The Goedel statement is in a formal language, and if it really is there and its correct translation to english is a self referent sentence then there must somewhere be a referential identity defining the goedel sentence! And that Referential identity must be a Liar Identity, and therefore the rules of logic has been broken!Ken G said:The translated arithmetic is just arithmetic, it can be no more or less inconsistent than arithmetic itself. It is an arithmetical statement that, if a proof could be found that the statement was true as an arithmetic statement, it would demonstrate conclusively and without doubt that arithmetic is inconsistent. Hence, if we assume arithmetic is not inconsistent, we must hold that no proof of that arithmetic statement is possible. That renders the statement empirically true when translated back to English. What all this proves is that it is impossible to make a seamless transition from the syntax of arithmetic to the semantics that we wish to associate with arithmetic to lift it out of the rules of pure logic and bring it into contact with the truths that actually make arithmetic useful and are why we teach it in school.
Hey! I like that: You are the first to admit that I have a method! But it SOLVES not "removes" the paradox.Ken G said:In other words, your method of removing the paradox
Er... don't you mean UNdecidable?Ken G said:In other words, your method of removing the paradox]does not remove the purpose of the Godel theorems. Arithmetic is still either incomplete or inconsistent whenever we attempt to marry syntax and semantics, which is the ultimate goal of arithmetic. It doesn't really matter if logic is saved or not, it is the purpose of logic that is under attack, and it seems to have no defense other than arithmetic serves its purpose and we can continue to assume it is consistent, even if it includes semantically true statements that are logically decidable.
This is not true! "by being a liar sentence, it is a liar identity, because it refers to itself."Ken G said:The alternative is that arithmetic is inconsistent (either because its axioms are or because logic isn't what it's cracked up to be), which seems far worse and we will never accept that unless we have to. Saving logic is a footnote to all that, it just rules out that last possibility in the parentheses.Most people regard the Godel sentence as satisfying both roles at once-- it is a liar sentence, and by being a liar sentence, it is a liar identity, because it refers to itself. Your liar identity is nothing but the explicit recognition that the Godel sentence is self-referential, which most people take as implicit in the Godel sentence. I realize that you are being more careful to explicitly separate the sentence from its self-referential character, but everyone agrees that the self-referential character is the troublesome part, not the sentence itself.f.
No I have shown that their self-referential character is well defined!Ken G said:It would be easy enough to rule out self-referential statements on the grounds that their self-referential character is not well posed,
This was not necessary...Ken G said:but the Godel proof circumvents that by translating the sentence into arithmetic, so it cannot be ruled out as an arithmetic statement.
Here your statement has at least two interpretations...And next is your conclusion...Hmmm...And Again...Hmmmm!Ken G said:This shows that the problem appears when we attempt to attach semantic meaning to arithmetic statements, but that's the whole point of arithmetic,
So I can't follow you here...I just declare that I oppose.Ken G said:so the Godel proof is indeed a valid limitation on what we would like arithemetic to be. That limitation is normally expressed that we must regard arithmetic as incomplete, if we want it to be consistent, and if we want to attach semantic meaning to syntactic sentences.
And the same here...Sigh... it was interesting!Ken G said:Sure, you recover a syntactic structure by disassociating it with any semantic content. But the issue behind the Godel proof, and paradoxes in general, is the effort to connect syntax with semantics. It is easy to prove that the syntax defines a consistent tautology, what is at issue is whether or not we encounter difficulties when attaching semantic meaning to the syntax. It was hoped we would not, Godel proved that we do. That is also the "point" of a true paradox, to expose the difficulties in attaching semantics to any sufficiently rich syntactic structure.
Ken G said:This is a valid question, and a long thread, so I don't know if it was taken up. But I think it's fair to include, with the question "why does anything exist?", the question "why ask why in the first place?"
But those two things are saying the same thing: a language is not consistent with logic because it allows a liar sentence to be constructed. The liar sentence is self-referential, which breaks the rules of logic. You claim that a language cannot break the rule of logic because the liar sentence is not self-referential. But it clearly is self-referential, and this has nothing at all to do with logic, it has to do with meaning. The goal of language is to infuse syntax with meaning, so for language to succeed, logic must fail, or vice versa. That's all Tarski is saying as well, you are not disagreeing-- you are merely choosing a different side in the conflict (logic over meaning), but it is the existence of the conflict that is relevant, not which side we choose.sigurdW said:Alfred Tarski for instance: He said that natural languages (and all semantically closed languages) are inconsistent because the Liar Paradox can be derived in them, And I oppose! No Liar Paradox can be derived in natural language without breaking the rules of Logic!
