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    Thread: Epistemological Relativism

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      Epistemological Relativism

      The purpose of Science is not the establish the most accurate depiction of reality possible. Its purpose is to enable the mind to most easily assign value to various assertions. An assertion supported by scientific evidence is not more true than an assertion void of evidence, it is simply a more valuable idea to utilize when making decisions.

      The factual universe is outside the realm of the subjective experience. The subjective experience is capable only of behaving in whichever way it can find to be most advantageous. Science enables the organism to discover the most statistically advantageous model to base decisions upon, not the most accurate depiction of reality in general.

      A friend of mine disagrees with me in this particular regard. He believes that the most accurate assertion of reality is not necessarily the most functional. He cites organized religion to argue that irrational ideas are often more capable of functioning and propagating than rational ideas. Benefit is therefore not related to Truth. I disagree, I believe the only means we have to find the most accurate depiction of reality is to observe the most successful behavior. Or rather that it is impossible for the subjective mind to ascertain something which is more true than something else, and therefore the goal of the organism is to find success, not truth. Discovering the most accurate depiction of reality possible is only beneficial so far as it serves the function of the observer. The Scientific Method increases an organisms chances of success by providing a more stable foundation to influence their behavior than Dogmatic Tradition. Ideas such as belief, right, wrong, true and false are antiquated in my mindset. I am interested in the practices the organism utilizes in order to prosper.

      For example we know ethics is typically considered relative unless it is conflated with piety. I consider ethics to be an intuitive development of Game Theory, and research on Game Theory shows that the most advantageous behavior includes compassion, fairness and other ethical ideals. In other words ethics are the tactics which are most advantageous when considering the complexity of life and the length of time it takes for certain processes to reach fruition. Ethics are the tactics for those wishing to with-hold instant gratification and seek out success on a larger scale than their own personal gain, or more precisely in search of a sustainable and more advantageous gain than what is delivered through opportunism, such as a more stable and prosperous society.
      Last edited by Omnis Dei; 03-12-2012 at 08:24 AM.
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      Rational Spiritualist DrunkenArse's Avatar
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      Quote Originally Posted by Omnis Dei View Post
      A friend of mine disagrees with me in this particular regard. He believes that the most accurate assertion of reality is not necessarily the most functional. He cites organized religion to argue that irrational ideas are often more capable of functioning and propagating than rational ideas. Benefit is therefore not related to Truth.
      Am I just drunk or is your friend not very on point here?

      How do the propensities of rational and irrational ideas for spreading pertain to which of them is a more accurate description of reality? Why does the most accurate idea have to be the one that best propagates? And what is even meant by an accurate model of reality?
      Previously PhilosopherStoned

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      One thing I can tell you is that your response to my posts displays a very inaccurate reflection of my opinion.

      My friend used plate tectonics as an example for his claim. There's this theory that the poles are shifting, the earth is expanding, its hollow, whatever you want. These theories are all blatantly opposed to scientific evidence. To uphold these claims in the face of all scientific evidence to the contrary is, in my friend's opinion, more wrong than to agree with the conclusions implied by the evidence.

      In my opinion, there's no way to judge a subjective opinion or experience as a less accurate depiction of reality than another. That means that someone's opinion that Hamsters created the universe is no less objectively accurate than the current consensus made by astrophysicists. When it comes to someone's subjective model of reality, accuracy in relationship to actual reality is simply an invalid concept. A more valid comparison between differing opinions is the value they serve the individual. This means that if someone believes eagles shat out the universe in order to cool themselves, and that opinion serves them or society in regard to widescale evolution, then its more valuable than an opinion which was not as productive, whether or not the latter opinion had more scientific evidence supporting it.

      I look forward to seeing you miss the point and misconstrue my argument again.

      Everything works out in the end, sometimes even badly.


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      Quote Originally Posted by PhilosopherStoned View Post
      Am I just drunk or is your friend not very on point here?

