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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 15, 2020 19:27:54 GMT
What I wrote about people not thinking, was not referring to you and what you wrote. It was just a general statement about people overall. I see the real struggle in society as being between the mindless majority and the conscious minority.
As for your Norwegian sentences:
(Folk is that they think what they do - is living in a chaotic time.
Folk er det de tenker for de gjør er lever i a kaotisk tid.)
Eh... I didn't understand that. Folk=people. So you wrote: "People are what they think they do. -Living in a chaotic time." I can't make sense of that.
(I have a question: what a premise I wrote?
Jeg har a spørre: hva en forutsett jeg skrev?)
My preferred translation would be: Jeg har et spørsmål. Hva mener du jeg forutsatte i hva jeg skrev?"
(=What do you believe I premised in what I wrote?)
(Execuse me for mistakes. I apologize if I made mistakes.
Unnskyld meg for feiler. Jeg beklager lagte mange feiler.)
My translation: Jeg beklager hvis jeg har gjort feil.
Or, rather, since I presume it refers to having written something wrong, and since you used the word "mange"=a lot, it would be: Jeg beklager hvis jeg har skrevet mye feil. (=I am sorry if have written a lot that is incorrect.)
(Skrevet=written)
What Gödel's proof illustrates is that logic is useless unless one always have a clear idea about what exactly is the meaning of the concepts we analyse logically, when we try to understand their relation to one another. If there is no clarity in what the concepts mean, such as for example, what is a positive property and why does being godlike have to include all positive properties, then the logical reasoning that follows is of limited value.
What Kurt Gödel actually thought about God isn't revealed in his proof of God's existence.
Richard Nixon would ultimately be the soul which his brain allowed to be conscious and could exercise free will. Nixon wasn't his choices, but the soul that made those choices. Had he been reborn in a world identical to the one he was born in on Earth, he would be likely to manifest himself in that world with traits similar to how he manifested in this world, and had he been reborn in a different environment , his choices could have been dramatically different, and he might have become a defender of democracy. A clone of Richard Nixon wouldn't be Richard Nixon. Who you are is your soul, not your physical being. Your brain is the landscape your soul maneuvers in, and which set the limitations for what choices you can make. But the brain itself is not your soul.
... You know it's not easy to understand even basics of language with not a native language (learning Norwegian with English). Yes, I do agree, the phrases I tried to construct were poorly constructed in English (I was still thinking Ukrainian trying to do i). I found not a bad site LearningNorwegian101. Also, I found a site that was made just by one person in Russian, and thus site is huuuge. I mean it seems the one did lotta work. However there were critics (certainly, Norwegians) who pointed the developer for his mistakes. He did them. Anyway, it's not only useful and interesting to learn a language, but - I think in my poor examples it can be seen - that we require to know the underlying, core logic behind the language or its parts to use it effectively, or just to be able to use it. In English we put -s at the end, while, as I understood, in Norwegian we put -(e)r, -e, and, in definite, -ene. Depending on the end of the word, and also there are another cases when a vowel omits. I think such underlying laws might be not only helpful to be more creative, but for better understanding each other. As someone once said "Tell me something and I will see you", so artists, poets, writers and the other creators are almost always trying to represent their core hesitations, feelings, even thougts, and language helps them with it. If one hasn't been heard he'd better to take care about to improve his expressive manners. And a reciever should care about it to - trying to have heard the one. To Gödel: we need to have right meaning, and yet it might happen that a person A and a person B are talking with each other rendering to different things. I mean either they understand each other just because they somehow feel each other (intuitive talk: when A person expects ehat B will say, and one will do it), or the language they use allow variety of meanings such as: we can address from P to Q1, Q2, ..., Qn, and from a set Q to R. In such a situation A could utter "P" rendering to "Qi", while B understands one as if A through "P" refers to "Qj". Surprisingly, they both have succeeded in/at "R". By this I was going to show that in some cases equally of meaning is not necessary. To logically understanding: yes, it seems even effective, than just a plain formalization. It reminds Wittgenstein's phrase: “For a large class of cases of the employment of the word ‘meaning’—though not for all—this word can be explained in this way: the meaning of a word is its use in the language” (Philosophical Investigations p. 43). Nixon: Ok, a doppelganger of Nixon could be Nixon-democrate, but if there were no Nixon-republican we would never know what was like for Nixon to not be Nixon. Having got Nixon-r(epublican) we have learned (understood?) what the "other" one might be. If we never had the one there would be ni chances to claim anything about that "potential" Nixon. - You've said previously that if we never seen a thing (we have never known anything about of its possibility of being known; before we knew the one for us it was the same as the things that never existed), we can never exemplify it, right? So, here's the same. That was what Kripke had been trying to tell (and again, I can't appeal to his theory much as long as I don't remember it for sure). Again to Gödel: formalizing what he said makes our investigation on his proof quite clearer, and if before the research there were N undefined terms, and after some... let us call it "some actions" or "some work"... actions we got N-K (K<N), then some luck smiled at us.
Good luck with learning Norwegian. Yes it's very important when learning a language that you understand its structure. So it's much better that you go from Russian, which is similar to Ukrainian, to Norwegian, than from English to Norwegian.
I presume you were referring to inflections. Here's one example:
English: To drive, driving, drove, have driven
Norwegian: Å kjøre, kjører, kjørte, har kjørt
Wittgenstein's definition of a word's meaning is not problematic to me in what it literally states, but in what it implies. One way or another, every word gets its meaning from how its used in the language. In fact, it's trivially true to the point of being pointless to state. However, what is being implied is that there is no source for the meaning of a word than the development of the language in which it's used. It subtlety exclude the possibility for some words to get their meaning from an inner universal world of concepts, as a universal foundation for all languages. And in this way, it also rejects that thought comes before language. According to Wittgenstein, not even God can read one's thoughts. One's words and one's thoughts are the same, and if one's words get their meaning from the development of language, our thoughts get their meaning from the development of language as well. Rather than seeing the brilliant individual as the driver of the development of language, by being able to translate one's thoughts into words, the process of language development becomes a form of mysticism instead. Something that cannot be deeply analysed, only described. His conclusion doesn't differ in essence from the one he arrived at in tractacus, where he claimed that it's not meaningful to discuss philosophy. He later rejected the reasoning in tractacus, and went on a quest to find another rationalisation for why philosophical analysis is pointless.
As for Nixon. To me it doesn't matter whether we learn about him being a conservative or not. His existence doesn't depend on our perception of him. Even if he was isolated at a spot in the universe separated in time and space from everyone else, trapped inside his own Hubble radius, he would still exist. He would exist because he has consciousness. He's a subject, not an object. He doesn't need to be observed to exist.
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Post by Eugene 2.0 on Aug 15, 2020 20:48:27 GMT
... You know it's not easy to understand even basics of language with not a native language (learning Norwegian with English). Yes, I do agree, the phrases I tried to construct were poorly constructed in English (I was still thinking Ukrainian trying to do i). I found not a bad site LearningNorwegian101. Also, I found a site that was made just by one person in Russian, and thus site is huuuge. I mean it seems the one did lotta work. However there were critics (certainly, Norwegians) who pointed the developer for his mistakes. He did them. Anyway, it's not only useful and interesting to learn a language, but - I think in my poor examples it can be seen - that we require to know the underlying, core logic behind the language or its parts to use it effectively, or just to be able to use it. In English we put -s at the end, while, as I understood, in Norwegian we put -(e)r, -e, and, in definite, -ene. Depending on the end of the word, and also there are another cases when a vowel omits. I think such underlying laws might be not only helpful to be more creative, but for better understanding each other. As someone once said "Tell me something and I will see you", so artists, poets, writers and the other creators are almost always trying to represent their core hesitations, feelings, even thougts, and language helps them with it. If one hasn't been heard he'd better to take care about to improve his expressive manners. And a reciever should care about it to - trying to have heard the one. To Gödel: we need to have right meaning, and yet it might happen that a person A and a person B are talking with each other rendering to different things. I mean either they understand each other just because they somehow feel each other (intuitive talk: when A person expects ehat B will say, and one will do it), or the language they use allow variety of meanings such as: we can address from P to Q1, Q2, ..., Qn, and from a set Q to R. In such a situation A could utter "P" rendering to "Qi", while B understands one as if A through "P" refers to "Qj". Surprisingly, they both have succeeded in/at "R". By this I was going to show that in some cases equally of meaning is not necessary. To logically understanding: yes, it seems even effective, than just a plain formalization. It reminds Wittgenstein's phrase: “For a large class of cases of the employment of the word ‘meaning’—though not for all—this word can be explained in this way: the meaning of a word is its use in the language” (Philosophical Investigations p. 43). Nixon: Ok, a doppelganger of Nixon could be Nixon-democrate, but if there were no Nixon-republican we would never know what was like for Nixon to not be Nixon. Having got Nixon-r(epublican) we have learned (understood?) what the "other" one might be. If we never had the one there would be ni chances to claim anything about that "potential" Nixon. - You've said previously that if we never seen a thing (we have never known anything about of its possibility of being known; before we knew the one for us it was the same as the things that never existed), we can never exemplify it, right? So, here's the same. That was what Kripke had been trying to tell (and again, I can't appeal to his theory much as long as I don't remember it for sure). Again to Gödel: formalizing what he said makes our investigation on his proof quite clearer, and if before the research there were N undefined terms, and after some... let us call it "some actions" or "some work"... actions we got N-K (K<N), then some luck smiled at us.
Good luck with learning Norwegian. Yes it's very important when learning a language that you understand its structure. So it's much better that you go from Russian, which is similar to Ukrainian, to Norwegian, than from English to Norwegian.
I presume you were referring to inflections. Here's one example:
English: To drive, driving, drove, have driven
Norwegian: Å kjøre, kjører, kjørte, har kjørt
Wittgenstein's definition of a word's meaning is not problematic to me in what it literally states, but in what it implies. One way or another, every word gets its meaning from how its used in the language. In fact, it's trivially true to the point of being pointless to state. However, what is being implied is that there is no source for the meaning of a word than the development of the language in which it's used. It subtlety exclude the possibility for some words to get their meaning from an inner universal world of concepts, as a universal foundation for all languages. And in this way, it also rejects that thought comes before language. According to Wittgenstein, not even God can read one's thoughts. One's words and one's thoughts are the same, and if one's words get their meaning from the development of language, our thoughts get their meaning from the development of language as well. Rather than seeing the brilliant individual as the driver of the development of language, by being able to translate one's thoughts into words, the process of language development becomes a form of mysticism instead. Something that cannot be deeply analysed, only described. His conclusion doesn't differ in essence from the one he arrived at in tractacus, where he claimed that it's not meaningful to discuss philosophy. He later rejected the reasoning in tractacus, and went on a quest to find another rationalisation for why philosophical analysis is pointless.