I can accept this as a thesis,but its not very supported.apeiron said:It is a key question because it gets us to our epistemological limits - or rather the limits of a certain epistemology!
Ahem...I thought it was sentences supposed to express statements that could be or not be well formed?apeiron said:This may be why people get uncomfortable. They feel secure in having a method of accounting for the world. Then they discover it suddenly runs out of road. The choice then is either to honestly question their prior beliefs or to declare any further explorations as "unanswerable questions" or "abstract nonsense".
This is what you so clearly state about syntactic paradoxes. You have a universal method for making well-formed statements. And suddenly there is a crisis because - as with the liar paradox - it hits a limit.
And what is an "off-thread conversation?apeiron said:And also in the other off-thread conversation about Bohmian interpretations. Again there is a belief in a method of explanation that hits a limit (and Bohmian mechanics is where people just keep digging anyway).
Why "crisis", isn't "problem" enough?apeiron said:So there are these well-accepted foundational crises in Godelian incompleteness and Quantum weirdness. And I should mention here the Hard Problem which is taken as the foundational crisis of mind science. Yet for some reason the "why anything" question is being treated by some here as not also a standard foundational crisis.
Sorry but "clearly" youre unclear.apeiron said:What the "why anything" question in particular draws attention to is the incompleteness of models of causality based on effective cause - the idea that every event is the result of a chain of events. In physics, this "syntax" gives us the various mechanics, the various models founded on the principle of locality. All useful models, but all limited by the ultimate restrictions of their syntax and unable to talk about the larger semantics that so clearly embeds them.
I think your tecnique can be improved, why not try giving some examples now and then?apeiron said:So when confronted by the "why anything?" paradox, there are two lessons.
The first is the discovery that a familiar epistemology does indeed have hard limits. For it, some questions don't even compute. It finds itself making nonsensical statements about "nothing existing" - well-formed statements, but clearly detached from any proper semantic grounding.
I wait eagerly for your results in exploringapeiron said:The second lesson ought to be that causality is larger than people stuck within a certain paradigm may have believed it to be. And so the correct response is to explore those larger models, hoping to find the syntax that can unlock that semantics. Is there a better way to talk about reality which brings the two parts of the epistemological method - models and their measurements, ideas and their impressions, syntax and their semantics - back into an orderly relationship?
Nope. No fact! Goedel did prove a conjunction... an either or statement.apeiron said:But it still is a curious situation. Why does the "why anything?" question provoke hostility to a much greater degree than Godelian incompleteness or Quantum weirdness.
I suppose with Godel, people might take comfort in the fact it proves we are smarter than our logics (Penrose's position for example).
First time we agree.apeiron said:And maths could carry on producing more maths regardless.
Lol!apeiron said:It was seen as a problem about where maths came from rather than where it was going.
With Quantum weirdness, many people perhaps are comforted by the feeling that eventually it will get explained away. They will be able to make a locality-preserving explanation stick. They will be able to break through the Planck-scale and unify QFT and GR. Although also there is the counter-fact that QM is just so concretely successful as a model. It actually can be used for making technology. So all the metaphysical challenges can be shoved aside, as in the Copenhagen interpretation, and the method simply employed - a case of using the syntax without worrying about the embedding semantics. Although, as has been mentioned, logical positivism or scientific pragmatism is still a definite philolosophy.
Anybodys guess?apeiron said:But the "why anything" question gets people's goats. Maybe this is because it seems quasi-religious - it was a reason that gods and other kinds of prime movers were invented. Yet actually even a cursory examination of the question shows that god-style explanations fail as just another variant of effective cause reasoning.
So maybe its time has not properly come? Cosmology is quite a new science really. People are still working through the motions of trying to conjure something out of nothingness, as with the tunnelling out of a quantum vacuum. They are still hoping to demonstrate reality as a necessary mathematical fact, as with string theory, or alternatively, reduce it to some ultimate mathematical contingency, as with Tegmark's multiverse.
I would like to know what you mean by: the lack of semantic content in apparently well-formed statements like "nothing exists"apeiron said:Science looks busy in this area. And so there is hope. And when the foundational crisis - the lack of semantic content in apparently well-formed statements like "nothing exists" - is pointed out, the response switches to "oh well, limits are limits, whereof what we cannot speak, thereof we should remain silent, etc." Shush child, don't mention the emperor forgot his pants.
