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Post by Elizabeth on Aug 8, 2020 5:57:23 GMT
Heard this recently from someone who likes philosophy and loved the quote. What are your thoughts of it?
To search for God with logical proof .. is like searching for the Sun with a Lamp. Sufi poverb
I think it makes all the sense in the world. Good job Sufi...whoever/whatever you are. I say this because people are searching for it the wrong way. Turn the lamp off and find the light of the sun. Turn off the way you think your logic works and find how things truly work.
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Post by karl on Aug 8, 2020 6:10:35 GMT
The existence of God can't be logically deduced. Belief in God is an introspective experience. Similarly, free will can't be logically deduced either. It's something we intuitively sense.
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Post by Eugene 2.0 on Aug 8, 2020 6:53:01 GMT
Some - natural theologists, like R. Swinburne or A. Plantinga - believe that it's possible to derivate very existence of God from some axioms and some other concepts. I really don't know if this is to be possible.
But the quote - I do like. It's seriously pretty cool, because of its too obviousness. I guess there must be some people who collect such phrases.
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Post by karl on Aug 8, 2020 8:05:40 GMT
Some - natural theologists, like R. Swinburne or A. Plantinga - believe that it's possible to derivate very existence of God from some axioms and some other concepts. I really don't know if this is to be possible. But the quote - I do like. It's seriously pretty cool, because of its too obviousness. I guess there must be some people who collect such phrases.
Here's Kurt Gödel's attempt. In my view, its weakness is that it premises that there is no distinction between what we can imagine and what's actually real. It's like saying: "What we imagine as God must exist within our imagination." I think this reflects a deeper aspect of Gödel's understanding of reality. I don't think he made a proper distinction himself between what may be observed introspectively, and what we observe in the external world. To him, exploring the world of introspection was just as much a science as physics. And, in fact, may even take precedent over natural sciences. He even stated to a young physics student once: "I don't believe in natural science."
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: If a property is positive, then its negation is not positive.
Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is positive
Axiom 6: For any property P, if P is positive, then being necessarily P is positive.
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.
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Post by Eugene 2.0 on Aug 8, 2020 9:50:03 GMT
Some - natural theologists, like R. Swinburne or A. Plantinga - believe that it's possible to derivate very existence of God from some axioms and some other concepts. I really don't know if this is to be possible. But the quote - I do like. It's seriously pretty cool, because of its too obviousness. I guess there must be some people who collect such phrases.
Here's Kurt Gödel's attempt. In my view, its weakness is that it premises that there is no distinction between what we can imagine and what's actually real. It's like saying: "What we imagine as God must exist within our imagination." I think this reflects a deeper aspect of Gödel's understanding of reality. I don't think he made a proper distinction himself between what may be observed introspectively, and what we observe in the external world. To him, exploring the world of introspection was just as much a science as physics. And, in fact, may even take precedent over natural sciences. He even stated to a young physics student once: "I don't believe in natural science."
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: If a property is positive, then its negation is not positive.
Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is positive
Axiom 6: For any property P, if P is positive, then being necessarily P is positive.
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.
Yes! Thank you for this add. Because Godel had the version too. First of all, I do agree about how did you said about the distinction Godel tried to draw. I'm not sure, but Rorty, I've been recently read his "Philosophy and the Mirror of Nature", in Ch. II said that Kant and many other philosophers wasn't correctly with distinction external and internal mental representations i.e. concepts and intuitions. The firsts are what is almost always has no contradictions, its almost ideal and well-structured - what we bear in our minds. The other one is quite shaky and not fully-comprehensible, because of material-like nature of it (being honestly, I can't say I get these descriptions well). In yours, if I understood it correctly, "can be imagined" and "the real" must be distinct in the premises, because "conceivable" (="what can be imagined") doesn't imply "the real". They say there are also some theories of multiverse. I don't the stuff, and content of it properly, 'cause I didn't study it, but I guess it's correct to say that the theories have modal logics, i.e. they're using "plural worlds" concepts. If so, then the proof of Godel might be magnified. (Also, I've heard that Godel said that he believes in a priori truths only. And A. Tarski said that too. Recently I've met on the Net one of Tarski's students John Corcoran. He's been publishing his articles and works almost all the time. He asked me to translate some works into Ukrainian or Russian... My laziness hasn't allowed me yet to start it. But I'd like to. From his articles it becomes more clear that Tarksi and Gogel were friends and cooperated together. In the Net there are also photos of Godel and Tarski as two friends.) And also to the positiveness. Isn't this adjective to be sorta subjective? If so, then where be many Gods. And as soon as I know it's not positive to have two Gods that contradict each other (I have to choose), then it's not positive (one of those God must be not positive). Thanks again for presenting the detailed proof of Godel. I haven't seen anything like this before. Just heard of it.
