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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 Eugene 2.0 on Aug 10, 2020 21:09:01 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.
Throughout last two decades we know that Lovecraft wasn't only novelist. He wrote many essays, letters, comedy/fun stories, and did in some other genres too. The theme of the fear is wide. The most featured essay of it is "Supernatural Horror in Literature" (1925-27). Then were some letters (I can't remember specifically, but I do know that this info can be found in S. T. Joshi's bio of Lovecraft. Joshi made one of the fullest description of Lovecraft life. I read it book of Lovecraft's bio where each day of life of Lovecraft was described) where he continued this theme. In many books of him like "Call of Cthulhu", "At Mountains of Madness", "Pickman's Model" and many other he made partially some notes on it. Therefore there are many quotes from those novels. The favourite of mine (I don't know the place of it in the novels; I caught it in the 2006 game "Call of Cthulhu: Dark Corners of the Earth"): "Horror - the true horror that paralyzes the mind and scars it with nightmares - is never truly healed".
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Post by karl on Aug 12, 2020 10:21:42 GMT
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 =)
I didn't discover this post before now. I missed it due to that clicking on this link just lead me to your last post about Lovecraft.
Yes, the existence of a colour does premise the existence of an observer, since a colour is something that is consciously experienced. However, in this I need to make the distinction between the potential of being observed and actually being observed. Let's say that those animals who see utraviolet see a colour that is fundamentally different from the colours we see. (That doesn't necessarily have to be the case. When we see violet, which is a frequency higher than blue, we're not seeing anything different from violet as a mix between blue and red. But, again, let's say that ultraviolet is an entirely new colour.) Then imagine that all conscious beings that are able to see it suddenly die. That doesn't mean the colour ceases to exist. The colour still exists in that it has the potential of being observed. So, yes, what you could hear before still exists, even if you can't hear it the same way now.
A colour or a particular sound, or a thought, or whatever, may exist even if there doesn't exist anyone in the universe right now able to think, hear, see, smell, or feel it. It has potential existence. What I was referring to is what can't be observed in anyway by anyone at anytime.
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Post by Eugene 2.0 on Aug 12, 2020 11:14:19 GMT
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 =)
I didn't discover this post before now. I missed it due to that clicking on this link just lead me to your last post about Lovecraft.
Yes, the existence of a colour does premise the existence of an observer, since a colour is something that is consciously experienced. However, in this I need to make the distinction between the potential of being observed and actually being observed. Let's say that those animals who see utraviolet see a colour that is fundamentally different from the colours we see. (That doesn't necessarily have to be the case. When we see violet, which is a frequency higher than blue, we're not seeing anything different from violet as a mix between blue and red. But, again, let's say that ultraviolet is an entirely new colour.) Then imagine that all conscious being that are able to see it suddenly die. That doesn't mean the colour ceases to exist. The colour still exists in that it has the potential of being observed. So, yes, what you could hear before still exists, even if you can't hear it the same way now.
A colour or a particular sound, or a thought, or whatever, may exists even if there doesn't exist anyone in the universe right now able to think, hear, see, smell, or feel it. It has potential existence. What I was referring to is what can't be observed in anyway by anyone at anytime.
Hmm... that ultraviolet example is bright. (Sometimes I forget to add a link by putting a comment down below.) Then you're referring to a thing for what there's no observers exist. Let's say that all the potential things sooner or later would be observed. (Maybe, because of all the possible combinations that our Universe even can be constructed would be passed (would be reached? - I don't know what a verb can I put here).) I think it's clear that all that things must have an observed to be observed. Because, would it have any sense if there wouldn't be any? However, it might be there wouldn't be any observers for some reason. How to understand such a collision then? I think that such a argumentation finally gets us to a thought that's been uttered by Protagoras: "A person (an observer) is a measure of what exist". Actually, we have to correct it with Kantian speculations that there must be fitted brains/a mind for us to be able to measure something. And also the last thought may lead to what Hegel said after that the absolute mind can achieve any information from the Universe. So, this question also requires us to set what kind of knowledge is appropriated to claim that there exists something that is unable to be seen, and hence, to be unable to be understood, comprehended, and (conceptually) conceived.
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Post by karl on Aug 12, 2020 13:46:06 GMT
I didn't discover this post before now. I missed it due to that clicking on this link just lead me to your last post about Lovecraft.
Yes, the existence of a colour does premise the existence of an observer, since a colour is something that is consciously experienced. However, in this I need to make the distinction between the potential of being observed and actually being observed. Let's say that those animals who see utraviolet see a colour that is fundamentally different from the colours we see. (That doesn't necessarily have to be the case. When we see violet, which is a frequency higher than blue, we're not seeing anything different from violet as a mix between blue and red. But, again, let's say that ultraviolet is an entirely new colour.) Then imagine that all conscious being that are able to see it suddenly die. That doesn't mean the colour ceases to exist. The colour still exists in that it has the potential of being observed. So, yes, what you could hear before still exists, even if you can't hear it the same way now.
A colour or a particular sound, or a thought, or whatever, may exists even if there doesn't exist anyone in the universe right now able to think, hear, see, smell, or feel it. It has potential existence. What I was referring to is what can't be observed in anyway by anyone at anytime.
Hmm... that ultraviolet example is bright. (Sometimes I forget to add a link by putting a comment down below.) Then you're referring to a thing for what there's no observers exist. Let's say that all the potential things sooner or later would be observed. (Maybe, because of all the possible combinations that our Universe even can be constructed would be passed (would be reached? - I don't know what a verb can I put here).) I think it's clear that all that things must have an observed to be observed. Because, would it have any sense if there wouldn't be any? However, it might be there wouldn't be any observers for some reason. How to understand such a collision then? I think that such a argumentation finally gets us to a thought that's been uttered by Protagoras: "A person (an observer) is a measure of what exist". Actually, we have to correct it with Kantian speculations that there must be fitted brains/a mind for us to be able to measure something. And also the last thought may lead to what Hegel said after that the absolute mind can achieve any information from the Universe. So, this question also requires us to set what kind of knowledge is appropriated to claim that there exists something that is unable to be seen, and hence, to be unable to be understood, comprehended, and (conceptually) conceived.
I need to emphasise again that the context for me even referring to a colour that cannot be observed, is that within Gödel's proof the concept of existence wasn't defined. Therefore we cannot just presume that Gödel premised that for something to exist, it must be observable. In fact, it could very well be that 'being observed' is what's within the concept of being exemplified. If, however, it was premised that something needs to be observable in order to exist, then being exemplified must mean something else. And the only option I can think of is that it refers to being exemplified in the real world. However, this is an interpretation I doubt is correct. I think the core of the proof is that Gödel never made a distinction between extrospection and introspection, between what's real and what's imagined.
So let me stress that my view is that if something can't potentially be observed, it doesn't exist. However, this needs a qualifier. Even if something can't be observed directly, its effects may be observed.