Damn its late...Just a few comments now and theKen G said:But those two things are saying the same thing: a language is not consistent with logic because it allows a liar sentence to be constructed. The liar sentence is self-referential, which breaks the rules of logic. You claim that a language cannot break the rule of logic because the liar sentence is not self-referential. But it clearly is self-referential, and this has nothing at all to do with logic, it has to do with meaning. The goal of language is to infuse syntax with meaning, so for language to succeed, logic must fail, or vice versa. That's all Tarski is saying as well, you are not disagreeing-- you are merely choosing a different side in the conflict (logic over meaning), but it is the existence of the conflict that is relevant, not which side we choose.
There was always the freedom to adjust logic, it doesn't matter what version is used-- the problem is not resolvable by changing logic. If we allow self-reference in logic, then logic itself is what is broken. If we don't, we can save logic, but the connection with the semantics of language is still broken in the way I mentioned above. Either way, we cannot have a system that does everything we'd like, and that is the fundamental issue-- which evil we choose as the lesser when faced with these limitations is a subjective matter, what we must acknowledge is the existence of the limitation.sigurdW said:First: Your statement that "The liar sentence is self-referential, which breaks the rules of logic." At the time of Tarski Logic was Classical logic allowing self reference! Again: At the time there was no no breach of logic if a sentence was self referent. Now they are excluded so now is different.
Actually I thought that was pretty clear, so let me give you my understanding of what that means. The reductionist approach to physics, where we break everything down to its smallest parts and try to understand the action of everything in terms of elementary interactions between those parts, can be thought of as a kind of syntactic approach. We are trying to understand nature by understanding her syntax, a chain of local causes adding up to one big Cause. But the word "understand" implies a semantic content, which seems impossible to obtain by consideration of pure syntax, just as you could not understand this sentence by analyzing how letters combine to form words or how words are ordered in a sentence. You must have experience, something global or transcendant, to reference, in order to have any hope of following the collisions of meaning in this sentence. An understanding of nature may require similar higher-level processing techniques.sigurdW said:Sorry but "clearly" youre unclear.apeiron said:What the "why anything" question in particular draws attention to is the incompleteness of models of causality based on effective cause - the idea that every event is the result of a chain of events. In physics, this "syntax" gives us the various mechanics, the various models founded on the principle of locality. All useful models, but all limited by the ultimate restrictions of their syntax and unable to talk about the larger semantics that so clearly embeds them.
You said this right after he did give an example. The example was the statement "nothing exists." That's an example of a syntactically well formed statement, which, in a perfect world, would allow its semantic elements to merge in a semantically meaningful way. But we know that doesn't always happen. Lesser difficulties emerge from statements like "green is hot", which require a rather special context to avoid being nonsense. But "nothing exists" seems to assert a claim that is not sheer nonsense, but it encounters semantic bugbears if we dig into it. It confronts us with the problem that our words might not really mean anything in any kind of absolute or unimpeachable way, we find that language is itself a kind of bumbling collision of ideas that somehow manages to make sense but is not guaranteed to be well founded.sigurdW said:I think your tecnique can be improved, why not try giving some examples now and then?
The sentence "nothing exists" has two interpretations: it might mean that there is an object called "nothing" and that said object does not exist, or it means that for any object x then x does not exist. Its a question of how language works, to extend concepts of language to apply to nature seems a risky business. Analogue thinking should be avoided if possible.Ken G said:Actually I thought that was pretty clear, so let me give you my understanding of what that means. The reductionist approach to physics, where we break everything down to its smallest parts and try to understand the action of everything in terms of elementary interactions between those parts, can be thought of as a kind of syntactic approach. We are trying to understand nature by understanding her syntax, a chain of local causes adding up to one big Cause. But the word "understand" implies a semantic content, which seems impossible to obtain by consideration of pure syntax, just as you could not understand this sentence by analyzing how letters combine to form words or how words are ordered in a sentence. You must have experience, something global or transcendant, to reference, in order to have any hope of following the collisions of meaning in this sentence. An understanding of nature may require similar higher-level processing techniques.You said this right after he did give an example. The example was the statement "nothing exists." That's an example of a syntactically well formed statement, which, in a perfect world, would allow its semantic elements to merge in a semantically meaningful way. But we know that doesn't always happen. Lesser difficulties emerge from statements like "green is hot", which require a rather special context to avoid being nonsense. But "nothing exists" seems to assert a claim that is not sheer nonsense, but it encounters semantic bugbears if we dig into it. It confronts us with the problem that our words might not really mean anything in any kind of absolute or unimpeachable way, we find that language is itself a kind of bumbling collision of ideas that somehow manages to make sense but is not guaranteed to be well founded.