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Post by karl on Aug 8, 2020 10:42:31 GMT
Here's Kurt Gödel's attempt. In my view, its weakness is that it premises that there is no distinction between what we can imagine and what's actually real. It's like saying: "What we imagine as God must exist within our imagination." I think this reflects a deeper aspect of Gödel's understanding of reality. I don't think he made a proper distinction himself between what may be observed introspectively, and what we observe in the external world. To him, exploring the world of introspection was just as much a science as physics. And, in fact, may even take precedent over natural sciences. He even stated to a young physics student once: "I don't believe in natural science."
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: If a property is positive, then its negation is not positive.
Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is positive
Axiom 6: For any property P, if P is positive, then being necessarily P is positive.
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.
Yes! Thank you for this add. Because Godel had the version too. First of all, I do agree about how did you said about the distinction Godel tried to draw. I'm not sure, but Rorty, I've been recently read his "Philosophy and the Mirror of Nature", in Ch. II said that Kant and many other philosophers wasn't correctly with distinction external and internal mental representations i.e. concepts and intuitions. The firsts are what is almost always has no contradictions, its almost ideal and well-structured - what we bear in our minds. The other one is quite shaky and not fully-comprehensible, because of material-like nature of it (being honestly, I can't say I get these descriptions well). In yours, if I understood it correctly, "can be imagined" and "the real" must be distinct in the premises, because "conceivable" (="what can be imagined") doesn't imply "the real". They say there are also some theories of multiverse. I don't the stuff, and content of it properly, 'cause I didn't study it, but I guess it's correct to say that the theories have modal logics, i.e. they're using "plural worlds" concepts. If so, then the proof of Godel might be magnified. (Also, I've heard that Godel said that he believes in a priori truths only. And A. Tarski said that too. Recently I've met on the Net one of Tarski's students John Corcoran. He's been publishing his articles and works almost all the time. He asked me to translate some works into Ukrainian or Russian... My laziness hasn't allowed me yet to start it. But I'd like to. From his articles it becomes more clear that Tarksi and Gogel were friends and cooperated together. In the Net there are also photos of Godel and Tarski as two friends.) And also to the positiveness. Isn't this adjective to be sorta subjective? If so, then where be many Gods. And as soon as I know it's not positive to have two Gods that contradict each other (I have to choose), then it's not positive (one of those God must be not positive). Thanks again for presenting the detailed proof of Godel. I haven't seen anything like this before. Just heard of it.
Yes. This touches upon a discussion we've had earlier. When we're referring to lifeless objects like, for example, a stone, it's not so obvious how to make a distinction between the real object and how we perceive it. Berkley made a very good argument for that there cannot be such a distinction. We believe in the existence of a stone because we can observe it, and the stone has no consciousness, so what does it even mean for it to have an existence outside of our consciousness? Well, it may indirectly influence other objects, or conscious beings for that matter, that we, in turn observe. But what if the stone is somewhere beyond the Hubble radius, where it cannot influence anything in our part of the universe in any way? One could make the claim that it's meaningless to state that it actually exists, when its existence cannot be perceived, directly or indirectly. However, that does not apply with the object in question if it is a subject with consciousness. Even if I could make the argument that a stone doesn't exist if it cannot influence anyone's conscious experience, I cannot make the argument that your existence depends on someone observing you. This is why I care not for the Schrödinger's cat thought experiment, for the cat knows itself whether it's being poisoned.
As I pointed out in a previous discussion, a world outside of the Hubble radius can be said to exist, if it's inhabited by conscious subjects. And the realisation that there exists a reality independent of my conscious experience, is to have discovered the meaning of objectivity. The difference between a God that only exists within our imagination, and a God that independently exists, is that the latter is conscious. And what is conscious may exercise will, one way or another. Gödel's proof doesn't state whether the God that is proven to exist has consciousness.
