God and Gödel’s Theorem of Incompleteness
Offline Disclaimer:
Before I start, I would like to say that to the best of my knowledge, this argument is original to me and that I intend to publish it eventually. Other theists feel free to use this argument in private settings, but please be honest and source me (and allow me to publish it eventually. This argument has taken me quite some time to assemble.) Also please inform me if it is actually not original.
Oh, atheists, I am posting this here to see how this argument stands up to something approaching real scrutiny. I'm just as much after valid criticisms as anything else (and if this argument is a doozy, I would like to know that, too and why.)
Also, this argument isn't a "proof of God" so much as it is an argument against the alternative.
Sources: Wikipedia (for initial drafting purposes only) and Stanford Encyclopedia of Philosophy (online) Considering how famous Gödel’s Theorems of Incompleteness are (and how differently different sources phrase them) feel free to note that this work is improperly cited. The only reason I don't cite from the horse's mouth is that I can't read German (I've read that Gödel was reluctant about several translations of his own work.)\
OUTLINE:
Part 1: The Argument
Introduction
Section 1: Gödel’s First Theorem of Incompleteness
Section 2: Gödel’s Second Theorem of Incompleteness
Section 3: Applying "God" as a Completion of Physics and Logic
Part 2: Foreseen Criticisms and Rebuttals:
Section 1: Preventing Ad Infinitum Regressions
Section 2: Is the Application of Gödel’s Theorem to Physics/Logic a Valid Application?
Section 3: Can Quantum Mechanics Create an Exception?
Introduction
If the observable universe was created by non-teleologically based forces, then it follows that our own reason would be self-attesting. I have argued (at length) with Todangst over this point. Likewise, if the universe itself were a collection of forces acting with no teleological intention, it follows that those forces themselves are self-attesting.
By contrast, IF the observable universe was created by a force with teleological intention, it follows that neither logic, nor the forces of the universe itself would be self-attesting.
Begin with the following assertion assumed to be true "Physics itself is complete [regardless of the state of our understanding of it.]" also known as Leplace's Demon.
Section 1: Gödel’s First Theorem of Incompleteness:
"If [system] P is ω-consistent, then there is a sentence which is neither provable nor refutable from P." (From Stanford Encyclopedia of Philosophy)
Starting from this, we see that in terms of formal provability, neither the functions of logic nor the forces of the universe can account for themselves. Assuming that all that is is physical, then in the realm of logic, we see that logic will produce true statements that are not provable within logic itself. Ergo far from being "self-attesting" logic cannot even prove all statements it regards as true to be true (and is therefore incomplete.)
Things do not improve when this is applied to the physical forces. Again, we can see that there will be statements regarded as true that cannot be proven as true within the realm of the physical forces.
But, if all that is is physical, then it is impossible for a true statement to not be provable by the forces of physics. There is no higher axiomatic system to invoke given monistic materialism.
Section 2: Gödel’s Second Theorem of Incompleteness
"If P is consistent, then Con(P) is not provable from P." (from Stanford Encyclopedia of Philosophy)
Applying this to logic and physical forces, it can be seen that it is logically improper to even use logic or the forces of physics as their own proof-system. They are incurably incomplete.
(This can be seen even more clearly with the Wikipedia wording.)
Section 3: Applying "God" as a Completion of Logic and Physics
For the sake of argument, define "God" as "a substance that has no place, mass, charge, or other means of direct physical influence, y exerts physical effects."
Importing "God" into Logic allows logic to function consistently; under the pretext that logic itself is understood to be incomplete. The same holds true for physical forces. Statements that were true, but could not be proven in either system can now be proven by importing "God." Indeed, a view of either physics or logic without "God" (or an analogous feature) is inescapably either incomplete (the first theorem of incompleteness) or is inconsistent (the second theorem of incompleteness.)
Part 2: Foreseen Criticisms and Rebuttals
Section 1: Preventing Ad Infinitum Regressions.
"God" completing logic and physics is all well and good, but what system will complete the axioms that "God" cannot possess? Is there an axiomatic system higher than God, even?
In this feature, this argument is analogous to the first cause argument, with the definite exception that a stop is possible in this case. There are at least two solutions that both stop Gödel’s Theorems from applying to everything in sight. One is that "God" Himself has a multiplicitous nature; the other is that "God" is not able to be logically probed.
Assuming "God" has a multiplicitous nature, then we are not looking at a singular entity, but rather several peer entities. Assuming that no one entity of God has a total axiomatic solution, then it follows that the statements that cannot be proven in one entity are provable in the other and vice-versa. This solution is admittedly circular, but both Gödel’s Theorem and "God's" finality are satisfied.
Conversely, it is possible that "God" is just not logically able to be probed. This solution explains that Gödel’s Theorem no longer applies to "God," but gives no specific mechanism on how it no longer applies.
Section 2: Is the Application of Gödel’s Theorem to Physics/Logic a Valid Application?
The wikipedia entry on Gödel’s Theorems of Incompleteness has an entry that reads as follows:
"Stanley Jaki followed much later by Stephen Hawking and others argue that (an analogous argument to) Gödel's theorem implies that even the most sophisticated formulation of physics will be incomplete, and that therefore there can never be an ultimate theory that can be formulated as a finite number of principles, known for certain as "final".
I have not traced the citations given to credible citations:
Jaki: http://pirate.shu.edu/~jakistan/JakiGodel.pdf
Hawking: http://www.damtp.cam.ac.uk/strings02/dirac/hawking/
Given that Gödel’s Theorem explicitly applies to any system that involves arithmetic (beyond "the most trivial systems"
it follows that all symbolic mathematics (including logic) follow suit. It also follows that physics itself follows suit insofar as it is modeled via mathematics.
Presently I see no reason why it should not apply, so I see no reason to compartmentalize my understanding of the universe.
Section 3: Can Quantum Mechanics Create an Exception?
All this "Importing 'God" business is complicated, not to mention suspicious. Is it possible that we can invoke quantum unpredictability to assert that the universe itself is inconsistent within bounds?
Quantum mechanics is not "inconsistent within bounds" it is not predictable beyond probabilities. It is still computable and, like all the other laws of physics discussed here, modeled with mathematics on the assumption of consistency.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
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I'm sorry to say it's not. Sorry only because you say you've worked on it for so long.
Gödel's theorem is more about demonstrating that we'll never have exhaustive knowledge. The rest of the material looks like a "god in the gaps" set-up.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Can an all knowing, all powerful god exist while Godel Theorem is true?
