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  1. #21

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    Nocturne pretty much said what I wanted to say regarding this, and used words I wouldn't have thought of.

    But I am going to pick a small nit regarding the example of 2+2=4 in base 10 while 2+2=10 in base 4.

    These do not constitute different subjective perceptions of reality, but simply slightly different ways of writing mathematical facts. It is like saying II+II=IV in Roman numerals. They are simply different notations. 10 in base 4 is 4 in base 10, not "ten" (in a way independent of base).

    The deception occurs because "2" is used in both notational systems, but base 4 only has symbols 0,1,2, abd 3.

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  2. #22
    Senior Member wildcat's Avatar
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    Quote Originally Posted by athenian200 View Post
    I was just thinking about how many people believe that it is possible to know something in a objective manner. However, this is not true, not even of perceptions. Everything we can know or express to ourselves inherently has a subjective element, because it is processed through subjective filters.

    An example many people use to show that we can have objective knowledge is the mathematical notion that 2+2=4. However, this formulation is in fact subjective in several ways. First, it assumes that the person is using decimal, standard mathematical notation, and agrees on the meaning of each number. For instance, just by switching to quaternary, I could make 2+2=10. Now the person might argue that this is actually the same answer because you can acheive the same result with physical objects. But this is also subjective, because you would first have to agree on what should be defined as an object. With what we consider to be two books, we have to agree that it is the set of pages, ink, ideas, atoms, etc, that we have somehow defined as a book, separately from it's surrounding environment. Also, the idea of counting does not change anything about the books, it simply is part of how we define our perception of them. The idea that the two books are independent entities is part of a limitation in how human beings process reality. Truthfully, we cannot say that anything exists outside of our perception of it. Everything that we can communicate is based on a shared set of assumptions and rules for processing things that we somehow accrue over the course of our lives. Even this communication is entirely subjective, based on my perception of reality, language, and logic.

    Even if we assumed that things that we perceive exist outside our perception, we still must acknowledge that we only comprehend something by superimposing a subjective impression onto it, and examining that. For instance, if our understanding is correct, what we call "red" exists in nature, but only as a material that reflects light particles within a certain band of the electromagnetic spectrum. To a being that perceived the electromagnetic spectrum differently, we would be able to explain "red" to them, but they might not understand what that particular perception really means to us, because what "red" means to us has more to do with the subjective impression it makes on us, rather than how light particles respond to it.

    So how can anything truly be objective? It can't. Why do some people claim that they can say something objectively, when all knowledge is subjective?

    What does this mean?
    It means any measurement pertains to the subject alone- not to the object.
    The object is beyond reach.

  3. #23
    Oberon
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    Quote Originally Posted by athenian200 View Post
    I was just thinking about how many people believe that it is possible to know something in a objective manner. However, this is not true, not even of perceptions. Everything we can know or express to ourselves inherently has a subjective element, because it is processed through subjective filters...

    ...So how can anything truly be objective? It can't. Why do some people claim that they can say something objectively, when all knowledge is subjective?

    What does this mean?
    You are correct in saying that "Everything we can know or express to ourselves inherently has a subjective element...," because knowledge and expression are functions of perception, and perception is necessarily subjective.

    However, our understanding that we cannot remove the filter of subjectivity through which we perceive reality does not by any means prove that there is no objective reality...it just means that, conceptually, we can't get there from here.

    One might be tempted to say "But an objective reality that is impossible to perceive is utterly useless to us; it's the same as it not existing at all, for all practical purposes." To believe so would be a great mistake.

  4. #24
    Oberon
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    Quote Originally Posted by ygolo View Post
    Nocturne pretty much said what I wanted to say regarding this, and used words I wouldn't have thought of.

    But I am going to pick a small nit regarding the example of 2+2=4 in base 10 while 2+2=10 in base 4.

    These do not constitute different subjective perceptions of reality, but simply slightly different ways of writing mathematical facts. It is like saying II+II=IV in Roman numerals. They are simply different notations. 10 in base 4 is 4 in base 10, not "ten" (in a way independent of base).

    The deception occurs because "2" is used in both notational systems, but base 4 only has symbols 0,1,2, abd 3.
    An applicant for an accounting position at a Fortune 500 company was once asked the question "What is two plus two?"

    His answer was "How much do you want it to be?"

    He got the job.

  5. #25
    Oberon
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    Quote Originally Posted by Jack Red View Post
    And thank god I found you people. I was starting to feel like I was going insane.
    Having found us by NO means guarantees that you are not going insane. In fact, it may stack the odds against you.