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Post by Eugene 2.0 on Aug 8, 2020 15:05:20 GMT
Yes! Thank you for this add. Because Godel had the version too. First of all, I do agree about how did you said about the distinction Godel tried to draw. I'm not sure, but Rorty, I've been recently read his "Philosophy and the Mirror of Nature", in Ch. II said that Kant and many other philosophers wasn't correctly with distinction external and internal mental representations i.e. concepts and intuitions. The firsts are what is almost always has no contradictions, its almost ideal and well-structured - what we bear in our minds. The other one is quite shaky and not fully-comprehensible, because of material-like nature of it (being honestly, I can't say I get these descriptions well). In yours, if I understood it correctly, "can be imagined" and "the real" must be distinct in the premises, because "conceivable" (="what can be imagined") doesn't imply "the real". They say there are also some theories of multiverse. I don't the stuff, and content of it properly, 'cause I didn't study it, but I guess it's correct to say that the theories have modal logics, i.e. they're using "plural worlds" concepts. If so, then the proof of Godel might be magnified. (Also, I've heard that Godel said that he believes in a priori truths only. And A. Tarski said that too. Recently I've met on the Net one of Tarski's students John Corcoran. He's been publishing his articles and works almost all the time. He asked me to translate some works into Ukrainian or Russian... My laziness hasn't allowed me yet to start it. But I'd like to. From his articles it becomes more clear that Tarksi and Gogel were friends and cooperated together. In the Net there are also photos of Godel and Tarski as two friends.) And also to the positiveness. Isn't this adjective to be sorta subjective? If so, then where be many Gods. And as soon as I know it's not positive to have two Gods that contradict each other (I have to choose), then it's not positive (one of those God must be not positive). Thanks again for presenting the detailed proof of Godel. I haven't seen anything like this before. Just heard of it.
Yes. This touches upon a discussion we've had earlier. When we're referring to lifeless objects like, for example, a stone, it's not so obvious how to make a distinction between the real object and how we perceive it. Berkley made a very good argument for that there cannot be such a distinction. We believe in the existence of a stone because we can observe it, and the stone has no consciousness, so what does it even mean for it to have an existence outside of our consciousness? Well, it may indirectly influence other objects, or conscious beings for that matter, that we, in turn observe. But what if the stone is somewhere beyond the Hubble radius, where it cannot influence anything in our part of the universe in any way? One could make the claim that it's meaningless to state that it actually exists, when its existence cannot be perceived, directly or indirectly. However, that does not apply with the object in question if it is a subject with consciousness. Even if I could make the argument that a stone doesn't exist if it cannot influence anyone's conscious experience, I cannot make the argument that your existence depends on someone observing you. This is why I care not for the Schrödinger's cat thought experiment, for the cat knows itself whether it's being poisoned.
As I pointed out in a previous discussion, a world outside of the Hubble radius can be said to exist, if it's inhabited by conscious subjects. And the realisation that there exists a reality independent of my conscious experience, is to have discovered the meaning of objectivity. The difference between a God that only exists within our imagination, and a God that independently exists, is that the latter is conscious. And what is conscious may exercise will, one way or another. Gödel's proof doesn't state whether the God that is proven to exist has consciousness.
I mentioned about bishop Berkeley today... but I don't remember in which post exactly. Hmm... Berkeley was too strong and unmerciful to the materialists, and perhaps, left no chances to them. I've read a joke-shape logical task from Smullyan. It says: "If the boiler isn't watched (viewed, observed), it won't boil". To unprove it I have to watch on the boiler; else, I don't really know what's wrong with it (to the Schrёdinger's cat). I believe in matter in my own way. All that is a matter is everything we can handle with. We can shape it how we want and so on. If I can shape the one (make a little move, make a little change, use it, push it...), then this one is a material, the matter; else - I have no sure. Samuel Johnson, as it's been said, tried to argue to George Berkeley pushing a rock on a road with some force. Berkeley answered that philosophy is never be refuted through kicking. Maybe relating to philosophy Berkeley was right, but was he right about our knowledge? If we kicked a rock in out life (or made anything, that allowed us to conclude that there's a matter), then we don't need Berkeley's view anymore. Why? Because Berkeley's view is what we'd been holding till we did something (that allowed us to suppose that there's a matter). We don't have any solid knowledge about our material world, because we never sure about the work of its laws, and if there are such laws. Meanwhile I tried to formalize Gёdel's proof. That is what I've got. Def 1: God-like(x)≡!