Isn't any god that is all knowing a violation of Godel's theorem?
An all powerful God has the power to prove all theorems of mathematics. He can make a formal system that is both complete and consistent.
So therefore if God, Godel's theorem has a contradiction. If Godel's theorem is true, then no God.
Seems to me your definition of God is the dude that can violate the laws of logic and Godel's theorem.
So all you've proven is that it is irrational and illogical to have the concept of God in your mind.
Taxation is the price we pay for failing to build a civilized society. The higher the tax level, the greater the failure. A centrally planned totalitarian state represents a complete defeat for the civilized world, while a totally voluntary society represents its ultimate success. --Mark Skousen
I thought as much. Even if it is a variant of the "god in the gaps" argument, that doesn't change the validity of this particular form (about like it is also a variation of the first cause argument.) So is the application of Godel's Theorem of Incompleteness to the gaps argument original specifically?
EDIT: Godel's Theorem is also not a demonstration that we will never have exhaustive knowledge. It is simply that truth outruns formal provability. These two statements are fundamentally different. The one implies incomplete knowledge of a single system, the other implies that there must be a higher proof-system still.
Also, as an added paradox, how is it possible for a universe considered to be finite (about 15 billion light-years across) to have an infinite amount of knowledge to it?
This criticism has already been answered in the original post.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
I'm not sure. I've seen it a couple of times already, that's all. I wouldn't be able to point you at a publication. It doesn't tend to hold water, since it rightly demonstrates the limitations of logic ... which says little of the physical sciences, which are based on statistics and probability.
You're absolutely right - I was being a bit too general for a discussion about logic. To be honest, I'm more of an information theory (and thus probability) type, so absolute proofs of things don't do much for me. On the one hand, Gödel did us a favour by taking the wind out of the perfectionism that bore logical positivism, but on the other hand, the common perception is that Gödel somehow disproved the usefulness of logic ... which doesn't really make sense.
I'm not sure where you got "infinite amount of knowledge". Is that an interpretation of Gödel's? Did I just miss something?
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Having re-read your argument, I can see why todangst would disagree with your premise.
From my perspective, the weakness here is an assumption of the absolute consistency of our reason by definition. It's a false dichotomy. Either we must have total and perfect self-attestation or the universe was created by a "force with teleological intention". It's just too much of a jump. Especially when the majority of the observable universe reinforces the conclusions we reach through the application of logic and experimentation. Yes, there are limitations, but that doesn't jump us immediately to a "force with teleological intention". That would be one of an infinite number of possibilities within the gaps of our ignorance.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Maybe you can enlighten me on how it was rebutted. All you said in your supposed rebuttal was that Godel Theorem can not be applied to God. So you have no rebuttal, all you did was restate the criticism. If Godel's theorem can't be applied to the question of god, why even create this post?
Taxation is the price we pay for failing to build a civilized society. The higher the tax level, the greater the failure. A centrally planned totalitarian state represents a complete defeat for the civilized world, while a totally voluntary society represents its ultimate success. --Mark Skousen
This isn't exactly a "stupid" thing to say, but it is most definitely careless. Logic reaches its conclusions with absolute certainty (assuming you follow correct reasoning rules.) However, statistical analysis cannot reach any conclusions with certainty. If logic has limitations that do not apply to statistical analysis, then not only does it follow that some things cannot be proven as true as Godel's Theorem suggests, but rather that nothing can even be proven. Logic is incomplete, and any higher analysis relies on non-definitive statistics.
To quote Mark Twain "There are lies, then there are damn lies, then there's statistics."
The admittance of not being able to know anything is a pretty big concession.
Isn't that what you just did? Who needs Gödel when we have you? (somewhat sarcastic)
In actuality we are stuck with the non-finality of logic, so just as Gödel said, truth outruns proof. I suppose that this could be called a "faith" of sorts that is unavoidable by virtue of being human. (I post this knowing that it will create a stir and quite possibly a few ad hominems.)
What we have is either that both logic and natural forces (understood as axiomatic systems) are incomplete or inconsistent. On the assumption that this argument isn't fundamentally flawed in some way that I am totally unaware of, this dichotomy isn't a false one. It's taken straight from the theorem(s). I hope that it's obvious why inconsistent isn't a viable option for any kind of scientific method analysis to take place, with or without statistical analysis. (Although it would explain a lot for the universe itself to be inconsistent.)
The wording on the introduction may need some work, granted.
No. I said that one of the possible stops was that logic cannot be applied to God. I also said that this position satisfies Gödel's theorems, even though it doesn't particularly explain anything.
Conversely, another stop that satisfies Gödel's theorems and allows logic to remain functional is for "God" to not be a singular axiomatic system. Gödel's theorems only apply to single axiomatic systems, or one system on each "level." If there were multiple markedly different systems within a single "level", then Gödel's theorems no longer apply.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
Why worry about satisfying Godel's theorem in your arguments? This theorem was arrived at by applying the laws of logic. But then you claim that God could be a being that does not exist within the realm of logic and mathematics.
These "markedly different systems" don't obey any rules of logic and mathematics, they can only exist in the imagination. God can only exist in some Alice in Wonderland, not in the real of logic and reason. So Godel's theorem implies that one must suspend logic and reason to believe in a all knowing, all powerful god.
Taxation is the price we pay for failing to build a civilized society. The higher the tax level, the greater the failure. A centrally planned totalitarian state represents a complete defeat for the civilized world, while a totally voluntary society represents its ultimate success. --Mark Skousen
Hmmm...
I think that it would be good to work through a book of Formal Logic and work through Godel's theorem before you started using it.
There are countless scholars who saw the conclusion of Godel's theorem but because they hadn't properly studied it they didn't understand what those words meant in the context of logic.
First Order Logic is a logical language that can be used to describe the rules of arithmetic. (The Peano Axioms)
Godel's proof was to show that "This sentance cannot be proved" could be constructed with this language.
There we had a sentence that had to be true but could not be provable through the system of first order logic.
So Godel's proof was that there were certain types of sentences in language that were true but not logically provable.
The next question was where else we might find these special kinds of sentences.
It appears that some have been found in abstract mathematics but I've yet to come across such a sentence in a proposition of physics.
The sentence involves self reference - that is it says something about itself.
I've yet to come across this in a meaningful hypothesis about physics.