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Post by Eugene 2.0 on Aug 12, 2020 16:29:30 GMT
Hmm... that ultraviolet example is bright. (Sometimes I forget to add a link by putting a comment down below.) Then you're referring to a thing for what there's no observers exist. Let's say that all the potential things sooner or later would be observed. (Maybe, because of all the possible combinations that our Universe even can be constructed would be passed (would be reached? - I don't know what a verb can I put here).) I think it's clear that all that things must have an observed to be observed. Because, would it have any sense if there wouldn't be any? However, it might be there wouldn't be any observers for some reason. How to understand such a collision then? I think that such a argumentation finally gets us to a thought that's been uttered by Protagoras: "A person (an observer) is a measure of what exist". Actually, we have to correct it with Kantian speculations that there must be fitted brains/a mind for us to be able to measure something. And also the last thought may lead to what Hegel said after that the absolute mind can achieve any information from the Universe. So, this question also requires us to set what kind of knowledge is appropriated to claim that there exists something that is unable to be seen, and hence, to be unable to be understood, comprehended, and (conceptually) conceived. I need to emphasise again that the context for me even referring to a colour that cannot be observed, is that within Gödel's proof the concept of existence wasn't defined. Therefore we cannot just presume that Gödel premised that for something to exist, it must be observable. In fact, it could very well be that 'being observed' is what's within the concept of being exemplified. If, however, it was premised that something needs to be observable in order to exist, then being exemplified must mean something else. And the only option I can think of is that it refers to being exemplified in the real world. However, this is an interpretation I doubt is correct. I think the core of the proof is that Gödel never made a distinction between extrospection and introspection, between what's real and what's imagined.
So let me stress that my view is that if something can't potentially be observed, it doesn't exist. However, this needs a qualifier. Even if something can't be observed directly, its effects may be observed. This is necessary right that you're turning back this discussion to the Godel's problem (I've almost forgot about it =)). Also, please don't take any offenses by my continuously repeating the same thing - about nonexistence of things. Losting in translations may be the reason of this long talk, although I think it's because of my ignorance or non-understanding of some things. Anyway, exemplification is exactly at what our attention has to be directed, because Godel, it seems, wanted us to maintain it. All I could say here is that the question is getting be complicated, than previously, yet they lead us to the problems that were being highly observed (in their specific way) during Neoplatonism. Due to your explanations I see now (I suppose to) that what Godel's proof is about - even manifestating the existence of something, it's not enough to just claim it, but it requires us to get what kind of it we're looking for. Here, "kind" or "type" is how do we measure its existence as the supposed thing will have been found. By the way, the sentence "If something can't be observed directly, its effects may be observed" gives us a thought what "directly" means? 1. The observer + a thing observed = he observes it directly. 2. The observer + a tool + a thing observed = he doesn't observe it directly. 3. The observer has increased his sight ability → a) he's reached a tool; b) he's not reached any tools. a) The observer + a thing observed = he doesn't observe it directly b) The observer + a thing observed = he observes it directly. 4. The observer has advanced his thinking skills → c) he's reached a tool; d) he's not reached any tools. c) The observer + a thing observed = he doesn't observe it directly. d) The observer + a thing observed = he observes it directly. 5. (After having advanced his thinking skills) he uses or doesn't use a tool: e) The observer + a thing observed = he observes it directly. f) The observer + a tool + a thing observed = he doesn't observe it directly. I think what have we gotten here is two things: there might be natural physical tools and natural mind tools. In case of advancing skills would it be better for us to understand something? Seems it would, however it's not all what we could get here. There's also a fact that before and after the advancing the existence of something may change somehow. Trying to show it clearly, let a thing A has p, q, r, and s properties, while B has five: p, q, r, s, and t. These things also have structures that are similar to each other, but to define B we have to have more advance sight to do it. So, it must be seen than if one has more advanced ability of sight he's able to distinguish A from B, and to have seen B itself, while someone else who has no such an advanced sight is able to see just A, but not having a chance to see B. About six years ago I was watching the night skies trying to find and to trace Saturn. I had a not bad, but a not good for Astronomy telescope; I had a hunter looking-glass. I don't remember how much power it has; perhaps 75%? It was certainly lower, than 100 times magnifying, but I don't remember how many times. So, to see it I previously read a special book. It said to be able to see it with some not powerful telescope one didn't had to enough watching it, but one had to do some procedures before it (trying his eyes getting use to the darkness, and so on). And it was also needed to watch not directly at the planet, but to lightly right or left (up or down) - to access his focal vision. I was glad I could do it. So, yes as soon as I had tried to watch it using focal sight it was done. I couldn't distinct it from the other planets (in this particularly case; surely, I knew it was Saturn, yet I didn't watch its very famous circle). As for me, un-existential exemplification (if this what Godel meant) is just a mess. How does it possible at all? To have an example I must be able to observe it, or there's no examples. Here, in Godel's proof, the exemplification must be taken as an important add to any other propositions (that are taken as exemplified). So, if P is an exemplified proposition, it should have P+an example. And certainly that examples cannot be taken as formal examples. Being unable to use direct languages already, we've been transferred to either natural languages, or some meta-languages.
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Post by karl on Aug 12, 2020 17:23:05 GMT
I need to emphasise again that the context for me even referring to a colour that cannot be observed, is that within Gödel's proof the concept of existence wasn't defined. Therefore we cannot just presume that Gödel premised that for something to exist, it must be observable. In fact, it could very well be that 'being observed' is what's within the concept of being exemplified. If, however, it was premised that something needs to be observable in order to exist, then being exemplified must mean something else. And the only option I can think of is that it refers to being exemplified in the real world. However, this is an interpretation I doubt is correct. I think the core of the proof is that Gödel never made a distinction between extrospection and introspection, between what's real and what's imagined.