It could probably mean a hundred somewhat different things, in fact. Those are two, but there's also meanings like, the term existence is unclear enough that we cannot assert that anything does it. But that might also mean we cannot assert that for any x that x does not exist because we just can't tell. Or, maybe we think the word "exists" is perfectly clear, but the term "thing" is giving the problem and cannot be associated in an unambiguous way with the clear notion of "existence". So if that were the meaning, it would be more like "no things exist," but maybe ideas do, or maybe Platonic forms do, but they are not regarded as things.sigurdW said:The sentence "nothing exists" has two interpretations: it might mean that there is an object called "nothing" and that said object does not exist, or it means that for any object x then x does not exist.
Yes, it is risky, and this is its purpose. It is supposed to be risky, attempting to communicate involves taking risks. I'd say this very thread makes that clear enough! And attempting to communicate about nature is also risky, because we know we will never completely succeed, but we do have our small victories.Its a question of how language works, to extend concepts of language to apply to nature seems a risky business.
On the contrary, that's what thinking is. All thought that is expressed in language is analog thinking, because all language involves drawing analogies, that's exactly what semantics means.Analogue thinking should be avoided if possible.
The purpose of the term "syntax" is to focus on the structure separately from the meaning. So no, meaning is not involved, to whatever extent that separation can be made. That the separation is artificial is a big part of what I've been saying.Also I feel uncomfortable with the concept "syntax" it seems to have to do with joining together words irrespectively of their meanings... but isn't meaning indirectly involved?
The syntax of "nothing exists" is noun-verb. If it doesn't have that syntax, that's how we spot something wrong. Whether or not that noun goes with that verb, or what it means when those words collide, is a matter of semantics, and that's where language gets tricky. That's also where mathematical logic gets tricky-- when we want the mathematical constructs to mean something, not just be correctly syntactically combined.So what use is there in having the concept of "syntax" if it can't spot there's something wrong with the sentence?
Sure, that's common in language: "my name is Ken," or "it is raining now." These statements are contextual, provisional, and goal-oriented-- which is common for semantic usefulness.Read the following : "You are reading this text." When you read it the sentence is true, but left alone it is not true. The truth and therefore perhaps also the meaning of the sentence depends of something not within the sentence.
No! It is ok with selfreference, it does not make logic inconsistent.Ken G said:If we allow self-reference in logic, then logic itself is what is broken.
The topic is Ancient! A fellow named Parmenidesbohm2 said:Why there is something rather than nothing?
What about this indirect subtraction argument against this position posted in post 114 and mentioned in the Rickles piece:sigurdW said:The topic is Ancient! A fellow named Parmenides
gave around three thousand years ago a satisfactory treatment of the problem.
He claimed that the statement:" Nothing is." is self contradictory and therefore not true!
On Explaining ExistenceMetaphysical nihilism (MN)
1. There is a world with a finite number n of concrete objects (accessible from our own: i.e. possible relative to ours). Call this world wn.
2. The existence of any object o in wn is contingent.
3. The non-existence of o does not imply the existence of another object o'.
4. There is a world, wn-1, accessible from wn containing exactly one less object than wn. There is a world accessible from wn-1, w(n-1)-1, containing exactly one less object than wn-1.
5. By iterating the above procedure (i.e. by repeated ‘subtractions’) we arrive at a world wn-m = wmin, accessible from wn, that contains exactly one object.
6. Therefore, by steps 2, 3, 4, from wmin there is an accessible world, wnil = wn-m-1, containing no objects at all (= MN).
Metaphysical nihilism (MN)
1. There is a world with a finite number n of concrete objects (accessible from our own: i.e. possible relative to ours). Call this world wn.
2. The existence of any object o in wn is contingent.
3. The non-existence of o does not imply the existence of another object o'.
4. There is a world, wn-1, accessible from wn containing exactly one less object than wn. There is a world accessible from wn-1, w(n-1)-1, containing exactly one less object than wn-1.
5. By iterating the above procedure (i.e. by repeated ‘subtractions’) we arrive at a world wn-m = wmin, accessible from wn, that contains exactly one object.
6. Therefore, by steps 2, 3, 4, from wmin there is an accessible world, wnil = wn-m-1, containing no objects at all (= MN).
I don't see the similarity.audioloop said:hmm.. very similar to. cosmological argument
bohm2 said:I don't see the similarity.
MarcoD said:No. By similar reasoning, the number 3 cannot exist since on a scale of real numbers, it has probability 0 of existing.