Right...
The 'forces of physics' aren't 'things' you use to prove things with.
They themselves are descriptions of the physical world.
In the same way, logic isn't a 'physical force' - it's just a method for separating truth from falsity.
Logic starts with 'self evident rules' - i.e. rules that we are all naturally using anyway when we discuss things - heck, they're embedded into our language!!
While these are both well respected physicists, it's quite possible that the roots of logic, being a different area of expertise to their own specialty, have also failed to understand the theorem.
Nonetheless, I shouldn't pre-judge them without hearing their arguments in detail.
Perhaps physics at it's most complex does gradually make use of Godel sentences - ones that cannot be proved or disproved.
Although I would still be surprised, if you were to find such sentences in a scientific theory then I would be refuted on this point.
Looking at the argument:
It is quite true that Logical Language allows for sentences to be constructed that are true but unprovable, and it's quite true that Mathematical theory does contain propositions of this type, so far we have no reason to believe that such propositions will also appear in physics. Physics is a mathematical model but it doesn't necessarily use all mathematical propositions in it's description so there's no reason to think a priori that physics will have such sentences.
Such a sentence would have to be discovered.
Again, I think you need to study logic.
I don't think that you understand what most of these words mean in the context of logic and I'm not sure you fully understand what logic is.
I mean, what would it even mean to 'import' God into logic?
First Order Logic is simply a language with rules, rules that happen to be present in our natural language of debate.
I mean, I guess you could define God as some rule of debate, but that would be a far cry from the omni-potent being that Christians talk of.
I think I have some issues here too, but I want to be sure I understand you first.
If you could explain what you mean by "self attesting" then that would help me.
(Not that you've mis-used that phrase - it's just not one I'm familiar with!)
Let's put things this way. I never said there was a solution that would satisfy you. I said there were two solutions that satisfied the theorems of incompleteness. Do you see the dichotomy?
Besides, I am at least two steps ahead of you. Once you understand how either of these solutions I have presented satisfy the theorems of incompleteness -something that may take a while- I have a good guess about what argument you will use to counter it. I even have a rebuttal ready for it.
No. I'm not bluffing.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
Am I to understand that you have a PhD in the implications of Godel's Theorems as well? (just kidding.)
Perhaps it would be a good idea to not make a first post on a thread a baseless assertion of my ignorance. Perhaps one day you will also come to the realization that theists hold the positions they do out of ignorance is a stereotype, and as such is bound to have exceptions. I'll go ahead and tell you my credentials in this field, even though I doubt that you will do likewise.
I have read many scholarly and semi-scholarly (namely Godel, Escher, Bach) works on Godel's Theorems of Incompleteness (including a modern translation of his work and numerous AI arguments for and against that invoke it.) I've even heard it invoked by an Oxford professor studying the philosophy of mind (via the Teaching Company)
I have also had informal logic in high school and "dabbled in the formal stuff." My local college, however, does not offer formal logic as a course...but on the other hand, I never said that this was a formal proof. I just invoked a theorem from formal logic.
In all honesty, I don't understand the formal proof of Godel's theorems much better than I understand the tenzer analysis that proves the theories of relativity. I personally doubt that any more than a very slight minority of this forum understand those.
That said, pulling rank won't help much here. There is a great deal of debate in philosophical circles that as to exactly what Godel's theorems mean.
Also, that statement of yours reeks of a source, considering that it assumes the liar paradox understanding of the theorems- an aspect we have yet to touch on in this thread. Could you cite it?
Used as it's own proof-system. One of my points in this thread is that nothing can be self-attesting and still consistent with Godel's theorems of incompletenss.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
So, in theory, if we invoke God we'll get a Theory of Everything?
That makes no sense.
It's a shame that Chaos Lord isn't here as he has done some very intensive study of it.
I've been taken through it in a university course and have worked through the proof.
I've not worked through the original text but have worked through a good course which is closely linked to Jeffery's book. and I think that the particular route of proof we took is covered in his other book
I did Mathematics joint with Philosophy at Nottingham University.
Although I won't pretend I was a master at the subject - I got a 2:2.
I don't intend to use this in my arguments though - I find arguments from authority to be lame.
Where I say you've misunderstood it, I don't expect you to take my word for it and be convinced - it's just the way I see it, my 2c on this debate.
But I do have some background in this subject so you might find that other logicians who read your argument bring forward similar complaints.
Or maybe I'm wrong...
The only way to find out is to study formal logic properly and pwn me the proper way!
I wasn't prejudging you as a theist here.
All my criticism was based on your arguments and what seemed to be your understanding of the theorem.
It made me think you had misunderstood the theorem.
That's fair enough.
Although I did work through the proof at the time, I certainly wouldn't be able to recite it by heart and working through it again would be difficult stuff.
My objection is purely as follows:
The words used Godel's conclusion are defined within formal logic, so it's quite difficult to understand what he even means unless you have a strong grounding in formal logic.
It's all logical jargon that's difficult to make sense of unless you're really familiar with the subject of formal logic.
That's why I recommend working through the formal proof as doing so will teach you the context of the thesis at hand and help your understanding of it.
Godel is perhaps the most abused and misunderstood in theory because people know that it is mathematically proven but fail to understand the thesis that has been proven.
There might be debate over the full logical consequences and applications, but there should be absolutely no debate over what the theorems mean.
The whole point of the theorem was that it used the most clear and perfect, technical, mathematical language they have for logic.
The terms such as 'completeness' and 'soundness' were defined in the context of mathematical logic.
Again, you can find these definitions from the book I linked to above.
You're right that there are more paths to the conclusion than the liar paradox.
Nonetheless, my point still stands:
Godel's theorem of truths that cannot be proved applied to particular sentences with particular properties.
There is no application in physics until you find a sentence relevent to physics with these properties.
Fair enough.
I don't hold anything to be "Self Attesting".
My 'defense' of logic is a bit like Descarte's defense of the general accuracy of perception - it's something that needs to be in place before any kind of thought/debate/communication is possible so if we are thinking/debating/communicating then logic must be already in place.
Like I said before, it's a shame that Chaos Lord isn't around.
He really does know Godel's theorem and is an expert on Logic in general.
I'm just slightly informed in comparison.
My criticisms are based on my loose knowledge of Logic and the Theorem.
He would've been able to have given you something much more detailed.
I stand corrected. I was using the two synonymously.