So let me stress that my view is that if something can't potentially be observed, it doesn't exist. However, this needs a qualifier. Even if something can't be observed directly, its effects may be observed. This is necessary right that you're turning back this discussion to the Godel's problem (I've almost forgot about it =)). Also, please don't take any offenses by my continuously repeating the same thing - about nonexistence of things. Losting in translations may be the reason of this long talk, although I think it's because of my ignorance or non-understanding of some things. Anyway, exemplification is exactly at what our attention has to be directed, because Godel, it seems, wanted us to maintain it. All I could say here is that the question is getting be complicated, than previously, yet they lead us to the problems that were being highly observed (in their specific way) during Neoplatonism. Due to your explanations I see now (I suppose to) that what Godel's proof is about - even manifestating the existence of something, it's not enough to just claim it, but it requires us to get what kind of it we're looking for. Here, "kind" or "type" is how do we measure its existence as the supposed thing will have been found. By the way, the sentence "If something can't be observed directly, its effects may be observed" gives us a thought what "directly" means? 1. The observer + a thing observed = he observes it directly. 2. The observer + a tool + a thing observed = he doesn't observe it directly. 3. The observer has increased his sight ability → a) he's reached a tool; b) he's not reached any tools. a) The observer + a thing observed = he doesn't observe it directly b) The observer + a thing observed = he observes it directly. 4. The observer has advanced his thinking skills → c) he's reached a tool; d) he's not reached any tools. c) The observer + a thing observed = he doesn't observe it directly. d) The observer + a thing observed = he observes it directly. 5. (After having advanced his thinking skills) he uses or doesn't use a tool: e) The observer + a thing observed = he observes it directly. f) The observer + a tool + a thing observed = he doesn't observe it directly. I think what have we gotten here is two things: there might be natural physical tools and natural mind tools. In case of advancing skills would it be better for us to understand something? Seems it would, however it's not all what we could get here. There's also a fact that before and after the advancing the existence of something may change somehow. Trying to show it clearly, let a thing A has p, q, r, and s properties, while B has five: p, q, r, s, and t. These things also have structures that are similar to each other, but to define B we have to have more advance sight to do it. So, it must be seen than if one has more advanced ability of sight he's able to distinguish A from B, and to have seen B itself, while someone else who has no such an advanced sight is able to see just A, but not having a chance to see B. About six years ago I was watching the night skies trying to find and to trace Saturn. I had a not bad, but a not good for Astronomy telescope; I had a hunter looking-glass. I don't remember how much power it has; perhaps 75%? It was certainly lower, than 100 times magnifying, but I don't remember how many times. So, to see it I previously read a special book. It said to be able to see it with some not powerful telescope one didn't had to enough watching it, but one had to do some procedures before it (trying his eyes getting use to the darkness, and so on). And it was also needed to watch not directly at the planet, but to lightly right or left (up or down) - to access his focal vision. I was glad I could do it. So, yes as soon as I had tried to watch it using focal sight it was done. I couldn't distinct it from the other planets (in this particularly case; surely, I knew it was Saturn, yet I didn't watch its very famous circle). As for me, un-existential exemplification (if this what Godel meant) is just a mess. How does it possible at all? To have an example I must be able to observe it, or there's no examples. Here, in Godel's proof, the exemplification must be taken as an important add to any other propositions (that are taken as exemplified). So, if P is an exemplified proposition, it should have P+an example. And certainly that examples cannot be taken as formal examples. Being unable to use direct languages already, we've been transferred to either natural languages, or some meta-languages.
If Gödel's proof operates with a concept of existence that doesn't necessitate observability, then exemplification is observability. So I don't see it as Gödel opens up for what you refer to as "un-existential exemplification". See it as two forms of existence:
1. Existence that isn't observable, and hence can't be exemplified. 2. Existence that is observable, and hence can be exemplified.
When I referred to direct and indirect observation, I knew I was getting into difficult territory. We can start off with what's easy to state:
1. I observe directly the colour blue.
2. A quark, if it exists, doesn't exist in free form, and my only be observed indirectly, for example in that it makes up matter, and we can observe matter.
Getting into exactly what is direct observation and what is indirect observation, does eventually become a matter of semantics.
When I observe the colour blue, is that me directly or indirectly observing the electromagnetic waves that cause my eyes to see blue? It depends on what definition one starts off with.
It would be possible to insist on a strict definition of direct observation to mean only that which manifests directly within our consciousness. This illustrates how difficult it is to dismiss those who claim that there is no distinction between the external and the internal world. After all, everything we observe directly, by that definition, we may also observe through memory or through imagination. So how exactly are we to distinguish between what we observe introspectively and what we observe through our senses? And yet, we do sense the difference. When we're awake, we know we're not dreaming.
One way by which we recognise the external world is by the laws it follows. We discover that others have existence independently from ourselves by observing that our will and imagination can't force their choices. At the same time, we observe the similarities between them and ourselves, and identify that just like how we can make our own choices, so can they. And as we can be independent from them, they can be independent from us. It's this realisation; That other individuals have an independent existence from ourselves, that is the true discovery of objectivity.
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Post by Eugene 2.0 on Aug 13, 2020 0:14:08 GMT
This is necessary right that you're turning back this discussion to the Godel's problem (I've almost forgot about it =)). Also, please don't take any offenses by my continuously repeating the same thing - about nonexistence of things. Losting in translations may be the reason of this long talk, although I think it's because of my ignorance or non-understanding of some things. Anyway, exemplification is exactly at what our attention has to be directed, because Godel, it seems, wanted us to maintain it. All I could say here is that the question is getting be complicated, than previously, yet they lead us to the problems that were being highly observed (in their specific way) during Neoplatonism. Due to your explanations I see now (I suppose to) that what Godel's proof is about - even manifestating the existence of something, it's not enough to just claim it, but it requires us to get what kind of it we're looking for. Here, "kind" or "type" is how do we measure its existence as the supposed thing will have been found. By the way, the sentence "If something can't be observed directly, its effects may be observed" gives us a thought what "directly" means? 1. The observer + a thing observed = he observes it directly. 2. The observer + a tool + a thing observed = he doesn't observe it directly. 3. The observer has increased his sight ability → a) he's reached a tool; b) he's not reached any tools. a) The observer + a thing observed = he doesn't observe it directly b) The observer + a thing observed = he observes it directly. 4. The observer has advanced his thinking skills → c) he's reached a tool; d) he's not reached any tools. c) The observer + a thing observed = he doesn't observe it directly. d) The observer + a thing observed = he observes it directly. 5. (After having advanced his thinking skills) he uses or doesn't use a tool: e) The observer + a thing observed = he observes it directly. f) The observer + a tool + a thing observed = he doesn't observe it directly. I think what have we gotten here is two things: there might be natural physical tools and natural mind tools. In case of advancing skills would it be better for us to understand something? Seems it would, however it's not all what we could get here. There's also a fact that before and after the advancing the existence of something may change somehow. Trying to show it clearly, let a thing A has p, q, r, and s properties, while B has five: p, q, r, s, and t. These things also have structures that are similar to each other, but to define B we have to have more advance sight to do it. So, it must be seen than if one has more advanced ability of sight he's able to distinguish A from B, and to have seen B itself, while someone else who has no such an advanced sight is able to see just A, but not having a chance to see B. About six years ago I was watching the night skies trying to find and to trace Saturn. I had a not bad, but a not good for Astronomy telescope; I had a hunter looking-glass. I don't remember how much power it has; perhaps 75%? It was certainly lower, than 100 times magnifying, but I don't remember how many times. So, to see it I previously read a special book. It said to be able to see it with some not powerful telescope one didn't had to enough watching it, but one had to do some procedures before it (trying his eyes getting use to the darkness, and so on). And it was also needed to watch not directly at the planet, but to lightly right or left (up or down) - to access his focal vision. I was glad I could do it. So, yes as soon as I had tried to watch it using focal sight it was done. I couldn't distinct it from the other planets (in this particularly case; surely, I knew it was Saturn, yet I didn't watch its very famous circle). As for me, un-existential exemplification (if this what Godel meant) is just a mess. How does it possible at all? To have an example I must be able to observe it, or there's no examples. Here, in Godel's proof, the exemplification must be taken as an important add to any other propositions (that are taken as exemplified). So, if P is an exemplified proposition, it should have P+an example. And certainly that examples cannot be taken as formal examples. Being unable to use direct languages already, we've been transferred to either natural languages, or some meta-languages.