      How do the propensities of rational and irrational ideas for spreading pertain to which of them is a more accurate description of reality? Why does the most accurate idea have to be the one that best propagates? And what is even meant by an accurate model of reality?
      You're not drunk, but maybe you are in our subjective world according to Omnis. Yes, yes I think you are drunk and the idea that you have not ingested mass quantities of alcohol which effect your body does not invalidate my perception that you are drunk.

      Theories blatantly opposed to scientific evidence in the natural world are what psychologists like to call "delusions." The premise that the world was created by hamsters has no grounding in factual evidence of the natural world. And I don't know where you get the idea that science is a value assigning discipline. Science isn't normative. There are no values in it.
      'What is war?...In a short sentence it may be summed up to be the combination and concentration of all the horrors, atrocities, crimes, and sufferings of which human nature on this globe is capable' - John Bright

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      I never said there were. My claim is simply that true and false are not determinable from a subjective standpoint. There is not subjective opinion which is more in line with the objective reality than another. The only way in which one subjective viewpoint can be better than another is by the value it serves the individual's decision making process.

      Example: There is no guarantee the sun will rise tomorrow, but I hold the premise that the sun will rise tomorrow as a more valuable basis for my decision making than the premise that it will not. Evidence such as inferring the sun will rise based on what it has done previously and the evidence of a revolving earth gives that premise a greater statistical advantage than the premise that the sun will not rise.

      Because industrial London led to lichen free trees, dark peppered moths are more statistically advantageous than light peppered moths. And they most likely will continue to be for some time to come, but that doesn't make the light colored mutation less valid than the dark one, simply less valuable based on the environment it is situated in. Simply because dark peppered moths currently hold the advantage, that doesn't mean the mutation should just go away forever. In fact one day the lichen may grow back and the advantage will switch back.

      Whatever the case, the example is meant to show you the difference between the absolutist right/wrong worldview and the relativist advantageous/disadvantageous worldview. Rational, logical thinking doesn't imply what is right, it only reveals a more statistically advantageous basis for decisions which is inherently subjective and relative. One can still choose to experiment, and in fact many of the views we accept today started as explorations of ideas outside the traditional worldview. These ideas were tested for evidence but that didn't make them true, in the relativist view, it merely gained them more statistical advantage.

      Everything works out in the end, sometimes even badly.


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      Quote Originally Posted by Omnis Dei View Post
      I never said there were. My claim is simply that true and false are not determinable from a subjective standpoint. There is not subjective opinion which is more in line with the objective reality than another. The only way in which one subjective viewpoint can be better than another is by the value it serves the individual's decision making process.

      Example: There is no guarantee the sun will rise tomorrow, but I hold the premise that the sun will rise tomorrow as a more valuable basis for my decision making than the premise that it will not. Evidence such as inferring the sun will rise based on what it has done previously and the evidence of a revolving earth gives that premise a greater statistical advantage than the premise that the sun will not rise.

      Because industrial London led to lichen free trees, dark peppered moths are more statistically advantageous than light peppered moths. And they most likely will continue to be for some time to come, but that doesn't make the light colored mutation less valid than the dark one, simply less valuable based on the environment it is situated in. Simply because dark peppered moths currently hold the advantage, that doesn't mean the mutation should just go away forever. In fact one day the lichen may grow back and the advantage will switch back.

      Whatever the case, the example is meant to show you the difference between the absolutist right/wrong worldview and the relativist advantageous/disadvantageous worldview. Rational, logical thinking doesn't imply what is right, it only reveals a more statistically advantageous basis for decisions which is inherently subjective and relative. One can still choose to experiment, and in fact many of the views we accept today started as explorations of ideas outside the traditional worldview. These ideas were tested for evidence but that didn't make them true, in the relativist view, it merely gained them more statistical advantage.

      You are conflating science with subjectivity. If you were to be saying "You can't prove my favorite ice cream flavor is true or false" then I (and I think Stoned) would not really have a problem with what you are saying. Preferences such as this are subjective and it is based on aesthetics, not logic.

