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  1. #41
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by MARKOM
    Spoiler part is not really showing well on safari. It's blue box with blue text, I was wondering what it is until I highlighted it with painting the area... Anyway concession seems to be your interpretation still. I know what you mean with it thou (99% sure, since you are going to ask it soon), but you probably don't know what I meant with the sentence or you don't want to look at it that way for some reason. See, I'm discussing that exact thing with CliveStaples, how Santa Clause is true and why Jack is taller than Tom is sometimes true, and sometimes it is not true. If you can't see how the meaning of the words, their relation to observed world a posteriori and the way, how words are used is changing the game, then I need to learn the language you speak and try to use it, lol.
    you can't mistake the inherent limitations on language to be an inherent limitation on logic.
    Just because "jack" can refer to a million different people (all named Jack) doesn't mean that logic is somehow limited. At that point your only arguing the meaning of terms, equivocating terms and other logical fallacies.

    In other words,when you say A=/=A, you are not talking about the same thing and thus not addressing the argument.

    So, the language is simply the vehicle for communicating meaning and intention. If I intend A to = 1 and you understand it to mean 2, then A+A=2 is going to be false as you understand it and true as I communicate it. The problem is not with the logic or the argument, but with clarity of meaning.

    Quote Originally Posted by MARKOM
    but you probably don't know what I meant with the sentence or you don't want to look at it that way for some reason.
    No I understand what your saying, I'm making a point. As long as you hold that A=/=A then I can read your words to be whatever I wish and I will be 100% correct, or at least you could never prove me wrong.
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  2. #42
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by CliveStaples View Post
    No, you've introduced Q. The axiom is about p. if($P = TRUE) {$P = TRUE}
    Yes, sorry, I made a quantum leap to previously used "if and only if" case by reading this part too fast. One more question: why do you need set P twice, I see no meaning for that, once it's set, it's set, extra is tautology. What I would do next is comparison...

    Quote Originally Posted by CliveStaples View Post
    I have no idea what programming language you're using; in Java, the negation operator is ! (so if P = TRUE, !P = FALSE). Using this convention, If (P = TRUE) then (!!P = TRUE)
    Thanks for explanation. See how much effort it can take to really get the meant purpose of the pretty simple clauses One more time:

    2) If p is true, then "p is false" is false. That is, p is logically equivalent to ~~p.

    if ($P = TRUE) {
    echo !!$P === $P ? 'T' : 'F';
    }
    Run: http://codepad.org/w5ih1oid

    But again I don't see, why this is regarded as axiom? To me it's more like self refering clause, that can be seen more simply: echo $P ? 'T' : 'F';

    It's PHP language here, I may translate these to Python or Lisp, maybe Node.js at least to see, if it brings any other interesting things. I've never looked programming languages from this point of view, because I've just been working, not philosophizing or theorizing, lol.

    Quote Originally Posted by CliveStaples View Post
    No, you read it wrong. The axiom is this:

    If "p is true" is true and "if p is true, q is true" is true, then "q is true" is true.

    if (p AND if(p=TRUE){q=TRUE}){q=TRUE}
    Oh, you are using , for AND. Is this common practice? To me it's more clear to use AND because on the last part of the sentence you say "true, then" and using AND there is weird so to say. Translation:

    if ($P) {
    if ($P = TRUE) {
    $Q = TRUE;
    }
    $Q = TRUE;
    }
    It is little better, but it is still unclear why you call P alone at first, it could be anything? To me this is much simpler and reduces to:

    if ($P = TRUE) {
    $Q = TRUE;
    }
    Which now is same as we have talked on if and only if case. But what you seem to do in first hand is that practically you make nested clauses there, which is an example of recursiveness. But I can't see why it is used here. How and why do you introduce P without any value for the first time?

    Quote Originally Posted by CliveStaples View Post
    Lol, that's the point. Arithmetic is simply a collection of axioms together with statements that a provable from those axioms.
    So tell me how basic and other axioms are derived, decided and if axioms can be used to create other axioms, or should it be called other term in that case? I suppose conclusions or anything can be regarded as axiom when you use it as an obvious, no need to define claim, occuring either by deliberate, or by nature of language. Quoting you (and me):

    Quote Originally Posted by CliveStaples View Post
    Because if it is always true that "Axioms can always be questioned further and further infinitely in a free thinking world", then that itself is an axiom.
    Axiom seems to be a definition too, starting point, basic premise. This is something I've addressed before. Beside that questioning doesn't equal prooving (or disprooving) AND that structure of language form is often axiomatic althought not intended ALSO the claim has something to do with sematic levels. I need to bring up longer reasoning for this now, which itself is nothing new, but my way to understand and explain, what it means when we say, that "it's just semantics". It is also resembles even not accurately same the semantic shift in sentence like "Do women need to worry about man-eating sharks?" http://en.wikipedia.org/wiki/Equivocation and furthermore, it's refering to problem of limited expression space, reductivism and infinite definition cycle, very much the Trilemma itself. On "man-eating sharks" you jump from human to males, because it is semantically ambigious term.

    First of all, if you cannot test it ie. apply to other concrete level, then there is no way to see the truth value and there should be no reason to claim and use axioms at all until its just for fun and mental exercise. It would be as meaningless (which is different to totally meaningless btw.) than a claim, that God is behind the galaxy. Might be, might not.