If Gödel's proof operates with a concept of existence that doesn't necessitate observability, then exemplification is observability. So I don't see it as Gödel opens up for what you refer to as "un-existential exemplification". See it as two forms of existence:
1. Existence that isn't observable, and hence can't be exemplified. 2. Existence that is observable, and hence can be exemplified.
When I referred to direct and indirect observation, I knew I was getting into difficult territory. We can start off with what's easy to state:
1. I observe directly the colour blue.
2. A quark, if it exists, doesn't exist in free form, and my only be observed indirectly, for example in that it makes up matter, and we can observe matter.
Getting into exactly what is direct observation and what is indirect observation, does eventually become a matter of semantics.
When I observe the colour blue, is that me directly or indirectly observing the electromagnetic waves that cause my eyes to see blue? It depends on what definition one starts off with.
It would be possible to insist on a strict definition of direct observation to mean only that which manifests directly within our consciousness. This illustrates how difficult it is to dismiss those who claim that there is no distinction between the external and the internal world. After all, everything we observe directly, by that definition, we may also observe through memory or through imagination. So how exactly are we to distinguish between what we observe introspectively and what we observe through our senses? And yet, we do sense the difference. When we're awake, we know we're not dreaming.
One way by which we recognise the external world is by the laws it follows. We discover that others have existence independently from ourselves by observing that our will and imagination can't force their choices. At the same time, we observe the similarities between them and ourselves, and identify that just like how we can make our own choices, so can they. And as we can be independent from them, they can be independent from us. It's this realisation; That other individuals have an independent existence from ourselves, that is the true discovery of objectivity.
Thank you, Karl, for this really interesting discussion. I don't even remember when I discussed it with such an interest. This talk has opened my eyes wider to some areas I have never been to. Surely, QL theme must also be included. The quantity of themes which may come from the variety of questions and an amount of hypothesis above are positively increasing, and I'm very glad to watch it to. I. An exemplification, in my opinion, can be touched to a couple of these themes in logic and, particularly, in PL: a) ontologization of things by or with logic; b) what can be implied from an example or exemplified from a premise? The first one is tough for me to raise it here and know (as a part in was being used by us during the conversation not once). The second is: 1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa The first formula is not an exemplification, yet it might be looked like. I don't remember exactly the results of Gödel, but it's quite close to this result that ⋄∃xPx (it's possible that there exists at least one object that has P as its property) where Px is positively, well, holy, etc. ⋄∃xPx allows to be ∃xPx, or ~∃xPx. This seems to be a close proof to a Swinburne's one where thr last one told that existence of God is higher than 50%. (Yet in Gödel's case, there's no calculations.) II. Speaking of which, those two examples (no observation "~O" → no exemplified "~E"; observationalnees O → exemplifiedness E) have even more, than these two forms. They could be this: a) O→E b) O→~E c) ~O→E d) ~O→~E I think that (d) is the most clear and agreed bu us, (a) is quite unclear and agreed a little; (b) and (c) are the most doubtful and also agreed as such. III. We need to define and formulate things as completely and exhaustive as it possible - to prevent many occasional and non-occasional dismisses. So, this question is such which importance must be put firstly. Yet many not do this for their reasons (or maybe they cannot?). I like when a compromise can be reached, it's cool, while I know many who don't. IV. Ladt two paragraphs are magnificent and touched contemporariness. Of these things I have some thoughts: 1) Imagination without reflection is empty 2) Reflective imagination is a start point to be able naming it (imagination) 3) Ruling of reflected imaginations with names/concepts - conceivableness 4) The power of imagination measures through conceivability ... x) The question of how to know the outside world is the question of how to rule your conceivability. Partially (x) is determined through logic laws, but being an imagination it can't be said it has no flaws. V. Knowing the laws of our Nature is what really pushes us toward something good. So, I do agree here without a hesitation.
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Post by karl on Aug 13, 2020 12:49:40 GMT
If Gödel's proof operates with a concept of existence that doesn't necessitate observability, then exemplification is observability. So I don't see it as Gödel opens up for what you refer to as "un-existential exemplification". See it as two forms of existence:
1. Existence that isn't observable, and hence can't be exemplified. 2. Existence that is observable, and hence can be exemplified.
When I referred to direct and indirect observation, I knew I was getting into difficult territory. We can start off with what's easy to state:
1. I observe directly the colour blue.
2. A quark, if it exists, doesn't exist in free form, and my only be observed indirectly, for example in that it makes up matter, and we can observe matter.
Getting into exactly what is direct observation and what is indirect observation, does eventually become a matter of semantics.
When I observe the colour blue, is that me directly or indirectly observing the electromagnetic waves that cause my eyes to see blue? It depends on what definition one starts off with.
It would be possible to insist on a strict definition of direct observation to mean only that which manifests directly within our consciousness. This illustrates how difficult it is to dismiss those who claim that there is no distinction between the external and the internal world. After all, everything we observe directly, by that definition, we may also observe through memory or through imagination. So how exactly are we to distinguish between what we observe introspectively and what we observe through our senses? And yet, we do sense the difference. When we're awake, we know we're not dreaming.
One way by which we recognise the external world is by the laws it follows. We discover that others have existence independently from ourselves by observing that our will and imagination can't force their choices. At the same time, we observe the similarities between them and ourselves, and identify that just like how we can make our own choices, so can they. And as we can be independent from them, they can be independent from us. It's this realisation; That other individuals have an independent existence from ourselves, that is the true discovery of objectivity.
Thank you, Karl, for this really interesting discussion. I don't even remember when I discussed it with such an interest. This talk has opened my eyes wider to some areas I have never been to. Surely, QL theme must also be included. The quantity of themes which may come from the variety of questions and an amount of hypothesis above are positively increasing, and I'm very glad to watch it to. I. An exemplification, in my opinion, can be touched to a couple of these themes in logic and, particularly, in PL: a) ontologization of things by or with logic; b) what can be implied from an example or exemplified from a premise? The first one is tough for me to raise it here and know (as a part in was being used by us during the conversation not once). The second is: 1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa The first formula is not an exemplification, yet it might be looked like. I don't remember exactly the results of Gödel, but it's quite close to this result that ⋄∃xPx (it's possible that there exists at least one object that has P as its property) where Px is positively, well, holy, etc. ⋄∃xPx allows to be ∃xPx, or ~∃xPx. This seems to be a close proof to a Swinburne's one where thr last one told that existence of God is higher than 50%. (Yet in Gödel's case, there's no calculations.) II. Speaking of which, those two examples (no observation "~O" → no exemplified "~E"; observationalnees O → exemplifiedness E) have even more, than these two forms. They could be this: a) O→E b) O→~E c) ~O→E d) ~O→~E I think that (d) is the most clear and agreed bu us, (a) is quite unclear and agreed a little; (b) and (c) are the most doubtful and also agreed as such. III. We need to define and formulate things as completely and exhaustive as it possible - to prevent many occasional and non-occasional dismisses. So, this question is such which importance must be put firstly. Yet many not do this for their reasons (or maybe they cannot?). I like when a compromise can be reached, it's cool, while I know many who don't. IV. Ladt two paragraphs are magnificent and touched contemporariness. Of these things I have some thoughts: 1) Imagination without reflection is empty 2) Reflective imagination is a start point to be able naming it (imagination) 3) Ruling of reflected imaginations with names/concepts - conceivableness 4) The power of imagination measures through conceivability ... x) The question of how to know the outside world is the question of how to rule your conceivability. Partially (x) is determined through logic laws, but being an imagination it can't be said it has no flaws. V. Knowing the laws of our Nature is what really pushes us toward something good. So, I do agree here without a hesitation.