As for Nixon. To me it doesn't matter whether we learn about him being a conservative or not. His existence doesn't depend on our perception of him. Even if he was isolated at a spot in the universe separated in time and space from everyone else, trapped inside his own Hubble radius, he would still exist. He would exist because he has consciousness. He's a subject, not an object. He doesn't need to be observed to exist.
Jeg er hyggelig å se deg igjen. As Norwegian is a German group language for those who learn English it ought to be easier to understand it. And the inflection you mentioned support my words. Wittgenstein: your view is indeed wide on this matter, I don't even know what else to add here. Maybe for how children understand something and deaf-mutes do it? I don't remember exactly, but I guess it was John Searle who said elsewhere (on one's magazine pages) that dogs acted like humans except for controlling their language syntax; i.e. a dog can't inverse a phrase, but a person can. I guess that Wittgenstein's thought is a pretty simple. He said on it in "The Brown Book" that Frefe was anger on those who thinked that depending on a mood your thoughts might change (here, mood is taken as a direct cause of mental states). So, to clearly know how the words acted one had to try to use them. And - without a check we cannot (and not be able to) understand how to coordinate (=to check?... I can't choose a good verb here. Correspond would be ok, but I'm not sure) something with something else. "X" is known if "X" can be differentiated from "Y", or else "X" might be "Y". Also it looks like a primal function determination: any X1 or any X2 have to realise in Y, while no X doesn't have to realise in two or more Y'ses. So, the violence of the function is broken if we're thinking we can think "the pure X" without any Y'ses. To know "how to use smth", as I presume, could be arranged from the other point: to know something else (given that this 'smth else' is being compared with the previous investigated thing). On Nixon again: Jeg vil gjerne be om unnskyldning, det er min skyld - Jeg burde ikke ha gjort det: skriv kaotiske tingene om Nixon. I hope you'll agree on it - not knowing Nixon (lets imagine there were no Nixon ever) we can't say anything about him. Common sense tells us if there had been Nixon, but nobody would know about him a thing, nonetheless he would exist. But as we don't know him we cannot say anything about him anything. We even don't know if he's republican or democrat. Hence, to get a knowledge about him we have to (being able to) recognise him, separating him from the others (else - we wouldn't be sure). What is that act of separating, but an essentially tagging him. Having tagged him we stock him with some essential properties that only them Nixon can have to be recognizable. The more important that Nixon's Thought Experiment is not about to deny existence, but to show that there are a posteriori truths. I don't even sure did I do good starting using this example here. However, I like this discussion! - It's already helped me to understand many things. Ha det!
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Post by karl on Aug 16, 2020 9:29:18 GMT
Good luck with learning Norwegian. Yes it's very important when learning a language that you understand its structure. So it's much better that you go from Russian, which is similar to Ukrainian, to Norwegian, than from English to Norwegian.
I presume you were referring to inflections. Here's one example:
English: To drive, driving, drove, have driven
Norwegian: Å kjøre, kjører, kjørte, har kjørt
Wittgenstein's definition of a word's meaning is not problematic to me in what it literally states, but in what it implies. One way or another, every word gets its meaning from how its used in the language. In fact, it's trivially true to the point of being pointless to state. However, what is being implied is that there is no source for the meaning of a word than the development of the language in which it's used. It subtlety exclude the possibility for some words to get their meaning from an inner universal world of concepts, as a universal foundation for all languages. And in this way, it also rejects that thought comes before language. According to Wittgenstein, not even God can read one's thoughts. One's words and one's thoughts are the same, and if one's words get their meaning from the development of language, our thoughts get their meaning from the development of language as well. Rather than seeing the brilliant individual as the driver of the development of language, by being able to translate one's thoughts into words, the process of language development becomes a form of mysticism instead. Something that cannot be deeply analysed, only described. His conclusion doesn't differ in essence from the one he arrived at in tractacus, where he claimed that it's not meaningful to discuss philosophy. He later rejected the reasoning in tractacus, and went on a quest to find another rationalisation for why philosophical analysis is pointless.
As for Nixon. To me it doesn't matter whether we learn about him being a conservative or not. His existence doesn't depend on our perception of him. Even if he was isolated at a spot in the universe separated in time and space from everyone else, trapped inside his own Hubble radius, he would still exist. He would exist because he has consciousness. He's a subject, not an object. He doesn't need to be observed to exist.
Jeg er hyggelig å se deg igjen. As Norwegian is a German group language for those who learn English it ought to be easier to understand it. And the inflection you mentioned support my words. Wittgenstein: your view is indeed wide on this matter, I don't even know what else to add here. Maybe for how children understand something and deaf-mutes do it? I don't remember exactly, but I guess it was John Searle who said elsewhere (on one's magazine pages) that dogs acted like humans except for controlling their language syntax; i.e. a dog can't inverse a phrase, but a person can. I guess that Wittgenstein's thought is a pretty simple. He said on it in "The Brown Book" that Frefe was anger on those who thinked that depending on a mood your thoughts might change (here, mood is taken as a direct cause of mental states). So, to clearly know how the words acted one had to try to use them. And - without a check we cannot (and not be able to) understand how to coordinate (=to check?... I can't choose a good verb here. Correspond would be ok, but I'm not sure) something with something else. "X" is known if "X" can be differentiated from "Y", or else "X" might be "Y". Also it looks like a primal function determination: any X1 or any X2 have to realise in Y, while no X doesn't have to realise in two or more Y'ses. So, the violence of the function is broken if we're thinking we can think "the pure X" without any Y'ses. To know "how to use smth", as I presume, could be arranged from the other point: to know something else (given that this 'smth else' is being compared with the previous investigated thing). On Nixon again: Jeg vil gjerne be om unnskyldning, det er min skyld - Jeg burde ikke ha gjort det: skriv kaotiske tingene om Nixon. I hope you'll agree on it - not knowing Nixon (lets imagine there were no Nixon ever) we can't say anything about him. Common sense tells us if there had been Nixon, but nobody would know about him a thing, nonetheless he would exist. But as we don't know him we cannot say anything about him anything. We even don't know if he's republican or democrat. Hence, to get a knowledge about him we have to (being able to) recognise him, separating him from the others (else - we wouldn't be sure). What is that act of separating, but an essentially tagging him. Having tagged him we stock him with some essential properties that only them Nixon can have to be recognizable. The more important that Nixon's Thought Experiment is not about to deny existence, but to show that there are a posteriori truths. I don't even sure did I do good starting using this example here. However, I like this discussion! - It's already helped me to understand many things. Ha det!
I agree that if we know nothing about Nixon, we can't know that he exists.
By posteriori truths I presume you mean knowledge about the real world based on what we may observe. The posteriori knowledge we have come in the form of probabilities. When we assume the sun will still shine tomorrow, it's not because we know it, but because we can conclude that it's very unlikely that it won't. This is based on what we've been being able to deduce from observation
Our starting point is the induction principle, which is a synthetic knowledge a priori. A simplified way to present it would be that if you conduct experiment A and get result B, then for every time you repeat A and still get B, you become more and more convinced that next time you repeat A you will get B. This can't be proven. It's simply something we regards as self-evident. We can't, for example, state that the induction principle is true because it's proven to work, for that would be to use the induction principle to prove the induction principle. What the induction principle in reality is expressing, is that we expect there to be order in the universe.
But the induction principle can never be used to deduce anything with 100% certainty. As the famous example goes, there is always the possibility that a black swan shows up. Similarly, even if you conduct the same experiment a billion times, something might change so that one day it starts yielding a different result. We can't even know that the laws we believe to have identified won't change. We don't know, for example, that the speed of light won't change.
As for Wittgenstein, yes one's mood might change one's thoughts, and also what one means by uttering the same sentence. Our inner world of thoughts is far more complex than what can be expressed even by a modern language. So we try to use the words we think are closest to what we want to express, and we further attempt to convey that meaning through tone of voice, facial expression and body language. And sometimes one's inner thoughts are actually far more primitive and simplistic than the words one uses to express them. Like the eloquent person who attempts to rationalise his petty selfishness. One thing Hitler knew how to do, was to make people feel that their most primitive and vile desires actually expressed something refined and deep. Lenin did the same, when he urged the poor farmers to take their anger and frustrations out on the wealthier farmers in the name of class struggle and equality.
There is a distinction that's important to make. "an emotion changing a thought", to me, simply means to go from one thought to another. Or to go from one composition of thoughts to another. However, that is probably not what Wittgenstein means. What I think he's aiming for is to make it seem as if a thought can't be clarified. For how could it, if it's so organic that it keeps changing?
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Post by Eugene 2.0 on Aug 17, 2020 13:06:42 GMT
karlI apologize for late commenting. Now I'm not using keyboard so as soon as I plug it I'll be in touch. Actually I had read it and thinked a lot. This theme starts making me see many things I've never seen before.