In all honesty, I don't think of this argument as a "proof of God." It's just a thought-provoker...and I wanted to see some more heavy-handed criticisms of my connections than I received on the other forum I put this on.
Strong grounding? I have little grounding in formal logic, but I came to my understanding of it with about the same difficulty as I did the Relativity theories (even without the helpful little diagrams all over the internet.)
It would explain a bit if I had a close-but-incorrect idea of what the theorems meant. I've always understood them in the following way: Truth outruns provability in any given system, ergo a single system cannot claim to be complete. If it does claim to be complete, it is inconsistent with itself at some point.
This looks to be a criticism I'm looking for, but I don't understand it, yet. Could you clarify what specific properties are involved before Gödel's Theorems apply?
I was under the general impression that Gödel's Theorems applied to all systems that involved arithmetic beyond "the most trivial of systems."(Stanford Encyclopedia of Philosophy) The argument to physics is "guilt by association" so to speak, because of it's liberal use of mathematics.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
"define "God" as "a substance that has no place, mass, charge, or other means of direct physical influence, y exerts physical effects."
Um.... huh?
Why not define God as a mystical, magic bus that makes Universes? It would work just as well.
Once again, we witness the Incredible Shrinking God.
Imagine the people who believe such things and who are not ashamed to ignore, totally, all the patient findings of thinking minds through all the centuries since the Bible was written. And it is these ignorant people, the most uneducated, the most unimaginative, the most unthinking among us, who would make themselves the guides and leaders of us all; who would force their feeble and childish beliefs on us; who would invade our schools and libraries and homes. I personally resent it bitterly.
Isaac Asimov
OK, I have to understand what you mean by God. Is God all powerful and all knowing? What if any are his deficiencies? If he is, then he is by definition a violation of Godel's Theorem. This god can create theory systems that are complete and consistent. This can prove that there is no god higher that himself, another violation of Godel. So therefore if god, Incompleteness Theorem is false.
Or could our universe be like the Matrix, some programmers and scientists created a virtual world for us to live in, but these beings don't know if they also live in a Matrix and are bound by the laws of logic and Godel's Theorem.
Taxation is the price we pay for failing to build a civilized society. The higher the tax level, the greater the failure. A centrally planned totalitarian state represents a complete defeat for the civilized world, while a totally voluntary society represents its ultimate success. --Mark Skousen
Not to sound condescending but this could have more easily and concisely be summed up as: "If logic cannot be used to prove itself, then God must have created logic along with everything else in the universe."
Again, that's the god of the gaps argument.
I may be way off, but my understanding of Gödel is that any language that is complete is capable of expressing unprovable truth statements. Here, "completeness" requires the ability to describe arbitrary complex systems within a domain.
So, though mathematics may fall under the pervue of Gödel, physics does not. Physics is merely a complex system which uses mathematics as its descriptor. The fact that mathematics is also capable of presenting unprovable truths has nothing to do with physics, other than the small potential that those truths may apply to an extant process or interaction. However, since we've never run across one of these, there's no reason to assume that physics expresses an unprovable truth.
Put another way, all physics is expressed as mathematics; but all mathematics is not an expression of physics.
Again, I may be way off on this. I too have read Gödel, Escher, Bach, and so only have a layman's understanding. I have neither the expertise nor the patience to work through his proof.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind." - PZ Myers
I don't usually chime in on Godel threads basically because I like incompleteness, I think it's great that mathematical systems run out of play, as long as there's always room for more, there's more, right? Sounds like fun to me, sign me up.
A little humour - Isn't the turing response to the Godel statement logicianish for the Jewish name of god? In-utterable... and Godel's conclusion logicianish for the Hindu name for God. Neti neti?
I don't think there is any point using Godel's Incompleteness to prove or disprove God, it would be more useful in proving miracles, ie not very really. However, not altogether being humorous any more, there is a certain possibility that one can prove incompleteness itself is what has been historically referred to as God, and it would be a really radical turn from the usual - 'this doesn't fit', therefore God, so frequently pumped out by apologetics these days.
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Yeah. I've noticed that nowdays when I come out with arguments, I less expect them to nail the matter but still end up learning lots from them anyhow.
More or less.
Being pedantic, the simply system of propositional logic is complete, but that's not a system strong enough of expressing the axioms of arithmetic.
So for First Order language, the one we tend to use for Mathematics, it is possible to construct sentences that are true but not provable.
Any language capable of expressing the axioms of arithmetic is capable of constructing these sentences, and in Mathematical theory such propositions have been encountered.
However, when we use mathematics as the language of physics, we're not going to be using all of mathematics.
Mathematics explores a lot that bares no relevence to physics whatsoever.
I'm not an absolute expert on this subject, but all the examples of "unprovable truths" I came across were either self-referencial propositions or followed from them.
Logic and mathematics explore all the grammatical possibilities of language.
Physics, on the other hand, sticks to describing the physical world and thereby doesn't get embroiled in such word-play.
I personally can't imagine a self-referencing proposition having a place a scientific theorem.
For those of us with virtually zero ability to detect subtlety, I'm thinking of a Christian doctrine about God that -because of it's extremely counter-intuitive nature- has had more heresies associated it than I can count with my fingers and is defined by "The three Persons of God are connected in a way that allows them to be one without confusion, division, mixture, or separation."
Is that clear enough?
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
Eh? Propositional logic < Arithmetic? I always thought of logic as a unique form of a math.
Could you give an example of the last statement (or a source that would give examples)? That sounds like something I should explore.
We won't actually know exactly what parts of mathematics we're using until someone clarifies what the relationship between physics and the abstract mathematics that we use to model it is. The relationship has been noted many times, but it doesn't look like it will be solved in the near-future....
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
Nah. Logic is more fundamental than mathematics.
Mathematics is a system based on axioms that are defined within a logical system.
The idea is that every truth in mathematics follows from these axioms.
Propositional Logic isn't sophisticated enough to construct the axioms of mathematics but First Order Logic is.
Godel showed that any logical language capable of constructing the axioms of arithmetic would be incomplete.
It's fairly straight forward really...
Mathematics tends to be split into 'pure' and 'applied'.
Pure is the exploration of the axiomatic system.
Applied is where we apply the results of Pure to real life situations.
Mathematics can be applied to a real life situation where some mathematical propositions describe something about reality.