      However you are saying scientific knowledge of the natural world is based upon relative observations, but it isn't. If we were to stand in the same spot, all things being equal, we would we the same distance from the sun or would have the same measurements of its size. Science is agent-neutral meaning it that its truth isn't dependent upon the individual on hand.
      'What is war?...In a short sentence it may be summed up to be the combination and concentration of all the horrors, atrocities, crimes, and sufferings of which human nature on this globe is capable' - John Bright

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      The nice thing about measuring is that it provides good statistical advantage to base decisions upon. But you're conflating the measurements made by the subjective observer with the measurements existing in objective reality. The epistemological relativist point of view is that if 500 people were to measure something and 499 get one measurement and 1 person gets a different measurement, the 1 person's measurement is not objectively wrong, their assessment simply isn't advantageous compared to the 99.5% majority and decisions made related to the measurement are preferable if based upon the result of the 499 rather than the one.

      Or, when using science to negate dogmatism, if 499 people were to make a claim without proof and 1 person made a claim backed up by a mountain of evidence, the value would go to the one. This is not objectively true, it's simply my advice based on my relativist perspective. I would assign more value to evidence than no evidence. But I would not assign truth to evidence.

      The core principle here is that objective truth is an impossible idea, and that functionality is a preferable goal. The goal is not to find out what objectively is, but would would best serve you.
      Last edited by Omnis Dei; 03-15-2012 at 10:38 AM.

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      Quote Originally Posted by Omnis Dei View Post
      The nice thing about measuring is that it provides good statistical advantage to base decisions upon. But you're conflating the measurements made by the subjective observer with the measurements existing in objective reality. The epistemological relativist point of view is that if 500 people were to measure something and 499 get one measurement and 1 person gets a different measurement, the 1 person's measurement is not objectively wrong, their assessment simply isn't advantageous compared to the 99.5% majority and decisions made related to the measurement are preferable if based upon the result of the 499 rather than the one.

      Or, when using science to negate dogmatism, if 499 people were to make a claim without proof and 1 person made a claim backed up by a mountain of evidence, the value would go to the one. This is not objectively true, it's simply my advice based on my relativist perspective. I would assign more value to evidence than no evidence. But I would not assign truth to evidence.

      The core principle here is that objective truth is an impossible idea, and that functionality is a preferable goal. The goal is not to find out what objectively is, but would would best serve you.

      Because there is no subjective reality toward measurements. A foot is 12 inches...everywhere. It's a priori. If 500 people were to measure something and one gets it wrong, then that is called variation. This is because of user error in engaging in the measurement. That is why I said, all other things being equal.

      Your core principle that "objective truth is an impossible idea" is a performative contradiction because the fact that there is no objective truth is itself an objective truth about the world. Congratulations.

      Honestly, save yourself some time. Just get over this relativity phase.
      'What is war?...In a short sentence it may be summed up to be the combination and concentration of all the horrors, atrocities, crimes, and sufferings of which human nature on this globe is capable' - John Bright

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      Being condescending isn't going to make you any better at arguing your viewpoint, in fact it makes you appear dismissive which strikes me as though you don't have much confidence in your own viewpoint because you're unwilling to argue it.

      A foot being 12 inches is abstract, and abstraction can be absolute in the frame that it's devised in. But abstract truth is limited to circular logic. Something becomes true because we deemed it as such for the sake of being able to communicate effectively, not because it's true in any real sense. When someone claims a foot is not 12 inches (or 2+2=5, or any other abstract ideas) that also doesn't make them objectively wrong, it simply makes them a bad communicator, unwilling to play by the agreed upon rules. These things still have nothing to do with objective reality.

      The idea that objective truth is an impossible is, in fact, contradictory with epistomological relativism, and I knew that when I said it. Epistomogological relativism would hold that an absolutist is no more wrong than a relativist. This in itself is a paradox in the philosophy, for a relativist to argue their viewpoint they must also argue that absolutism is as equal as their own viewpoint. I broke those rules in my attempt to communicate with you that it's impossible to discover objective truth as the subjective observer. I believe that explanation should be more clear.

      Everything works out in the end, sometimes even badly.


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      Rational Spiritualist DrunkenArse's Avatar
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      Quote Originally Posted by Omnis Dei View Post
      One thing I can tell you is that your response to my posts displays a very inaccurate reflection of my opinion.
      ...