RaptorWizard said:The reason as to why there is something rather than nothing is because the all is mind; the Universe is mental, meaning that it is consciousness and the way that this energy is focused into form that determines our reality, the greatest goal of them all being perception.
bohm2 said:Think of all the possible ways that the world might be, down to every detail. There are infinitely many such possible ways. All these ways seem to be equally probable—which means that the probability of anyone of these infinite possibilities actually occurring seems to be zero, and yet one of them happened. “Now, there’s only one way for there to be Nothing, right?” There are no variants in Nothing; there being Nothing at all is a single state of affairs. And it’s a total state of affairs; that is, it settles everything—every possible proposition has its truth value settled, true or false, usually false, by there being Nothing. So if Nothing is one way for reality to be, and if the total number of ways for reality to be are infinite, and if all such infinite ways are equally probable so that the probability of anyone of them is [essentially] zero, then the probability of ‘there being Nothing’ is also [essentially] zero.” Because there are an infinite number of potential worlds, each specific world would have a zero probability of existing, and because Nothing is only one of these potential worlds—there can be only one kind of Nothing—the probabilily of Nothing existing is zero.
Diffy said:This probability argument bugs me. There are only an infinite number of choices for reality because there is something versus nothing.
So why is it not a 50/50 chance of having something versus having nothing. Why is it that we should include all the possibilities of what reality could be. And who is to say what is not reality is something that could be (or could have been) reality. There is certainly no evidence.
You might want to look at post 180. The authors in those links make the same point you are arguing for, I think. From one of the links in post 180:Diffy said:This probability argument bugs me. There are only an infinite number of choices for reality because there is something versus nothing. So why is it not a 50/50 chance of having something versus having nothing. Why is it that we should include all the possibilities of what reality could be. And who is to say what is not reality is something that could be (or could have been) reality. There is certainly no evidence.
When you win the lottery ticket it may be reasonable to infer that other people bought a ticket but, in any case, the very idea of winning a lottery presupposes that other tickets exist and that the winning ticket has been drawn more or less randomly from the collection of tickets. By contrast, our universe being the way it is (“winning the lottery”) does not presuppose that other universes (with different properties) exist-our evidence is simply neutral in this respect. Furthermore, we have no a priori right to presuppose that the values of the parameters characterizing our universe are bestowed on it by some random process-and so no right to presuppose a probability distribution (uniform or otherwise) of the outcomes. Therefore, a judgment of what is natural to infer from our universe being as it is (with us in it) hangs in the air.
chiro said:Here is a question for you: if you haven't observed something yourself, does that mean it doesn't exist?
Evo said:This is the kind of question that makes me bang my head on my desk. Why do people spend time on such useless questions? Oh, I know, philosophy asks the questions that don't need to be asked. <bangs head on desk>
Carry on.
FreeMitya said:I'm OK with whatever inspires people to think.
Alcatrace IV said:That doesn't explain why things in the ; it merely hints at the nature of interpretive perception
You're reducing the problem from that of the physical to that of the mental and . however, the problem of existence is indifferent to that dichotomy; the phantasms of our haunting have not yet left us in rest. If everything is good, why does good exist? If is only mind, how come the mind exists? Surely, reasoning is not necessary of - otherwise, could simply be factored into nothing but the rational in itself and that is certainly untrue
Why Anything? Why This?If all these worlds exist, we can ask why they do. But, compared with most other cosmic possibilities, the All Worlds Hypothesis may leave less that is unexplained. For example, whatever the number of possible worlds that exist, we have the question, ‘Why that number?’ That question would have been least puzzling if the number that existed were none, and the next least arbitrary possibility seems to be that all these worlds exist. With every other cosmic possibility, we have a further question. If ours is the only world, we can ask: ‘Out of all the possible local worlds, why is this the one that exists?’ On any version of the Many Worlds Hypothesis, we have a similar question: ‘Why do just these worlds exist, with these elements and laws?’ But, if all these worlds exist, there is no such further question...
Though the All Worlds Hypothesis avoids certain questions, it is not as simple, or unarbitrary, as the Null Possibility...Of all the cosmic possibilities, the Null Possibility would have needed the least explanation. As Leibniz pointed out, it is much the simplest, and the least arbitrary. And it is the easiest to understand. It can seem mysterious, for example, how things could exist without their existence having some cause, but there cannot be a causal explanation of why the whole Universe, or God, exists. The Null Possibility raises no such problem. If nothing had ever existed, that state of affairs would not have needed to be caused.