We find mathematical propositions that describe some part of reality and then we can work out what other mathematical propositions follow from them.
e.g. Give a particle a position in time and space, and a velocity, and the mathematical relation between position and velocity, from there we can work out how the position of the particle will change as time changes.
From our basic grasp of language, we know what kind of sentences we use to describe reality.
These sentences don't tend to have quirks like Self-Reference that Godel sentences have.
So a Godel sentence won't be applicable to physics.
If I could move on a bit; the usual way people try to apply Godel is to say "God's existence could be such a proposition", but they would have to demonstrate that questions about God had a characteristics of Godel sentences. The thing is, the Godel sentences are word play really and couldn't describe anything of reality so I can't see this argument every working.
Yours was slightly different though.
Yours was to try and prove that physics was incomplete and therefore God could be used to complete it.
So it seemed your argument was to try and put physics into some kind of logical crisis and postulate God as a solution.
Even if physics turned out to be 'incomplete', i.e. allow for propositions of a Godel type, this would simply mean that there are physical truths that we can't logically prove.
(That would be very strange as physics is based on empirical observation rather than logical consequences of axioms!!)
My first point would be that the odd Godel proposition in physics would hardly be a crisis - people could quite easily accept it as incomplete.
My second point would be Todangst's age old objection to placing God as the solution.
What difference could 'God' make to logic?
That sounds about right to me.
But I've only taken a university module...
ChaosLord, where art thou?
Whoa. Physics (itself, not our modeling of it) is based on "empirical observation?"
I didn't know an inanimate object could observe. (joke)
Seriously, though. In order for physics to be able to be an inanimate and consistent system it must be some kind of a system based on axioms (even if we can't ever prove what those specific axioms are, but rather just observe their effects.) What other alternative is there?
Correct me if I'm wrong as well, but I didn't think that Godel's Theorems always referred back to logic, but rather the system being studied. So if it were to apply to physics, logic wouldn't be the comparison system as that logic is an axiomatic system subordinate to physics. Physics itself would be the comparison system. (This is a terribly awkward wording, but I can't express it any better.)
This would explain the connection between pure mathematics and physics (pure mathematics are subordinate axiomatic systems) but it makes Godel's Theorem apply to physics itself, so we would wind up with my original paradox that physics is either inconsistent or incomplete.
Again, there's probably a bug here, but I don't know what it is.
EDIT: I thought you guys didn't like wikipedia.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
You've lost me...
Godel's theorem applies to a logical system, i.e. a logical language with methods of proof.
After all, it's the method of proof by which a system is considered sound (that all provable statements are true) and complete (that all true statements are provable).
That's the only context within which the word 'incomplete' means anything within the context of Godel's Incompleteness Theorem.
Arithmetic is a system of axioms that can be expressed in a logical language.
I guess a system of physics would be a system of propositions about the natural world.
Not sure where 'axioms' would come into this...
The facts in physics aren't deduced from a priori logical axioms.
Because the propositions of physics are descriptions on how the world is; given how we use descriptive language, it doesn't involve the grammatical tie-ups that lead to the paradoxes required for Godel statements.
You've stated the relationship, and that relationship is sufficient for incompleteness to affect physics. The mathematical systems used to model physics are incomplete and sound. That is, the physicist observes relata describes the relation in an existing axiomatic system, uses that system to predict logical relationships that follow from the original observation, tests the predicted variables and if the variables match the model survives a round. Godels theorem tells us that you can't find a perfect system of axioms for deducting physics, that is, a model can survive for a long time and the axioms that support it can be an incredibly sound system but eventually you will build another leg because that system will be unable to comply with something that exists within it. It won't be able to give you an answer to your question. It doesn't necessarily mean the answer will be true, Godels statement can be true or false, but the system created from logic will be unable to say.
Now the Godel statement is a generalisation of many possible statements, and most of the known ones don't intrude on anything but pure mathematics, one that does intrude on physics is the second incompleteness theorem - consistency. Proof of consistency is: No A exists in this system such that both A and ~A can be proved. Basically saying, none of your results will negate your system. Because it's a Godel statement, the system can't answer it. The way this affects physics is that basically, such systems are what we use to say things about the world and they can't promise us they won't throw up anomalies which require new systems to be derived in order to understand them. That doesn't mean that we will necessarily encounter anomalies in each system or that we will necessarily come across unprovable truths. It says essentially that our mathematical systems are incapable of making the guarantee that we will not, thus they are incomplete. But you have to know that this stipulation of a system guaranteeing it's own consistency does not immediately translate into inconsistency in the system. The consistency statement is one possible Godel sentence, it's not the same as the original proof of incompleteness.
So in summary, Godels First incompleteness theorem guarantees the existence things a mathematical system cannot say, ie there is at least one thing. The second Incompleteness theorem says that you can't ask a mathematical system to prove it's own consistency, which physics doesn't do, by extension it could be dubious to rely on the systems consistency, which physics does do, because the system cannot guarantee it won't throw out things you never imagined it could, which physics is basically used to by now cause the universe does the same thing to it on a regular basis.
Theist badge qualifier : Gnostic/Philosophical Panentheist
www.mathematicianspictures.com
Okay, maybe I wasn't clear. In the physical sciences, there is always measurement. When you measure something, there's always a margin of error. Always. Interacting with the physical world cannot be perfect. I can say that an object is 70cm long within a certain margin of error. That doesn't stop us from saying the object is 70cm long, because we have lives to live outside of the measurement of a single object. We cannot have exhaustive knowledge that would bring us to definitively state anything without some margin of error. That's what I mean by "based on statisitics".
Second, logic has as its reference point the physical world to reinforce it. Its basic rules can be tested on known quanities in the physical world and then applied, since there is no reference point other than the physical world for the purposes of objective testing. Repeated testing reduces the margin of error. That process also involves statistics by necessity.
Certainly, if that's what I said. Except it isn't. I admitted that we cannot know anything absolutely, only within a margin of error.
Why would it be "faith"? If truth outruns proof, then everything I've said makes sense. Maybe you misunderstood me because I didn't present my case clearly enough. Or maybe you think my application of probability isn't appropriate in certain cases?
If your idea of "inconsistent" is what I've presented as "incorporating a margin of error", then maybe that's where our communication is breaking down. I don't see evidence for absolutes. Certainly absolutes are helpful for framing problems (ie by simplifying them), but it doesn't mean that the logic itself gets to trump reality. Asking questions like "is logic correct?" is ridiculous because logic is just a tool for discussion.