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Post by Eugene 2.0 on Aug 17, 2020 21:12:25 GMT
karlWittgenstein: - I agree on it. Except for some details. Well, there's no doubt that some changes occur, because - as our experience may prompt us about it - behaviour of a person may change by some reasons. And again, it's not strongly positive. Firstly, sometimes we continue to do what we'd better stop doing it (breaking habits). - They looked for weakness points of persons. This example is great to show how the mechanism of propaganda works. Another person can count on using rhetoric speeches to manipulate one's behaviour. They say (I don't know it well) that it's impossible to control some things though. Murdering or another things are impossible to be taught with a hypnoses suggestions. - Well, that's indeed an important theme, because here is seen what exactly problems may occur during such an investigation for those philosophers. As far as I know, when Frege told about "stability" of a thought he meant that "2+2=4" is eternally true. It's impossible for us to wake up in the morning tomorrow saying: "Oh, today 2+2=5!". Are there any transferring or leaping from one thought to another, and what kind of mechanism is it? - I really don't know. Seems it's an area of psychology. But what Wittgenstein was trying to save Frege's thought was that as if we judged about a thought by its meaning, and a cause of meaning its a thought (a concept, a proposition), then to know the meaning is to know how it uses in general or particular ways. And here's another problem occurs - about using the method of induction. Behaviouristic way out of Wittgenstein manifested that perhaps there is no meaning at all. Saul Kripke, as far as I know, tried to save Wittgenstein's position by explaining our a posteriori truths by how I have already said about that. So, in general, what about Wittgenstein's thought on it? - We have to show the meaning of a word by using it. When A utters a (complex) sign B in some situation C, pointing on D, then the meaning of B to A is D that takes place in the situation C (or smth like that). Kripke: - Me too. Probability of a posteriori claims are those, because any proposition P (for example, water is boiling at 100*C) in another world might be different. - Russell, in one of his lectures of Mathematical Logics, said that in each induction there is an implicit premise N, that tells that "All of the rest premises is enough to make a (technical) conclusion". It also can be seen if we start thinking about it in this manner: X1, X2, ..., Xn -> A1 X1, X2, ..., Xn, Xn+1 -> A2 ... X1, X2, ..., Xn, Xn+k -> Ak Where Ak - is kinda limit or the most possible conclusion. So, for each conclusion: X1, X2, ..., Xn, Xn+i -> An+i We implicitly add that there's enough premises (A1...An+i) premises to make this (n+i) conclusion. - In what Kripke wanted to show there's no induction. It's true that our conclusions of the world is by inductions. However, it doesn't infer our investigations. Why? Because, if once we knew how to differ water from something else, we got the knowledge of how to compare this thing (water) from the other ones. Usually, we differ things. And if the next thing would not be a water (not H20, for instance), so we would claim it comparing it to the water - our knowledge of this thing. Maybe it become possible to make trips to Saturn where "the water" was found. Then we arrived to the planet we wanted to check whether or not that was water. The same about Nixon. As soon as we know this knowledge it's been badged or tagged as it is. Surely, Nixon could be different, but that Nixon we know was him and nobody else. He started to be the measure for next Nixon. Conclusion about Nixon is not under induction, is a conceptual characteristic. Nixon could be republican, and if he were the one, when the other possible Nixons would be compared to Nixon-republican. Kripke explained it by referring us to such a thing as the reference, standard, the model. Before atomic investigations we used a meter that was determined like what it was, and the standard of him was in Paris's famous scientific museum. It could happen (by someone's fault) that the meter had been replaced with another one. What would we do then? - Probably nothing. We couldn't do anything. The same is with Mona Lisa. If someone did steal the portrait and changed it, and then replaced it, then we - oh oh - we couldn't do anything. However, there was at least one episode when the books were burned, but its texts were saved - Confucian's teachings. They say the ones who remembered them then wrote it again. (The same was rumoring about Qur'an.) Directly local we can't aim simple things and then measure it all with it like we used to to with logic or math: we never stop using x+y=y+x for next times to compare it with next things. Unfortunately, such things as Quantum Logic or Non-classical Logic break our hope down, because the Nature keeps some secrets that logically don't suit them well. Putnam: Later Putnam objected Kripke's decision by giving an example of the Twin-Earth. Imagine the Twin-Earth where everything is the same as in its original (the Earth), but the water is XYZ, and not H2O. Some criticized Putnam for this just thought-experiment freely comparing, however, Putnam was trying to show that it might happen when we thought that H2O was water, but it was XYZ. What to do in this situation? Practically to arrange it, we try to use coherent decisions: we try to equip not one, but few things to be sure that we're at the right direction. At final we try to have the powerful tool: the formal system that allows us to do this (to analyze). As Godel proved that such a system has flaws, then Frege's dreams were over. Important note: I could make some gross mistakes. That's why I have to consider my review as personal and subjektive.
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Post by karl on Aug 18, 2020 13:33:16 GMT
karl Wittgenstein: - I agree on it. Except for some details. Well, there's no doubt that some changes occur, because - as our experience may prompt us about it - behaviour of a person may change by some reasons. And again, it's not strongly positive. Firstly, sometimes we continue to do what we'd better stop doing it (breaking habits). - They looked for weakness points of persons. This example is great to show how the mechanism of propaganda works. Another person can count on using rhetoric speeches to manipulate one's behaviour. They say (I don't know it well) that it's impossible to control some things though. Murdering or another things are impossible to be taught with a hypnoses suggestions. - Well, that's indeed an important theme, because here is seen what exactly problems may occur during such an investigation for those philosophers. As far as I know, when Frege told about "stability" of a thought he meant that "2+2=4" is eternally true. It's impossible for us to wake up in the morning tomorrow saying: "Oh, today 2+2=5!". Are there any transferring or leaping from one thought to another, and what kind of mechanism is it? - I really don't know. Seems it's an area of psychology. But what Wittgenstein was trying to save Frege's thought was that as if we judged about a thought by its meaning, and a cause of meaning its a thought (a concept, a proposition), then to know the meaning is to know how it uses in general or particular ways. And here's another problem occurs - about using the method of induction. Behaviouristic way out of Wittgenstein manifested that perhaps there is no meaning at all. Saul Kripke, as far as I know, tried to save Wittgenstein's position by explaining our a posteriori truths by how I have already said about that. So, in general, what about Wittgenstein's thought on it? - We have to show the meaning of a word by using it. When A utters a (complex) sign B in some situation C, pointing on D, then the meaning of B to A is D that takes place in the situation C (or smth like that). Kripke: - Me too. Probability of a posteriori claims are those, because any proposition P (for example, water is boiling at 100*C) in another world might be different. - Russell, in one of his lectures of Mathematical Logics, said that in each induction there is an implicit premise N, that tells that "All of the rest premises is enough to make a (technical) conclusion". It also can be seen if we start thinking about it in this manner: X1, X2, ..., Xn -> A1 X1, X2, ..., Xn, Xn+1 -> A2 ... X1, X2, ..., Xn, Xn+k -> Ak Where Ak - is kinda limit or the most possible conclusion. So, for each conclusion: X1, X2, ..., Xn, Xn+i -> An+i We implicitly add that there's enough premises (A1...An+i) premises to make this (n+i) conclusion. - In what Kripke wanted to show there's no induction. It's true that our conclusions of the world is by inductions. However, it doesn't infer our investigations. Why? Because, if once we knew how to differ water from something else, we got the knowledge of how to compare this thing (water) from the other ones. Usually, we differ things. And if the next thing would not be a water (not H20, for instance), so we would claim it comparing it to the water - our knowledge of this thing. Maybe it become possible to make trips to Saturn where "the water" was found. Then we arrived to the planet we wanted to check whether or not that was water. The same about Nixon. As soon as we know this knowledge it's been badged or tagged as it is. Surely, Nixon could be different, but that Nixon we know was him and nobody else. He started to be the measure for next Nixon. Conclusion about Nixon is not under induction, is a conceptual characteristic. Nixon could be republican, and if he were the one, when the other possible Nixons would be compared to Nixon-republican. Kripke explained it by referring us to such a thing as the reference, standard, the model. Before atomic investigations we used a meter that was determined like what it was, and the standard of him was in Paris's famous scientific museum. It could happen (by someone's fault) that the meter had been replaced with another one. What would we do then? - Probably nothing. We couldn't do anything. The same is with Mona Lisa. If someone did steal the portrait and changed it, and then replaced it, then we - oh oh - we couldn't do anything. However, there was at least one episode when the books were burned, but its texts were saved - Confucian's teachings. They say the ones who remembered them then wrote it again. (The same was rumoring about Qur'an.) Directly local we can't aim simple things and then measure it all with it like we used to to with logic or math: we never stop using x+y=y+x for next times to compare it with next things. Unfortunately, such things as Quantum Logic or Non-classical Logic break our hope down, because the Nature keeps some secrets that logically don't suit them well. Putnam: Later Putnam objected Kripke's decision by giving an example of the Twin-Earth. Imagine the Twin-Earth where everything is the same as in its original (the Earth), but the water is XYZ, and not H2O. Some criticized Putnam for this just thought-experiment freely comparing, however, Putnam was trying to show that it might happen when we thought that H2O was water, but it was XYZ. What to do in this situation? Practically to arrange it, we try to use coherent decisions: we try to equip not one, but few things to be sure that we're at the right direction. At final we try to have the powerful tool: the formal system that allows us to do this (to analyze). As Godel proved that such a system has flaws, then Frege's dreams were over. Important note: I could make some gross mistakes. That's why I have to consider my review as personal and subjektive.
Unless I misunderstood what you wrote, you seem to be referring to mathematical induction. When I was referring to the induction principle, I meant empirical, not mathematical induction. Bertrand Russell gives an explanation of empirical induction in his book "problems of philosophy".
As for Wittgenstein. Let's start with the statement 2+2=4. This resembles an expression people sometimes use, which goes like this: "I put two and two together." Let's, for the sake of this argument, pretend that expression includes the answer, so that it would be as follows: "I put two and two together and got four." Now that statement looks as if it's synonymous with the statement "2+2=4". But is it?
Someone studying Wittgenstein told me that Wittgenstein once sat in a restaurant with someone who uttered the statement: "It's cold in here." Wittgenstein realised that the statement wasn't just an expression of the temperature in the room, but meant something beyond that. The person was making a statement about the psychological atmosphere, just as much as about the physical temperature.
Similarly, the statement "I put two and two together and got four." wouldn't be a pointless reminder of that 2+2=4. For example, imagine the following conversation:
A: How did you figure out that his wife had cheated on him? B: I noticed that their son looks remarkably like the postman, so I put two and two together...
One could also imagine that "2+2=5" becomes a standard expression. Imagine the following statement:
"We falsely expect the world to make sense, but sometime 2+2=5."
Is the person uttering it actually claiming that 2+2 sometimes equals 5? No. It's just a way of saying that the world doesn't always seem to make logical sense.
So how one states something, and the context within which one states it, are deciding factors for what thought, or composition of thoughts, lie behind the statement: "2+2=4". For example, by adding an extra layer of meaning. It's not the eternal truth of "2+2=4" that is being altered. It's just that the statement is used in such a way that it conveys something beyond that mathematical truth. The mathematical thought "2+2=4" isn't, and cannot, be altered by context and emotion.
The key point is that all of this can be depicted and explained. We can reduce the composition of thoughts behind each statement to its smaller parts and explain the underlying meaning. When I invented the expression: "Sometimes 2+2=5", many people would, given the context, pick up its meaning. And the meaning wouldn't be confined to that context. I could reuse it in another context as follows:
A: "Women make no logical sense." B: "Within the world of female psychology, sometimes 2+2=5."
Again, it can be depicted, analysed and reduced to its smaller parts. All it's an expression of, is that people can find ways to combine thoughts in an attempt to describe different aspects of a very complex reality. And it's because we understand the meaning of the different elements as clear thoughts, that we can change the composition and come up with new ways of expressing ourselves. This is possible only because thought comes before language. Rather than being confined by what ways the statement "2+2=5" have been used to far, and only seek to describe its use, we pick up the essence of it, and come up with new ways of using it.
Physicist: "When a conventional theory tells us that 2+2=5, we know there must be something we haven't understood."
