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Thread: Logical Possibility

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    Re: AW: Re: Logical Possibility

    Quote Originally Posted by Pervitinist View Post
    ...


    To draw a conclusion for my question whether it is logically possible that 5+5=11:

    Since it is logically possible that what we hold to be logically possible is the outcome of a higher consciousness - or let's be traditional and call it a Cartesian genius malignus - restricting our epistemic access to the realm of actual logical possibilities, the claim that it is logically impossible that 5+5=11 is logically possible is unfounded.

    But does that mean that it is logically possible that 5+5=11?

    We can't make this claim either, because in order to do so we would have to exclude the logical possibility that e.g. the genius malignus G that restricts our access to the realm of logical possibilities might himself be subjected to another genius malignus G* restricting G's access to the realm of logical possibilities.

    As long as the logical possibility of G being deceived by G* cannot be excluded, G might be wrong in thinking that he is deceiving us about the logical possibility of 5+5=11.

    So, provided that there is no third genius malignus G** fooling around with G* - our conviction that it is logically impossible that 5+5=11 might be not only

    (a) induced by the genius malignus G
    but also
    (b) true due to G's being misled by G*.
    Conclusion:

    (1) We cannot positively claim that 5+5=11 is logically impossible because we cannot exclude the logical possibility of being misled in our judgement by a genius malignus G.
    (2) We cannot positively claim that 5+5=11 is logically possible because we cannot exclude the logical possibility that G is misled by another genius malignus G*.
    Still,

    (3) We have the strong intuition that 5+5=11 is in some sense impossible (provided that we use the decimal system, the common semantics of mathematical symbols etc.)
    The question is: Is this impossibility logical or merely mathematical?

    Another question is: Does the concept of logical possibility make sense after all in view of skeptical arguments like the ones sketched above or does it rather reduce to some kind of common sense/intuitive or pragmatic possibility?
    This is a great example of the Uncertainty Constant in action.

    With respect to question #1.) The possibility is metaphysically contingent upon access to what genius malignus knows that we do not. There is no contradiction involved in saying that we can--we just don't know how.

    I may be genious malignus. You may be him. However, he may not know that I/you/we are he! (a conundrum...)

    Mathematically, however, it doesn't matter how complex it gets from 1+1: the mathematics behind String Theory still work within the rules, the laws, of the known universe (even though malignus may have exactly the ontological status we have applied to him in this example). Therefore, its mathematical impossibility is, and will remain, that. (Think Newtonian physics/Relativity: math 'works').


    With respect to question #2.) Logical possibility has the leisure to operate in the highest levels of abstraction (ergo its necessity in Traditionalist Metaphysics), as well as the most banal deductions of probability and deduction (e.g. the sun dawned today, it will do so tomorrow): it is both pragmatic and 'useless'.
    "...The moral man is a lower species than the immoral, a weaker species; indeed - he is a type in regard to morality, but not a type in himself; a copy...the measure of his value lies outside him. ... I assess the power of a will by how much resistance, pain, torture it endures and knows how to turn to its advantage; I do not account the evil and painful character of existence a reproach to it, but hope rather that it will one day be more evil and painful than hitherto..." (Nietzsche)

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    Re: Logical Possibility

    Quote Originally Posted by Pervitinist View Post
    Since it is logically possible that what we hold to be logically possible is the outcome of a higher consciousness.
    What is the logical argument for the "logically possible" 'higher consciousness'?
    Why are there beings at all, & why not rather nothing?
    [Leibniz/Heidegger]

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