view which requires one to eliminate the notion of senses or consciousness as well as claim that quantum randomness is the result of PRNGs, not random oracles (which result naturally within the UDA view, or in the more restricted MWI view), that could salvage your theory partially, but wait, you're a subjective idealist, thus you will reject any theory that rejects the mind's existence, meaning that you are stuck in a tight corner - either ultrafinitism has to give or the subjective idealism has to give, at least if you don't want to keep increasing the bound endlessly just to satify all observations - there is even an experiment in the future which we could perform to show that such a bound is non-sense, but it's a bit too early to talk about that and I'm not going to bother talking about it either as you refused to even read anything I referenced.

The notion of probability is well-defined in the ultrafinist case, even much more well-defined than in the classical finitist case. Technically you could even compute it if you had... just more resources than your current upper bound (but still finite), ahahaha.

>>187
What? What does this have to do with God
Why does a scientist care why his theory doesn't predict the existence of God?

reality is what I obtain by deduction and induction through senses and thought.
How did you obtain the "deduction" and "induction" themself?

Cantor did pioneer an important mathematical technique - diagonalization
"important" for whom? I dont see its importance or relevance to the observable reality.

it's not like the people that wrote that work are unknown and you cannot check their credentials and reputations: almost all are professors and have Ph. d's., and more than half are even well-known within their fields.
Sorry, but Phd wont confirm your theory. Phd is just a title, you can buy if you have enough money and/or time.

I figured that if you're not educated enough to understand some of those papers (even though some are not hard at all to understand), a novel from a good hard sci-fi author on the subject would at least make it easier for you to understand certain concepts.
There is a reason I'm not educated - I cant enter education due to disagreement with concepts of Set Theory and modern mathematics. A sci-fi novel wont fix that.

The author is so serious about his work being as accurate as possible that he even wrote a manual on general realitivy and quantum mechanics
What did you say?! The novelist is so serious, he even wrote comments on other sci-fi novels to supplement his Electric Boogaloo? Sounds like a typical case of copyright infringement. Einstein's family will sue him for stealing fantasy worlds and characters. It's like when you take Lord of The Rings and make sequel, without having license from the owner.

>>188
Now consider all the possible Turing-equivalent programs that define some laws of physics, up to your favorite upper bound.
Sorry, you're using unrestricted quantifier "all" again.

Some such program may represent the laws of physics of our world, but you see, there's a memory limit, so it will only run a finite number of steps (or will loop).
What wrong with looping? It's a very robust way to make something work well without imposing artificial borders.

first-person indeterimism and the quantum laws that would follow would become severly limited (given the UDA view) and would be likely to contradict our current observations
I dont understant what is "first-person indeterimism" or "the quantum laws", but some time ago I heard that science is just a bunch hypotheses based on experiment data. You're fast to make a dogma from a hypothesis.


The notion of probability is well-defined in the ultrafinist case, even much more well-defined than in the classical finitist case. Technically you could even compute it if you had... just more resources than your current upper bound (but still finite), ahahaha.
In my definition, the probability is just a ratio of "hits" to the total "shots". But mathematician define probability as some crazy calculus construct.