∃xP(x) (!x - exclusively positive) Def 2: A(x)≡∀B□[B(x)]≡.A⊃B Def 3: □[∃x??⊃□∀E]? - this definition is weird and uncompleted. I don't know how Godel has formulated it. A1: E(x)⊃P(x)⊃.~E(x)⊃~P(x) A2: P(x)⊃.ϕ(x)⊃P(x) (why there this axiom here? it's pretty obvious) A3: God-like(x)⊃P(x) A4: P(x)⊃□P(x) (I can't say this argument is obvious; one of Frege's theorem was □ϕ⊢ϕ) A5: □∃xϕ(x)⊃P(x) (This axiom perhaps is needed to be filled with quantor of second-order logic ∀ϕ) A6: ∀p[P(p)⊃□P(p)] T1: ⊢ P(p)⊃.{~[P(p)&~P(p)]&!∃pP(p)} (equivalence for "i.e."?..) C1: ~[God-like(p)&~God-like(p)]&∃pGod-like(p) (isn't it too strictly to get it? it must be the same to say A5, but it has one route: from antecedent to consequent, not vice versa; we can't derive from P(x)⊃God-like(x)) T2: ⊢ God-like(x)⊃!∃xGod-like(x) (I am not sure here) T3: ⊢ □{~[God-like(x)&~God-like(x)]&∃xGod-like(x)}
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Post by karl on Aug 9, 2020 5:32:12 GMT
Yes. This touches upon a discussion we've had earlier. When we're referring to lifeless objects like, for example, a stone, it's not so obvious how to make a distinction between the real object and how we perceive it. Berkley made a very good argument for that there cannot be such a distinction. We believe in the existence of a stone because we can observe it, and the stone has no consciousness, so what does it even mean for it to have an existence outside of our consciousness? Well, it may indirectly influence other objects, or conscious beings for that matter, that we, in turn observe. But what if the stone is somewhere beyond the Hubble radius, where it cannot influence anything in our part of the universe in any way? One could make the claim that it's meaningless to state that it actually exists, when its existence cannot be perceived, directly or indirectly. However, that does not apply with the object in question if it is a subject with consciousness. Even if I could make the argument that a stone doesn't exist if it cannot influence anyone's conscious experience, I cannot make the argument that your existence depends on someone observing you. This is why I care not for the Schrödinger's cat thought experiment, for the cat knows itself whether it's being poisoned.
As I pointed out in a previous discussion, a world outside of the Hubble radius can be said to exist, if it's inhabited by conscious subjects. And the realisation that there exists a reality independent of my conscious experience, is to have discovered the meaning of objectivity. The difference between a God that only exists within our imagination, and a God that independently exists, is that the latter is conscious. And what is conscious may exercise will, one way or another. Gödel's proof doesn't state whether the God that is proven to exist has consciousness.
I mentioned about bishop Berkeley today... but I don't remember in which post exactly. Hmm... Berkeley was too strong and unmerciful to the materialists, and perhaps, left no chances to them. I've read a joke-shape logical task from Smullyan. It says: "If the boiler isn't watched (viewed, observed), it won't boil". To unprove it I have to watch on the boiler; else, I don't really know what's wrong with it (to the Schrёdinger's cat). I believe in matter in my own way. All that is a matter is everything we can handle with. We can shape it how we want and so on. If I can shape the one (make a little move, make a little change, use it, push it...), then this one is a material, the matter; else - I have no sure. Samuel Johnson, as it's been said, tried to argue to George Berkeley pushing a rock on a road with some force. Berkeley answered that philosophy is never be refuted through kicking. Maybe relating to philosophy Berkeley was right, but was he right about our knowledge? If we kicked a rock in out life (or made anything, that allowed us to conclude that there's a matter), then we don't need Berkeley's view anymore. Why? Because Berkeley's view is what we'd been holding till we did something (that allowed us to suppose that there's a matter). We don't have any solid knowledge about our material world, because we never sure about the work of its laws, and if there are such laws. Meanwhile I tried to formalize Gёdel's proof. That is what I've got. Def 1: God-like(x)≡!∃xP(x) (!x - exclusively positive) Def 2: A(x)≡∀B□[B(x)]≡.A⊃B Def 3: □[∃x??⊃□∀E]? - this definition is weird and uncompleted. I don't know how Godel has formulated it. A1: E(x)⊃P(x)⊃.~E(x)⊃~P(x) A2: P(x)⊃.ϕ(x)⊃P(x) (why there this axiom here? it's pretty obvious) A3: God-like(x)⊃P(x) A4: P(x)⊃□P(x) (I can't say this argument is obvious; one of Frege's theorem was □ϕ⊢ϕ) A5: □∃xϕ(x)⊃P(x) (This axiom perhaps is needed to be filled with quantor of second-order logic ∀ϕ) A6: ∀p[P(p)⊃□P(p)] T1: ⊢ P(p)⊃.{~[P(p)&~P(p)]&!∃pP(p)} (equivalence for "i.e."?..) C1: ~[God-like(p)&~God-like(p)]&∃pGod-like(p) (isn't it too strictly to get it? it must be the same to say A5, but it has one route: from antecedent to consequent, not vice versa; we can't derive from P(x)⊃God-like(x)) T2: ⊢ God-like(x)⊃!∃xGod-like(x) (I am not sure here) T3: ⊢ □{~[God-like(x)&~God-like(x)]&∃xGod-like(x)}
The key to understanding Gödel's thinking lies in the first theorem:
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
To state that exemplification is the same as consistency could be justified as follows: I would have no conception of blue if the colour blue was never exemplified. So if I claim that there exists a colour no one has ever seen, one could state that this colour, as a property, is not consistent.