    What is more interesting here is that you go to the levels of presentation language in reasoning like this "...if it is always true..." and you refer to sentence itself. It is represented on "Omnipotence paradox": http://en.wikipedia.org/wiki/Omnipotence_paradox

    An omnipotent being creates a universe which follows the laws of Aristotelian physics. Within this universe, can the omnipotent being create a stone so heavy that the being cannot lift it?
    There are a lot of explanations and ways to see the paradox. I will see it from linquistical point of view. I will break down the problem to something like the presentation level (or the semantic meta level) and the meaning level or even the producer and the product level. On "if it is true that Axioms can be questioned, it's an axiom" you jump from meaning to language semantics and phrasing, from product to producer. Which one would you question, producer or product? It is also linked to identity problem, since identity is just an artificial referee to either itself (A is A) or other level (A is B). Using this as analogy in computer language identifier (A) refers to memory block or address (B). They have another reality behind so to say. As well natural language identifiers (A's) have their meaning (B's) behind. Now I think they are different levels or "worlds" in more wide and ambigious phrasing and we often get mixed with them in logical reasoning and conversations. Referring can target to each of the levels (maybe there can be even more levels than supposed two but let it be other discussion).

    One solution is to hypothesize that referring from higher level to lower is acceptable and causes no problems in logical sense (truth value is a different problem). Referring from lower to higher or to same level causes recursiveness thus infinite regression and also self defeating problem. One funny related example is the clause "You can know recursiveness by knowing recursiveness first". Or you put a word recursive to the vocabulary, and explain it "See the word self referring". Then you go to the word self-refering, you read "See the word recursive". Some logic says, they explain nothing, because they are self referring. But what happens in reality they both together produces a loop and gives a real world example and meaning for the words (actually words are just analogies after analogies forming recursive "neural" net after all). Realization is the exit from the loop in this case, but at the same time is a way back in. Result spreads to different levels, presentation and meaning.

    Second example. Girl sees an object on the ground, it's beautiful and unique, resembling nothing seen before. She gives object a name "skirei". Day after she goes to her mom and says excited, I found a "scirei". Should mom say, hey there is nothing called skirei, don't be funny? Then she lifts up the object from pocket and shows "skirei" and they both are amuzed of the beauty of the object. "Scirei" had a meaning to the girl, and after the episode word has a meaning to mom too. A lot of symbols exists, maybe infinitely, they can have a real meaning which points to something observable, or some collection of other terms, symbols and concepts. If some of the basic symbols don't have (I'm not sure if this is possible at all) or they don't refer observable or measurable ground, then they are pure language and logic, are subject to logical fallacies and should have regarded different way than symbols that has observable and measurable counterparts.

    Natural language and many of the computer languages in grammar level are recursive. It seems to be a fundamental principle on nature, I see it almost everywhere especially all neural related. That's why I suspect, that some sort of linear logic (or maybe it should be identified with other word) has a fundamental problem, when used to explain the world UNTIL it has a measurable counterpart with it's axioms. And that's the level where most of the debates also evolves, forgetting or not seeing / understanding the meaning behind the presentation OR on the other hand not being able to express the meaning very well.

    Quote Originally Posted by CliveStaples View Post
    What might be less obvious to you is that this notion extends to infinite collections--and that there are different sizes of infinities, given this method of counting.
    At least in computer languages it could be mutable or immutable list, in this case it was mutable list (array) indeed.
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  3. #43
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by markom View Post
    Yes, sorry, I made a quantum leap to previously used "if and only if" case by reading this part too fast. One more question: why do you need set P twice, I see no meaning for that, once it's set, it's set, extra is tautology. What I would do next is comparison...
    Exactly, it's a tautology. That is, you accept that "P = P" (P always has the same Boolean value as P) is always true.

    Thanks for explanation. See how much effort it can take to really get the meant purpose of the pretty simple clauses One more time:

    2) If p is true, then "p is false" is false. That is, p is logically equivalent to ~~p.



    Run: http://codepad.org/w5ih1oid

    But again I don't see, why this is regarded as axiom? To me it's more like self refering clause, that can be seen more simply: echo $P ? 'T' : 'F';

    It's PHP language here, I may translate these to Python or Lisp, maybe Node.js at least to see, if it brings any other interesting things. I've never looked programming languages from this point of view, because I've just been working, not philosophizing or theorizing, lol.
    I don't know what "echo" means.

    P = ~~P is called the axiom of non-contradiction; ~P and P can never have the same truth value. The reason why there are expressions for this in programming languages, and why it seems so obvious when you're coding in a programming language, is that the programming languages were built with the assumptions and axioms of Boolean logic.

    Oh, you are using , for AND. Is this common practice? To me it's more clear to use AND because on the last part of the sentence you say "true, then" and using AND there is weird so to say. Translation:
    No, I wasn't using "," for "and". Do you not speak English?

    Think of a sentence like "If you're going, I'm going." There is an implicit 'then' in the sentence; it really means "If you are going, then I am going." Then "," doesn't mean "and". "If you're going, I'm going" doesn't mean "If you're going and I'm going." That wouldn't make any sense.

    It is little better, but it is still unclear why you call P alone at first, it could be anything? To me this is much simpler and reduces to:



    Which now is same as we have talked on if and only if case. But what you seem to do in first hand is that practically you make nested clauses there, which is an example of recursiveness. But I can't see why it is used here. How and why do you introduce P without any value for the first time?
    Okay, you seem really confused by this.

    Think of P as a variable that can have either the value 1 or 0.

    "If P, then Q" means that whenever P=1, Q must also equal 1.
    "P is true" means P=1.
    "Q is true" means Q=1.