Thank you. It's an interesting discussion.
I don't quite understand your use of symbols.
a) O→E b) O→~E c) ~O→E d) ~O→~E
Is this a correct interpretation of it:
a) Being observable implies existence. b) Being observable implies non-existence. c) Not being observable implies existence. d) Not being observable implies non-existence.
If that is correct, then b) and c) make no sense. And d) is redundant, since it logically follows from a).
1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa
My confusion here may be a matter of my own ignorance. What does Fx, Fy, and Fa mean within this context?
∀x = For all x ∃x = There exists an x
For all x, Fx implies Fy For all x, Fx implies Fa There exists an X so that Fx implies Fa
I really don't understand the meaning of this, but, again, it might be just due to me not being familiar with this use of symbols.
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Post by Eugene 2.0 on Aug 13, 2020 18:03:42 GMT
Thank you, Karl, for this really interesting discussion. I don't even remember when I discussed it with such an interest. This talk has opened my eyes wider to some areas I have never been to. Surely, QL theme must also be included. The quantity of themes which may come from the variety of questions and an amount of hypothesis above are positively increasing, and I'm very glad to watch it to. I. An exemplification, in my opinion, can be touched to a couple of these themes in logic and, particularly, in PL: a) ontologization of things by or with logic; b) what can be implied from an example or exemplified from a premise? The first one is tough for me to raise it here and know (as a part in was being used by us during the conversation not once). The second is: 1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa The first formula is not an exemplification, yet it might be looked like. I don't remember exactly the results of Gödel, but it's quite close to this result that ⋄∃xPx (it's possible that there exists at least one object that has P as its property) where Px is positively, well, holy, etc. ⋄∃xPx allows to be ∃xPx, or ~∃xPx. This seems to be a close proof to a Swinburne's one where thr last one told that existence of God is higher than 50%. (Yet in Gödel's case, there's no calculations.) II. Speaking of which, those two examples (no observation "~O" → no exemplified "~E"; observationalnees O → exemplifiedness E) have even more, than these two forms. They could be this: a) O→E b) O→~E c) ~O→E d) ~O→~E I think that (d) is the most clear and agreed bu us, (a) is quite unclear and agreed a little; (b) and (c) are the most doubtful and also agreed as such. III. We need to define and formulate things as completely and exhaustive as it possible - to prevent many occasional and non-occasional dismisses. So, this question is such which importance must be put firstly. Yet many not do this for their reasons (or maybe they cannot?). I like when a compromise can be reached, it's cool, while I know many who don't. IV. Ladt two paragraphs are magnificent and touched contemporariness. Of these things I have some thoughts: 1) Imagination without reflection is empty 2) Reflective imagination is a start point to be able naming it (imagination) 3) Ruling of reflected imaginations with names/concepts - conceivableness 4) The power of imagination measures through conceivability ... x) The question of how to know the outside world is the question of how to rule your conceivability. Partially (x) is determined through logic laws, but being an imagination it can't be said it has no flaws. V. Knowing the laws of our Nature is what really pushes us toward something good. So, I do agree here without a hesitation.
Thank you. It's an interesting discussion.
I don't quite understand your use of symbols.
a) O→E b) O→~E c) ~O→E d) ~O→~E
Is this a correct interpretation of it:
a) Being observable implies existence. b) Being observable implies non-existence. c) Not being observable implies existence. d) Not being observable implies non-existence.
If that is correct, then b) and c) make no sense. And d) is redundant, since it logically follows from a).
1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa
My confusion here may be a matter of my own ignorance. What does Fx, Fy, and Fa mean within this context?
∀x = For all x ∃x = There exists an x
For all x, Fx implies Fy For all x, Fx implies Fa There exists an X so that Fx implies Fa
I really don't understand the meaning of this, but, again, it might be just due to me not being familiar with this use of symbols.
Hmm.... yes. It is my fault. I had to not be so close-minded to imagine that what kind of formal system I use is what I used to use... There are things I feel I ought to explain. First of all, I want to admire that my usage of such a language to explain something is more likely to be mine interpretation, and that's why it's about for objectivity to be lost completely by this language. Ok, first things first, I'll try to do my best. a) O→E b) O→~E c) ~O→E d) ~O→~E a) Being observable implies existence. b) Being observable implies non-existence. c) Not being observable implies existence. d) Not being observable implies non-existence. Yes, it is a perfect interpretation. (Just a tiny add: I put "observation" and "exemplification" as words, but it not what I'd meant indeed. I used an elliptic form of sentence to short that "observation" is "something that is observable" and "a thing that is exemplified". Propositions have a meaning of being either false, or true, yet just words don't have the meaning "true", "false", they have a meaning of being "correct" or "incorrect" placeholders.) The interpretation is correct except for a view that (d) is logically implied by (a). Actually, it could be, and it might be. Or, in other words, there's nothing unusual to happen for (d) to be implied by (a), but as a logical requirement this isn't correct. Taking P→Q we can say that this formula is true either when P is false, or Q is true. (The formula is false only if P is true, and Q is false.) And that's the main rule of implication. No other forms, such as P→~Q, ~P→Q, and ~P→~Q when doing by this, don't repeat the meaning of the formula. For example, P→Q: 1→1 = 1 1→0 = 0 0→0 = 1 0→0 = 1 P→~Q: 1→1 = 0 1→0 = 1 0→1 = 1 0→0 = 1 As we can see the set of meaning in the first formula [1;0;1;1] is not the same as in the second [0;1;1;1], and that's why both of them are not equivalent, and, therefore, they can't be mutually interchangeable. Logical opposition to P→Q is ~Q→~P. These two formulas are identical: ~Q→~P: 1→1 = 1 1→0 = 0 0→1 = 1 0→0 = 1 (The next set of formulas, like Fy, Fx, I'll explain in the next post.)
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Post by karl on Aug 13, 2020 18:10:49 GMT
Thank you. It's an interesting discussion.
