The Illusory Paradox: A Formal Analysis of Nonduality and Duality

Discussion in 'Advanced Applied Math' started by Earl, Sep 4, 2023.

  1. Earl

    Earl

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    The Illusory Paradox: A Formal Analysis of Nonduality and Duality


    Abstract

    The metaphysical debate between nondual and dual perspectives has surfaced an apparent paradox that has remained unresolved in previous philosophical arguments. Through formal symbolic logic, this paper demonstrates that the alleged paradox stems solely from mutually contradictory assumptions, revealing it to be an illusion requiring no solution. Resolving this illusion of paradox illuminates the necessity of questioning assumptions and employing analytic methods to evaluate absolute claims rationally.


    Introduction

    The metaphysical debate between nondual and dual conceptions of reality has spanned philosophies and centuries (Smith, 1999; Jones, 2005). Nondual schools assert an undifferentiated unity as the fundamental nature of existence, while dualists like Descartes claim apparently irreducible divisions such as subject/object and mind/matter. At the heart of this debate lies an apparent paradox concerning the very possibility of nonduality given the manifest perception of separation and multiplicity. Specifically, dualism claims the self-evident experience of dualities renders nondualism an impossibility, yet nonduality denies any separation or division as mere illusion (Parsons, 2019). This seeming mutual exclusivity creates a conceptual tension that has resisted definitive resolution (Grier, 2007). Prior philosophical attempts at reconciling this central paradox through rhetorical arguments have failed to achieve consensus, with thinkers falling substantially into one metaphysical camp or the other (Albahari, 2009). This paper contends that formal symbolic logic provides the means to break the impasse by demonstrating the supposed paradox as merely an illusion stemming from contradictory premises, rather than requiring harmonization or choice between competing perspectives. By elucidating the precise assumptions underlying the paradox through formal abstraction and unpacking their logical relationships, the analysis reveals their mutual incoherence and thereby dissolves the necessity of solving an apparent dilemma that under scrutiny reveals no actual paradox at all.


    Symbolic Logic Formulation

    To rigorously assess this scenario, nonduality and duality can be formulated as formal logic propositions:


    Let A = "Reality is nondual"

    Let B = "Duality exists"


    In propositional logic, negation is represented by the ¬ symbol:

    ¬A = "Reality is not nondual (is dual)"
    ¬B = "Duality does not exist"


    First, the seeming paradox arises through the conjunction of:

    A∧¬B

    Which asserts nonduality is true AND duality does not exist. But this contradicts the very definitions, creating incoherence.

    The alternative conjunction:

    ¬A∧B

    Asserts nonduality is false AND duality exists. This is also incoherent, violating the law of non-contradiction by affirming two mutually exclusive claims.

    Any conjunction of A and ¬B or their negations will result in a contradictory premise. From here, various apparent paradoxes can be derived, such as:

    ¬A∧B → ¬B

    But this relies upon an inherently contradictory premise.

    All such derivations reveal nothing more than the incoherence embedded within contradictory premises. No actual logical paradox exists wherein a true dilemma requires solution. The central "paradox" between nonduality and duality dissolves under formal analysis, exposing the illusion stemming from false assumptions and conflated levels of discourse.
     
    Earl, Sep 4, 2023
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  2. Earl

    conway

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    It is beyond doubt that duality exist...

    up/down...positive/negative...etc...

    therefore non-duality most also exist, as it is the opposite of duality.

    The assumption that mathematics, or Boolean algebra can solve all things...is what is false.

    Consider the nature of Infinity. Many paradoxes arise from it. This does not mean that Infinity does not exist.

    Lastly....paradoxes only exist from a "limited perspective" of the problem given. Given a perfect perceptive no paradoxes exist.

    Consider the concept of LOVE. It is the greatest of all things. Yet mathematics cannot touch it or describe it. Clearly it exist....I am not talking about oxytocin. Consider....

    Does dopamine exist...therefore I am happy. Or am I happy therefore dopamine exist.

    Mathematicians MUST accept, that there are truths that mathematics cannot define, or explain.

    Thus I am a philosopher...not a mathematician.
     
    conway, Dec 15, 2023
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  3. Earl

    HallsofIvy

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    Mathematicians KNOW what mathematics IS.
    Therefore they do NOT expect everything to be mathmatics or to be able to define everything in term of mathematics.
     
    HallsofIvy, Jan 5, 2024
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    e.jane.aran and conway like this.
  4. Earl

    conway

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    So you agree...no paradox exists here. Nor can mathematics deal with this concept. Just like they cannot deal with the concept of love.

    Thank you for your continuing debate. It is very much appreciated!
     
    conway, Jan 5, 2024
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  5. Earl

    e.jane.aran

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    No, Halls was saying that your alleged conflict does not in fact exist: No mathematician thinks that all of existence can be reduced to mathematical theorems.

    And it's insulting of you, frankly, to say that mathematicians are incapable of love, or that the concept of love somehow drives us insane.
     
    e.jane.aran, Jan 5, 2024
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  6. Earl

    conway

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    Perhaps that was Halls point. In any case I did not say mathematicians are incapable of love. Or that the concept drives you insane.

    I said mathematics cannot define it. It cannot touch it. You are reading to fast, and getting viscous.

    Yet I will do my best to learn to love you!

    Your intelligence is greatly appreciated.
     
    conway, Jan 5, 2024
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  7. Earl

    e.jane.aran

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    Then what did you mean, specifically, by the following?
    Then you stated:
    I wasn't reading "to[sic] fast". Quite to the contrary, I read deliberatively, and responded directly.

    I have no idea what you mean when you say that I am "having a thick, sticky consistency between solid and liquid; having a high viscosity". Is this a way of saying that I'm stupid ("thick")?
     
    e.jane.aran, Jan 6, 2024
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    conway likes this.
  8. Earl

    conway

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    "They" being mathematicians...cannot use math to define love. I meant to spell vicious. Thank you for continuing to give me the opportunity to better myself, and my own concept of love.

    If you truly wish to be mean...just ignore me.

    Thank your for your time.
     
    conway, Jan 6, 2024
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