    If all you had was "If P, then Q", then you wouldn't know whether Q=1. This axiom establishes that if you know P=1, and if you know that "whenever P=1, Q must also equal 1", then you know Q=1. Without setting P=1, you don't trigger the requirement that Q=1.


    Are you not comfortable working with clear, easy examples? Take P = "I am in London", Q = "I am in England". "If P, then Q" means "If I am in London, then I am in England." Do you understand so far? I think working with an actual example will make the principles I'm talking about much clearer.

    So tell me how basic and other axioms are derived, decided and if axioms can be used to create other axioms, or should it be called other term in that case? I suppose conclusions or anything can be regarded as axiom when you use it as an obvious, no need to define claim, occuring either by deliberate, or by nature of language. Quoting you (and me):
    Axioms aren't derived. Anything derived from axioms is called a "theorem".

    Axioms don't have to be 'obvious', either. But most axiom systems will have 'obvious' axioms, since most people agree on whether 'obvious' statements are true. And if lots of people agree that the axioms of a system are true, then the system has results that apply to a lot of people.

    That's the strength of the axiomatic approach; let S is a system with a collection of axioms A = {a1, a2, ..., ak}. Suppose that I give a proof that, if you assume that every axiom in A is true, then some statement P must also be true. This shows that anyone who accepts a1, a2, ..., ak as true must also accept P as true on pain of contradiction.

    The weakness of the axiomatic approach is that it doesn't really have to show that a1, a2, ..., ak are true, or even plausible.

    Axiom seems to be a definition too, starting point, basic premise. This is something I've addressed before. Beside that questioning doesn't equal prooving (or disprooving) AND that structure of language form is often axiomatic althought not intended ALSO the claim has something to do with sematic levels. I need to bring up longer reasoning for this now, which itself is nothing new, but my way to understand and explain, what it means when we say, that "it's just semantics". It is also resembles even not accurately same the semantic shift in sentence like "Do women need to worry about man-eating sharks?"

    http://en.wikipedia.org/wiki/Equivocation and furthermore, it's refering to problem of limited expression space, reductivism and infinite definition cycle, very much the Trilemma itself. On "man-eating sharks" you jump from human to males, because it is semantically ambigious term.

    First of all, if you cannot test it ie. apply to other concrete level, then there is no way to see the truth value and there should be no reason to claim and use axioms at all until its just for fun and mental exercise. It would be as meaningless (which is different to totally meaningless btw.) than a claim, that God is behind the galaxy. Might be, might not.

    What is more interesting here is that you go to the levels of presentation language in reasoning like this "...if it is always true..." and you refer to sentence itself. It is represented on "Omnipotence paradox": http://en.wikipedia.org/wiki/Omnipotence_paradox



    There are a lot of explanations and ways to see the paradox. I will see it from linquistical point of view. I will break down the problem to something like the presentation level (or the semantic meta level) and the meaning level or even the producer and the product level. On "if it is true that Axioms can be questioned, it's an axiom" you jump from meaning to language semantics and phrasing, from product to producer. Which one would you question, producer or product? It is also linked to identity problem, since identity is just an artificial referee to either itself (A is A) or other level (A is B). Using this as analogy in computer language identifier (A) refers to memory block or address (B). They have another reality behind so to say. As well natural language identifiers (A's) have their meaning (B's) behind. Now I think they are different levels or "worlds" in more wide and ambigious phrasing and we often get mixed with them in logical reasoning and conversations. Referring can target to each of the levels (maybe there can be even more levels than supposed two but let it be other discussion).

    One solution is to hypothesize that referring from higher level to lower is acceptable and causes no problems in logical sense (truth value is a different problem). Referring from lower to higher or to same level causes recursiveness thus infinite regression and also self defeating problem. One funny related example is the clause "You can know recursiveness by knowing recursiveness first". Or you put a word recursive to the vocabulary, and explain it "See the word self referring". Then you go to the word self-refering, you read "See the word recursive". Some logic says, they explain nothing, because they are self referring. But what happens in reality they both together produces a loop and gives a real world example and meaning for the words (actually words are just analogies after analogies forming recursive "neural" net after all). Realization is the exit from the loop in this case, but at the same time is a way back in. Result spreads to different levels, presentation and meaning.
    I don't think there's a semantic "meta-level" going on. From a linguistics/language point of view, you have a whole bunch of well-formed sentences. Some of these well-formed sentences will be true--like "Barack Obama was elected President of the United States in 2008"--and some will be false--like "John McCain was elected President of the United States in 2008".

    Now, what you've done is made some statement that is quantified over the set of well-formed sentences. You said something like, "Any axiom can be infinitely questioned." Now, this statement itself (let's call it S) is a well-formed sentence.

    Suppose S ("Any axiom can be infinitely questioned) is always true. Since S is a well-formed sentence, it can be taken as an axiom. Then since S is true, and S is an axiom, "S can be infinitely questioned" must also be true. So why should I believe that S is true?

    If S is not always true, then there's some axiom that can't be infinitely questioned. So S must be false.


    Second example. Girl sees an object on the ground, it's beautiful and unique, resembling nothing seen before. She gives object a name "skirei". Day after she goes to her mom and says excited, I found a "scirei". Should mom say, hey there is nothing called skirei, don't be funny? Then she lifts up the object from pocket and shows "skirei" and they both are amuzed of the beauty of the object. "Scirei" had a meaning to the girl, and after the episode word has a meaning to mom too. A lot of symbols exists, maybe infinitely, they can have a real meaning which points to something observable, or some collection of other terms, symbols and concepts. If some of the basic symbols don't have (I'm not sure if this is possible at all) or they don't refer observable or measurable ground, then they are pure language and logic, are subject to logical fallacies and should have regarded different way than symbols that has observable and measurable counterparts.