For instance, I have a friend who can consistently argue, using modal logic, that he does not have a head. That does not invalidate his ownership of a head.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Thanks, Strafio - I probably should have just quoted you in my last reply.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
...Come again? (I read the rest of the paragraph and didn't see how it proved this. In fact, I didn't see how it had anything to do with this at all.)
Incomplete means that we don't know where it came from, but sound means:
Apparently to declare something "sound" we must know where it came from, but if it is "incomplete" we really don't know that.
(**bewildered expression**)
So logic's ability to prove things with certainty is...useless? If we can't tell anything about the universe except within a "margin of error," but we actually have no way of determining how big the margin of error is, so then everything we think about the universe could be dead wrong in finality and we would be woefully ignorant of it and not have a clue how to prove otherwise.
For the way we model physics, that's true, but I can't see how it is possible for any kind of a system that Godel's Theorems can act upon to exist in the first place unless in finality physics itself is a system that Godel statements can be made in.
Basically I am drawing a dichotomy between the way we understand physics, and the way physics itself must be.
EDIT: I'm starting to get the idea that we (myself and Strafio) have different epistemological connections attached to the word "physics." As near as I can tell, Strafio has only one: the human attempt to empirically model nature with mathematical equations and models. I have two: Strafio's concept, but then also the idea that physics has an axiomatic nature apart from the human understanding that the human empirical modeling is a struggle to encapsulate.
Regardless of which is correct, the dual concept of physics is a prerequisite to following this argument.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
Sigh. We do have a way of determining the margin of error. Look it up.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
I see this has degraded into a typical "we can't know anything" argument.
The 'truth' value of a statement or proposition within a deductive system such as logic or mathematics is determined by whether it is or is not consistent with the axioms (assumptions) of the particular formal system. Godel showed that in sufficiently expressive formal systems it is possible to make statements that cannot be decided.
Even in basic logic, if a proposition A is a statement about the proposition itself, you have the same problem, ie you cannot 'prove' logic is valid using logic. Godel just used a formal system expressive enough to express this such an ultimately undecidable statement entirely within the terms of the system itself.
It is only within such formal systems that absolutely 'true' statements can be made, since they depend only on precise definitions and whatever 'logically' follows from such definitions. All the elements that can be manipulated within the formal system are precisely known, by definition.
When in comes to statements about the Universe, where we know little or nothing with ABSOLUTE certainty, we can PROVE virtually nothing in the mathematical/logical sense, only establish and attempt to refine probabilities and likelihoods, which is at the heart of science. In this context, logic and math are vital tools to manipulate and analyse simplified models of reality ( 'theories' ) to test how well they map to reality and help us determine where and how to look for further data/observations which will usefully add to the models descriptive and predictive power.
So arguments based purely on formal systems such as logic and math cannot prove anything about the external reality, they require actual observational data as input, andf as HisWillness said, that will always have a degree of uncertainty. Deductions from logic and math about the implications of observational data will only be 'true' to the extent that the input data accurately and completely describes all relevant phenomena.
We have a whole set of tools in probability theory for setting bounds on the likelihood of any given statement or deduction accurately corresponding to 'reality'. 'Prove' doesn't come into it, at least in the strict logical sense, except about the internal consistency of a particular logical or math theorem.
The 'truth' that the sum of the internal angles of a triangle is equal to 180 degrees is absolutely true GIVEN the axioms of Euclidean geometry, including the one that one and only one straight line can be drawn through a given point such that it will never meet another given line that does not already pass thru the same point. Thsi last axiom is not necessarily true in our Einstenian Universe of curved space-time.
So don't confuse the provable 'truths' of math with any assertions about reality, such as there is (or is not) a God. All we can do is set finite bounds of probability.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Let me get this straight, BobSpence1, science is entirely dominated by empirical and statistical data that can be studied until statistics essentially proves things, but conversely logic can prove abstract things with certainty.
Granted that no abstract thing exists in the physical universe, doesn't this make logic...superfluous? (or irrelevant)
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
'Abstract thing' is not a really comprehensible phrase. Abstractions don't exist as 'things', unless you include ideas as things, which just makes your statement about them empty and/or circular.
Abstractions are ideas, concepts, ideal/simplified relationships between, and properties of, perceived real-world, or imagined, entities, and so are essential tools of our thought and reasoning about the physical universe. They 'exist' as patterns of thought, relationships between other ideas or patterns of thought, and so CANNOT be meaningfully said to 'exist' apart from the physical universe where our ideas exist as patterns of brain activity.
Logic is an ESSENTIAL tool for testing whether any proposition or conclusion is consistent (or not) with some other statements or propositions. It is a formalised description of the minimal rules of structured, coherent thought.
Pattern, Structure, Process, Interaction, Attributes, etc, involving matter and energy, and aggregations of such, are essential aspects of a complete account of THE universe. 'Physical' is a unnecessary qualification. Science, 'naturalism' if you like, is NOT just about matter and energy, it's about the patterns and structures and interactions of partially independent entities such as the whole hierarchy of material 'entities' from quarks to protons/neutrons/electrons to atoms, molecules, chemical compounds, rocks planets stars galaxies, living organisms...
I get a sense you make be mired in out-of-date Platonic fallacies of reification of abstractions in their own 'plane of reality' or some such philosophical nonsense.
BTW, science is a process of studying ANY data, observations, reports, to establish its reliability, consistency with other data, requiring a degree of statistical analysis where uncertainty is significant. The only 'data' that is rejected is unverifiable 'data' or testimony that does not have independent corroboration to some degree. It doesn't strictly 'prove' things, just establishes (at best) that various relationships ( IF this AND that THEN this, as a very simple case ) are extremely likey to be the case, or ultimately occur, etc.
So there is deductive truth, which is either absolutely certain or completely undecidable (in the case of Godel statements), but doesn;t tell us anything positive about real-world assertions, just allows us to reject ones that amount to logical contradictions.
Then there is scientific 'truth', which is provisional, incomplete, but in many cases sufficiently consistent with reality to be extremely useful.
What's left is speculation - Philosophy, Theology, with no ultimate 'truth' value at all.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
I just noticed the old 'infinite regression' thing got a mention.
This is only a problem for someone who assumes that a 'cause' must always be at least as 'great' or 'greater than' the effect it 'causes', in at least some dimension, which is an unwarranted assumption, since we see examples all the time of massive events triggered by minor variations in some thing, like sea surface temperature rises helping to trigger a hurricane, or the butterfly effect idea on other weather events, or the idea of the last snowflake triggering an avalanche.
