Can You Prove Paradox Exists?

Discussion in 'General Philosophy' started by steampunk, May 10, 2012.

  1. steampunk Registered Senior Member

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    Can you prove that paradox exists?

    I think this is impossible. But you can try if you like. I will try to argue that you are just confused. Let's go.
     
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  3. Epictetus here & now Registered Senior Member

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    Paradox -noun
    1. a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.
    2. a self-contradictory and false proposition.
    3. any person, thing, or situation exhibiting an apparently contradictory nature.
    4. an opinion or statement contrary to commonly accepted opinion.(http://dictionary.reference.com/browse/paradox)

    Since a paradox is merely an abstract notion, a statement about something, then it exists only in the same way any abstract idea can be said to exist.

    Marriage, for instance, is merely an abstract notion; it has no physical presence or form, but would you say that marriage does not exist? All right? Now ask your wife!
     
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  5. Emil Valued Senior Member

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    A paradox is a statement or group of statements that lead to a contradiction or a situation which (if true) defies logic or reason, similar to circular reasoning. (http://en.wikipedia.org/wiki/Paradox)

    I do not think a paradox can be proved .
    Just as you cannot prove a self-evidence.
     
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  7. steampunk Registered Senior Member

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    Well what about Zeno's paradox's, which Aristotle points out in this quote:

    Another way a person could say this same paradox:

    If you turn a page half way, then cut the remaining distance in half and repeat, you can see that there are an infinite amount of points existing between any two points. So, how is it that one can ever turn a page fully if one must pass an infinite number of points?

    Aristolean physics creates such a paradox, but Newtonian Physics clears it up. Would anyone like to argue for Aristotle? I will argue for Newton.

    But, we don't have to argue Zeno if you don't want to. We can argue any paradox.
     
  8. Rav Valued Senior Member

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    In the end I don't really think that there is such a thing as a paradoxical reality. Whenever we encounter something that looks like such, it's either because we are misunderstanding it, or because it's fiction.
     
  9. Emil Valued Senior Member

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    Prove that 3 is not greater than 5.
     
  10. Buddha12 Valued Senior Member

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    Freedom of speech.

    If I say something that is a threat to someone becuse I do not care for them I'm put into jail someimes for saying what I think. Is this not a paradox of freedom of speech?:shrug:
     
  11. Rav Valued Senior Member

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    is less than:

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    It doesn't matter what symbols we use to represent an amount of apples (or anything else), it's always true in reality.
     
  12. steampunk Registered Senior Member

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    We could look at this two different ways:

    1. There are no exceptions to Freedom of Expression

    2. There are exceptions to Freedom of Expression

    These are examples of some real world exceptions :
    http://en.wikipedia.org/wiki/Censorship_in_the_United_States

    If there are no exceptions, we can say you have the freedom of expression no matter what and all expression is protected. Don't mix this with you also have the responsibly for effects of how expression is naturally received by others. If you confused these two, you are in the illusion of a paradox. So, if you hurt or significantly threaten a person who is innocent, you can do this freely, but you may incite them to defend themselves, and therefore you may be hurt yourself or charged with a crime.

    If there are exceptions, then the reason for the exception is that the very nature of the act is not in the category freedom. When harming or making a significant threat of harm toward a person, you take their Freedom away, buy forcing them have to live in defense, which means they cannot express themselves in a way of their choice otherwise. Your expression is not free in nature if it takes freedom from another. So, threats do not fit the category free and therefore is not free expression. Confusing non-free expression with free expression by not categorizing them properly creates the illusion of a paradox.
     
    Last edited: May 11, 2012
  13. Emil Valued Senior Member

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    The question is if you can prove/demonstrate a self-evidence/axiom or a paradox which contradicts a self-evidence/axiom.
     
    Last edited: May 10, 2012
  14. Buddha12 Valued Senior Member

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    But threats are just a form of free speech and does not take away any others rights because they can and do defend themselves if they so choose with their own freedom of saying what they think. So if I say that a certain product is a bad thing to buy it could take away that products ability to sell on the market which would be the same as threatening someone with a lawsuit or other ramification. Again freedom of speech is something that is a paradox as we can't put limits upon it for then it wouldn't be free speech any longer but another paradox that we make.
     
  15. Yazata Valued Senior Member

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    5,902
    The English word 'paradox' is derived from the Greek for 'contrary to opinion'.

    Here are some of the ways that the word 'paradox' is used. (I'm more or less paraphrasing a few highlights from the 'Oxford Guide to Philosophy' pp 678-681, especially the remarks by James Cargile of the U. of Virginia, author of 'Paradoxes' (1979 Cambridge U. Press).