This doesn't mean that the conventional theory actually gave 5 as the answer to 2+2, but that there is something in the theory that doesn't add up logically.
So the meaning of a sentence is the composition of its individual elements, which have been put together by the creative mind. -The creative mind, which through introspection have been able to identify the underlying thoughts of the sentences that we utter.
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Post by Eugene 2.0 on Aug 18, 2020 14:51:39 GMT
karlNo, I wasn't referring to math induction. For me, in a weak sense, all that is not deduction - is one of forms of induction. Specifically, the math induction is what was given in the 5th axiom of Peano (at least, it is said in the preface to Landau L. "Basics of Analysis"). Well, I know this essay of Russell, I've reread it recently. I'd say Russell tried to convince us that there was a principle of induction. Looked like he speculated about signs and things (i.e. round epistemological problems). My note on the induction in the previous comments was most technically - I just wanted to say that if there are some premises that are not enough to make a conclusion, there is another one (an implicit one) that we add to this. Russell told about the induction I've been mentioning in his "Philosophy of Logical Atomism" (Chapter V. General Propositions and Its Existence, somewhere in the middle of the text; I'm using Russian translation of this text. I think the bibliographical references I'd give wouldn't help much.) The poly-meaningfulness of Wittgenstein's understanding is quite possible. I'm not objecting it. Actually, many strings of Wittgenstein's work I don't get as, for instance, Russell's. Well, I supposed I wanted to express not exactly Wittgensteian personal position, but rather his style of defending the thought of Frege. I don't think that what Wittgenstein said about the expression of that man is so extravagant and new. The short discussion you wrote - it's cool! Surely, this can happen, but why this happens? Because either there was violated one of semantics standard (for instance, "remarkably" was "my sense on it was too strong to make a mistake. I never did such a mistake before", and "cheated" was "playing one of card games", while that A wrongly assumed that "cheated" was "a wife making something adult-like with not her husband"), or it was a violation one of Grice's maxims. I don't remember them exactly, but there was one like this: A: What's your impressions? How did she sing? B: Well, she looked nice. So, I'd say that Wittgenstein probably just scoffed at his vis-a-vis. Sometimes I ask myself weren't a few Wittgenstein's works brochures of anecdotes? I wouldn't mix our primarily intentions and meanings with possible meanings. I guess that at each moment of our lives we can imagine that all what is going on is just the Matrix, or a delusion, or that all what is going on is a circus, etc. However, all such solipsistics or skeptical thoughts don't get us far. Why not to trust to induction for making possible to achieve something? Need to change a bulb, hardly makes me read Whitman or Shakespeare to get some info about it. Extra info (meaning) can be found as soon as there are many ways to get it from (there could be much more explanations, I give just some): a) the form of symbols; b) associations (one symbol reminds me another, so...); c) funny coincidences of syllables; d) wish to appear a funny guy;... and many more. In the different contexts we have to use different meanings. Well, I can't agree on our inability to reduce or doing something with meanings. What makes me thing that? First of all, I cannot disagree that that "meaning-thing" problem has no flaws. It certainly has, and not sureness and not stability of a meaning shows this problem nicely. However, I can't imagine that there's nothing more, except for just meanings, words, and things. Each context is either a game, or a formal system (it depends on has in or not logical rules). For an informal system like "women logic" (I thought that only Slavic women are illogical. Aren't the women from other regions of the Earth illogical too?). Maybe we haven't learned yet how to recognize contexts, and how to explicate sense from something (what is the sense of life? or - Doesn't a life has any sense?) Reduction is not the only one possible route. Actually, the reduction method has such a flaw as "small men". Scientists like Helmholtz sometimes did such a mistake (not intentionally). This view is to think that, for instance, behind our mind there are small men who control us. Such a view, obviously leads us to infinite reduction of this fact. And this occurs because it's not easy for us to comprehend levels of being in many situations. "I am a liar" - is one of such examples. There might be some levels. Maybe our ability of focusing (e.g. making our eyes to see something closer or farther) helps us here, or maybe it makes us understand things incorrectly. This appeared that what xxxxxxxxx tried to say that Nothing is a relation between things, while I was addressing this to that Nothing is a substitution for a thing. So, 9x said if there are A and B, "and" is Nothing. My view is that if there are A and B, then to the phrase "there is no C" is the same to say "there is Nothing" (it must be seen more clear if there were not A and B, and then the phrase "there are no A and B" would be the same as "there is Nothing" (="we haven't found any A's and B's")). I brought this part of discussion here to show that nor me, nor 9x wanted not to refer to meta-level or not to use reduction. There's also two important addition to protect reduction. First of all, it's important where to live: of the planet Earth, or in the desert of Kara-Kum. If one challenged with such a choice, what would he chose? Another one, is to look at the trolley problem from a point of such points of view: what if there there cabbages instead of people (laying down the rails being tied)? what if there were five robots? what if there were five vast complexes of electrons? what if there were laying five pieces of organic stuff? I think that form the ethical point such methods as reduction get us back to the previous start positions (before Wittgenstenian skepticism). "This is possible only because thought comes before language" - However, as Rorty ("Philosophy and the Mirror of Nature". Chapter about Declining of Epistemology) said that Wittgensteinians (and Wittgenstein himself) along with the Ordinary Language philosophers that there were no thoughts till appearance of language. (Also, I wouldn't insist on this fact. Maybe I took the passage some incorrectly. Nevermind.) The version of the (creative) mind is indeed good. Anyway, for me the mind is nothing without methods it's able to use. Without it - he's an empty organic stuff, right? That's why I insist on methodological position over any elses.
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Post by karl on Aug 18, 2020 15:07:46 GMT
karl No, I wasn't referring to math induction. For me, in a weak sense, all that is not deduction - is one of forms of induction. Specifically, the math induction is what was given in the 5th axiom of Peano (at least, it is said in the preface to Landau L. "Basics of Analysis"). Well, I know this essay of Russell, I've reread it recently. I'd say Russell tried to convince us that there was a principle of induction. Looked like he speculated about signs and things (i.e. round epistemological problems). My note on the induction in the previous comments was most technically - I just wanted to say that if there are some premises that are not enough to make a conclusion, there is another one (an implicit one) that we add to this. Russell told about the induction I've been mentioning in his "Philosophy of Logical Atomism" (Chapter V. General Propositions and Its Existence, somewhere in the middle of the text; I'm using Russian translation of this text. I think the bibliographical references I'd give wouldn't help much.) The poly-meaningfulness of Wittgenstein's understanding is quite possible. I'm not objecting it. Actually, many strings of Wittgenstein's work I don't get as, for instance, Russell's. Well, I supposed I wanted to express not exactly Wittgensteian personal position, but rather his style of defending the thought of Frege. I don't think that what Wittgenstein said about the expression of that man is so extravagant and new. The short discussion you wrote - it's cool! Surely, this can happen, but why this happens? Because either there was violated one of semantics standard (for instance, "remarkably" was "my sense on it was too strong to make a mistake. I never did such a mistake before", and "cheated" was "playing one of card games", while that A wrongly assumed that "cheated" was "a wife making something adult-like with not her husband"), or it was a violation one of Grice's maxims. I don't remember them exactly, but there was one like this: A: What's your impressions? How did she sing? B: Well, she looked nice. So, I'd say that Wittgenstein probably just scoffed at his vis-a-vis. Sometimes I ask myself weren't a few Wittgenstein's works brochures of anecdotes? I wouldn't mix our primarily intentions and meanings with possible meanings. I guess that at each moment of our lives we can imagine that all what is going on is just the Matrix, or a delusion, or that all what is going on is a circus, etc. However, all such solipsistics or skeptical thoughts don't get us far. Why not to trust to induction for making possible to achieve something? Need to change a bulb, hardly makes me read Whitman or Shakespeare to get some info about it. Extra info (meaning) can be found as soon as there are many ways to get it from (there could be much more explanations, I give just some): a) the form of symbols; b) associations (one symbol reminds me another, so...); c) funny coincidences of syllables; d) wish to appear a funny guy;... and many more. In the different contexts we have to use different meanings. Well, I can't agree on our inability to reduce or doing something with meanings. What makes me thing that? First of all, I cannot disagree that that "meaning-thing" problem has no flaws. It certainly has, and not sureness and not stability of a meaning shows this problem nicely. However, I can't imagine that there's nothing more, except for just meanings, words, and things. Each context is either a game, or a formal system (it depends on has in or not logical rules). For an informal system like "women logic" (I thought that only Slavic women are illogical. Aren't the women from other regions of the Earth illogical too?). Maybe we haven't learned yet how to recognize contexts, and how to explicate sense from something (what is the sense of life? or - Doesn't a life has any sense?) Reduction is not the only one possible route. Actually, the reduction method has such a flaw as "small men". Scientists like Helmholtz sometimes did such a mistake (not intentionally). This view is to think that, for instance, behind our mind there are small men who control us. Such a view, obviously leads us to infinite reduction of this fact. And this occurs because it's not easy for us to comprehend levels of being in many situations. "I am a liar" - is one of such examples. There might be some levels. Maybe our ability of focusing (e.g. making our eyes to see something closer or farther) helps us here, or maybe it makes us understand things incorrectly. This appeared that what xxxxxxxxx tried to say that Nothing is a relation between things, while I was addressing this to that Nothing is a substitution for a thing. So, 9x said if there are A and B, "and" is Nothing. My view is that if there are A and B, then to the phrase "there is no C" is the same to say "there is Nothing" (it must be seen more clear if there were not A and B, and then the phrase "there are no A and B" would be the same as "there is Nothing" (="we haven't found any A's and B's")). I brought this part of discussion here to show that nor me, nor 9x wanted not to refer to meta-level or not to use reduction. There's also two important addition to protect reduction. First of all, it's important where to live: of the planet Earth, or in the desert of Kara-Kum. If one challenged with such a choice, what would he chose? Another one, is to look at the trolley problem from a point of such points of view: what if there there cabbages instead of people (laying down the rails being tied)? what if there were five robots? what if there were five vast complexes of electrons? what if there were laying five pieces of organic stuff? I think that form the ethical point such methods as reduction get us back to the previous start positions (before Wittgenstenian skepticism). "This is possible only because thought comes before language" - However, as Rorty ("Philosophy and the Mirror of Nature". Chapter about Declining of Epistemology) said that Wittgensteinians (and Wittgenstein himself) along with the Ordinary Language philosophers that there were no thoughts till appearance of language. (Also, I wouldn't insist on this fact. Maybe I took the passage some incorrectly. Nevermind.) The version of the (creative) mind is indeed good. Anyway, for me the mind is nothing without methods it's able to use. Without it - he's an empty organic stuff, right? That's why I insist on methodological position over any elses.