But the property of being God-like is a collection of properties. This would be the equivalent of stating that the concept of a unicorn is not consistent if it doesn't exist. But the fundamental difference between the concept of the unicorn and the concept of the colour no one has seen, is that a unicorn consists for properties that are all individually exemplified.
However, if one disregards the distinction between the real world and the world of imagination, then this becomes irrelevant. Being God-like means having all positive properties, and since all positive properties can be exemplified individually, the property of having all positive properties can also be exemplified, as in, imagined.
You wondered about Axiom 2. The reason for axiom 2 is that it's needed for knowing that consistency (being exemplified) is a positive property. If consistency is not a positive property, then it cannot be part of being god-like, since being god-like only consists of positive properties.
As for axiom 4: I think we are to see it as self-evident within the context of God only having positive properties. Like, if God have the power to change the world, then there cannot be ambiguity to whether that is a positive or not. This is no Gnostic God. This is God as the deity perceived as flawless. "positive" is not just the mathematical positive, but also means "good".
My own view about the existence of a stone, is that a stone does exists independently from my own consciousness, but it doesn't exist independently from any consciousness. The stone exists in its potential for being observed by some conscious being, whether directly or indirectly in how the stone may affect other objects or subjects. And if there exists an uninhabited universe out there, it could be said to exist if it's observed by God.
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Post by Eugene 2.0 on Aug 9, 2020 23:38:59 GMT
I mentioned about bishop Berkeley today... but I don't remember in which post exactly. Hmm... Berkeley was too strong and unmerciful to the materialists, and perhaps, left no chances to them. I've read a joke-shape logical task from Smullyan. It says: "If the boiler isn't watched (viewed, observed), it won't boil". To unprove it I have to watch on the boiler; else, I don't really know what's wrong with it (to the Schrёdinger's cat). I believe in matter in my own way. All that is a matter is everything we can handle with. We can shape it how we want and so on. If I can shape the one (make a little move, make a little change, use it, push it...), then this one is a material, the matter; else - I have no sure. Samuel Johnson, as it's been said, tried to argue to George Berkeley pushing a rock on a road with some force. Berkeley answered that philosophy is never be refuted through kicking. Maybe relating to philosophy Berkeley was right, but was he right about our knowledge? If we kicked a rock in out life (or made anything, that allowed us to conclude that there's a matter), then we don't need Berkeley's view anymore. Why? Because Berkeley's view is what we'd been holding till we did something (that allowed us to suppose that there's a matter). We don't have any solid knowledge about our material world, because we never sure about the work of its laws, and if there are such laws. Meanwhile I tried to formalize Gёdel's proof. That is what I've got. Def 1: God-like(x)≡!∃xP(x) (!x - exclusively positive) Def 2: A(x)≡∀B□[B(x)]≡.A⊃B Def 3: □[∃x??⊃□∀E]? - this definition is weird and uncompleted. I don't know how Godel has formulated it. A1: E(x)⊃P(x)⊃.~E(x)⊃~P(x) A2: P(x)⊃.ϕ(x)⊃P(x) (why there this axiom here? it's pretty obvious) A3: God-like(x)⊃P(x) A4: P(x)⊃□P(x) (I can't say this argument is obvious; one of Frege's theorem was □ϕ⊢ϕ) A5: □∃xϕ(x)⊃P(x) (This axiom perhaps is needed to be filled with quantor of second-order logic ∀ϕ) A6: ∀p[P(p)⊃□P(p)] T1: ⊢ P(p)⊃.{~[P(p)&~P(p)]&!∃pP(p)} (equivalence for "i.e."?..) C1: ~[God-like(p)&~God-like(p)]&∃pGod-like(p) (isn't it too strictly to get it? it must be the same to say A5, but it has one route: from antecedent to consequent, not vice versa; we can't derive from P(x)⊃God-like(x)) T2: ⊢ God-like(x)⊃!∃xGod-like(x) (I am not sure here) T3: ⊢ □{~[God-like(x)&~God-like(x)]&∃xGod-like(x)}
The key to understanding Gödel's thinking lies in the first theorem:
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
To state that exemplification is the same as consistency could be justified as follows: I would have no conception of blue if the colour blue was never exemplified. So if I claim that there exists a colour no one has ever seen, one could state that this colour, as a property, is not consistent.
