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  1. #91

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    I would say logic, at least formal logic, is limited in tangible ways.

    1. First and foremost, to use any formal logic, the semantics (the "model" if you will), has to be well defined, and fixed. Note the semantics can be quite complicated, if you want, but simpler semantics are easier to use.

      A lot of times, even people making "logical" arguments, even when using formal means to do it, and even when every premise looks the same, different conclusions can be drawn due to differing semantics.

      Think of it this way, if it'll help. When someone writes a C-compiler with different semantics but the same grammar, very different results are possible from the same program. This is actually a very real problem that programmers face (luckily only in extreme cases). Hardware designers use "synthesizers" (which are basically compilers for hardware) and well as simulators that work on the same language (verilog or VHDL usually). Sometimes the synthesized circuit exhibits different behavior from the circuit input to the synthesizer, because the synthesizer and simulator used semantics that were incompatible.

    2. Formal logic is further limited by the fact that to say anything with substance...that is anything that is not a tautology (and even the truth of tautologies are dependent on the semantics), it needs the use of "axioms" or "postulates" or something of that sort.

    3. There are further limits to the completeness and consistency of formal systems. To put the results of these types of things in simple terms...a formal system that is self-consistent, may not be able to extract all that is true in the real life system it is meant to represent.


    This is not meant to be an exhaustive list by an means. I believe the limits placed on calculating mechanisms of logic, by physics has already been discussed.

    With all that said, the combination of human ingenuity and formal logic has produced the information age, without which we wouldn't be able to have this sort of conversation. Compiler designers come face-to-face with all the limitations of logic I mentioned, but have devised ingenious ways to circumvent these problems for practical cases.

    We have then further used our logical capabilities (enhanced by machines of our creation) to start to decode the very "code" of life.

    Not to say that it was logic alone that achieved these things, but formal logic played very crucial roles.

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  2. #92
    Senior Member Moiety's Avatar
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    Quote Originally Posted by Ragingkatsuki View Post
    I see. But you are looking towards the infinite future.
    I'm just saying logic itself evolves. Just like humans. Logic actually evolves much faster than humans.

    But yes, for me the answer to such an non-contextualized question would always be in infinite terms.

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    Quote Originally Posted by Sytpg View Post
    I'm just saying logic itself evolves. Just like humans. Logic actually evolves much faster than humans.

    But yes, for me the answer to such an non-contextualized question would always be in infinite terms.
    The capability of logic evolves faster than humans do because there is simply not enough man power/computer power/etc to logically process things at a rate which we discover them.

    Logic can reason with pretty much anything that is. Everything has a reason whether it is accepted, known, acknowledged, ignored, etc. Everything is logical, but we dont have the time to logically understand everything.

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    Quote Originally Posted by Ragingkatsuki View Post
    Well I'm not really saying logic is faulty. I'm just saying it could have limits and so we only logically come to a conclusion within those limits. I'm guessing that it's a pretty strange concept to grasp. But anyways, it's interesting to talk about.

    I see. But you are looking towards the infinite future.
    Yes. Actually, had no intention to walk into an argument over semantics. Had more than enough argument to last me a lifetime. If you're asking whether bigger things exists outside of logic, I can only echo an earlier reply: God. Unfortunately, I can't prove his existence, so I must stick to the belief that all things have the potential of being rationally understood.

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    Quote Originally Posted by poki View Post
    The capability of logic evolves faster than humans do because their is simply not enough man power/computer power/etc to logically process things at a rate which we discover them.

    Logic can reason with pretty much anything that is. Everything has a reason whether it is accepted, known, acknowledged, ignored, etc. Everything is logical, but we dont have the time to logically understand everything.
    Yes I mostly agree.

    But I'd really like to stress out the importance of the fact that logic is a human "construct". So in that sense it would always be unlimited. When there's a barrier, you change the rules and introduced new principles to make it make sense again. Like quantum physics.

    For hundreds of years 1+1 = 2, was just that. But then some guy thought it had to be explained to he "constructed" a reason for it.

    Everything may not be logical, but humans will always envision a way in which they might be. That's why logic is not unlimited.

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    Quote Originally Posted by poki View Post
    The capability of logic evolves faster than humans do because there is simply not enough man power/computer power/etc to logically process things at a rate which we discover them.

    Logic can reason with pretty much anything that is. Everything has a reason whether it is accepted, known, acknowledged, ignored, etc. Everything is logical, but we dont have the time to logically understand everything.
    I don't think logic can reason towards an action that is illogical aka purely emotional.

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    Quote Originally Posted by krunchtime View Post
    Yes. Actually, had no intention to walk into an argument over semantics. Had more than enough argument to last me a lifetime. If you're asking whether bigger things exists outside of logic, I can only echo an earlier reply: God. Unfortunately, I can't prove his existence, so I must stick to the belief that all things have the potential of being rationally understood.
    I see. Alright then.

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    Quote Originally Posted by Ragingkatsuki View Post
    I don't think logic can reason towards an action that is illogical aka purely emotional.
    Logic on its own doesn't even have a reason to reason towards an action. You need a person using logic and with a goal, to do that. Even a program needs a goal.

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    Quote Originally Posted by Sytpg View Post
    Logic on its own doesn't even have a reason to reason towards an action.
    So logic is illogical?

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    Quote Originally Posted by Ragingkatsuki View Post
    So logic is illogical?
    Illogical =/= emotional. Is an electrons trajectory illogical? Is psychology not the logical study of emotions?

    And no, logic is not illogical. Logic is a tool, a system. "Action" based on logic is something only a human, or a human constructed program can do.

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