I need to clarify that I wasn't, by any means, trying to express Wittgenstein's view of language. I was expressing my own. Wittgenstein did not acknowledge that one can clarify thoughts as the basis for language. His view was that one can't read one's own thoughts, and that even God can't read them. Instead, what we utter may only be described, but not actually analysed.
My point with my last and previous posts in regards to Wittgenstein, is to explain why I regard his conclusions as false. I see him as making observations about how language works which are superficially correct, but drawing the wrong conclusions.
To put mathematical and empirical induction in the same category makes no sense to me, as I see them as distinctly separate from each other. Empirical induction leads to probabilities, and those probabilities aren't even certain. This is outside the world of mathematical analysis.
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Post by Eugene 2.0 on Aug 18, 2020 15:37:50 GMT
karl No, I wasn't referring to math induction. For me, in a weak sense, all that is not deduction - is one of forms of induction. Specifically, the math induction is what was given in the 5th axiom of Peano (at least, it is said in the preface to Landau L. "Basics of Analysis"). Well, I know this essay of Russell, I've reread it recently. I'd say Russell tried to convince us that there was a principle of induction. Looked like he speculated about signs and things (i.e. round epistemological problems). My note on the induction in the previous comments was most technically - I just wanted to say that if there are some premises that are not enough to make a conclusion, there is another one (an implicit one) that we add to this. Russell told about the induction I've been mentioning in his "Philosophy of Logical Atomism" (Chapter V. General Propositions and Its Existence, somewhere in the middle of the text; I'm using Russian translation of this text. I think the bibliographical references I'd give wouldn't help much.) The poly-meaningfulness of Wittgenstein's understanding is quite possible. I'm not objecting it. Actually, many strings of Wittgenstein's work I don't get as, for instance, Russell's. Well, I supposed I wanted to express not exactly Wittgensteian personal position, but rather his style of defending the thought of Frege. I don't think that what Wittgenstein said about the expression of that man is so extravagant and new. The short discussion you wrote - it's cool! Surely, this can happen, but why this happens? Because either there was violated one of semantics standard (for instance, "remarkably" was "my sense on it was too strong to make a mistake. I never did such a mistake before", and "cheated" was "playing one of card games", while that A wrongly assumed that "cheated" was "a wife making something adult-like with not her husband"), or it was a violation one of Grice's maxims. I don't remember them exactly, but there was one like this: A: What's your impressions? How did she sing? B: Well, she looked nice. So, I'd say that Wittgenstein probably just scoffed at his vis-a-vis. Sometimes I ask myself weren't a few Wittgenstein's works brochures of anecdotes? I wouldn't mix our primarily intentions and meanings with possible meanings. I guess that at each moment of our lives we can imagine that all what is going on is just the Matrix, or a delusion, or that all what is going on is a circus, etc. However, all such solipsistics or skeptical thoughts don't get us far. Why not to trust to induction for making possible to achieve something? Need to change a bulb, hardly makes me read Whitman or Shakespeare to get some info about it. Extra info (meaning) can be found as soon as there are many ways to get it from (there could be much more explanations, I give just some): a) the form of symbols; b) associations (one symbol reminds me another, so...); c) funny coincidences of syllables; d) wish to appear a funny guy;... and many more. In the different contexts we have to use different meanings. Well, I can't agree on our inability to reduce or doing something with meanings. What makes me thing that? First of all, I cannot disagree that that "meaning-thing" problem has no flaws. It certainly has, and not sureness and not stability of a meaning shows this problem nicely. However, I can't imagine that there's nothing more, except for just meanings, words, and things. Each context is either a game, or a formal system (it depends on has in or not logical rules). For an informal system like "women logic" (I thought that only Slavic women are illogical. Aren't the women from other regions of the Earth illogical too?). Maybe we haven't learned yet how to recognize contexts, and how to explicate sense from something (what is the sense of life? or - Doesn't a life has any sense?) Reduction is not the only one possible route. Actually, the reduction method has such a flaw as "small men". Scientists like Helmholtz sometimes did such a mistake (not intentionally). This view is to think that, for instance, behind our mind there are small men who control us. Such a view, obviously leads us to infinite reduction of this fact. And this occurs because it's not easy for us to comprehend levels of being in many situations. "I am a liar" - is one of such examples. There might be some levels. Maybe our ability of focusing (e.g. making our eyes to see something closer or farther) helps us here, or maybe it makes us understand things incorrectly. This appeared that what xxxxxxxxx tried to say that Nothing is a relation between things, while I was addressing this to that Nothing is a substitution for a thing. So, 9x said if there are A and B, "and" is Nothing. My view is that if there are A and B, then to the phrase "there is no C" is the same to say "there is Nothing" (it must be seen more clear if there were not A and B, and then the phrase "there are no A and B" would be the same as "there is Nothing" (="we haven't found any A's and B's")). I brought this part of discussion here to show that nor me, nor 9x wanted not to refer to meta-level or not to use reduction. There's also two important addition to protect reduction. First of all, it's important where to live: of the planet Earth, or in the desert of Kara-Kum. If one challenged with such a choice, what would he chose? Another one, is to look at the trolley problem from a point of such points of view: what if there there cabbages instead of people (laying down the rails being tied)? what if there were five robots? what if there were five vast complexes of electrons? what if there were laying five pieces of organic stuff? I think that form the ethical point such methods as reduction get us back to the previous start positions (before Wittgenstenian skepticism). "This is possible only because thought comes before language" - However, as Rorty ("Philosophy and the Mirror of Nature". Chapter about Declining of Epistemology) said that Wittgensteinians (and Wittgenstein himself) along with the Ordinary Language philosophers that there were no thoughts till appearance of language. (Also, I wouldn't insist on this fact. Maybe I took the passage some incorrectly. Nevermind.) The version of the (creative) mind is indeed good. Anyway, for me the mind is nothing without methods it's able to use. Without it - he's an empty organic stuff, right? That's why I insist on methodological position over any elses.
I need to clarify that I wasn't, by any means, trying to express Wittgenstein's view of language. I was expressing my own. Wittgenstein did not acknowledge that one can clarify thoughts as the basis for language. His view was that one can't read one's own thoughts, and that even God can't read them. Instead, what we utter may only be described, but not actually analysed.
My point with my last and previous posts in regards to Wittgenstein, is to explain why I regard his conclusions as false. I see him as making observations about how language works which are superficially correct, but drawing the wrong conclusions.
To put mathematical and empirical induction in the same category makes no sense to me, as I see them as distinctly separate from each other. Empirical induction leads to probabilities, and those probabilities aren't even certain. This is outside the world of mathematical analysis.
I apologize for misunderstanding. However, Wittgenstein did many jokes in his works. Because the discussion began to be monologue-monologue structure it became harder for me to explicit sense of it. And I think if was my fault to start taking aside thoughts as Wittgenstein's, Kripke's and Putnam's. Anyway, do you think it is possible to see somehow our thoughts (to make our thoughts be somehow visible)? On math induction: 5th of Peano: a) it is true for 1; b) if it is true for n, then it must be true for n+1. thesis: 1+2+...+n = n(n+1)/2 a) 1 = 1(1+1)/2 b) If 1+2+...+n = n(n+1)/2, then 1+2+...n+n+1 = n+1(n+1+1)/2 ') n(n+1)/2 = (n^2+n)/2 '') (n+1)(n+2)/2 = (n^2+n)+2(n+1)/2 = (n^2+n)/2 + 2(n+1)/2 = (n^2+n)/2 + n+1 ''') n+1 = n+1 Yeah, it looks like not a trivial induction. Usually, induction shows as the reversed implication (Cohen, Nagel "An Introduction to Logic and Scientific Methods", 1936): Deduction: if p⊃q deduces q when and only when p⊃q is given as true, and p is true; Induction: if p⊃q induces p when and only when p⊃q is given as true and q is true. Math induction doesn't look like the one. So, probably, yeah, this is not the usual induction.
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Post by karl on Aug 18, 2020 16:04:41 GMT
I need to clarify that I wasn't, by any means, trying to express Wittgenstein's view of language. I was expressing my own. Wittgenstein did not acknowledge that one can clarify thoughts as the basis for language. His view was that one can't read one's own thoughts, and that even God can't read them. Instead, what we utter may only be described, but not actually analysed.
My point with my last and previous posts in regards to Wittgenstein, is to explain why I regard his conclusions as false. I see him as making observations about how language works which are superficially correct, but drawing the wrong conclusions.
To put mathematical and empirical induction in the same category makes no sense to me, as I see them as distinctly separate from each other. Empirical induction leads to probabilities, and those probabilities aren't even certain. This is outside the world of mathematical analysis.
I apologize for misunderstanding. However, Wittgenstein did many jokes in his works. Because the discussion began to be monologue-monologue structure it became harder for me to explicit sense of it. And I think if was my fault to start taking aside thoughts as Wittgenstein's, Kripke's and Putnam's. Anyway, do you think it is possible to see somehow our thoughts (to make our thoughts be somehow visible)? On math induction: 5th of Peano: a) it is true for 1; b) if it is true for n, then it must be true for n+1. thesis: 1+2+...+n = n(n+1)/2 a) 1 = 1(1+1)/2 b) If 1+2+...+n = n(n+1)/2, then 1+2+...n+n+1 = n+1(n+1+1)/2 ') n(n+1)/2 = (n^2+n)/2 '') (n+1)(n+2)/2 = (n^2+n)+2(n+1)/2 = (n^2+n)/2 + 2(n+1)/2 = (n^2+n)/2 + n+1 ''') n+1 = n+1 Yeah, it looks like not a trivial induction. Usually, induction shows as the reversed implication (Cohen, Nagel "An Introduction to Logic and Scientific Methods", 1936): Deduction: if p⊃q deduces q when and only when p⊃q is given as true, and p is true; Induction: if p⊃q induces p when and only when p⊃q is given as true and q is true. Math induction doesn't look like the one. So, probably, yeah, this is not the usual induction.
Yes, I know the Peano axioms and mathematical deduction. We discussed this a long time ago in relation to Kurt Godel's incompleteness theorem. It's so long ago I can't remember the name of the thread.