    Natural language and many of the computer languages in grammar level are recursive. It seems to be a fundamental principle on nature, I see it almost everywhere especially all neural related. That's why I suspect, that some sort of linear logic (or maybe it should be identified with other word) has a fundamental problem, when used to explain the world UNTIL it has a measurable counterpart with it's axioms. And that's the level where most of the debates also evolves, forgetting or not seeing / understanding the meaning behind the presentation OR on the other hand not being able to express the meaning very well.
    What "measurable counterpart with its axioms"? It seems like you're just throwing words together. Do you not speak English?

    At least in computer languages it could be mutable or immutable list, in this case it was mutable list (array) indeed.
    No computer language can express infinitely large arrays, since every programming language deals with finite memory.
    If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard
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  4. #44
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by CliveStaples View Post
    The weakness of the axiomatic approach is that it doesn't really have to show that a1, a2, ..., ak are true, or even plausible.
    That's what Agrippa told and was the source of the whole critics. If they don't show true (maybe you mean truth instead) values, then why to use them and how do you verify they work?

    Quote Originally Posted by CliveStaples View Post
    I don't think there's a semantic "meta-level" going on. From a linguistics/language point of view, you have a whole bunch of well-formed sentences. Some of these well-formed sentences will be true--like "Barack Obama was elected President of the United States in 2008"--and some will be false--like "John McCain was elected President of the United States in 2008"
    These are not comparative sentence, because they are not refering to itself. Proper sentence for comparing would be "John McCain says: I'm a liar". Now if he is a liar, then he can't tell the truth so sentence must be false. So the sentence is false, so he is not a liar which contradicts his own words, and so and so on. Apparently to be true sentence, he didn't mean given sentence was false, maybe everything else. You need to resolve situation by extra definitions or meta levels if you don't use extra definitions. I recommend using meta levels because definitions sends you to define more and more infinitely.

    Quote Originally Posted by CliveStaples View Post
    Now, what you've done is made some statement that is quantified over the set of well-formed sentences. You said something like, "Any axiom can be infinitely questioned." Now, this statement itself (let's call it S) is a well-formed sentence.

    If S is not always true, then there's some axiom that can't be infinitely questioned. So S must be false.
    See above reply and then consider these additions: I wrote "Axioms can always be questioned further and further infinitely in a free thinking world". It can be taken as axiom if you want, I have nothing against that. It can also be taken not an axiom, but a statement, so you can freely question it without getting into paradoxes, because it doesn't carry any exact binary logic value. Then if you take it as an ultimate axiom, you can always put at the end of the axiom part: "if and only if you don't question itself" if it satisfies someones logic better. You can also take is as antiaxiom, when it means you can never question anything, not even itself. And finally Gödel way you can conclude, that truth machine called perfect divine logic couldn't find out the true value of the statement, so it's not perfect and there is someone, who's smarter than logic

    Quote Originally Posted by CliveStaples View Post
    What "measurable counterpart with its axioms"? It seems like you're just throwing words together. Do you not speak English?
    What speaking has to do with writing and reading? I'm not native. If you get frustrated you don't need to answer, or if you want to know the meaning, then ask. It's not very constructive to start a debate if you don't know what other is saying or meaning at first.

    Quote Originally Posted by CliveStaples View Post
    No computer language can express infinitely large arrays, since every programming language deals with finite memory.
    There was no claim about the size of the arrays, just mutability of them. If finite memory is the reason for not being able to do that, then humans shouldn't be able to do that either, cause we have just a finite number of neurons and "capacity of brains is constrained by deterioration with age and the finite life time of mortals." http://learnmem.cshlp.org/content/3/5/341.full.pdf
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  5. #45
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by markom View Post
    That's what Agrippa told and was the source of the whole critics. If they don't show true (maybe you mean truth instead) values, then why to use them and how do you verify they work?
    I already explained the strengths of the axiom system. Did you not understand that part?

    These are not comparative sentence, because they are not refering to itself. Proper sentence for comparing would be "John McCain says: I'm a liar". Now if he is a liar, then he can't tell the truth so sentence must be false. So the sentence is false, so he is not a liar which contradicts his own words, and so and so on. Apparently to be true sentence, he didn't mean given sentence was false, maybe everything else. You need to resolve situation by extra definitions or meta levels if you don't use extra definitions. I recommend using meta levels because definitions sends you to define more and more infinitely.



    See above reply and then consider these additions: I wrote "Axioms can always be questioned further and further infinitely in a free thinking world". It can be taken as axiom if you want, I have nothing against that. It can also be taken not an axiom, but a statement, so you can freely question it without getting into paradoxes, because it doesn't carry any exact binary logic value. Then if you take it as an ultimate axiom, you can always put at the end of the axiom part: "if and only if you don't question itself" if it satisfies someones logic better. You can also take is as antiaxiom, when it means you can never question anything, not even itself. And finally Gödel way you can conclude, that truth machine called perfect divine logic couldn't find out the true value of the statement, so it's not perfect and there is someone, who's smarter than logic



    What speaking has to do with writing and reading? I'm not native. If you get frustrated you don't need to answer, or if you want to know the meaning, then ask. It's not very constructive to start a debate if you don't know what other is saying or meaning at first.