But the property of being God-like is a collection of properties. This would be the equivalent of stating that the concept of a unicorn is not consistent if it doesn't exist. But the fundamental difference between the concept of the unicorn and the concept of the colour no one has seen, is that a unicorn consists for properties that are all individually exemplified.
However, if one disregards the distinction between the real world and the world of imagination, then this becomes irrelevant. Being God-like means having all positive properties, and since all positive properties can be exemplified individually, the property of having all positive properties can also be exemplified, as in, imagined.
You wondered about Axiom 2. The reason for axiom 2 is that it's needed for knowing that consistency (being exemplified) is a positive property. If consistency is not a positive property, then it cannot be part of being god-like, since being god-like only consists of positive properties.
As for axiom 4: I think we are to see it as self-evident within the context of God only having positive properties. Like, if God have the power to change the world, then there cannot be ambiguity to whether that is a positive or not. This is no Gnostic God. This is God as the deity perceived as flawless. "positive" is not just the mathematical positive, but also means "good".
My own view about the existence of a stone, is that a stone does exists independently from my own consciousness, but it doesn't exist independently from any consciousness. The stone exists in its potential for being observed by some conscious being, whether directly or indirectly in how the stone may affect other objects or subjects. And if there exists an uninhabited universe out there, it could be said to exist if it's observed by God.
Thank you for this detailed explanation. I'll try to turn back to this a bit later. Now I wanted to check the 1st: the consistency. p is inconsistent iff it implies e.g. q&~q. Having no experience of a particular colour - isn't it inconsistent (theoretical view)? Maybe it is for usual conditions, but modally it can be overcome: the non-exemplified consistency is possible. About the axioms: thanks again for paying attention to my remarks. I wanted to understand how to construct relevant formulas. I guess the 50% of success in such proofs is their smooth and fitted shape. And there are some problems of mine, because I don't get along well with all that notation techniques.
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Post by karl on Aug 10, 2020 7:01:29 GMT
The key to understanding Gödel's thinking lies in the first theorem:
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
To state that exemplification is the same as consistency could be justified as follows: I would have no conception of blue if the colour blue was never exemplified. So if I claim that there exists a colour no one has ever seen, one could state that this colour, as a property, is not consistent.
But the property of being God-like is a collection of properties. This would be the equivalent of stating that the concept of a unicorn is not consistent if it doesn't exist. But the fundamental difference between the concept of the unicorn and the concept of the colour no one has seen, is that a unicorn consists for properties that are all individually exemplified.
However, if one disregards the distinction between the real world and the world of imagination, then this becomes irrelevant. Being God-like means having all positive properties, and since all positive properties can be exemplified individually, the property of having all positive properties can also be exemplified, as in, imagined.
You wondered about Axiom 2. The reason for axiom 2 is that it's needed for knowing that consistency (being exemplified) is a positive property. If consistency is not a positive property, then it cannot be part of being god-like, since being god-like only consists of positive properties.
As for axiom 4: I think we are to see it as self-evident within the context of God only having positive properties. Like, if God have the power to change the world, then there cannot be ambiguity to whether that is a positive or not. This is no Gnostic God. This is God as the deity perceived as flawless. "positive" is not just the mathematical positive, but also means "good".
My own view about the existence of a stone, is that a stone does exists independently from my own consciousness, but it doesn't exist independently from any consciousness. The stone exists in its potential for being observed by some conscious being, whether directly or indirectly in how the stone may affect other objects or subjects. And if there exists an uninhabited universe out there, it could be said to exist if it's observed by God.
Thank you for this detailed explanation. I'll try to turn back to this a bit later. Now I wanted to check the 1st: the consistency. p is inconsistent iff it implies e.g. q&~q. Having no experience of a particular colour - isn't it inconsistent (theoretical view)? Maybe it is for usual conditions, but modally it can be overcome: the non-exemplified consistency is possible. About the axioms: thanks again for paying attention to my remarks. I wanted to understand how to construct relevant formulas. I guess the 50% of success in such proofs is their smooth and fitted shape. And there are some problems of mine, because I don't get along well with all that notation techniques.
I just want to clarify that I was referring to a colour no one has seen and no one will ever see. It's a colour no one will ever be able to imagine. (And, to not complicate things, lets also, for this example, rule out the existence of God, so we don't have to bother with the possibility of God being able to imagine this colour. ) Is then the very concept of that colour consistent? If something can't be exemplified in either the imagined or the real world, is that "something" even a meaningful concept?