I think all our thoughts are visible introspectively, but no, I don't think all our thoughts can be made visible outside of introspection. I can write one as "1", but I can't make visible the thought it's meant to express. In that example, it doesn't matter, for as long as everyone understands what thought "1" is referring to. I see another person's thought indirectly through symbols. This is what's so great about mathematics. Many of its concepts are thoughts universally shared. If I show a picture of a circle, I can probably point to it and tell a person unfamiliar with geometric shapes: "This is a circle", with no further explanation. I probably don't have to explain that it's not the colour I drew it in that makes the circle, nor is it its size, or whatever background paper I was using. The circle is understood as an abstract concept. This I can also do when referring to "free will". But here we face a problem. What if someone disputes the existence of free will? Then we'd have to try to express our thought about free will. This is where we face the limitation of language. It will always depend on that we all tap into the same inner world of concepts. If someone simply declares that the concept of free will is meaningless, we have no words, no imagery to point to, no analysis to present to explain it. Only indirectly may we make a case for it. For example, that the uncertainty principle makes it a possibility. -And that it might be that free will is linked to uncomputable sets of numbers. But that isn't expressing free will itself.
Language always depends on common understanding. Imagine someone stating the following:
"I don't think I have a self, because the self just mirrors the processes in the brain, and the brain is continuously changing."
Then I would declare I know the person is wrong, because I have an introspective sense of the self, or, rather, the core of the self, as something indivisible and unchanging. But if the other person doesn't, or pretends that he/she doesn't, I would not be able to prove that person wrong.
In a meaningful discussion I am therefore always dependent, not only on that the person I discuss with is honest with me, but that he/she is honest with him/herself. One should never have as a premise for a discussion that if person A thinks person B is wrong, that person A should be able to prove it, if he/she is right. For very often that is not the case, and based on the misconception that language can express anything meaningful convincingly to those who respect facts and logic. Rather, language may express what's meaningful to those who respect facts and logic as well as having spent their lives acquiring self-insight through introspection. For it is through introspection that one clarifies the thoughts upon which language is ultimately based.
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Post by jamesskywalker on Aug 18, 2020 16:16:26 GMT
You can’t search the “sun”. First of all, you can’t get there. Second of all, how are you gunna get inside and look around? it’s too hot!
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Post by Eugene 2.0 on Aug 18, 2020 17:41:17 GMT
I apologize for misunderstanding. However, Wittgenstein did many jokes in his works. Because the discussion began to be monologue-monologue structure it became harder for me to explicit sense of it. And I think if was my fault to start taking aside thoughts as Wittgenstein's, Kripke's and Putnam's. Anyway, do you think it is possible to see somehow our thoughts (to make our thoughts be somehow visible)? On math induction: 5th of Peano: a) it is true for 1; b) if it is true for n, then it must be true for n+1. thesis: 1+2+...+n = n(n+1)/2 a) 1 = 1(1+1)/2 b) If 1+2+...+n = n(n+1)/2, then 1+2+...n+n+1 = n+1(n+1+1)/2 ') n(n+1)/2 = (n^2+n)/2 '') (n+1)(n+2)/2 = (n^2+n)+2(n+1)/2 = (n^2+n)/2 + 2(n+1)/2 = (n^2+n)/2 + n+1 ''') n+1 = n+1 Yeah, it looks like not a trivial induction. Usually, induction shows as the reversed implication (Cohen, Nagel "An Introduction to Logic and Scientific Methods", 1936): Deduction: if p⊃q deduces q when and only when p⊃q is given as true, and p is true; Induction: if p⊃q induces p when and only when p⊃q is given as true and q is true. Math induction doesn't look like the one. So, probably, yeah, this is not the usual induction.
Yes, I know the Peano axioms and mathematical deduction. We discussed this a long time ago in relation to Kurt Godel's incompleteness theorem. It's so long ago I can't remember the name of the thread.
I think all our thoughts are visible introspectively, but no, I don't think all our thoughts can be made visible outside of introspection. I can write one as "1", but I can't make visible the thought it's meant to express. In that example, it doesn't matter, for as long as everyone understands what thought "1" is referring to. I see another person's thought indirectly through symbols. This is what's so great about mathematics. Many of its concepts are thoughts universally shared. If I show a picture of a circle, I can probably point to it and tell a person unfamiliar with geometric shapes: "This is a circle", with no further explanation. I probably don't have to explain that it's not the colour I drew it in that makes the circle, nor is it its size, or whatever background paper I was using. The circle is understood as an abstract concept. This I can also do when referring to "free will". But here we face a problem. What if someone disputes the existence of free will? Then we'd have to try to express our thought about free will. This is where we face the limitation of language. It will always depend on that we all tap into the same inner world of concepts. If someone simply declares that the concept of free will is meaningless, we have no words, no imagery to point to, no analysis to present to explain it. Only indirectly may we make a case for it. For example, that the uncertainty principle makes it a possibility. -And that it might be that free will is linked to uncomputable sets of numbers. But that isn't expressing free will itself.
Language always depends on common understanding. Imagine someone stating the following:
"I don't think I have a self, because the self just mirrors the processes in the brain, and the brain is continuously changing."
Then I would declare I know the person is wrong, because I have an introspective sense of the self, or, rather, the core of the self, as something indivisible and unchanging. But if the other person doesn't, or pretends that he/she doesn't, I would not be able to prove that person wrong.
In a meaningful discussion I am therefore always dependent, not only on that the person I discuss with is honest with me, but that he/she is honest with him/herself. One should never have as a premise for a discussion that if person A thinks person B is wrong, that person A should be able to prove it, if he/she is right. For very often that is not the case, and based on the misconception that language can express anything meaningful convincingly to those who respect facts and logic. Rather, language may express what's meaningful to those who respect facts and logic as well as having spent their lives acquiring self-insight through introspection. For it is through introspection that one clarifies the thoughts upon which language is ultimately based.
:)))) My way is quite opposite. I remember almost every posts of yours and mine. Yes, my memory and attention might've got not a few errors. Anyway, this started from exemplification, positive deities, and Godel's vision on many of that things that he was supposed to have proven that God exists by his proof. Our believe is important thing, I guess, and this is just one reason that is okay, and there's no need such an attention to what Godel tried to do. However, his attempts were just like an artist picture, he was likely to wish to make something interesting. Well, I don't know. No, not exactly of his incompleteness, but this theme was raised once or a couple of times. Actually, I don't think it might help us here (the incompleteness), because - any formal (logical) system, i.e. Principia Mathematica's type which contains a plain arithmetics either is incomplete, or it necessary has a theorem that cannot be proven by its own methods (or the theorem that is seemed to be built with the axioms and theorems, however it is not, and it doesn't belong to this system). As far as I know Godel used his number notation to show this. Honestly, I never did this prove again. I've tried, but all that tries to start it ended with nothing. All I watched is light versions of the prove. I think I have to try to re-prove it. Okay, the "1", and the circle. Well, I don't see a way to show a thought either, except for to draw it or to express like the mathematicians do. The concepts they address to are usually plain and universally understood. Free will. Correct me if I wrong, but I think that theme is important to you, right? Well, I don't know much about it, because my interest lays much aside of it, however I've always been hoping for that we have the free will. If we don't, then it's not very good for us. For instance, how to explain we're responsible for our sins? Some people say that even if we think there's the free will, we still cannot affirm it. What if, they say, all what's been happening to everything is just a script or it goes by a pre-written scenario? It's like each type of explanation can be re-written as a movie. And if our actions can be viewed as a movie (things should go like that), then there's no free will. I think that this time another Putnam's objection can be used here. He proposed "Brains in Vat" mind experiment, where we're nothing, but brains with electrodes and we're manipulated my evil crazy scholars. He said that: so what, it cannot prove anything (maybe I'm wrong, I should've re-read his opinion on it in details again). But, nevermind, I think that this view - about a movie "free will" - doesn't disprove anything. I think I have to support the view about the limits of our expression of the free will. It seems to be it, but I don't know much about uncomputable number of sets, or, namely, how do they relate to it? Could you explain it further? I guess it also may be helpful on Godel. Free will surely has to be taken as a positive thing. About the short dialogue. Aye. That person surely doesn't know the self. But doesn't he know himself? This also might be found an interesting: what makes us to understand something as short, and what as long processes? The person in this dialogue says that "he doesn't know self...", because "...self is continuously changing". And we can ask him again: "What makes him think that <<the self>> is a point?" or "why does he think that <<self>> at some moment?". One thing X started to exist at time T1, and finished at T2. We can describe this thing either ways: to say that if this x is "X", then "it started to exist at time T1...", or if "this thing x started to exist at time T1...", then "...". So, addressing to self has to be wider, than just a moment. Usually, we don't know what is at particular moment, or that particular moment. Science don't say about exactly moments, except for prediction to have this "y" at "0,5" when "x" at "-1", or like that. I guess even this is not the best; science is trying to escape such detailed prediction, so it attempts to present a function what describe a behaviour of "y" depending on "x". Approximation is optional. There's also a view - that you provided at the last passage on this - that if the person declared his unable to view self, then it wouldn't be sure for us to disagree with a person. I think that if that person each time, at each moment of his life, tried to observe if there was the self, he probably couldn't do it, because "self is beyond a moment". But what we obviously could do was to describe the bio of that person. We could write the history of his life. That's why, I guess, usually we've got plenty enough of histories of lives, but we don't have "selves". Even the word "the spirit", I guess, illustrates this. Because what is the spirit? - It's like a ghost, like a fog, or a dim. We can't see it, we somehow only feel his presence. And, except for any other things, why do we try to capture the self? Are we gonna try to catch the time itself? Richard Rorty, I mentioned couple of times, also shook his head saying that such a pursuing might be ended as a ghost hunting. "Language may express what's meaningful to those who respect facts and logic as well as having spent their lives acquiring self-insight through introspection" - I join this view. This was said pretty strongly. So, the language can be seemed as a tool. The same as for the logical language. If Godel's intuition was guided by something else, and finally found the tool, it (his intuition) tried to express itself through the language... I'm not manifesting the essence of that intuition, I just typed it in such a style. And that - a tool to pronounce it in such a way - was an ability of the language. However, I should mastering it to be able use it properly in different places to make an expression (if I need to).
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Post by karl on Aug 18, 2020 18:32:10 GMT
Yes, I know the Peano axioms and mathematical deduction. We discussed this a long time ago in relation to Kurt Godel's incompleteness theorem. It's so long ago I can't remember the name of the thread.
