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Thread: Logical Possibility

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    Logical Possibility

    In his 'An Introduction to Philosophical Analysis', John Hospers makes the distinction between three types of 'possibility';

    i) Empirical possibility,

    ii) Technical possibility, and

    iii) Logical possibility

    Unfortunately, much non-philosophical thinking stops at the first two, and sees things only in terms of either empirical and technical possibility.

    However, Philosophy deals in the main with Logical possibility[LP].

    Nietzsche's eternal recurrence of the same could be seen as an example of a LP.

    The 'eternal recurrence' says that events from the past will recur again in the future in exactly the same way, and in exactly the same form, as they did in the past.

    Those who recoil from this notion may not be aware of LP.

    With LP the philosopher is able to open up the world of thought to untold possibilities.

    But LP does not mean that 'anything' is possible, of course; it means that, as long as no self-contradiction is involved in a proposition, then the proposition is a LP.
    In other words, anything 'logical' is possible.

    Hospers argues for example, that time travel is not a LP.
    However, in the process of so doing, he demonstrates that 'the eternal recurrence of the same' is a LP.

    "It is logically possible that history might suddenly start repeating itself: that on January 1, 2006, all of our modern buildings & machinery would disappear & we would find ourselves among sand & pyramids & the world of 3, 000 BC.
    This repetition is logically possible [though not empirically, to the best of our present knowledge], but it would be a repetition with a difference: the first time you were there [3,000 BC], you weren't there; & the second time [AD 2006], you were.
    This would not be a case of literally going back in time to 3,000 BC: it would be a case of history repeating itself [with a slight difference], with the world of 2006".
    [Hospers, ib., page 173-, slightly adapted]

    So feel free to anounce your logical possibilities here in the Philosophy forums!

    Wiki article;
    http://en.wikipedia.org/wiki/Logical_possibility
    Last edited by Moody; Monday, October 2nd, 2006 at 11:08 AM. Reason: left out the word 'not' - slight mistake!
    Why are there beings at all, & why not rather nothing?
    [Leibniz/Heidegger]

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    AW: Logical Possibility

    Is it logically possible that 5+5=11?

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    AW: Logical Possibility

    Quote Originally Posted by Pervitinist View Post
    Is it logically possible that 5+5=11?
    Of course it is! All we need to do is move away from a decimal system and take away a random number except 1 and 5
    Ceterum censeo Iudaeam esse delendam.

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    AW: Logical Possibility

    Quote Originally Posted by Illuminatus View Post
    Of course it is! All we need to do is move away from a decimal system and take away a random number except 1 and 5
    Good point. But what if we keep the decimal system?

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    AW: Logical Possibility

    Quote Originally Posted by Pervitinist View Post
    Good point. But what if we keep the decimal system?
    Then we just change the order of the numbers
    Ceterum censeo Iudaeam esse delendam.

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    AW: Logical Possibility

    Quote Originally Posted by Illuminatus View Post
    Then we just change the order of the numbers
    LOL! Well, let me put it differently: It is empirically impossible (at least without taking psychedelic drugs) to add five apples to five apples and get eleven apples. But is it also logically impossible? If so, why?

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    AW: Logical Possibility

    There are various ways:
    For example one apple could suddenly due to a anomalia in the space-time-continuum or somebody completly unrelated throws an apple to your apples etc
    Ceterum censeo Iudaeam esse delendam.

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    Re: AW: Logical Possibility

    Quote Originally Posted by Pervitinist View Post
    LOL! Well, let me put it differently: It is empirically impossible (at least without taking psychedelic drugs) to add five apples to five apples and get eleven apples. But is it also logically impossible? If so, why?
    No, it is not logically possible. Logically possible is whatever can exist without logical contradiction. Thus, it's logically possible that you could have wings tomorrow and be able to fly, but it's not logically possible that 5+5=11 or that you are omnipotent and omniscient at the same time.
    .

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    Re: Logical Possibility

    1.) It is logically possible that we live in the best of all possible worlds.

    2.) It is logically possible that the world, as we know it, is the creation of a consciousness beyond our own and governs what we believe to be our own consciousness.

    3.) It is logically possible that this consciousness that governs our consciousness imposes restrictions upon the world as we know it, such that logical contradiction exists as logically possible in a world in which it is so, without us being able to say that x, which is a logical contradiction in the world as we know it, is a logical possibility in the world as it ontologically is; as the world as we know it is limited by the imposition of a higher governing consciousness.

    The rub:

    The governing consciousness imposing restrictions on our consciousness such that we unable to make logically possible a logical contradictory, limits our knowledge of the extent to which logical possibility applies to this world, which might be the best of all possible worlds, is metaphysically contingent upon access to what lay beyond the consciousness which governs our own: a world is possible in which logical contradiction is an illusion; it may be our own.

    This does not involve a contradiction.

    A particular, and more practical, illustration of uncertainty as a constant as seen in Quantum Mechanics:

    http://plato.stanford.edu/entries/qt-uncertainty/
    "...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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    AW: Re: Logical Possibility

    Thanks for this enlightening line of argument!

    Quote Originally Posted by Suut View Post
    The governing consciousness imposing restrictions on our consciousness such that we unable to make logically possible a logical contradictory, limits our knowledge of the extent to which logical possibility applies to this world, which might be the best of all possible worlds, is metaphysically contingent upon access to what lay beyond the consciousness which governs our own: a world is possible in which logical contradiction is an illusion; it may be our own.

    This does not involve a contradiction.
    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?

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