      I look forward to seeing you miss the point and misconstrue my argument again.
      Ditto. I was giving you an argument to use against your friend's perspective since you apparently were unable to spot the fallacy. Your friend apparently doesn't know how rationality works anymore than you do since his argument is about on par with what I would expect from you. Did you find a problem (that you have failed to explicate) with my rebuttal of your friend's position or was assuming that I was opposed to your opinion just a knee-jerk reaction on your part?

      Quote Originally Posted by Laughing Man View Post
      And I don't know where you get the idea that science is a value assigning discipline. Science isn't normative. There are no values in it.
      Science is absolutely a normative, value assigning discipline. It's primary normative tools are predictive power and falsifiability. The values it assigns are related to the explanatory power of the hypothesis under consideration. This is why creationists get laughed at if they manage to slither into a biology department.

      Good thing too. A disipline that can't do these things isn't much of a discipline, is it?

      Quote Originally Posted by Laughing Man View Post
      However you are saying scientific knowledge of the natural world is based upon relative observations, but it isn't. If we were to stand in the same spot, all things being equal, we would we the same distance from the sun or would have the same measurements of its size.
      The idea that objective observation is even possible is one of those assumptions which lay at the heart of the rational materialist model. It is only in our experience that such measurements do not depend on who carries them out. It makes the universe much cleaner to think about and is a very useful assumption but this does not make it objectively true.
      Previously PhilosopherStoned

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      Quote Originally Posted by Omnis Dei View Post
      Being condescending isn't going to make you any better at arguing your viewpoint, in fact it makes you appear dismissive which strikes me as though you don't have much confidence in your own viewpoint because you're unwilling to argue it.
      I just don't have much tolerance for nihilism because so many who find out what it is waste their intellectual power trying to promote it because its groovy or something like that.

      Quote Originally Posted by Omnis Dei View Post
      A foot being 12 inches is abstract, and abstraction can be absolute in the frame that it's devised in. But abstract truth is limited to circular logic. Something becomes true because we deemed it as such for the sake of being able to communicate effectively, not because it's true in any real sense. When someone claims a foot is not 12 inches (or 2+2=5, or any other abstract ideas) that also doesn't make them objectively wrong, it simply makes them a bad communicator, unwilling to play by the agreed upon rules. These things still have nothing to do with objective reality.
      Actually it makes them objectively wrong because it is beyond logic to show that 2.0000+2.00000 equals anything but 5. Math is based on logic, logic is universal and inescapable. There is no such thing as an illogical mind because we wouldn't be able to perceive it, understand it or interact with it.

      Quote Originally Posted by Omnis Dei View Post
      The idea that objective truth is an impossible is, in fact, contradictory with epistomological relativism, and I knew that when I said it. Epistomogological relativism would hold that an absolutist is no more wrong than a relativist. This in itself is a paradox in the philosophy, for a relativist to argue their viewpoint they must also argue that absolutism is as equal as their own viewpoint. I broke those rules in my attempt to communicate with you that it's impossible to discover objective truth as the subjective observer. I believe that explanation should be more clear.
      So now you are saying that objective truth being impossible is contrary to epistomological relativism? It Sounds like you need to hash out what you really believe before this conversation continues.
      'What is war?...In a short sentence it may be summed up to be the combination and concentration of all the horrors, atrocities, crimes, and sufferings of which human nature on this globe is capable' - John Bright

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      Quote Originally Posted by PhilosopherStoned View Post
      Science is absolutely a normative, value assigning discipline. It's primary normative tools are predictive power and falsifiability. The values it assigns are related to the explanatory power of the hypothesis under consideration. This is why creationists get laughed at if they manage to slither into a biology department.

      Good thing too. A disipline that can't do these things isn't much of a discipline, is it?
      Actually it is not. Humans can place value upon scientific studies but science itself does not place value on itself or its study. Science can show you what happens when you put two hydrogens and an oxygen together but it does not say why you should put it together nor if it is good to do so etc.