I think all our thoughts are visible introspectively, but no, I don't think all our thoughts can be made visible outside of introspection. I can write one as "1", but I can't make visible the thought it's meant to express. In that example, it doesn't matter, for as long as everyone understands what thought "1" is referring to. I see another person's thought indirectly through symbols. This is what's so great about mathematics. Many of its concepts are thoughts universally shared. If I show a picture of a circle, I can probably point to it and tell a person unfamiliar with geometric shapes: "This is a circle", with no further explanation. I probably don't have to explain that it's not the colour I drew it in that makes the circle, nor is it its size, or whatever background paper I was using. The circle is understood as an abstract concept. This I can also do when referring to "free will". But here we face a problem. What if someone disputes the existence of free will? Then we'd have to try to express our thought about free will. This is where we face the limitation of language. It will always depend on that we all tap into the same inner world of concepts. If someone simply declares that the concept of free will is meaningless, we have no words, no imagery to point to, no analysis to present to explain it. Only indirectly may we make a case for it. For example, that the uncertainty principle makes it a possibility. -And that it might be that free will is linked to uncomputable sets of numbers. But that isn't expressing free will itself.
Language always depends on common understanding. Imagine someone stating the following:
"I don't think I have a self, because the self just mirrors the processes in the brain, and the brain is continuously changing."
Then I would declare I know the person is wrong, because I have an introspective sense of the self, or, rather, the core of the self, as something indivisible and unchanging. But if the other person doesn't, or pretends that he/she doesn't, I would not be able to prove that person wrong.
In a meaningful discussion I am therefore always dependent, not only on that the person I discuss with is honest with me, but that he/she is honest with him/herself. One should never have as a premise for a discussion that if person A thinks person B is wrong, that person A should be able to prove it, if he/she is right. For very often that is not the case, and based on the misconception that language can express anything meaningful convincingly to those who respect facts and logic. Rather, language may express what's meaningful to those who respect facts and logic as well as having spent their lives acquiring self-insight through introspection. For it is through introspection that one clarifies the thoughts upon which language is ultimately based.
))) My way is quite opposite. I remember almost every posts of yours and mine. Yes, my memory and attention might've got not a few errors. Anyway, this started from exemplification, positive deities, and Godel's vision on many of that things that he was supposed to have proven that God exists by his proof. Our believe is important thing, I guess, and this is just one reason that is okay, and there's no need such an attention to what Godel tried to do. However, his attempts were just like an artist picture, he was likely to wish to make something interesting. Well, I don't know. No, not exactly of his incompleteness, but this theme was raised once or a couple of times. Actually, I don't think it might help us here (the incompleteness), because - any formal (logical) system, i.e. Principia Mathematica's type which contains a plain arithmetics either is incomplete, or it necessary has a theorem that cannot be proven by its own methods (or the theorem that is seemed to be built with the axioms and theorems, however it is not, and it doesn't belong to this system). As far as I know Godel used his number notation to show this. Honestly, I never did this prove again. I've tried, but all that tries to start it ended with nothing. All I watched is light versions of the prove. I think I have to try to re-prove it. Okay, the "1", and the circle. Well, I don't see a way to show a thought either, except for to draw it or to express like the mathematicians do. The concepts they address to are usually plain and universally understood. Free will. Correct me if I wrong, but I think that theme is important to you, right? Well, I don't know much about it, because my interest lays much aside of it, however I've always been hoping for that we have the free will. If we don't, then it's not very good for us. For instance, how to explain we're responsible for our sins? Some people say that even if we think there's the free will, we still cannot affirm it. What if, they say, all what's been happening to everything is just a script or it goes by a pre-written scenario? It's like each type of explanation can be re-written as a movie. And if our actions can be viewed as a movie (things should go like that), then there's no free will. I think that this time another Putnam's objection can be used here. He proposed "Brains in Vat" mind experiment, where we're nothing, but brains with electrodes and we're manipulated my evil crazy scholars. He said that: so what, it cannot prove anything (maybe I'm wrong, I should've re-read his opinion on it in details again). But, nevermind, I think that this view - about a movie "free will" - doesn't disprove anything. I think I have to support the view about the limits of our expression of the free will. It seems to be it, but I don't know much about uncomputable number of sets, or, namely, how do they relate to it? Could you explain it further? I guess it also may be helpful on Godel. Free will surely has to be taken as a positive thing. About the short dialogue. Aye. That person surely doesn't know the self. But doesn't he know himself? This also might be found an interesting: what makes us to understand something as short, and what as long processes? The person in this dialogue says that "he doesn't know self...", because "...self is continuously changing". And we can ask him again: "What makes him think that <<the self>> is a point?" or "why does he think that <<self>> at some moment?". One thing X started to exist at time T1, and finished at T2. We can describe this thing either ways: to say that if this x is "X", then "it started to exist at time T1...", or if "this thing x started to exist at time T1...", then "...". So, addressing to self has to be wider, than just a moment. Usually, we don't know what is at particular moment, or that particular moment. Science don't say about exactly moments, except for prediction to have this "y" at "0,5" when "x" at "-1", or like that. I guess even this is not the best; science is trying to escape such detailed prediction, so it attempts to present a function what describe a behaviour of "y" depending on "x". Approximation is optional. There's also a view - that you provided at the last passage on this - that if the person declared his unable to view self, then it wouldn't be sure for us to disagree with a person. I think that if that person each time, at each moment of his life, tried to observe if there was the self, he probably couldn't do it, because "self is beyond a moment". But what we obviously could do was to describe the bio of that person. We could write the history of his life. That's why, I guess, usually we've got plenty enough of histories of lives, but we don't have "selves". Even the word "the spirit", I guess, illustrates this. Because what is the spirit? - It's like a ghost, like a fog, or a dim. We can't see it, we somehow only feel his presence. And, except for any other things, why do we try to capture the self? Are we gonna try to catch the time itself? Richard Rorty, I mentioned couple of times, also shook his head saying that such a pursuing might be ended as a ghost hunting. "Language may express what's meaningful to those who respect facts and logic as well as having spent their lives acquiring self-insight through introspection" - I join this view. This was said pretty strongly. So, the language can be seemed as a tool. The same as for the logical language. If Godel's intuition was guided by something else, and finally found the tool, it (his intuition) tried to express itself through the language... I'm not manifesting the essence of that intuition, I just typed it in such a style. And that - a tool to pronounce it in such a way - was an ability of the language. However, I should mastering it to be able use it properly in different places to make an expression (if I need to).
Just to clarify; When I stated that we've discussed the peano axioms before, I was not referring to this thread, but an earlier thread, many months ago (maybe even longer).
Uncomputable sets are the same as unenumerable sets; Sets of numbers that no algorithm may express. The proof of the incompleteness theorem involves proving that such a set exists. Another way to put it is that such a set, if it can be understood by a human being, is an example of something a human can understand, but not artificial intelligence.
I believe that such sets are directly linked to the question of free will and conscious understanding. -And I think consciousness, free will, and conscious understanding are all intimately linked. Consciousness is our experience of free will, and conscious understanding premises free will, as it always involves choice. When we choose what universal concepts to base our reasoning on, we are exercising our will. This is illustrated in the discussion about whether there is free will or not. Those who argue that there is not, often base their reasoning on the idea of a deterministic reality. The argument against determinism, based on quantum uncertainty, is dismissed by the claim that quantum uncertainty doesn't really play a role in the brain. Their starting point is the concept of science from the Newtonian days, when science was expected to have the power to explain and predict everything. The concepts they choose as their starting point aren't "false". They have their validity, but as any concept, they can be out of place within a certain context. But to determine what concepts one should have as the starting point of one's reasoning, is a matter of judgement, and what is the right choice is sometimes something one might not even be able to prove with whatever may be the present knowledge at the time. A choice has to be made.
The incompleteness theorem is proven by first demonstrating that there exists an algorithm that can express every possible computable arithmetic statement as a number series. Then one shows that there exists an enumerable set of numbers that is not decidable. Meaning, that there exists no algorithm that allows one to determine if any given number belongs to that set. One simply has to find the numbers by producing them with an algorithm. This, in turn, means that this set's complementary set is unenumerable.
My view is that universal concepts are not actually expressible in language, other than by attempting to talk about them to others, in hope that they connect with them introspectively the way the other person has. And that this is similar to how an unenumerable subset of natural numbers is not expressible by an algorithm.
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Post by Eugene 2.0 on Aug 18, 2020 21:41:43 GMT
))) My way is quite opposite. I remember almost every posts of yours and mine. Yes, my memory and attention might've got not a few errors. Anyway, this started from exemplification, positive deities, and Godel's vision on many of that things that he was supposed to have proven that God exists by his proof. Our believe is important thing, I guess, and this is just one reason that is okay, and there's no need such an attention to what Godel tried to do. However, his attempts were just like an artist picture, he was likely to wish to make something interesting. Well, I don't know. No, not exactly of his incompleteness, but this theme was raised once or a couple of times. Actually, I don't think it might help us here (the incompleteness), because - any formal (logical) system, i.e. Principia Mathematica's type which contains a plain arithmetics either is incomplete, or it necessary has a theorem that cannot be proven by its own methods (or the theorem that is seemed to be built with the axioms and theorems, however it is not, and it doesn't belong to this system). As far as I know Godel used his number notation to show this. Honestly, I never did this prove again. I've tried, but all that tries to start it ended with nothing. All I watched is light versions of the prove. I think I have to try to re-prove it. Okay, the "1", and the circle. Well, I don't see a way to show a thought either, except for to draw it or to express like the mathematicians do. The concepts they address to are usually plain and universally understood. Free will. Correct me if I wrong, but I think that theme is important to you, right? Well, I don't know much about it, because my interest lays much aside of it, however I've always been hoping for that we have the free will. If we don't, then it's not very good for us. For instance, how to explain we're responsible for our sins? Some people say that even if we think there's the free will, we still cannot affirm it. What if, they say, all what's been happening to everything is just a script or it goes by a pre-written scenario? It's like each type of explanation can be re-written as a movie. And if our actions can be viewed as a movie (things should go like that), then there's no free will. I think that this time another Putnam's objection can be used here. He proposed "Brains in Vat" mind experiment, where we're nothing, but brains with electrodes and we're manipulated my evil crazy scholars. He said that: so what, it cannot prove anything (maybe I'm wrong, I should've re-read his opinion on it in details again). But, nevermind, I think that this view - about a movie "free will" - doesn't disprove anything. I think I have to support the view about the limits of our expression of the free will. It seems to be it, but I don't know much about uncomputable number of sets, or, namely, how do they relate to it? Could you explain it further? I guess it also may be helpful on Godel. Free will surely has to be taken as a positive thing. About the short dialogue. Aye. That person surely doesn't know the self. But doesn't he know himself? This also might be found an interesting: what makes us to understand something as short, and what as long processes? The person in this dialogue says that "he doesn't know self...", because "...self is continuously changing". And we can ask him again: "What makes him think that <<the self>> is a point?" or "why does he think that <<self>> at some moment?". One thing X started to exist at time T1, and finished at T2. We can describe this thing either ways: to say that if this x is "X", then "it started to exist at time T1...", or if "this thing x started to exist at time T1...", then "...". So, addressing to self has to be wider, than just a moment. Usually, we don't know what is at particular moment, or that particular moment. Science don't say about exactly moments, except for prediction to have this "y" at "0,5" when "x" at "-1", or like that. I guess even this is not the best; science is trying to escape such detailed prediction, so it attempts to present a function what describe a behaviour of "y" depending on "x". Approximation is optional. There's also a view - that you provided at the last passage on this - that if the person declared his unable to view self, then it wouldn't be sure for us to disagree with a person. I think that if that person each time, at each moment of his life, tried to observe if there was the self, he probably couldn't do it, because "self is beyond a moment". But what we obviously could do was to describe the bio of that person. We could write the history of his life. That's why, I guess, usually we've got plenty enough of histories of lives, but we don't have "selves". Even the word "the spirit", I guess, illustrates this. Because what is the spirit? - It's like a ghost, like a fog, or a dim. We can't see it, we somehow only feel his presence. And, except for any other things, why do we try to capture the self? Are we gonna try to catch the time itself? Richard Rorty, I mentioned couple of times, also shook his head saying that such a pursuing might be ended as a ghost hunting. "Language may express what's meaningful to those who respect facts and logic as well as having spent their lives acquiring self-insight through introspection" - I join this view. This was said pretty strongly. So, the language can be seemed as a tool. The same as for the logical language. If Godel's intuition was guided by something else, and finally found the tool, it (his intuition) tried to express itself through the language... I'm not manifesting the essence of that intuition, I just typed it in such a style. And that - a tool to pronounce it in such a way - was an ability of the language. However, I should mastering it to be able use it properly in different places to make an expression (if I need to).