    There was no claim about the size of the arrays, just mutability of them. If finite memory is the reason for not being able to do that, then humans shouldn't be able to do that either, cause we have just a finite number of neurons and "capacity of brains is constrained by deterioration with age and the finite life time of mortals." http://learnmem.cshlp.org/content/3/5/341.full.pdf
    Okay, you obviously don't speak English, so I don't think this conversation is going to be very productive.
    If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by CliveStaples View Post
    I already explained the strengths of the axiom system. Did you not understand that part?
    Yes, and I agree with that. But it didn't solve liar paradox. It will be a paradox forever if you don't expand.

    Quote Originally Posted by CliveStaples View Post
    Okay, you obviously don't speak English, so I don't think this conversation is going to be very productive.
    Thank you so far CliveStaples
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by MindTrap028 View Post
    you can't mistake the inherent limitations on language to be an inherent limitation on logic.
    Just because "jack" can refer to a million different people (all named Jack) doesn't mean that logic is somehow limited. At that point your only arguing the meaning of terms, equivocating terms and other logical fallacies.
    You can't separate logic from language or more precicely defined set of symbols and rules using the symbols, which rules must be presented by other symbols because their meaning comes from association to other symbols which primarily will reduce to perceptions. Every thing is a model, take for example addition and substracting. It is an abstract model of (sequence of) operations. You have one finger and you bring other finger beside it, we can call it a group or set of two fingers. Association of 1 + 1 is called 2. By analogy you apply this to other meaningful things, like apples. Now a group of two apples can be divided half or taking one out from set of two you have one left or one each sides. All these are models applied by analogy to other situations. There is no divine logic behind this. Even "being" is a model, that involves interaction of monism, pluralism and nothingness. Many seem to think logic is something spiritual and separate from symbolic world, outside of it and somehow more real. That is strongly arguable.

    Quote Originally Posted by MindTrap028 View Post
    In other words,when you say A=/=A, you are not talking about the same thing and thus not addressing the argument.
    I assume you are using /= as !. All seems to use different language of their own. You can't simply dismiss "limitations on language" when talking about logic.

    Quote Originally Posted by MindTrap028 View Post
    So, the language is simply the vehicle for communicating meaning and intention. If I intend A to = 1 and you understand it to mean 2, then A+A=2 is going to be false as you understand it and true as I communicate it. The problem is not with the logic or the argument, but with clarity of meaning.
    As I said above, there is still symbol of + you didn't take on account, which also can be a problem, as well as symbol =. They both are simply agreed to mean some model of operation as I want to call it. Now the logic is purely dependant on aritmetic symbols and their meanings used in this case and can cause different results. Problem is with symbols, that we don't have agreement and that's why with different logic used to decipher the statement. Crucial question is: When is a sign a logical sign?

    Quote Originally Posted by MindTrap028 View Post
    No I understand what your saying, I'm making a point. As long as you hold that A=/=A then I can read your words to be whatever I wish and I will be 100% correct, or at least you could never prove me wrong.
    Bingo! You can always prove me wrong, this sentence and every other I have made, because you can always read words as you like and you can use your own logic! Nobody is stopping you, or is someone?

    Now the solution might come, if there is a certain logic, that is accepted by both parties, there are certain symbols, that are agreed to be used exactly by same meanings and there is someone, who's judging independently outside of us. Which throws us against three different problems, which I've addressed already on some of my replies. What comes to symbols, I want to say some more later on this reply.

    CliveStaples:

    I think two of the axioms were still open because of the language barrier, but they should be ok now, just a double check:

    1) If some proposition p is true, then "p is true" is true. That is, p is logically equivalent to p.

    $P = TRUE;
    echo $P == $P ? 'T' : 'F';
    Run: http://codepad.org/LyLvMJya

    But there is a possibility when comparison doesn't give TRUE value. That is when P refers to a function instead of variable. See scheme example:

    (define (P) (random 1000))
    (print (= (P) (P)))
    Run: http://codepad.org/WRC8XSSg

    Now comparison of P & P as functions will most probably give #f. Are P & P still equivalent?

    Under the hood of computing language and logic it is supposed, that equation of the two same pre-evaluated! object or symbol gives a result, that we mark with a symbol "true". True could be any other symbol, but true has a semantic value coming from etymology, that may confuce us to keep it same as a truth. From Mercian word origing "treowe" it means "faithful" http://www.etymonline.com/index.php?search=true

    This suggests, that actually there is no thing called truth, or true, just acceptance and faith on it. In science that faith or attached label and axiom is accepted and meaningful, because equations are meant to predict something useful, concrete and testable AND they work on prediction. Positive formalists almost religiously obey the doctrine, that there is no sense on philosophical discussions, that relates to Epistemology, Ethics and Metaphysics, because they are mathematically underivable. But they tend to forget social effects that philosophies and religions had and still seemingly have. Mass media as well as politics uses ideologies and blindness of people, which comes from fact they don't question things farer than very surface of their reality, to lead them to certain directions. Certainly philosophy and religion are not meaningless, it just happens that their answers has a value only in minds, which is not measurable and testable and is pure closed system logic, which means just opinions, which can be debated forever. In spite of having answers only on mind philosophies and religions are reflected to outer world however. But what is the correlation of words and world in this case, if symbols are just agreements and has no real base?