      Quote Originally Posted by PhilosopherStoned View Post
      The idea that objective observation is even possible is one of those assumptions which lay at the heart of the rational materialist model. It is only in our experience that such measurements do not depend on who carries them out. It makes the universe much cleaner to think about and is a very useful assumption but this does not make it objectively true.
      What other experience would there be that would not be dependent upon humans?
      'What is war?...In a short sentence it may be summed up to be the combination and concentration of all the horrors, atrocities, crimes, and sufferings of which human nature on this globe is capable' - John Bright

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      Rational Spiritualist DrunkenArse's Avatar
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      Quote Originally Posted by Laughing Man View Post
      Actually it makes them objectively wrong because it is beyond logic to show that 2.0000+2.00000 equals anything but 5.
      First off, is it 2.000 as a real number or 2 as an integer?

      2 + 2 = 1 is a true statement. Taken modulo 3.

      Quote Originally Posted by Laughing Man View Post
      Math is based on logic
      You should check out logicism. Essentially you are making a religious claim.

      tl;dr: math has not been logically reduced to logic.

      Quote Originally Posted by Laughing Man View Post
      logic is universal and inescapable.
      More of the rational materialist religion. It's a good religion and good, useful assumptions but that doesn't make them anything more than that.

      Quote Originally Posted by Laughing Man View Post
      There is no such thing as an illogical mind because we wouldn't be able to perceive it, understand it or interact with it.
      There is no such thing as a logical mind either.

      More on point though, your assertion that it doesn't exist (i.e. "no such thing") is itself based on the assumption that the only way for something to exist is if we can percieve it, understand it, or interact with it. This assumption isn't even necessary for rational materialism to function as one of the most distinguished of a number of possible models of reality. However, there's no way to have it be The One True Way though without this assumption.
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      Quote Originally Posted by Laughing Man View Post
      Actually it is not. Humans can place value upon scientific studies but science itself does not place value on itself or its study. Science can show you what happens when you put two hydrogens and an oxygen together but it does not say why you should put it together nor if it is good to do so etc.
      Science places value on specific scientific statements. It doesn't say why one should do something or if it's good. It says if the statement is correct or not. This is a valuation. With statistical inference it can say how likely it is for the statement to be correct. Statements of biblical creationism are rejected by the normative process of science and valued far less than statements that take place within the scope of evolutionary biology. Some of those will even be "de-valued" over time.

      Try to apply a little imagination.

      Quote Originally Posted by Laughing Man View Post
      What other experience would there be that would not be dependent upon humans?
      Any of the other number of sentient beings that exist. Aside from that (purposeful?) misunderstanding though, I was referring even to measurements made by two distinct humans. It is a matter of faith (assumption) that if they both make the same measurement correctly then they will get the same result. Like I said, it's a useful assumption but it is still an assumption.
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      If you make up math rules that don't make any sense any doesn't come out correctly mathematically, then yea you are wrong. You are always wrong. You are absolutely, 100% objectively wrong. We can easily prove you are wrong. Just because you try to act philosophical doesn't mean you are any less wrong.

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      Rational Spiritualist DrunkenArse's Avatar
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      Who's making up math rules that don't make sense?

      Why the strong reaction? Is having the sacred script of one of your choice religions questioned bothering you? Check the logicism wiki link. There is no serious way to claim that mathematics has been reduced to logic.

      Mathematical statements are also meaningless unless you specify in which context they are meant. 2 + 2 = 4 taken mod 5 or higher and in all fields which contain the integers. It comes to 0, 1 and 0 when taken mod 2, 3 and 4 respectively.

      So even in mathematics, context can change everything.
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      That isn't a different context, that is a different equation. Context doesn't really matter, leaving stuff out obviously does matters. You might as well say, 2+2=5 if you add one more. Though 2+2+1 is a totally different equation, than 2+2.

      Leaving something out and then adding it back in later doesn't prove math is flexible and changing, it only shows you made an error in the original problem.

      Doesn't matter if you believe in logicism or not, that doesn't change that math is logical.

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      Rational Spiritualist DrunkenArse's Avatar
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      Alric, you're having a hard time here. It helps to have a clue what you're talking about. There were no equations in the post to which you are responding. There were (as I said) various mathematical statements concerning the relation between objects and operators on said objects. The truth or falsity of those statements were dependent upon the context in which they were taken.