I don't quite understand your use of symbols.
a) O→E b) O→~E c) ~O→E d) ~O→~E
Is this a correct interpretation of it:
a) Being observable implies existence. b) Being observable implies non-existence. c) Not being observable implies existence. d) Not being observable implies non-existence.
If that is correct, then b) and c) make no sense. And d) is redundant, since it logically follows from a).
1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa
My confusion here may be a matter of my own ignorance. What does Fx, Fy, and Fa mean within this context?
∀x = For all x ∃x = There exists an x
For all x, Fx implies Fy For all x, Fx implies Fa There exists an X so that Fx implies Fa
I really don't understand the meaning of this, but, again, it might be just due to me not being familiar with this use of symbols.
Hmm.... yes. It is my fault. I had to not be so close-minded to imagine that what kind of formal system I use is what I used to use... There are things I feel I ought to explain. First of all, I want to admire that my usage of such a language to explain something is more likely to be mine interpretation, and that's why it's about for objectivity to be lost completely by this language. Ok, first things first, I'll try to do my best. a) O→E b) O→~E c) ~O→E d) ~O→~E a) Being observable implies existence. b) Being observable implies non-existence. c) Not being observable implies existence. d) Not being observable implies non-existence. Yes, it is a perfect interpretation. (Just a tiny add: I put "observation" and "exemplification" as words, but it not what I'd meant indeed. I used an elliptic form of sentence to short that "observation" is "something that is observable" and "a thing that is exemplified". Propositions have a meaning of being either false, or true, yet just words don't have the meaning "true", "false", they have a meaning of being "correct" or "incorrect" placeholders.) The interpretation is correct except for a view that (d) is logically implied by (a). Actually, it could be, and it might be. Or, in other words, there's nothing unusual to happen for (d) to be implied by (a), but as a logical requirement this isn't correct. Taking P→Q we can say that this formula is true either when P is false, or Q is true. (The formula is false only if P is true, and Q is false.) And that's the main rule of implication. No other forms, such as P→~Q, ~P→Q, and ~P→~Q when doing by this, don't repeat the meaning of the formula. For example, P→Q: 1→1 = 1 1→0 = 0 0→0 = 1 0→0 = 1 P→~Q: 1→1 = 0 1→0 = 1 0→1 = 1 0→0 = 1 As we can see the set of meaning in the first formula [1;0;1;1] is not the same as in the second [0;1;1;1], and that's why both of them are not equivalent, and, therefore, they can't be mutually interchangeable. Logical opposition to P→Q is ~Q→~P. These two formulas are identical: ~Q→~P: 1→1 = 1 1→0 = 0 0→1 = 1 0→0 = 1 (The next set of formulas, like Fy, Fx, I'll explain in the next post.)
Before I reply to the rest, I just feel a strong need to confirm one thing you wrote. Yes, a) doesn't imply d). Somehow my brain mixed it up, and read ~O→~E as meaning ~E→~O. And O→E does mean ~E→~O. It's actually a bit painful that I got something as basic as that wrong. And it's sad that you had to spend time and energy explaining it.
So b) meant:
"Being observable implies non-exemplification?"
Or did I misinterpret that?
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Post by Eugene 2.0 on Aug 13, 2020 18:38:01 GMT
karlI shall continue... No, it's not your ignorance (knowing logic for a physician is nonsense. It's kinda optional. There's a not bad book by Rudolph Karnap that is called "Philosophical Foundations of Physics" where he uses an apparatus of Mathematical Logic, but it's for Philosophical purposes only. There's no much need to use it, except for, maybe, thought experiments, some technical researches on increasing-decreasing temperature factors. Ok, not I'll try to explain them too. 1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa ∀x = For all x } yes ∃x = There exists an x } yes For all x, Fx implies Fy } yes For all x, Fx implies Fa } yes There exists an X so that Fx implies Fa } also, yes What I wanted to show is that depending on a type of a sentence (which one quantor it has, and has it) we need to understand what can we do with it. The rules of instantiation of generalization is the same as the rule of: is it logically allowed to turn a given particular sentence to a more wider form, or not? "For all" means - there must be some elements to satisfy this formula. However, the meaning of "for all" can be read as "for each", and also can be read as "for all (in general)". In the last sense it would be doubtful to say whether or not we might think there must be some elements to satisfy it. This one can be uttered in this way: any rules, orders, laws, not necessary must contain an element to take these rules, orders, laws as good and true. If there's a law that all the dog-eaters must be sent to the prison, and there are no dog-eaters it's ok, whenever they are or will be. Such formulas as Fy or Fx - and they might be read as "any y that is F" (e.g. "any y that eat potatoes at night"). This formula has a little problem being not quantified. Its sense isn't so clear as a quentified (for all x, there's an x...) formulas have. We can rewrite all Fy, Fx to the form: "__ eat potatoes at night", "___is cool". Such incomplete forms are nothing but a big question to us how to understand it. In the Predicate logic they're called "free variable predicates" or "free formulas". Usually, a logician is trying to get rid of them, or - he tries to show that such a formula depend on exactly this world (the formula is very likely to have a functional meaning/correlation with this particular world - and therefore, free variable is a sign of it. But the last one is not necessary. Generalization and instantiation are linked by the question of exemplification. To imply "there are some x" from "for all x" is to instantiate this particular x. Such formulas as "there's an x..." are which is more likely to has an example in this world, or else it's untrue. Indeed, what if say that "there's an y that is yellow" while there's no yellow things? It is a pure contradiction. More accurate to demonstrate it is to say that "there's an y that is yellow and can be presented for (a group of people who's been waiting for this action) now" while there are no such yellow things.
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Post by Eugene 2.0 on Aug 13, 2020 18:39:31 GMT
Hmm.... yes. It is my fault. I had to not be so close-minded to imagine that what kind of formal system I use is what I used to use... There are things I feel I ought to explain. First of all, I want to admire that my usage of such a language to explain something is more likely to be mine interpretation, and that's why it's about for objectivity to be lost completely by this language. Ok, first things first, I'll try to do my best. a) O→E b) O→~E c) ~O→E d) ~O→~E a) Being observable implies existence. b) Being observable implies non-existence. c) Not being observable implies existence. d) Not being observable implies non-existence. Yes, it is a perfect interpretation. (Just a tiny add: I put "observation" and "exemplification" as words, but it not what I'd meant indeed. I used an elliptic form of sentence to short that "observation" is "something that is observable" and "a thing that is exemplified". Propositions have a meaning of being either false, or true, yet just words don't have the meaning "true", "false", they have a meaning of being "correct" or "incorrect" placeholders.) The interpretation is correct except for a view that (d) is logically implied by (a). Actually, it could be, and it might be. Or, in other words, there's nothing unusual to happen for (d) to be implied by (a), but as a logical requirement this isn't correct. Taking P→Q we can say that this formula is true either when P is false, or Q is true. (The formula is false only if P is true, and Q is false.) And that's the main rule of implication. No other forms, such as P→~Q, ~P→Q, and ~P→~Q when doing by this, don't repeat the meaning of the formula. For example, P→Q: 1→1 = 1 1→0 = 0 0→0 = 1 0→0 = 1 P→~Q: 1→1 = 0 1→0 = 1 0→1 = 1 0→0 = 1 As we can see the set of meaning in the first formula [1;0;1;1] is not the same as in the second [0;1;1;1], and that's why both of them are not equivalent, and, therefore, they can't be mutually interchangeable. Logical opposition to P→Q is ~Q→~P. These two formulas are identical: ~Q→~P: 1→1 = 1 1→0 = 0 0→1 = 1 0→0 = 1 (The next set of formulas, like Fy, Fx, I'll explain in the next post.)