    1. 'Paradox' as a statement contradicting received opinion. Hence Socrates' "paradoxical" assertion that nobody ever knowingly does wrong, which contradicts everyone's opinion that people often knowingly do wrong. In this case, 'paradox' consists of a challenge to a widely held opinion.

    2. 'Paradox' as a Kantian-style 'antinomy'. Now the emphasis isn't on the statement that conflicts, but on the conflict itself. This kind of paradoxicality arises when two or more propositions are each considered logically unobjectionable in themselves, may be considered well founded and true, and perhaps even foundational to one's world view, but arguably are inconsistent with one another.

    3. 'Paradox' as vagueness or contradiction in criteria for classification. In scientific taxonomies we sometimes encounter 'paradoxical' examples that resist classification, not because we lack sufficient information about them, but because they possess characteristics that would place them into more than one taxonomical category.

    4. And there are the logical 'paradoxes'. These may in turn (following writers like P.F. Ramsey) divide into more than one subclass.

    4a. Logical paradoxes per-se, which are paradoxes of logical form. They would exist in a mathematical or formal logical system even when all of its constants and variables are uninterpreted. These might include Russell's paradox, the Burali-Forti paradox, and so on.

    4b. Semantic paradoxes, which depend on how we interpret the constants and variables. This subgroup would include the famous Liar, Berry's paradox and so on. Given a particular logical form, one interpretation of the variables might turn out to be paradoxical, while another isn't.

    Looking at the Liar, the difficulty isn't that the Liar's assertion (I am lying) contradicts any foundational beliefs of received opinion. (It's a seemingly unexceptional statement.) It's the more properly logical problem that it can't consistently be assigned a T or F truth-value. The difficulty arises from adopting a commonly accepted semantic interpretation of what a proposition (in this case "I am lying") means, and then applying the common principles of logic to it.

    Cargile notes that one of the first authors to discuss the Liar, Eubulides of Megara, used it to draw a very strong conclusion that rationalism fails, arguing that the basic logical standards of reasoning themselves are inconsistent. Few authors would agree with that today, but they aren't all agreed on precisely why it isn't so.
     
    Last edited: May 10, 2012
  16. wynn ˙ Valued Senior Member

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    There can be no real paradox because as we reason, we set out with the conviction that everything can and should be explainable, otherwise, we couldn't reason at all. This is then a self-fulfilling determination that leads us to understand things.
     
  17. Emil Valued Senior Member

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    I have the same opinion.
     
  18. Emil Valued Senior Member

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    The liar paradox is the statement "this sentence is false."

    The statement "this sentence is false" , can be written
    "This Sentence=false" and become:
    "This sentence" = "lie" .
    If we write "lie" as Boolean mathematics then
    "lie" = NOT "this sentence" (so "false" = "lie" = NOT "This Sentence")
    And the equation:
    "this sentence=false", become:
    "this sentence" = NOT "this sentence", what is an absurdity (x = NOT x)
     
  19. Cyperium I'm always me Valued Senior Member

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    I've often wondered how the universe could exist with all of the options it has without creating even a single paradox. I think this is in favor of a very simple principle that governs it all, that just can't be broken in any way conceivable no matter how the principle is applied.
     
  20. steampunk Registered Senior Member

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    Free is in the category of self-determinism. Threats are in the category of stopping self-determinism or significantly limiting it. Threats principally imply the taking of self-determinism. Confusing non-free ideas with free ideas implies a false paradox. Threats may fit in the category speech, but they are not in the category free. Therefore, threats can in no way be free speech.
     
  21. steampunk Registered Senior Member

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    How would you explain one object being in two different locations?
     
  22. Buddha12 Valued Senior Member

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    If I threaten someone with jail if they bother me for threatening me then I'm having freedom of speech just as much as the person doing the threats.


    What about light? It is shown to be a wave and a particle at the same time, how can that be other than a paradox?
     
  23. steampunk Registered Senior Member

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    I think the assumption is based upon the false assumption that energy is destroyed. When you apply the operator not, in a non-existence way, it subtly implies you are destroying that which it negates.

    Instead if you use affirmative reasoning and avoid negation's tricky violation of physics property, you would say false represents an order that is a subjective correlation vs. a objective correlation which is empirical.

    subject correlation - idea represents only a mental organisation of ideas, where those ideas are composed of things that have all physical correlations.

    objective correlation - idea that represents a mental organisation of ideas that has a physical correlation with world outside the mind

    'this sentence' can tentatively be stipulated as representing something that is only a subjective correlation. 'false' is a subjective correlation vs. the confusing 'is not a objective correlation'.

    If you talk about where things are, instead of saying they don't exist, it begins to clear up such things. Identify proximity and space vs. saying 'it's not there', say where it is and what it is vs. what it is not or where it is not.
     
    Last edited: May 11, 2012

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