>>189
Why does a scientist care why his theory doesn't predict the existence of God?
This has nothing to do with God. A limitative result could show for example "no theory of physics may have these and these properties", this result would be useful as it would lead to narrowing down on what the theories can be. The goal is to improve one's accuracy and negative results do that quite well. As for God, I already said, it's too undefined or too personally defined, it's not even worth talking about it scientifically, unless you give a particular definition.
How did you obtain the "deduction" and "induction" themself?
There are precise definitions of those terms formally and mathematically, but there is also the more common sense meaning of those terms. For example about induction: someone observes that a certain pattern is always followed by another - such as dropping a metal crate will cause a sound when the crate hits the floor. Or that you will observe that the sun rises each day and conclude that in all your past experiences it was all the case, thus you will hold that belief for now. Inductive reasoning actually comes rather naturally for humans and there are theories in cognitive sciences which show many parallels between our neocortex's hierarchical structure and some forms of bayesian/probabilistic networks. A more layman's introduction to some such high-level concepts could be found in the book "On Intelligence". I could also find some links to actual serious papers on the subject, but since you seem to be hostile to reading papers, I'm not going to waste more of my time locating copies of old papers I've read.
To put it differently, it's a both innate skill contained throughout our most basic reasoning facilities and also a learned skill when talking about formal versions.
"important" for whom? I dont see its importance or relevance to the observable reality.
Because you don't frame your theories about reality in math. Too bad most of your theories don't actually give any predictions whatsoever, so they're about as useless as the usual ``God'' hypothesis. Besides results which don't touch reality in any direct way, it can also be used to show the universality of the notion of computable function.
Sorry, but Phd wont confirm your theory. Phd is just a title, you can buy if you have enough money and/or time.
I never claimed so. I decide on what to believe in by my own judgement, and so should you.
There is a reason I'm not educated - I cant enter education due to disagreement with concepts of Set Theory and modern mathematics. A sci-fi novel wont fix that.
Maybe, but in this particular novel, he doesn't touch any set theoretic notions. He even entertains an ultrafinitistic view as a possible theory to explain one important event in the book, so you might like it (he also wrote a shorter story where he tries to consider the implications about what could the inconsistency of arithmetic mean in some such "impossible world").
What did you say?! The novelist is so serious, he even wrote comments on other sci-fi novels to supplement his Electric Boogaloo? Sounds like a typical case of copyright infringement. Einstein's family will sue him for stealing fantasy worlds and characters. It's like when you take Lord of The Rings and make sequel, without having license from the owner.
Haha. Except most scientific results are open and free (leaving aside silly paywalls). Also his book supplement is freely available on his site, not that you'll need it for this particular book.

>>191
Sorry, you're using unrestricted quantifier "all" again.
All within your define bound, it's a finite "all". Because you insist on using ultrafinitism, and I'm considering what consequences it would have to some theories.
I dont understant what is "first-person indeterimism" or "the quantum laws", but some time ago I heard that science is just a bunch hypotheses based on experiment data. You're fast to make a dogma from a hypothesis.
Not dogma, but I look at it like this, you have an established and well-verified physical theory. Now you consider a theory compeltly unrelated at first glance to it and you notice it gives the same consequences in a constructive manner without ever having asked for them or having built the theory artifically to give you those results. There is no dogma - every theory is a hypothesis, except when you have to rely on it for actual results, then you bet on it and you risk being wrong in some cases.
In my definition, the probability is just a ratio of "hits" to the total "shots". But mathematician define probability as some crazy calculus construct.
Extended forms of probability are like that, but here it's just a finite ratio, although possibly very big and intractable to calculate, yet still finite. You do get an uncomputable (thus your calculus construct) one when you do use an unbounded ontology though, but that's unavoidable in most non-trivial theories.

just poppin in to say I like ultra finitist in lisp sympta guy. What is your opinion on the natural numbers? How do you resolve always being able to add one to a number?

>>193
ultra finitist in lisp sympta guy
I'm not ultrafinitist.

What is your opinion on the natural numbers?
Haven't seen them.

How do you resolve always being able to add one to a number?
What is "always"?

>>191
This has nothing to do with God. A limitative result could show for example "no theory of physics may have these and these properties", this result would be useful as it would lead to narrowing down on what the theories can be. The goal is to improve one's accuracy and negative results do that quite well. As for God, I already said, it's too undefined or too personally defined, it's not even worth talking about it scientifically, unless you give a particular definition.
You can define "God" as anything you cant comprehend/sense. That way God is equivalent to Infinity/incompletness, which scientists care about.


There are precise definitions of those terms formally and mathematically, but there is also the more common sense meaning of those terms.
Common sense meaning has nothing to do with math. It's limited to our senses.

For example about induction: someone observes that a certain pattern is always followed by another - such as dropping a metal crate will cause a sound when the crate hits the floor.
When it's done in local, controlled and well understood environment. For example, crate wont cause sound, if it's dropped from outer space into the Sun.

you seem to be hostile to reading papers, I'm not going to waste more of my time locating copies of old papers I've read.
I cant understand them, because they are full of these cryptic "sets", together with mysterious "for all" and "there exist" wordings, buried under some ugly curly brace infix syntax, which isn't even context-free.

a learned skill when talking about formal versions.
Just like reciting Torah is a learned skill for a rabbi.

Because you don't frame your theories about reality in math. Too bad most of your theories don't actually give any predictions whatsoever
Wait! What are "my theories"? I do happen to agree with prof. Norman Wildberger on his rational-trigonometry, but he happen to demonstrate that geometry can be done without referencing "Infinity".

in this particular novel, he doesn't touch any set theoretic notions. He even entertains an ultrafinitistic view as a possible theory to explain one important event in the book, so you might like it
Author just recites what had been said already by George Berkeley a few centuries ago?