      Take it over Z or Z/nZ for n > 5 and 2 + 2 = 4. In Z/2Z and Z/4Z, 2 + 2 = 0. In Z/3Z, 2 + 2 = 1

      So 2 + 2 = 1 is false in Z but true in Z/3Z.

      You think that's weird?

      The ring Z/nZ has much more in common with Z than Z does with the rationals. Z/nZ will have (for n not prime) a non-trivial ideal structure whereas Q has no nontrivial ideals. So why is moving from Z to Q no big deal (as laughing man did by switching to 2.000 + 2.000 instead of 2 + 2) while a simple move to finite rings is?

      Why don't you accuse laughing man of making up weird mathematical rules? He's the one that's actually doing it.

      But you want an equation. Here's one.

      x2 + 1 = 0

      This equation has no solutions with x in the reals but has precisely two (i and -i) solutions in the complex numbers. It's the same equation (it lives in Z[X]. Ok actually the function x |-> x2 + 1 lives there but a little conflation is fine in this setting) but taken in two distinct contexts yields two distinct sets of solutions.

      So again, context matters even mathematics.


      Also, please note that the question of if logicism has achieved its goal or not is not a matter of "belief" any more than the correct proof of a theorem is. If it was done, then it would be done and everybody that knows enough to deserve an opinion would know it. It hasn't been done and hence nobody that knows enough to deserve an opinion would think of stating that mathematics has been reduced to logic.

      But you know better? Without knowing what an equation is?
      Last edited by PhilosopherStoned; 03-17-2012 at 01:43 AM.
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      If you say two things are equal to one another that is an equation. So yea, there was equations in the previous posts on this thread.

      Secondly I never said math is reduced to logic, I said math is logical. Which it is. The rules flow from logic and all make sense, it isn't random and chaotic or arbitrary in nature.

      If you are converting to another system of counting, the math still works perfectly fine just how it is. You just need to covert it. The reason you say all that other stuff, is because you have to, in order to tell people what you are doing, otherwise it become wrong.

      Even in your examples, the math is still working logically. Even imaginary numbers tell you something about what is going on in a given problem.

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      Philosopher Stoned:
      Why does the most accurate idea have to be the one that best propagates?
      This gave me the knee-jerk reaction that you misunderstood the post because I was arguing that in my view right and wrong are useless and in my view we are incapable of judging absolute reality in a truthful way (or rather that an illogical conclusion is just as correct and incorrect as a logical conclusion), we are only capable of perceiving reality to guide our decision making process. My friend argued against the idea that the most accurate idea is the one that best propagates, he claimed absolutists do far better than logicians at propagating. I argued that the most prosperous result is the most feasible way of creating the most accurate model to follow. Neither of us argued that the most feasible result or idea with best propagates is the most accurate perception of objective reality.

      Quote Originally Posted by Laughing Man View Post
      I just don't have much tolerance for nihilism because so many who find out what it is waste their intellectual power trying to promote it because its groovy or something like that.
      Then you should learn the difference between epistomological relativism and nihilism. See the above message I sent PhilosopherStoned. Nothing about my argument relates to nihilism because my perception leads me to determine comparative value, I simply don't believe there's any such thing as objective value nor objective right and wrong, nor objective truth to begin with. A nihilist would be someone who see's no value in anything period, possibly because life is an infinite but ultimately purposeless theater. If you want to rant about your disgust of this perception, there's a thread for that. This thread is intended to discuss the concept that logic stands upon its own circular logic, in that logic becomes truth because its logical, but not because it's true. It makes an assumption it has no right to make and the entire concept of logic is based upon a false postulate. Logic is a tool because it implies certain agreements one can use as a means of navigation.

      Actually it makes them objectively wrong because it is beyond logic to show that 2.0000+2.00000 equals anything but 5. Math is based on logic, logic is universal and inescapable. There is no such thing as an illogical mind because we wouldn't be able to perceive it, understand it or interact with it.
      Again, you're leaning upon the postulate that logic is truth without justifying why it's truth. You are containing the entire universe and reality and etc. within one, solitary toolset at your disposal.

