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The Meaningfulness of Logic

  1. Nov 2, 2007 #1
    I've been thinking about if logic is meaningful and if so, what makes logic meaningful. Or more precisely, what makes the assertion that logic is meaningless meaningless. Do you require logic to question the validity of logic or attempt to establish its invalidity (because otherwise words, prepositions etc. would be useless)? Or is that the result of the a priori adaptation of the meaningfulness of logic? If it requires logic to question the validity of logic, then that is an internal contradiction?
     
  2. jcsd
  3. Nov 3, 2007 #2
    But why would you ask if logic is meaningless to begin with?
    That question implores the person to think up a reason for it being meaningless.
    I think the answer to your question would become evident if you could find a reason for logic to be meaningless, but you can't so the question is meaningless.
     
  4. Nov 3, 2007 #3
    For something to be meaningful, it must have a purpose. The purpose of logic is to keep consistency. Without logic, things would be inconsistent. Therefore, If you need or want consistency, logic is required.

    Also, I am new here. =]
     
  5. Nov 3, 2007 #4
    Logic is simply a tool used to acquire a (self-)consistant view of the world. It is a useful tool, but to try to impart more `meaning' to it than that makes no more sense than trying to impart `meaning' to a hammer. They are both simply tools to be used to achieve a goal.
     
  6. Nov 5, 2007 #5
    I think that we use symbolic logic in an attempt to describe something inherent in reality that makes symbolic logic useful. Why is symbolic logic "useful"? It is because is help explain reality.
     
  7. Nov 7, 2007 #6

    jim mcnamara

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    FWIW - way back when I taught college we had a visiting linguist for a semester. Interesting guy. His specialty was Native American languages and logic systems.

    It turns out, according to him, that syllogisms could not exist and were illogical in two Northwest NA languages that he knew well. Since I'm acquainted with some NA languages, it sounded at least remotely plausible. Some NA languages have concepts that are close to impossible for non-speakers to get. Some phonemes as well.

    Anyway, plausible or not it raises the question: to what extent is our logic an artifact of language rather than something that is innate to the universe? Or would you prefer to dismiss the concept and say that the languages he cited were an aberration in the human "circle of reason"?

    Alonzo Church proved that Peano arithmetic was undecidable - meaning that following the axioms of Peano arithmetic did not allow for an algorithmically-derived answer for every all questions. This "no syllogism thing" is analogous in my opinion - you have a set of axioms, and a problem. The result in some circumstances is undecidable.

    YMMV.
     
  8. Nov 7, 2007 #7

    Hurkyl

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    Well, formal logic has its own language, and in principle, all logic would be done in that language. People use natural language simply because it's more familiar and more expedient. (And, of course, there are the people who never learned the formal stuff, which leads to unfortunate problems)
     
  9. Nov 7, 2007 #8

    jim mcnamara

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    You are exactly correct - and with first-order logic (if memory serves) Church proved that not all problems posed in first-order logic "semantics" are decidable. Is there a corollary that says 'all problems that exist are not able to be formed or asked'?

    The no syllogism thing limits the language, I think, in the not able to be formed context.
     
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