Once you allow that in a conceptual chain of 'causes', each earlier one may well be lesser in energy and/or duration, an infinite sequence of such will not require an infinite amount of time or energy, so there is no problem.
1 + 1/2 + 1/4 + 1/8 + to infinite number of terms = 2
So no need to invoke anything more than High School math there.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Bobspence already answered for me, so I'll just point you there, a system is sound when it does not contradict its axioms.
The Incompleteness theorem is specific in saying that a system can be sound up to a Godel statement, and in remaining sound it can have no answer to a Godel statement.
I don't see 'knowing where it comes from' implied in the definition you're giving me, BTW. How do you see that?
Theist badge qualifier : Gnostic/Philosophical Panentheist
www.mathematicianspictures.com
You can see my enthusiasm for that particular dead end. It's a good thing Bob showed up. Thanks, Bob!
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
And we can't even know that for sure.
Taxation is the price we pay for failing to build a civilized society. The higher the tax level, the greater the failure. A centrally planned totalitarian state represents a complete defeat for the civilized world, while a totally voluntary society represents its ultimate success. --Mark Skousen
Haha! Oh man.
Consider yourself punched in the shoulder.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
No problem - this topic covered a whole bunch of my pet peeves, so I couldn't resist.
This conflation of the truth values of deductive systems and real-world estimates of most-likely or most-productive/useful explanations or models of reality seems to me at the heart of so many arguments here. Talk of science can't PROVE x, or we can't PROVE our theories correspond to the TRUE nature of the Universe,,, arrrgghh!!!!
At least Science is a process of progressive refinement and filtering our stuff that is pure personal prejudice or pre-supposition, whereas Theology (and much Philosophy) thrive on building insubstantial palaces of the purest un-substantiated crap, almost entirely pre-suppositional and pulled-out-of-the-ass nonsense.
I so love Sam Harris' comment on Theology I quote in my sig.
BTW, I've been off the forums for a while due to sudden disruption in the company I was working for - hopefully things are stabilizing somewhat for me now... And I realize I need the therapy of expressing myself here and interacting with some great people, and some strange ones...
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
This is not a factual statement, it is a statement that you hold the philosophical position of monistic materialism. In the unlikely event that you would like to know some of the reasons I disagree with this position, I invite you to check out the Teaching Company course "Consciousness and it's Implications" lecture seven. Professor Robinson expresses the position far better than I, and is also far more qualified to make the criticism.
Face it, the instant I applied the FOL theorem of Godel's Theorems of incompleteness to physics itself, this became a philosophical discussion. If you really think that these fields are speculations without any "ultimate truth values," the logical course of action is to resign this thread, seeing as that it has no truth value.
I know you aren't going to do that.
Except that the butterfly effect is purely a rounding issue in computer atmospheric models. Assuming that it has anything to do with how complex systems actually work is another "unwarranted assumption." In the real world, things work this way:
In other words, viscosity means that all changes eventually be converted into heat which will be dissipated to the rest of the universe, and the smaller the change, the faster that conversion will take place.
EDIT: The very fact that you attempted to invoke the butterfly effect here betrays a fundamental misunderstanding of what is at issue, anyway. We are talking about formal proof systems here, not atmospherics.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
If this turns into metaphysics, I'm challenging someone to a deathmatch.
I wish I could find the quote by Nigel - he said it so succinctly. It was along the lines of science being the most successful epistemology by such leaps and bounds that it baffles the mind when people want to argue philosophically against it. Nigel? Where art thou?
I think everyone loves that quote. Okay, maybe not everyone, but it's a damn good quote.
Back to the loving arms of internet addiction.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Bring Professor Robinson on here, then. You might instead want to tell us what his philosophical positon is. You can use short hand, like "dualist antimaterialism" or something, but saying "there exists someone who can tell you you're wrong" isn't much of an argument.
Cute. But a far cry from addressing anything. Do you (or Professor Robinson) have an epistomology that works better than science? Something that, maybe, produces more in the way of truths that coincide with reality? Because I'd be all for that.
Sweet mother of mercy. Have you ever seen "math" before? "Purely a rounding issue"? Did you just call a novel branch of mathematics a "rounding issue"?
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Sir Valiant for Truth,
The instant you applied any aspect of Godel's theorems to physics you demonstrated your basic misunderstanding of the distinction between the formal systems that Godel's theorem applies to and the nature of scientific enquiry - not just physics.
And when will you get it thru your head that incompleteness is NOT about 'not knowing where it comes from', whatever that actually means, its about the inability to prove ALL statements within the system, that some statements are UNDECIDABLE.
And yes, that did make it a philosophical discussion - and into the area of pointless speculation.
The 'butterfly effect' is a slightly fanciful idea expressing a fundamental of non-linear systems involving feedback - also covered under the label of Chaos theory, involving infinite sensitivity to initial conditions, it most definitely is not an artefact of computer rounding error. Obviously the rounding error aspect does apply under many conditions, but there are systems where there are at least two quasi-stable states where the boundary in state-space between the regions is of zero width, so an infinitesimal change of relevant variable either way will determine the state the system adopts.
I raised that as the extreme example of effects being greater than the cause, which counters concern that 'infinite regress' necessarily impies actual infinities.
Your attempt to attach a formal axiomatic system as an aspect of physics is unjustified and gratuitous, and hence your whole argument is pointless. Physics uses formal systems in its models, but modelling physics itself in a formal system?? Clearly guaranteed to lead to a Godel problem because you are modelling a process which itself uses formal systems, inside a formal system....
So you don't really understand formal systems, Godel's theorems, chaos theory, the nature of science, ....
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
How nice to know that my well is poisoned. I feel so humbled that I shall restrict myself to asking the most meager of questions.
Might I ask how relevant to formal proof-systems the butterfly effect theory is?
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
I already explained that I raised it in the context of the infinite regress 'problem' which was raised in the OP - infinite causal regress is not a serious problem once you realize that 'causes' can be tiny relative to their 'effect'.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
So it seems you have this concept of 'physics itself' that needs discussion.
At the moment I have two complaints about it:
1) The 'human understanding of physics' is the physics that is relevent to our everyday life.
Everything we call 'scientific fact' in physics are propositions within this empirical model.
In what way does this 'physics itself' relate to 'physics as we understand it'?