      So now you are saying that objective truth being impossible is contrary to epistomological relativism? It Sounds like you need to hash out what you really believe before this conversation continues.
      Or you could stop using strawmen. Perhaps you should reread my post.

      it's impossible to discover objective truth as the subjective observer
      IE

      Logical conclusions based on perception =/= reality

      PS covered the rest. Props to PS
      Last edited by Omnis Dei; 03-17-2012 at 05:15 PM.

      Everything works out in the end, sometimes even badly.


    21. #21
      Rational Spiritualist DrunkenArse's Avatar
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      Quote Originally Posted by PhilosopherStoned View Post
      Z than Z does with the rationals. Z/nZ will have (for n not prime) a non-trivial ideal structure whereas Q has no nontrivial ideals. So why is moving from Z to Q no big deal (as laughing man did by switching to 2.000 + 2.000 instead of 2 + 2) while a simple move to finite rings is?
      protip: The ring Q[X] has much more in common with Z than any of the Z/nZ do. Z/nZ will always have a finite ideal structure whereas Z and Q[X] (or R[X] or C[X]) have infinite ideal structures. Or rather, for any n, one can cook up a strictly monotonic nesting of ideals n deep. Also, they both have an infinite amount of maximal (and hence, being Noetherian, prime) ideals. finally, I would just call Z/nZ Zn but that involves subscripts. LaTeX makes this stuff so much easier. To get subscripts one has to type tags or use the mouse. In LaTeX it's just _{n}. So much nicer. It should be an easy extension...

      This equation has no solutions with x in the reals but has precisely two (i and -i) solutions in the complex numbers. It's the same equation (it lives in Z[X]. Ok actually the function x |-> x2 + 1 lives there but a little conflation is fine in this setting) but taken in two distinct contexts yields two distinct sets of solutions.
      I'm being sloppier than I meant. The function x |-> x2 + 1 lives in R[x] not R[X]. It will be different depending on what solutions are allowed. x will belong to Z, Q or R when the equation has no solution and it will belong to C when it does. All four are different functions. I meant that we're solving the equation derived from the formal polynomial X2 + 1 which is what actually lives in Z[X] (The ring of formal polynomials over Z). This induces a function A -> A on any algebra, A, over Z. Setting that function equal to 0 makes an equation. So it's the same equation. They're different problems (if you're into taking tests) but it's the same equation. This is even more the case because all homomorphisms in sight have a trivial kernal and can be regarded as inclusion mappings; it's the same 0 (the one that's in Z) that's being solved for.

      But you know better? Without knowing what an equation is?
      I'm being a bit of a hypocrite here giving my view towards psychology (it's getting better) but I'm dead on with economics. Did you know that somebody got the Nobel Prize in economics for an incorrect result? Mathematically correct to be sure (to such an extent as such a thing exists in economics) but it didn't mirror reality.

      Quote Originally Posted by Alric View Post
      If you say two things are equal to one another that is an equation.
      No, that's a statement. An equation involves an unkown to be solved for.

      So yea, there was equations in the previous posts on this thread.
      No there weren't.

      Secondly I never said math is reduced to logic, I said math is logical.
      To say that 'math is logical' is very informal and hence, in the strict interpretation of the word, illogical. I assumed that you meant that formally, (i.e. in a logical sense) mathematics is logical, i.e. a subset of logic. It's not. Math uses logic (I love a good contrapositive proof myself, can't remember what the logicians call them (arguing the somethingorother I think)) but that doesn't make it logical any more than physics is mathematical. Of course if your primary interest is taking tests (and jumping through other people's hoops) then I suppose physics is mathematical (as long as you can cut basic calc) and math is logical. But whatevs. Math is no more made of logic than a car is made of socket wrenches.

      The rest of your post is addressed by pointing out that you don't know what math and logic are and are hence in no position to demand that your post is addressed without educating yourself or asking direct questions. I guess I'm a hypocrite concerning psychology. Hi DuB.