    As stated, in this level symbols doesn't need to have any relation to physical world, they don't need to correlate any certain objects. In western logic they live almost totally separate life, take for example P = Cat. P doesn't need to be P, nor it's not stated, that 'cat' has to be 'cat' any particular time or all the time. However 'cat' on formal language is a commonly accepted label for some object, we percept. According to Gödel, certain things doesn't have to be connected to physical reality at all. We can think paradoxes of set theory, that are presented by some symbols and think them at least as meaningful as sensational illusions are real to physics. I think this has even more firmly spiritualized the logic (Gödel was a mystic like Einstein anyway), trying to take symbols of logic away from signs and their natural origins. This is a dangerous shift.

    Some say Liar paradox and all similar are semantic paradoxes, which I think is true, but are not only semantic tricks. For many thinkers in antique and especially in orient paradoxes were a way to think and present certain things. They can be opened very many ways I've talked before, which I personally think can give nice insights of the world, human mind and logic. They urge us to jump out from system, outside of the box, to meta level and fall down the checkboard. Is this something spectacular? I don't think so, because logic itself applied on some arbitrary sentences we have discussed here already, it is something that is thought to be outside of the examined phrase, it's already on meta level, but we seem to forget it.

    In addition to that Gödel has proved by plain, althought rather complicated math, that logic and math is really incomplete. And still logic is used against logic, math is used against math, mind against mind, weapons against weapons, human against each others. Some say this is not possible, but it really is and that's what is happening all the time. Logic and questioning is used to find out fallacies and weak points on logical reasoning of some other, weather they are from the same sandbox or from the other. I have not read thru yet to speak understanding! the proof of Gödel: http://www.research.ibm.com/people/h...n00-goedel.pdf but I'm pretty sure it contains many interesting tidbits and realizations. You can get a sense of it by many other illustrations, like thinking the paradoxes of Liar, Agrippas and Fries Trilemma. Gödels incompleteness theory is compared to Pythagorean finding of square root of 2 to emphasize its importance.

    Ok, second and the last unsolved axiom was:

    3) If p is true, and if whenever p is true, q is true, then q is true. (If "p is true" is true and "if p is true, q is true" is true, then "q is true" is true.)

    Quote Originally Posted by CliveStaples View Post
    Consider the following argument:

    1. I am in London.
    2. If I am in London, I am in England.
    3. Therefore, I am in England.
    This sounds like a repeatition of Socrates / Man axiom. You are a member of something, which is a member of something else. I'm not sure, why it is concidered a different axiom then...

    class London {
    var $england = TRUE;
    }

    $city = new London();
    echo $city->england == TRUE ? 'T' : 'F';
    Run: http://codepad.org/o0khNt6k

    Compare:

    1) If all men are mortal, and if Socrates is a man, then "Socrates is mortal" is true (axiom of substitution).
    2) If London is in England, and you are in London, then "you are in England" is true.

    They are basicly same. You could say men are member of mortals, Sokrates is a member of men, so he is mortal. Slight difference is on plurality of men and singularity of London, but is it enough for different axiom?
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by MARKOM
    You can't separate logic from language or more precicely defined set of symbols and rules using the symbols, which rules must be presented by other symbols because their meaning comes from association to other symbols which primarily will reduce to perceptions. Every thing is a model, take for example addition and substracting. It is an abstract model of (sequence of) operations. You have one finger and you bring other finger beside it, we can call it a group or set of two fingers. Association of 1 + 1 is called 2. By analogy you apply this to other meaningful things, like apples. Now a group of two apples can be divided half or taking one out from set of two you have one left or one each sides. All these are models applied by analogy to other situations. There is no divine logic behind this. Even "being" is a model, that involves interaction of monism, pluralism and nothingness. Many seem to think logic is something spiritual and separate from symbolic world, outside of it and somehow more real. That is strongly arguable.
    How does that contradict what I said?
    I said "you can't mistake the inherent limitations on language to be an inherent limitation on logic."

    Quote Originally Posted by MARKOM
    I assume you are using /= as !. All seems to use different language of their own. You can't simply dismiss "limitations on language" when talking about logic.
    "When talking about logic" of course, but understanding logic yes.
    Suppose a language simply lacked the words that symbolize 1. Granted it would be a very primitive language, but logic itself wouldn't be thus limited.
    Only their access to it.


    Quote Originally Posted by MARKOM
    When is a sign a logical sign?
    When it is a sign of a concept.

    Quote Originally Posted by MARKOM
    Bingo! You can always prove me wrong, this sentence and every other I have made, because you can always read words as you like and you can use your own logic! Nobody is stopping you, or is someone?
    False, that is the fallacy of equivocation. I can not possibly prove you wrong if I never address what you are actually talking about.

    Quote Originally Posted by MARKOM
    Now the solution might come, if there is a certain logic, that is accepted by both parties, there are certain symbols, that are agreed to be used exactly by same meanings and there is someone, who's judging independently outside of us. Which throws us against three different problems, which I've addressed already on some of my replies. What comes to symbols, I want to say some more later on this reply.
    Your entire argument suffers the fallacy of equivocation. You have mistaken the symbols used to communicate logical ideas, with logic itself.
    We use language to communicate logic, but language is not logic itself. A world of no language would not be devoid of logic.
    To serve man.

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    Re: What is the most important question in philosophy?

    Quote Originally Posted by markom View Post
    This suggests, that actually there is no thing called truth, or true, just acceptance and faith on it.
    That maybe the case for the material world. But what empirically proves that our minds are fundamentally material?