Just to clarify; When I stated that we've discussed the peano axioms before, I was not referring to this thread, but an earlier thread, many months ago (maybe even longer).
Uncomputable sets are the same as unenumerable sets; Sets of numbers that no algorithm may express. The proof of the incompleteness theorem involves proving that such a set exists. Another way to put it is that such a set, if it can be understood by a human being, is an example of something a human can understand, but not artificial intelligence.
I believe that such sets are directly linked to the question of free will and conscious understanding. -And I think consciousness, free will, and conscious understanding are all intimately linked. Consciousness is our experience of free will, and conscious understanding premises free will, as it always involves choice. When we choose what universal concepts to base our reasoning on, we are exercising our will. This is illustrated in the discussion about whether there is free will or not. Those who argue that there is not, often base their reasoning on the idea of a deterministic reality. The argument against determinism, based on quantum uncertainty, is dismissed by the claim that quantum uncertainty doesn't really play a role in the brain. Their starting point is the concept of science from the Newtonian days, when science was expected to have the power to explain and predict everything. The concepts they choose as their starting point aren't "false". They have their validity, but as any concept, they can be out of place within a certain context. But to determine what concepts one should have as the starting point of one's reasoning, is a matter of judgement, and what is the right choice is sometimes something one might not even be able to prove with whatever may be the present knowledge at the time. A choice has to be made.
The incompleteness theorem is proven by first demonstrating that there exists an algorithm that can express every possible computable arithmetic statement as a number series. Then one shows that there exists an enumerable set of numbers that is not decidable. Meaning, that there exists no algorithm that allows one to determine if any given number belongs to that set. One simply has to find the numbers by producing them with an algorithm. This, in turn, means that this set's complementary set is unenumerable.
My view is that universal concepts are not actually expressible in language, other than by attempting to talk about them to others, in hope that they connect with them introspectively the way the other person has. And that this is similar to how an unenumerable subset of natural numbers is not expressible by an algorithm.
Such an uncountable set necessary has different type of relations, some mutual human-ish relations? Interesting things. When I say: "Consciousness is what can differ things", so it separates things, or it has it be separeted (triangulated, taken in parts, etc). And what has parts allows to direct attention on just one part. Therefore, partiated, analyzed, or separated a thing into parts is the same is to make a choice, or "making a choice" is interpretation of how do we go (closer) to the parts. We're able to part a thing starting from up, from down, etc. There might be plenty of ways how to do it, and exactly which way we're going is the same as how do we part the thing. No choices before partiating things don't exist. However, the word or the term "choice" is technical, and it usually means that "to make choice is to take this, or that to recieve that one" (or smth like that). There are different types of choices also. We can choose a part, but we're allowed to take another one, or two at the same time, or three, or these two, or those two, etc. It's the same as to undrstand how many combinations a set has. Why such algorithm is unenumerable? If we got this algorithm, we would numerate it according to the first algorithm of turning symbols of propositions to numbers, right?.. But we wouldn't be able to find exactly this statement... Oh, now I see. However, there's also another way of this task that was presented by Tarski. I don't know that in details. With all respects I can't see that free will somehow linked with this. Why? Free will is about of external, not internal abilities. If we would be butterflies, we wouldn't be able to think even with a piece of human brains. Brains doesn't mean - thinking. But some brains are indeed able to think. My opinion is that some brains try to do lotta work. Einstein did many tasks, he thinked a lot, didn't he? And many thinker did the same. The first one position is that one has free will only if the one has intellect. The more powerful one has, the more clearer one is able to see (choices). And again, brains should be trained, educated, etc. A newborn doesn't have any free will, but a child, if only he had been educated, has it, because he has mind on his shoulders.
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Post by karl on Aug 19, 2020 10:30:28 GMT
Just to clarify; When I stated that we've discussed the peano axioms before, I was not referring to this thread, but an earlier thread, many months ago (maybe even longer).
Uncomputable sets are the same as unenumerable sets; Sets of numbers that no algorithm may express. The proof of the incompleteness theorem involves proving that such a set exists. Another way to put it is that such a set, if it can be understood by a human being, is an example of something a human can understand, but not artificial intelligence.
I believe that such sets are directly linked to the question of free will and conscious understanding. -And I think consciousness, free will, and conscious understanding are all intimately linked. Consciousness is our experience of free will, and conscious understanding premises free will, as it always involves choice. When we choose what universal concepts to base our reasoning on, we are exercising our will. This is illustrated in the discussion about whether there is free will or not. Those who argue that there is not, often base their reasoning on the idea of a deterministic reality. The argument against determinism, based on quantum uncertainty, is dismissed by the claim that quantum uncertainty doesn't really play a role in the brain. Their starting point is the concept of science from the Newtonian days, when science was expected to have the power to explain and predict everything. The concepts they choose as their starting point aren't "false". They have their validity, but as any concept, they can be out of place within a certain context. But to determine what concepts one should have as the starting point of one's reasoning, is a matter of judgement, and what is the right choice is sometimes something one might not even be able to prove with whatever may be the present knowledge at the time. A choice has to be made.
The incompleteness theorem is proven by first demonstrating that there exists an algorithm that can express every possible computable arithmetic statement as a number series. Then one shows that there exists an enumerable set of numbers that is not decidable. Meaning, that there exists no algorithm that allows one to determine if any given number belongs to that set. One simply has to find the numbers by producing them with an algorithm. This, in turn, means that this set's complementary set is unenumerable.
My view is that universal concepts are not actually expressible in language, other than by attempting to talk about them to others, in hope that they connect with them introspectively the way the other person has. And that this is similar to how an unenumerable subset of natural numbers is not expressible by an algorithm.
Such an uncountable set necessary has different type of relations, some mutual human-ish relations? Interesting things. When I say: "Consciousness is what can differ things", so it separates things, or it has it be separeted (triangulated, taken in parts, etc). And what has parts allows to direct attention on just one part. Therefore, partiated, analyzed, or separated a thing into parts is the same is to make a choice, or "making a choice" is interpretation of how do we go (closer) to the parts. We're able to part a thing starting from up, from down, etc. There might be plenty of ways how to do it, and exactly which way we're going is the same as how do we part the thing. No choices before partiating things don't exist. However, the word or the term "choice" is technical, and it usually means that "to make choice is to take this, or that to recieve that one" (or smth like that). There are different types of choices also. We can choose a part, but we're allowed to take another one, or two at the same time, or three, or these two, or those two, etc. It's the same as to undrstand how many combinations a set has. Why such algorithm is unenumerable? If we got this algorithm, we would numerate it according to the first algorithm of turning symbols of propositions to numbers, right?.. But we wouldn't be able to find exactly this statement... Oh, now I see. However, there's also another way of this task that was presented by Tarski. I don't know that in details. With all respects I can't see that free will somehow linked with this. Why? Free will is about of external, not internal abilities. If we would be butterflies, we wouldn't be able to think even with a piece of human brains. Brains doesn't mean - thinking. But some brains are indeed able to think. My opinion is that some brains try to do lotta work. Einstein did many tasks, he thinked a lot, didn't he? And many thinker did the same. The first one position is that one has free will only if the one has intellect. The more powerful one has, the more clearer one is able to see (choices). And again, brains should be trained, educated, etc. A newborn doesn't have any free will, but a child, if only he had been educated, has it, because he has mind on his shoulders.
The brain is the landscape the soul maneuvers in, and the larger that landscape is, the more choices one may make. In the brain of a baby, the choices are limited. Acquiring insight manifests as a physical change in the structure of the brain, expanding the landscape, and increasing one's awareness. In metaphysics one often speaks of expanding consciousness, but with little effort to explain with any clarity what that entails. Expansion of consciousness is expansion of one's understanding. And increased understanding leads to expansion of one's free will. This is why sect leaders seek to suppress understanding in their followers, to keep their level of awareness low, in order to limit their inner freedom, which would otherwise have allowed them to make their own choices.
As for unenumerability. No algorithm is unenumerable. If a set is produced by an algorithm, it's enumerable by definition. But that a set is enumerable, doesn't always mean that the complementary of that set is enumerable as well. Imagine that you have an algorithm that produces and infinite subset of natural numbers, and the first numbers look like this:
112 - 7 - 65 -8646789 - 2 - and so on...
And let's say you ask the question: "Is the number 1 part of this set?"
If the set is not decidable, and if 1 is not part of the set, then there is no algorithm to tell you that 1 is not part of the set. What one can do to try to determine whether 1 is part of the set, is to run the algorithm that produces the set and see if 1 turns up. But since the set is infinite, even if one has produced a trillion members of that set and 1 doesn't show up, one can't know that it won't show up later. So this search for 1 would then go on for eternity without it showing up, without one ever being able to include that it's not a member of the set. So the fact that 1 is not part of the set is something that is true but unprovable.
The set of all the numbers that are not part of the original set is called the complementary set. In this set, 1 and any other number that never shows up when one runs the algorithm, are included. It's this set that's unenumerable.
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