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Post by Eugene 2.0 on Aug 10, 2020 8:08:53 GMT
Thank you for this detailed explanation. I'll try to turn back to this a bit later. Now I wanted to check the 1st: the consistency. p is inconsistent iff it implies e.g. q&~q. Having no experience of a particular colour - isn't it inconsistent (theoretical view)? Maybe it is for usual conditions, but modally it can be overcome: the non-exemplified consistency is possible. About the axioms: thanks again for paying attention to my remarks. I wanted to understand how to construct relevant formulas. I guess the 50% of success in such proofs is their smooth and fitted shape. And there are some problems of mine, because I don't get along well with all that notation techniques.
I just want to clarify that I was referring to a colour no one has seen and no one will ever see. It's a colour no one will ever be able to imagine. (And, to not complicate things, lets also, for this example, rule out the existence of God, so we don't have to bother with the possibility of God being able to imagine this colour. ) Is then the very concept of that colour consistent? If something can't be exemplified in either the imagined or the real world, is that "something" even a meaningful concept?
Now I see where I've failed. Unimaginable is neither consistent, nor inconsistent - according to Plato ("The Sophist", second before the last chapter); and it exists in a special ontological way by A. Meinong. Can't say I comprehend the last one (Meinong's) interpretation, but it is too close to: _ |- _ - this mean nothing implies nothing (it uses actively in the Sequencional Calculus). According to Plato the must br no meaning in such empty conceptions. Despite of it my intuition keeps saying that it must be the one. And it's important that there might be a draw line between absolutely unimaginable and occasionally unimaginable. (Absolutely non-comprehensive and occasionally non-comprehensive.) As soon as we don't even know how to draw such a line our answers have to make a stop here.
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Post by Eugene 2.0 on Aug 10, 2020 8:17:11 GMT
Also, turning back to the definition of inconsistency I have given, unimaginable (non-comprehensive or inconceivable) beyond of it.
I think it's interesting to compare such views with the ones Lovecraft had on the nature of nightmare, horror, and most notably on fear.
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Post by karl on Aug 10, 2020 10:26:29 GMT
I just want to clarify that I was referring to a colour no one has seen and no one will ever see. It's a colour no one will ever be able to imagine. (And, to not complicate things, lets also, for this example, rule out the existence of God, so we don't have to bother with the possibility of God being able to imagine this colour. ) Is then the very concept of that colour consistent? If something can't be exemplified in either the imagined or the real world, is that "something" even a meaningful concept?
Now I see where I've failed. Unimaginable is neither consistent, nor inconsistent - according to Plato ("The Sophist", second before the last chapter); and it exists in a special ontological way by A. Meinong. Can't say I comprehend the last one (Meinong's) interpretation, but it is too close to: _ |- _ - this mean nothing implies nothing (it uses actively in the Sequencional Calculus). According to Plato the must br no meaning in such empty conceptions. Despite of it my intuition keeps saying that it must be the one. And it's important that there might be a draw line between absolutely unimaginable and occasionally unimaginable. (Absolutely non-comprehensive and occasionally non-comprehensive.) As soon as we don't even know how to draw such a line our answers have to make a stop here. If I understood you correctly, then I agree. Let me also clarify that I was explaining how I saw Gödel's use of the term consistency. I would myself refer to a colour that can't be imagined as nonsense.
However, here's how one can make a case for that it's about consistency.
A: "There exists a colour that cannot be imagined." B: "If it cannot be imagined, it can't exist, so your statement contradicts itself."
My point was that I believed that I could make sense of how Gödel used it in the proof. One problem with the proof is that he neither defines "positive" nor "consistent". That is why I also gave my own interpretation for why he wrote that God has all positive properties.
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Post by karl on Aug 10, 2020 10:28:18 GMT
Also, turning back to the definition of inconsistency I have given, unimaginable (non-comprehensive or inconceivable) beyond of it. I think it's interesting to compare such views with the ones Lovecraft had on the nature of nightmare, horror, and most notably on fear.
And what did Lovecraft write about fear and nightmares? I have only read one book by him, and I can't remember any reference to that.
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Post by Eugene 2.0 on Aug 10, 2020 21:00:23 GMT
Now I see where I've failed. Unimaginable is neither consistent, nor inconsistent - according to Plato ("The Sophist", second before the last chapter); and it exists in a special ontological way by A. Meinong. Can't say I comprehend the last one (Meinong's) interpretation, but it is too close to: _ |- _ - this mean nothing implies nothing (it uses actively in the Sequencional Calculus). According to Plato the must br no meaning in such empty conceptions. Despite of it my intuition keeps saying that it must be the one. And it's important that there might be a draw line between absolutely unimaginable and occasionally unimaginable. (Absolutely non-comprehensive and occasionally non-comprehensive.) As soon as we don't even know how to draw such a line our answers have to make a stop here. If I understood you correctly, then I agree. Let me also clarify that I was explaining how I saw Gödel's use of the term consistency. I would myself refer to a colour that can't be imagined as nonsense.