2) The moment you start talking about 'physics itself', you're talking about something, you're describing something.
That is, you're just providing a model.
That's why I only take physics to be a model because as soon as you start talking about 'physics' you find that providing a model is what you're doing.
And if you're not doing that then what are you talking about and what relevence does it have to scientific fact?
3) You talked about 'physics itself' being an axiomatic system separate from understanding.
I think that this is seriously incoherent.
Think about what an axiomatic system is, what an axiom itself is.
It's a 'self evident' proposition that it true.
So it's a proposition that we evaluate as true.
Already we have imposed a 'system of understanding' on it.
Surely you must see the contradiction in talking about something beyond human understanding?
Are your words meaningful or complete nonsense?
If they're nonsense then let's carry on the conversation in the same tone - my rebutal will be "Ice yellow green five!! Pwned!!"
If, on the other hand, your words actually mean anything then we must both understand them and they must therefore be talking about something within understanding.
Post-modernists and other sceptics have often noted that language and logic is rooted within a system and then said "Then what must be outside this system."
The thing is, anything they say is within such a system so it's incoherent to even talk of there being an 'outside' of the system.
Descartes said "I think therefore I am"
A variation on this is "I think about it and therefore it is within understanding".
That's why it's a nonsense to talk about things existing 'beyond our understanding' because to be talking about it and making sense, you have to be understanding it.
You might as well be saying "ajjeeeba ajoooooba walla walla!" for all the sense/meaning/value of the words you are putting forth.
"Physics itself" isn't a concept original to me. In fact, I took the wording and the concept straight out of Leplace's Demon.
Only about as much as "pure mathematics" does. My entire position is that for "physics as we understand it" to even exist in the first place, "physics itself" must exist. Whether or not my assumption that "physics itself" is a First Order Logic and axiomatic system is up for some conjecture, but I cannot frankly see how it could not be both of those or a system with very similar rules that would not also negate the usefulness of all axiomatic and First Order Logic systems.
All I've said is that we can deduce some very specific things about physics with certainty via logic, something empirical observations cannot do.
It should also be noted that any assertion that we cannot know anything about physics in finality is a final statement, so is both self-defeating and is a conclusion derived from the nature of empirical observation combined with the assumption that empirical observation is the only legitimate way to study physics.
My assertion that we can use logic to know things about "physics itself" contradicts that assumption, to be sure, but please note that empirical observation and logic even if applied to the same field of physics could not even provide contradicting statements. Logic can only provide statements about "why," while empirical evidence can only provide statements about "how."
As that you are threatening "Pwnage," then before you summon Chuck Norris to roundhouse my face, allow me to give my totally honest interpretation of this statement and beat you to the punch.
I have a fundamentally different epistemological model of physics than you do. If I invoke an argument that involves one of the differences, anything I say immediately becomes nonsense to you, not necessarily because it really is nonsense, but because you no longer have the epistemological equipment required to follow it.
This actually finalizes the validity of my argument for any public setting. If I were to use this argument before an audience that was similar enough to my epistemological model of physics and you started asserting an argument they could follow is "nonsense," then they would come to the conclusion that you have an inadequate epistemological model, even if they didn't conveniently have the jargon down pat.
I am under no obligation to make you understand this argument, and if my explaination is correct, it is impossible for you to understand it anyway. The fact that I can both follow this argument, have led others through it, AND that I can explain why you think it's nonsense is enough for me because the ability to explain simultaneously forces a dichotomy between us and gives me the greater explanatory power.
EDIT: Things would have been different if you had said my argument was invalid because of a misunderstanding of terms, but you chose to say it was nonsense.
"Truth is the cry of all, but the game of the few." George Berkeley
"Truth is always strange — stranger than fiction." Lord Byron
Fixing the world, one dumb idea at a time.
Doesn't matter who invented it, that fact that you hold it is something that we need to do something about!
Pure mathematics isn't a 'thing' that 'exists'.
Mathematics is like a game - the axioms are the rules that determine how to play, how we determine whether propositions are true or false.
From there we work out which propositions are true and which ones are false.
Pure mathematics is when we look at mathematics for itself, not caring whether it has a real application.
Applied mathematics is when we use the results of pure mathematics to solve real problems.
Much of physics involves applied mathematics.
It's like the difference between theoretical physics and mainstream physics.
Mainstream physics has direct application to other problems wheras theoretical physics might bring results that mainsteam physics can use but is for now just for the sake of enthusiasm of physics with no garauntee of applications.
I don't think that you can use "pure maths" as an equivalent to "physics itself".
I thought that you might be thinking along these lines.
In real life, when we make a model it tends to be a model of something, something that itself isn't a model.
However, our language in mathematics/logic is slightly different - a model is any logical/mathematical construct that describes something.
You seem to be talking of the difference between "physics as we understand it" as our current model and "physics as it really is" as the ideal/perfect model that takes into account every event (even ones that humans haven't perceived).
Either one would be a model and would be described in language.
I actually disagree with this.
We can use logic to make inferences based on empirical justifications but I'd be surprised if you could come up with truly a priori propositions in physics.
There was once a belief that the structure of time and space was a priori (i.e. euclidean) but even that's been proved to be mistaken with Relativity.
But tell you what, if you can find some valid examples then you could prove me wrong on this.
Um... seeing as physics is a description of the perceived world, it's so much assumption as definition.
Our contact with with the perceived world is perception so clearly everything we know from it would be empirical.
Logic might dictate how we organise these perceptions and what we deduce from them but truth is always determined through empirical premises.
Fair enough. I was merely saying that you couldn't put physics outside all systems altogether.
You're right that your conclusions should follow from your epistemological model of physics but that model can be criticised itself.
I suspect that this model will have severe flaws that leave it incoherent - I guess we'll learn more as this debate goes on.
Given that you agree that "physics itself" is defined within a system, you agree that it is a model itself.
So how would it differ from the "physics as we understand it" model?
Maybe, as you seem to be suggesting, the ideal physics model will use differing language and discoveries.
However, I doubt that these changes will ever be enough to allow a Godel Sentence and here's why:
Whatever model we have it will be a description of reality and our descriptive use of language doesn't involve self referencing or anything else that would allow for a Godel sentence.
So unless you were to provide a revolution in linguistic philosophy that showed that a Godel sentence could crop up in our descriptive use of language then I don't think that you can make a case for them appearing in physics either.