Except most scientific results are open and free (leaving aside silly paywalls).
If Einstein's theory contains errors, then it could be a work of art.
http://en.wikipedia.org/wiki/Cartography#Cartographic_errors

you insist on using ultrafinitism
You should note, that I'm not an "ultrafinitist", I'm "subjective idealist". These terms are different, like "Atheist" vs "Agnostic"

All within your define bound, it's a finite "all".
Then there is nothing that will allow us to look "outside" the bound.

Not dogma, but I look at it like this, you have an established and well-verified physical theory.
Some time ago Newtonian Physics was a "well-verified physical theory" and it definitely confirmed ability to devide space into "infinitesimals".

that's unavoidable in most non-trivial theories.
The good thing is that "non-trivial theories" are avoidable.
http://en.wikipedia.org/wiki/Occam's_razor

>>194

Nevermind. I hate you. Sorry.

This thread is filled with infinite trolling.

This ''in lisp guy`` is like the worst autist i have ever seen.

>>194
You can define "God" as anything you cant comprehend/sense. That way God is equivalent to Infinity/incompletness, which scientists care about.
Fine then, then we can talk about some "ineffable" stuff, especially if that "ineffable" stuff has consequences. Such kind of stuff usually appears once you keep reducing and reducing things until you can't reduce anymore, and yet it's too simple to be able to explain in terms of anything else, but still can be reasoned about.
Common sense meaning has nothing to do with math. It's limited to our senses.
How do you think you learn about math or recursion?
When it's done in local, controlled and well understood environment. For example, crate wont cause sound, if it's dropped from outer space into the Sun.
Of course. It's not like we don't build fairly exhaustive models given our observations in a variety of environments.
I cant understand them, because they are full of these cryptic "sets", together with mysterious "for all" and "there exist" wordings, buried under some ugly curly brace infix syntax, which isn't even context-free.
Heh, if you're going to avoid talking about real things because you have problems with the the language used (or problems with notions in foundations of mathematics), you'll lose more, because those real things actually have consequences. You don't refuse to talk in English, but English is provably inconsistent as far as what sentences it allows you construct.
Just like reciting Torah is a learned skill for a rabbi.
Except one lets me make accurate predictions and the other is just mythology.
Wait! What are "my theories"? I do happen to agree with prof. Norman Wildberger on his rational-trigonometry, but he happen to demonstrate that geometry can be done without referencing "Infinity".
I considered your subjective idealism as a hypothesis. Ultrafinitism as a hypothesis. Do you really think that a strong form of ultrafinitism (which posits some finite upper bound for naturals) doesn't have severe limiting consequences as far as what physical law can be? As I said before, there's no problem with assuming some hard limits, but this might contradict some current theories which are (mostly) experimentally verified (such as quantum mechanics or general realitivity).
Author just recites what had been said already by George Berkeley a few centuries ago?
Not really. In the story, a highly unexpected/unusual event happens and one of the possible hypotheses that were thrown around was that they might have been wrong about that countable infinity after all and a finite upper bound might exist. (Maybe it would disappoint you, but I can easily see a solution to their problem which does not lead to ultrafinitism, although this wasn't really discussed in the book, it was mostly left as an open problem/cliffhanger; of course, some form of ultrafinitism in the ontology could explain that event as well).
If Einstein's theory contains errors, then it could be a work of art.
But pretty much all scientific theories are wrong. Some are just less wrong than the other. The goal of science is to get as close as possible to the least wrong theory, possibly reaching a true one. (They are of course applicable within their context, so they are mostly correct within the right context, but for example, general realitivity is likely wrong (and incomplete) regarding what happens singularities (big bang, black holes, etc), while quantum mechanics is wrong at the large scale as it includes no theory of gravity.)
You should note, that I'm not an "ultrafinitist", I'm "subjective idealist". These terms are different, like "Atheist" vs "Agnostic"
I wonder why does everyone consider you an ultrafinitist then? How did you manage to acquire this reputation? Does that mean you're merely agnostic about the existence of an infinity of finite natural numbers? Or that you posit an upper bound?
Then there is nothing that will allow us to look "outside" the bound.
Not entirely sure I understand what you mean by this. Given some max constant k and some particular definition of computation, such an ultrafinitist computationalist ontology will have radically different predictions than a classically finitist computationalist ontology. It may seem to you that they are unobservable, but if an upper limit does exist, it will have severe consequeces about what physical law is/can be.
Some time ago Newtonian Physics was a "well-verified physical theory" and it definitely confirmed ability to devide space into "infinitesimals".
Newtonian physics is not wrong given the right context, it's just more wrong than general relativity. Newtonian physics is not an absolute physical law - it's a local emergent law, same as most other physical laws we know right now, but that doesn't mean that the goal of physics isn't to find the full, consistent law which explains all local physical phenomena within one coherent/consistent formula/function/structure. Given that law, you have all kinds of other laws which emerge from it which are locally true within some context. Taking Newtonian Physics as ontological primitive would be an error in our world as evidence says otherwise.
The good thing is that "non-trivial theories" are avoidable. http://en.wikipedia.org/wiki/Occam's_razor
I use it too. Do you know why Occam's razor is more likely to lead to true theories? It has to do with probability theory - the probability of something having multiple disjoint properties is lower than just having some of those properties, especially if those properties explain exactly the same phenomena - in which case, the other parts become superflous.
When I talked about non-trivial theories I didn't mean that they are higher in complexity. Actually they are much lower in complexity than the ultrafinitistic version. If you want to judge complexity more objectively, you could use some formalized version such as Kolmogorov complexity, but then you probably won't like it because it's not computable (although there are ways to define approximations).