However, here's how one can make a case for that it's about consistency.
A: "There exists a colour that cannot be imagined." B: "If it cannot be imagined, it can't exist, so your statement contradicts itself."
My point was that I believed that I could make sense of how Gödel used it in the proof. One problem with the proof is that he neither defines "positive" nor "consistent". That is why I also gave my own interpretation for why he wrote that God has all positive properties.
Sorry for my misunderstanding that. I believe Godel used the definition of inconsistency as in "Principia Mathematica". So, in a wider sense, the theorem P is consistent iff it doesn't imply contradiction; in a narrow: iff P is not a tautology. A - colour that is unimaginable is, in my opinion, can be both: a) oxymoron; b) it's possible. I think (a) or (b) depend on do we need to rely on an observer? Because the colour is what must be observed by an observer. So, there must be an observer. An existence of color implies existence of a watcher. As in the case of the existence of an observer I think we need to understand that the observer is the one who is able to observe something (that he has to observe). Inability of approaching it denies all our construction of (b) - an existence of an observer. Just like in case when by a some reason I can't do what I've done before. - I have such an example. At the beginning of this August I lost an ability to hear well by one ear. It was my fault when I blew my nose doing it by both sides simultaneously. I did it not intentionally, but it made my ear to stop functioning as it were previously. Besides some strange high pitch voice occurred. Visiting doctor helped me, but I hadn't fixed it completely yet, and I don't even know about further. Surely, this circumstance teared me down, because the process of listening to the music or listening audiobooks have been changed. And my feeling of the process didn't make me a believer that the part of sound that I had heard before didn't exist anymore. Surely, that what I've been experiencing is what I believe to. The past is what quickly disappearing at each moment of our life. With the past our feelings are being carried out. But I do believe that even completely unimaginable things may be imagined if we will have gotten an ability to hear it or watch it. It's like in Lovecraft's novel "From Beyond". A doctor created the machine that allowed people to change their brain frequency (I don't remember what exactly it does, but it changed our physical feelings somehow). And it allowed a protagonist of the novel to meet some creepy creatures from the other dimensions. (By the way I highly recommend a movie by this novel "From Beyond" (1986) by S. Gordon. This movie is awesome horror by the time. It's one of my favourite.) Some problems with an ability of partially or fully acquiring something by our physiological parts of body may occur during our philosophical researches. I suppose one of this problem is: incomplete things seem to be completed. I think we do it all the time, it's, according to Kant or some psychologists, a phenomena of the apperception. We up-construct things to its "ideal" forms with our "previous" views on it. - On this I think that the phenomena is quite messy when we try to comprehend it closely. Saying that we up-construct things we wanted to say that indeed anything has particles/elements, and in turn the elements are grouped or somehow related to each other. And what makes them to be related? - "Something" that is not the elements; something different to the elements. The last one thought I tie with Predicate Logic Universal instantiation and Existential generalization, in particular a logical leap from ∀xPx to Py, and from Py to ∃xPx. I think that such an expression as Py (or Px) is incomplete, however it usually is understood by us as a completed one, a defined thing. We can't avoid it, because each such Fy is 𝑓x and i.e. some AxRBxR...RZx formula. The last one formula (we don't know exactly its composition, but we do know that it must be something like this) has another logic, e.g. A to Z must be presented as attributes to x, and, according to such a logic, if one alphabet letter would be gone, then it wouldn't be 𝑓x, and therefore Fy. All such a logic is cycling around the "y" (or "x" in the more generalized formula 𝑓x). As soon as we don't know the nature of it we can't be sure in our investigations. And the last chapter must be closer to the question of being and non-being or "existence" and "non-existence" and how can they be related, how can they deal to each other; and if there some logic behind them. The incompleteness of the formulas like Fy is what closer to "nothing" or unimaginable, than any other. Why? Because if we take sentences like "this sentence is true if it is non-uttered (non-explicit)" or "if this sentence is true it isn't written with Latin symbols" we get oxymoron or self-contradicted forms. By the way the word "true" here is a kind of substitute for "sentence is sentence": "this sentence is this sentence if it isn't uttered". ...Ok, I said lots of things. I hope it wasn't boring reading =)
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