      Omnis, I'm fairly drunk right now and in no shape to properly respond to your post) However I disagree with a few of your points (probably just semantics but nonetheless important) and will respond later. Peace.
      Last edited by PhilosopherStoned; 03-17-2012 at 11:23 PM.
      Previously PhilosopherStoned

    22. #22
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      No, you are totally wrong. Notice the first part of the word, equation. It comes from the word equal. If there is an equal sign and the statement is comparing two values then it is an equation. There doesn't have to be an unknown, and you don't have to solve it. You are totally wrong on this.

      Secondly, why are you assuming weird things? I said math is logical as in the rules of math are based in logic. As in the rules act in a predictable way, that are obtained through reason. Everything is orderly connected and thought out. If you prove anything in math, you can go through it step by step and see how it follows in a logical order.

      I never said math is a subset of logic, I said math is orderly and makes sense and is based entirely in reason, ie its logical.

      It makes me wonder if English is a secondary language for you. Since you don't know what an equation is, and use words in uncommon ways.

    23. #23
      Rational Spiritualist DrunkenArse's Avatar
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      Alric, you're probably a moron. I've never seen you say anything intelligent that someone else hasn't already told you. You probably never will. Your mind is far too riddled with assumptions and you think you know way to much to even contemplate doing any such thing. Just letting you know. And it's ok. The vast majority of people are so stupid that we would be living in huts and using fire for warmth if there weren't (very!) occasionally intelligent people to actually figure things out. After that, the stupid people can do stuff. Don't take credit above your class and know your place.

      I'll moderately concede that you're right about equations. (although see later where wikipedia asserts that many mathematicians back me up) So include 2 + 2 = 4 as an equation, you can squeeze it into the definition.

      Here's wikipedia backing me up: "Many mathematicians[2] reserve the term equation exclusively for the second type, to signify an equality which is not an identity. The distinction between the two concepts can be subtle;" Equation - Wikipedia, the free encyclopedia under the headings "identities".

      Here, the second type refers to statements that aren't always true and are only true for certain values of the unknowns. This implies in particular that there are unknowns (i.e. variables, i.e. independant variables) in one of the expressions or they would be constant functions and hence the relation would be true for all values.

      That's the way I was educated at least.

      Second, I'm not assuming weird things. I'm assuming mundane things that you don't have a clue about but that are at the core of your beliefs. How are you so sure of them if you don't even know. I'm only talking undergraduate (or maybe first year graduate) stuff here.

      You were asserting that math is logical. Formally it's not and that's what matters in math. You're stupid. I don't have to respond to you. You're beneath me and I'm better than you, you subhuman monkey.

      P.S. It doesn't matter if english is a second language for me because the second you wanted to start talking about math we stopped talking in english (where it's impossible to talk about math other than in the most masturbatory of ways) and started talking in mathematical enlish. This is where precision lays, this is where the power of the rational materialist model lays and this is where you substitute religion for clear thought and hard work.
      Last edited by PhilosopherStoned; 03-18-2012 at 01:22 AM.
      Previously PhilosopherStoned

    24. #24
      Rational Spiritualist DrunkenArse's Avatar
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      I hate people that think common sense is a good thing. They're almost as bad a creationists! Common sense is a prison in which small minds rot till the body that manufactures them dies.
      Previously PhilosopherStoned

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      Yea I am stupid, yet you need to look up 'equation' on Wikipedia in order to understand what it is? Then even though Wikipedia proved that you are an idiot and were wrong you tried to twist the wording to some how say you are right. Yet you are still wrong because your are taking the quote out of context.

      If you think 2+2=4 is an identity and most math people would call it an identity rather than an equation, then I think you are just hopeless. You are obviously just pulling things out of your ass.

      What they are talking about on Wikipedia is that something like A*0=0. That is an identity. As opposed to an equation which is A+0=0, which is an equation. BOTH are equations, but if you want to be more specific, one is an identity(true for all numbers), and one isn't an identity(true for one one set of numbers).

      You can insult me and call me stupid all you want, but even a 5th grader knows what an equation is, which apparently you do not.

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