  6. #26
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
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    Quote Originally Posted by ygolo View Post
    Nocturne pretty much said what I wanted to say regarding this, and used words I wouldn't have thought of.

    But I am going to pick a small nit regarding the example of 2+2=4 in base 10 while 2+2=10 in base 4.

    These do not constitute different subjective perceptions of reality, but simply slightly different ways of writing mathematical facts. It is like saying II+II=IV in Roman numerals. They are simply different notations. 10 in base 4 is 4 in base 10, not "ten" (in a way independent of base).

    The deception occurs because "2" is used in both notational systems, but base 4 only has symbols 0,1,2, abd 3.

    It's possible to come up with similar examples that display the original point though. For example 2+2=1 in modulus 3 arithmetic.
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  7. #27

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    Quote Originally Posted by The_Liquid_Laser View Post
    It's possible to come up with similar examples that display the original point though. For example 2+2=1 in modulus 3 arithmetic.
    Again this is a play on symbols. Similar to a play on words, or the logical fallacy of Equivocation

    Here you are using "=", to mean "congruent" rather than the typical meaning of "=" in the arithmetic taught in schools.



    Keep trying, I would like to see someone come up with a legitimately "different math" that isn't base of different premises or logical fallicies.

    Despite the fact that we humans can only really do "human math" (with the augmentation of whatever tools we chose), there is still good reason to call it "universal".

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

  8. #28
    Lex Parsimoniae Xander's Avatar
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    Quote Originally Posted by Maverick View Post
    Maybe, however what is the use of realizing this?

    We still need to build buildings and bridges, create systems, fly aeroplanes, research cures for diseases, ... and for that use it doesn't matter if what we know and our tools are not purely objective. They're sufficiently objective as to be able to be reliable, understandable, reproducible and useful to people who know nothing about each other, live in completely different parts of the world and speak different languages. There is no perfect state of objectivity but there are a number of things that are a hell of a lot less subjective than others.
    I like this line of thinking but I think your missing the point to existentialism and all this jive.

    If what you are given as truth is true then it is truth. Ergo it has no facets, no means to perceive it as anything but true. So why question it? Surely such would be futile and a waste of time.

    However if everything has some element of doubt to it (worrying and irritating as that may be) then you can question it, investigate it and feel justified in doing so. Sure this can lead to the often found depression (overuse of anything is bad mojo) or the inability to construct anything higher than a cup of tea but when used in moderation it can lead you to ask the question which no one else asked but needed asking in order to find the answer.

    Do you not find that many of the systems which you despair of are systems where you can see the things which are wrong but most others cannot? Does it not make sense that the reason for this is that they are accepting some precepts as truth and hence unquestionable? If so then would it not follow that by teaching that all things are questionable you are enabling those people to better question their surroundings (both their physical and mental surroundings) and to see some of those errors which are so blindingly obvious to you?
    Isn't it time for a colourful metaphor?

  9. #29
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
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    Quote Originally Posted by ygolo View Post
    Again this is a play on symbols. Similar to a play on words, or the logical fallacy of Equivocation

    Here you are using "=", to mean "congruent" rather than the typical meaning of "=" in the arithmetic taught in schools.



    Keep trying, I would like to see someone come up with a legitimately "different math" that isn't base of different premises or logical fallicies.

    Despite the fact that we humans can only really do "human math" (with the augmentation of whatever tools we chose), there is still good reason to call it "universal".
    If it's based on different premises then it is "different math". :P One system does not invalidate the other. They are both valid systems.

    It's been about ten years since I've studies rings, grous, and the like, but I believe that it's possible to develop a ring where 2 + 2 = 4 + a, "a" being a non-zero number. It's very possible to change the rules if you want to.
    My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14 - August 14)
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  10. #30

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    Quote Originally Posted by The_Liquid_Laser View Post
    If it's based on different premises then it is "different math". :P One system does not invalidate the other. They are both valid systems.
    Thats what I was getting at. They are both valid objectively. Neither is perceived differently based on the subject.

    Quote Originally Posted by The_Liquid_Laser View Post
    It's been about ten years since I've studies rings, groups, and the like, but I believe that it's possible to develop a ring where 2 + 2 = 4 + a, "a" being a non-zero number. It's very possible to change the rules if you want to.
    Yes. These are based on cosets. You can create divisor/factor rings and groups. But you are not "changing" the rules, you are playing a different game.

    Anyway. I guess we're off-topic a bit.

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

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