    Certainly philosophy and religion are not meaningless, it just happens that their answers has a value only in minds, which is not measurable and testable and is pure closed system logic, which means just opinions, which can be debated forever.
    Why is the mind only subject to a close system of logic? Are you saying that mind can't know truth?
    "The universe is immaterial-mental and spiritual.” --"The Mental Universe” | Nature
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by eye4magic View Post
    That maybe the case for the material world. But what empirically proves that our minds are fundamentally material?
    We should be somewhat sure, what we mean by mind and material on both ends, but I would say the objection, that mind and concepts and their development has a significant and traceable source on sensory and energic world and the counter evidence, that we have not been able to prove by empirical repeatable tests, that there is existence of mind without matter/vibrations, or outside of the own biological construction of body and brain. We have a feeling mind is separate, that can't be denied, but it is still a feeling which can be constructed and reasoned from material and neural sources. Similarly we can have a feeling, that mind is one with everything, which is more rare but true feeling as well, but it is still something, that can be constructed and reasoned from our brain. I think these are evidences pro "material".

    Quote Originally Posted by eye4magic View Post
    Why is the mind only subject to a close system of logic? Are you saying that mind can't know truth?
    Yes, thats basically what I'm saying. Think of how you interact with the world. You get information by senses, you collect data and compare it with other people on the world, who are making same, using their senses to get data from the world. This means all the energy exchange we get in form of light and radiations are transformed and transmutated to our body via sensory system plus represented on our brain and its neural network. Now can you see, how far we are from the true source of the information, direct knowing of the truth at this point already? And I'm not even counting concepts and signs and models we are mostly dealing on mind plus communication we are doing when we transfer information to other parties. How do you think mind can know the truth? By some mystic direct knowing, which for many means just being "super sure" what you think is right?

    But I'd like to rather talk that side of mind on conscious related thread, because it is a little bit different topic: http://www.onlinedebate.net/forums/s...gical-organism
    Last edited by markom; May 21st, 2012 at 06:45 AM.
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by MindTrap028 View Post
    How does that contradict what I said? I said "you can't mistake the inherent limitations on language to be an inherent limitation on logic."
    The point was, that logic is a part of semiotics, each of the logical argumentation structure and axiom can and must be be represented by a sign. I called that a model, because it more closely refers to a neural representation of the concept and doesn't need to be a visible or pictured symbol. It can be carried for example from mouth to mouth, it can be from any source of senses and combinations of senses and sequential, temporal model or pattern.

    You can try to extract logic from natural languages, but not from using symbols and signs. Thats why formal logical symbols were created: http://en.wikipedia.org/wiki/List_of_logic_symbols And because they all (natural languages, symbols and signs) deal with semantics and ontology, they deal with same problems as language, which problems / features are sign-object-interpretant triangular nature AND self refering, axiomatic and infinitely regressive nature. That is clear when you study semiotics.

    "Peirce's settled opinion was that logic in the broadest sense is to be equated with semeiotic (the general theory of signs), and that logic in a much narrower sense (which he typically called “logical critic”) is one of three major divisions or parts of semeiotic."

    http://www.scribd.com/manuel_moreno_...otic-and-Logic

    I think it is pretty valid because it is based on observations, which can be represented by modern brain and mind science. As I have told on previous posts, it is indeed true, that people either unconsciously or delibarately wants to separate logical operations from objects and subjects, like logic is beyond and superior and untouchable divine act. But from perspective of semiotics, they are all signs.

    Quote Originally Posted by MindTrap028 View Post
    Suppose a language simply lacked the words that symbolize 1. Granted it would be a very primitive language, but logic itself wouldn't be thus limited. Only their access to it.
    Because this is an imaginary situation, I can only say, logic would be very very limited in that case.

    Quote Originally Posted by MindTrap028 View Post
    When it is a sign of a concept.
    So when it is a sign of concept? How do you get concepts?

    Quote Originally Posted by MindTrap028 View Post
    False, that is the fallacy of equivocation. I can not possibly prove you wrong if I never address what you are actually talking about.
    Bingo nro. 2! You followed your logic and path of reasoning and found it false. Happened as I predicted. Theory seems to be useful, even if it is not right

    Quote Originally Posted by MindTrap028 View Post
    Your entire argument suffers the fallacy of equivocation. You have mistaken the symbols used to communicate logical ideas, with logic itself.
    We use language to communicate logic, but language is not logic itself. A world of no language would not be devoid of logic.
    My take on this is, that yes it is indeed! Logic is language is signs is semiotics. It's a meta language and it is nothing more than a computer language in modern days, which btw can be demonstrated much more easily than natural language can be demonstrated perfectly by computers.

    In group theory they speculate, that if you see a set of points for example stars, you can surround part of them to present a tennis racket. Tennis racket as an idea had to be somewhere. Of course the idea was somewhere, it was on your memory, some fuzzy pattern that you mirrored to the sky dots. Without the earlier learned pattern, you couldn't have realize it, or you would have created a new form like artists and given a some name for it. Now you seem to think logical representations are some ideas, that exists even if you didn't learn them by repeatance combined with neurophysical boundaries. Where comes logic, if it doesnt come from the world you sense and form the structure of your brains? Only way out from the cage is randomness ie. creativity. You try and test forms never been addressed before on your own path ways. That's something that is out of control, perhaps no logic at all, but sometimes it strikes very useful forms and you can use them logically and rationally on other circumstances if you like the idea. Or you throw them out to the garbage, that is the way nature seems to go forward.
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    Re: What is the most important question in philosophy?

    Quote Originally Posted by MARKOM
    Bingo nro. 2! You followed your logic and path of reasoning and found it false. Happened as I predicted. Theory seems to be useful, even if it is not right
    If you don't mind making and holding and admitting to forwarding a logically fallacious argument, then there is no discussion possible. You are willing to hold an inherently contradictory position, and thus there can be no discussion.