Before I reply to the rest, I just feel a strong need to confirm one thing you wrote. Yes, a) doesn't imply d). Somehow my brain mixed it up, and read ~O→~E as meaning ~E→~O. And O→E does mean ~E→~O. It's actually a bit painful that I got something as basic as that wrong. And it's sad that you had to spend time and energy explaining it.
So b) meant:
"Being observable implies non-exemplification?"
Or did I misinterpret that?
Yes. It is.
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Post by karl on Aug 13, 2020 19:51:06 GMT
karl I shall continue... No, it's not your ignorance (knowing logic for a physician is nonsense. It's kinda optional. There's a not bad book by Rudolph Karnap that is called "Philosophical Foundations of Physics" where he uses an apparatus of Mathematical Logic, but it's for Philosophical purposes only. There's no much need to use it, except for, maybe, thought experiments, some technical researches on increasing-decreasing temperature factors. Ok, not I'll try to explain them too. 1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa ∀x = For all x } yes ∃x = There exists an x } yes For all x, Fx implies Fy } yes For all x, Fx implies Fa } yes There exists an X so that Fx implies Fa } also, yes What I wanted to show is that depending on a type of a sentence (which one quantor it has, and has it) we need to understand what can we do with it. The rules of instantiation of generalization is the same as the rule of: is it logically allowed to turn a given particular sentence to a more wider form, or not? "For all" means - there must be some elements to satisfy this formula. However, the meaning of "for all" can be read as "for each", and also can be read as "for all (in general)". In the last sense it would be doubtful to say whether or not we might think there must be some elements to satisfy it. This one can be uttered in this way: any rules, orders, laws, not necessary must contain an element to take these rules, orders, laws as good and true. If there's a law that all the dog-eaters must be sent to the prison, and there are no dog-eaters it's ok, whenever they are or will be. Such formulas as Fy or Fx - and they might be read as "any y that is F" (e.g. "any y that eat potatoes at night"). This formula has a little problem being not quantified. Its sense isn't so clear as a quentified (for all x, there's an x...) formulas have. We can rewrite all Fy, Fx to the form: "__ eat potatoes at night", "___is cool". Such incomplete forms are nothing but a big question to us how to understand it. In the Predicate logic they're called "free variable predicates" or "free formulas". Usually, a logician is trying to get rid of them, or - he tries to show that such a formula depend on exactly this world (the formula is very likely to have a functional meaning/correlation with this particular world - and therefore, free variable is a sign of it. But the last one is not necessary. Generalization and instantiation are linked by the question of exemplification. To imply "there are some x" from "for all x" is to instantiate this particular x. Such formulas as "there's an x..." are which is more likely to has an example in this world, or else it's untrue. Indeed, what if say that "there's an y that is yellow" while there's no yellow things? It is a pure contradiction. More accurate to demonstrate it is to say that "there's an y that is yellow and can be presented for (a group of people who's been waiting for this action) now" while there are no such yellow things.
Ok, so let's see if I got it right.
1) ∀xFx→Fa 2) ∃xFx→Fa
I define a fundamentally new colour I will call Ultra.
x=plate, Fx=Any plate that's coloured only with Ultra, Fa=Will not contain either blue, red, or yellow.
∀xFx→Fa=All plates coloured only with Ultra will not contain either blue, red, or yellow.
∃xFx→Fa=There exists a plate coloured only with Ultra that will not contain either blue, red, or yellow.
In this instance, the last is crucial, for it establishes that Ultra is exemplified.
Is this correct usage of the formula?
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Post by Eugene 2.0 on Aug 13, 2020 20:27:11 GMT
karl I shall continue... No, it's not your ignorance (knowing logic for a physician is nonsense. It's kinda optional. There's a not bad book by Rudolph Karnap that is called "Philosophical Foundations of Physics" where he uses an apparatus of Mathematical Logic, but it's for Philosophical purposes only. There's no much need to use it, except for, maybe, thought experiments, some technical researches on increasing-decreasing temperature factors. Ok, not I'll try to explain them too. 1) ∀xFx→Fy 2) ∀xFx→Fa 3) ∃xFx→Fa ∀x = For all x } yes ∃x = There exists an x } yes For all x, Fx implies Fy } yes For all x, Fx implies Fa } yes There exists an X so that Fx implies Fa } also, yes What I wanted to show is that depending on a type of a sentence (which one quantor it has, and has it) we need to understand what can we do with it. The rules of instantiation of generalization is the same as the rule of: is it logically allowed to turn a given particular sentence to a more wider form, or not? "For all" means - there must be some elements to satisfy this formula. However, the meaning of "for all" can be read as "for each", and also can be read as "for all (in general)". In the last sense it would be doubtful to say whether or not we might think there must be some elements to satisfy it. This one can be uttered in this way: any rules, orders, laws, not necessary must contain an element to take these rules, orders, laws as good and true. If there's a law that all the dog-eaters must be sent to the prison, and there are no dog-eaters it's ok, whenever they are or will be. Such formulas as Fy or Fx - and they might be read as "any y that is F" (e.g. "any y that eat potatoes at night"). This formula has a little problem being not quantified. Its sense isn't so clear as a quentified (for all x, there's an x...) formulas have. We can rewrite all Fy, Fx to the form: "__ eat potatoes at night", "___is cool". Such incomplete forms are nothing but a big question to us how to understand it. In the Predicate logic they're called "free variable predicates" or "free formulas". Usually, a logician is trying to get rid of them, or - he tries to show that such a formula depend on exactly this world (the formula is very likely to have a functional meaning/correlation with this particular world - and therefore, free variable is a sign of it. But the last one is not necessary. Generalization and instantiation are linked by the question of exemplification. To imply "there are some x" from "for all x" is to instantiate this particular x. Such formulas as "there's an x..." are which is more likely to has an example in this world, or else it's untrue. Indeed, what if say that "there's an y that is yellow" while there's no yellow things? It is a pure contradiction. More accurate to demonstrate it is to say that "there's an y that is yellow and can be presented for (a group of people who's been waiting for this action) now" while there are no such yellow things.
Ok, so let's see if I got it right.