Cool new Jeans!

>>197
How do you think you learn about math or recursion?
I got recursion through exposure to Lisp system (XLisp at the time). I have never learned any math, because I haven't attened school. Everything I know about math is from wikipedia.org.

if you're going to avoid talking about real things because you have problems with the the language used...
Cant see how language about "infinity sets" could be used to talk about "real things".

Except one lets me make accurate predictions and the other is just mythology.
Cant see how "infinity" is accurate.


You don't refuse to talk in English, but English is provably inconsistent as far as what sentences it
"consistency" is a buzzword and in reality, there are no contradictions, except those we invent/define.

I considered your subjective idealism as a hypothesis
It's not. It's just a program (doctrine if you like), that helps me to avoid junk theories, like your "Set Theory".

Ultrafinitism as a hypothesis
I'm not an "ultrafinitist"

Do you really think that...
I don't "think". I prefer more animalistic way of seeing and interpreting things. That is: I either sense or not. No silly "consiousness"/"thinking".

strong form of ultrafinitism (which posits some finite upper bound for naturals) doesn't have severe limiting consequences as far as what physical law can be?
Can't see this. And I don't know the "phyisical law" to have an opinion.

I wonder why does everyone consider you an ultrafinitist then? How did you manage to acquire this reputation?
No idea.


Does that mean you're merely agnostic about the existence of an infinity of finite natural numbers? Or that you posit an upper bound?
That means I can't see them, thus can't have reasonable opinion about them, except that they are just buzzwords.

Not entirely sure I understand what you mean by this.
I mean that world is "closed", like in your http://en.wikipedia.org/wiki/Closure_(mathematics)
That is: no opcode will breach the userspace.

Newtonian physics is not wrong given the right context
The problem, there is no "right context" for newtonian physics.
"Newton saw a monotheistic God as the masterful creator whose existence could not be denied in the face of the grandeur of all creation."

When I talked about non-trivial theories I didn't mean that they are higher in complexity. Actually they are much lower in complexity

Trivial| Non-Trivial
-------|------------------------------------------------------------------------
lambda | inference, lambda cube, strongly normalizing, equality-qualified types,
       | algebraic types, existential types, phantom types, dependent types,
       | higher-kinded types, linear types, inductive types, unique types,
       | nominal types, recursive types, type classes, bounded quantification,
       | type annotations, principal types, higher-order abstract syntax,
       | generalized algebraic types, robinson unification, hindley-milner,
       | constrained types, polymorphic recursion, parametric polymorphism,
       | equivalence classes, type order, judgments, curry-howard isomorphism,
       | system t, system f, products, coproducts, categorial sum, call-by-name,
       | inhabited types, higher-rank impredicative polymorphism, covariance,
       | subtype polymorphism, ad-hoc polymorphism, predicative types,
       | signatures types, contravariance, affine types, structural subtyping...

>>199
because I haven't attened school. Everything I know about math is from wikipedia.org.
Well, this explains so much.