    Here you have admitted to committing a logical fallacy, but act as though it is a triumph.. there is no reasoning with that.

    You can have the last word.
    To serve man.

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    Re: What is the most important question in philosophy?

    Quote Originally Posted by MindTrap028 View Post
    If you don't mind making and holding and admitting to forwarding a logically fallacious argument, then there is no discussion possible. You are willing to hold an inherently contradictory position, and thus there can be no discussion.

    Here you have admitted to committing a logical fallacy, but act as though it is a triumph.. there is no reasoning with that.

    You can have the last word.
    Thank you for opportunity, I'm grateful I have a chance on free discussion board on topic started by myself

    Anyone can claim and defend with simple fallacy attacks, but that doesn't make certain logic or reasoning fallacious. If you cannot precicely show how argumention is fallacious by all means by comprehensive analysis of claims, plus you are just repeating same simple counter claims, then you are committing a fallacy of fallacy, which is very typical on conversations and often comes from the motivation just to show something is black and white, true or false without any other option, which actually is a real reason that makes discussions impossible. In addition to that claim on table is just a fraction of fraction of whole discussion and should not be even the center piece, thus not reason for imposibility of discussion in whole.

    Of "contradictory position", I thought that's the thing why there are debates. By contradictory positions you find other ways to see the topic and mirror it to your own point of view. If it doesn't make sense to you or you cannot understand it for some reason, then there is no reason to change opinion and view IF you ever happened to have a strict point of view to the topic in first place. If you don't understand, should you rather believe or try some more?

    So maybe it's time for conclusions and summary of the thread...

    I said on OP "from opponents view of point he is right and from my view of point I am right" That is something that almost always seem to be true UNTIL both sides makes an agreement that they are speaking on same meanings and they both accept the view of point. Objective of this thread and from same topic on other forums is similar: debate goes on and on (chosen view defines the view at the end) until artificial halt made by above mentioned agreement or outside judge or physical limits. One might say, what if you happen to understand you were wrong? But what is understanding but change of the viewpoint (standpoint) from above, beside or opposite to under to support controversial viewpoint (standpoint). I think there are nice openings on basic meanings of the orginal words itself when you think of it.

    One of the main point of OP was to ask if there is something wrong on circular reasoning, infinite regress, or unproven axioms AND if they can be avoided. One clear thing was, that we really can't avoid axioms in means of using some claims as true by default, with a disagreement if you can or cannot question axioms, because in my opinion you can and you should but not on "same breath" of course. You can carry argumentation that seems to keep some things obvious so argumentation / reasoning / thinking process / discussion can evolve. But at the same time you keep claims open so you can always go back and question any part of the claim. Questioning in this case means aspiration to find out truth value of the different parts of the argumentation. Questioning also means seeking if proposed logic keeps tight and unbreakable, thus it is also an attempt to find out fallacies and point them out precicely.

    What is unavoidable in this case, is that you are referring back to the original argumentation, yet to start infinite regression, that on the other hand can be avoided only by agreeing some axioms. It's all about balancing between these two.

    I'd say there is nothing wrong on axioms and regression, because they are major part of the logic. They just give logic some weak points. Circular reasoning to me is just other way to say an axiom. A is B because B is A. It is tautology like "if A, then A" is tautology. Now all these three seems mandatory for logic "Circular reasoning"" being just formally unaccepted way to present an axiom. But for some reason we don't like these three and they don't seem ok. Straight natural language forwards axiomatic approach if you don't use words like "i suppose", "i believe", "in my opinion", "maybe", "in some cases", and so forth all the time, which is just useless repeatition and waste of space.

    Problem comes not from well formed sentences as they all are such, but from the action to find out truth value of the statements. We kind of raise the perspective up and see whole case above (recalling the meaning of understanding) and try to find out if whole and each of the parts of the statement is true, not formally but by their real meaning, like:

    1) "if A, then A" -> is A true, why "if A, then A" is true and is the claim true of false.
    2) "A is B because B is A" -> is A really true, is B really true. is "A is B" really true
    3) "Johnny is the president of USA" -> claim is ok if taken as axiom. but is Johnny really the president of USA?
    4) "God lives in Sirius" -> again claim is ok if taken as axiom. but is there even God, what is Sirius, does God really live there, why is He living there?

    and so forth. What is pure logic, if you don't reflect it to the different measurable or observable situations, if you don't apply and cannot verify it? This is something that I mant when saying about "measurable counterpart with its axioms".

    To use logic to conclude something of the world (truth value of the claim) you need to make a certain paradigm shift like above and that is the point when different meta and presentation levels separates. You also step deeper to the swamp of semantics, ontology and semiotics. And that is not a problem, when there are real observations behind of the symbols and signs. Observation defines the truth value, not the logic. This is how the Liar paradox as well as Agrippa's paradox resolves. They are true on observation level which can be formulated as an argument on language presentation level, when they may contradict if self referred across the levels. Swamp is vertically less infinite on case of observational logic compared to debates settling on purely imaginary circular land of logic. Vertical observation based logic can still give huge room for discussion by levels of creation. Now the final question is, which sort of the infinity and incompleteness, vertical or horizontal you rather choose?
    Last edited by markom; May 22nd, 2012 at 02:15 AM.
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    Re: What is the most important question in philosophy?

    Where do we come from and why are we here?

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    Re: What is the most important question in philosophy?

    I have to say, that I'm interested to find out that too
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