1) ∀xFx→Fa 2) ∃xFx→Fa
I define a fundamentally new colour I will call Ultra.
x=plate, Fx=Any plate that's coloured only with Ultra, Fa=Will not contain either blue, red, or yellow.
∀xFx→Fa=All plates coloured only with Ultra will not contain either blue, red, or yellow.
∃xFx→Fa=There exists a plate coloured only with Ultra that will not contain either blue, red, or yellow.
In this instance, the last is crucial, for it establishes that Ultra is exemplified.
Is this correct usage of the formula?
2) ∃xFx→Fa - is correct 1) ∀xFx→Fa - yes. About x=plate. "x" are variables, and here "x" is rather a class, than an object. (It also has to be taken into account that there are some logical problems with all that, including the problem of universals; for instance, if "x" is a color, then to be with it? Because we cannot to put together plates and colors.) So, if x=plate, then a=plate. If ∀xFx means 'all x has a color Ultra', then Fa means 'a has a color Ultra', so if a є {x1, x2, x3, ..., xn-1, xn}, then ∀xFx means 'all plates has a color Ultra, and Fa means 'the plate has a color Ultra". And this example is interesting to notice, that Fa 'this plate has a color Ultra' is exemplification of ∀xFx. As not being a primarly a logician, I don't want to make an impression I know much all about it, so what I'm telling is not the necessary what a logician may tell. But I'll try to hold a view that many of exercise-books give. (Mathematicians are logicians, and as soon as physicians use math almost constantly: they are logicians too) - I got this example for a nice and indeed honoured book of M. Cohen, E. Nagel "An Introduction to Logic and Scientific Method" (1936 - the first publication). By this example (using indirect proof in syllogistics) they wanted to show that exemplification may be accepted just from nothing (I'll try to write down this example sometimes later). I guess that is a normal usage of formula, except for taking a distinction between variables and individuals (or constants). - And again, Predicate Calculus (or Predicate Logic) was taken as a manner of using Calculus. Sygmas, capital P (П), and many other came from Calculus to Predicate Logic. And plain Propositional Calculus (i.e. Propositional Logic) is also a kind of using algebraic symbols. At the beginning of XX century many logicians were mathematics, and vice versa. The development of logic was intensive. Frege and Russell, along with Hilbert, Peano, Whitehead, and some others directed their forced at the development as apparatus so first problems of mathematical logic. (About exemplification!) - An exemplification from ∃xFx to Fa seems not to be obvious, but more natural (?), because the sense of ∃xFx is a meaning that there is such x that F. - What does it mean (as I understand it)? - It means that if there is nothing left except for using ordinary, natural language, we will be able to say that ∃xFx spells as exemplification. ∀xFx, on the other hand, is quite different. From one side, it is, but there may be cases (as I said about laws, rules, claims, prescriptions... above) there it can't be strongly stick to the meaning of "there is an a that F...". So, usually, the first what many logicians are trying to do is to imply somehow many different formulas to understand the meaning of ∀xFx more clearly (to make ∀xFx be more clear, than before it). And also, there are some models in PL and some other forms of logic (Boolean type PL) where ∀xFx→Fa doesn't work. While ∃xFx→Fa works almost in every logical system (well, I don't know where it doesn't work). Thanks again for asking. I think I should repeat myself again that despite of what I know in logic, I won't recommend myself as a good explainer.
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Post by karl on Aug 13, 2020 20:50:01 GMT
Ok, so let's see if I got it right.
1) ∀xFx→Fa 2) ∃xFx→Fa
I define a fundamentally new colour I will call Ultra.
x=plate, Fx=Any plate that's coloured only with Ultra, Fa=Will not contain either blue, red, or yellow.
∀xFx→Fa=All plates coloured only with Ultra will not contain either blue, red, or yellow.
∃xFx→Fa=There exists a plate coloured only with Ultra that will not contain either blue, red, or yellow.
In this instance, the last is crucial, for it establishes that Ultra is exemplified.
Is this correct usage of the formula?
2) ∃xFx→Fa - is correct 1) ∀xFx→Fa - yes. About x=plate. "x" are variables, and here "x" is rather a class, than an object. (It also has to be taken into account that there are some logical problems with all that, including the problem of universals; for instance, if "x" is a color, then to be with it? Because we cannot to put together plates and colors.) So, if x=plate, then a=plate. If ∀xFx means 'all x has a color Ultra', then Fa means 'a has a color Ultra', so if a є {x1, x2, x3, ..., xn-1, xn}, then ∀xFx means 'all plates has a color Ultra, and Fa means 'the plate has a color Ultra". And this example is interesting to notice, that Fa 'this plate has a color Ultra' is exemplification of ∀xFx. As not being a primarly a logician, I don't want to make an impression I know much all about it, so what I'm telling is not the necessary what a logician may tell. But I'll try to hold a view that many of exercise-books give. (Mathematicians are logicians, and as soon as physicians use math almost constantly: they are logicians too) - I got this example for a nice and indeed honoured book of M. Cohen, E. Nagel "An Introduction to Logic and Scientific Method" (1936 - the first publication). By this example (using indirect proof in syllogistics) they wanted to show that exemplification may be accepted just from nothing (I'll try to write down this example sometimes later). I guess that is a normal usage of formula, except for taking a distinction between variables and individuals (or constants). - And again, Predicate Calculus (or Predicate Logic) was taken as a manner of using Calculus. Sygmas, capital P (П), and many other came from Calculus to Predicate Logic. And plain Propositional Calculus (i.e. Propositional Logic) is also a kind of using algebraic symbols. At the beginning of XX century many logicians were mathematics, and vice versa. The development of logic was intensive. Frege and Russell, along with Hilbert, Peano, Whitehead, and some others directed their forced at the development as apparatus so first problems of mathematical logic. (About exemplification!) - An exemplification from ∃xFx to Fa seems not to be obvious, but more natural (?), because the sense of ∃xFx is a meaning that there is such x that F. - What does it mean (as I understand it)? - It means that if there is nothing left except for using ordinary, natural language, we will be able to say that ∃xFx spells as exemplification. ∀xFx, on the other hand, is quite different. From one side, it is, but there may be cases (as I said about laws, rules, claims, prescriptions... above) there it can't be strongly stick to the meaning of "there is an a that F...". So, usually, the first what many logicians are trying to do is to imply somehow many different formulas to understand the meaning of ∀xFx more clearly (to make ∀xFx be more clear, than before it). And also, there are some models in PL and some other forms of logic (Boolean type PL) where ∀xFx→Fa doesn't work. While ∃xFx→Fa works almost in every logical system (well, I don't know where it doesn't work). Thanks again for asking. I think I should repeat myself again that despite of what I know in logic, I won't recommend myself as a good explainer.
Here's another attempt.
X=Plates coloured only with Ultra
Fx=X does not contain red, blue, or yellow
∀xFx→Fa = That all plates coloured only with Ultra contain neither red, blue, or yellow, implies that there exists a plate coloured only with Ultra that contains neither red, blue, or yellow.
Is this correct usage?
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