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Definition fo Logic!

  1. Jun 3, 2009 #1

    tgt

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    How is this definition ( I made up):

    Logic is the deductive (as opposed to empirical) science of all possible worlds.
     
  2. jcsd
  3. Jun 3, 2009 #2
    That definition is pretty murky.
     
  4. Jun 3, 2009 #3
    How about checking out some real definitions instead making things up?:

    "The analysis, without regard to meaning or context, of the patterns of reasoning by which conclusions are validly derived from sets of premises."

    Borowski and Borwein, Harper Collins Dictionary of Mathematics (1991).

    There are other more specific definitions citing axioms and rules of inference, all of them considerably better than yours
     
  5. Jun 3, 2009 #4

    tgt

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    Well, just say logic wasn't invented then I'd probably be interested to investigate (create) a field that has the definition that I gave. It's a first definition which usually is intuitive.
     
  6. Jun 3, 2009 #5
    Well, your definition describes aspects of the current state of theoretical physics. I suggest you investigate the Many Worlds interpretation of quantum mechanics.
     
  7. Jun 4, 2009 #6

    HallsofIvy

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    What is your definition of "science". In the usual definition, "a study that follows the scientific method", logic is not a science at all because it does not involve experimentation on the real world.
     
  8. Jun 4, 2009 #7

    tgt

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    From a modern view point, the terminologies have all been mixed up. But pretend it's 400BC before anything that resemble logic has been thought up of. Back in those days science and maths were closely linked and there wasn't the scientific method.
     
  9. Jun 4, 2009 #8
    What you're describing is the "natural philosophy" of classical ancient Greece. This was a mix of mathematics and logic with a kind of purely observational version of what we call science. Before 300 BC Aristotle had laid down a formal logic. Modern science dates from around the 16th century in western Europe. So is the pre-Aristotle world your ideal?

    I have a lot of respect for Pythagoras, Euclid, Plato, Aristotle and other outstanding thinkers of that time and place, but we have clearly progressed since then (although it wasn't a steady climb, at least in the West). It seems you crave an earlier simpler time. Better ignore my last suggestion and stay away from quantum mechanics and its various interpretations.

    EDIT: By the way, don't you think that mathematics and science are closely linked now?
     
    Last edited: Jun 5, 2009
  10. Jun 4, 2009 #9

    tgt

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    Well, if I was to put myself in that period which is without a lot of any theoretical maths then it would be interesting to work something in the area of the definition in the OP. Just to get some undisputable truth.



    They are closely connected but not as close as the ancients had thought.
     
  11. Jun 4, 2009 #10
    Indisputable truth?? You're winging off into deep metaphysical philosophy now. What makes you think these guys were any closer (to whatever your idea is) than we are now?

    EDIT: Would you agree that 2+3=5 at least, is a bit of indisputable truth?
     
    Last edited: Jun 4, 2009
  12. Jun 5, 2009 #11

    tgt

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    Probably indisputable truth in not just mathematics but other areas. That is why my definition has an empirical feel to it even though it shouldn't have anything to do with the world. I was trying to define something that includes more then just maths. It is a bit philosophical which isn't surprising as most philosophers enjoy logic more than maths.
     
  13. Jun 5, 2009 #12
    Your OP offers a definition of logic as a science which is strictly deductive (not empirical) and deals with "all possible worlds". Don't you see all the contradictions here? Halls of Ivy already shot down your view that logic is a science. If it is strictly deductive, how can it have an "empirical" feel? And what in heaven's name does "all possible worlds" mean if you say it shouldn't have anything to do with the (any?) world. What are the possible worlds? Observable worlds? A multiverse? Braneworlds? Parallel universes? Everything the human mind can conceive (EHMCC)? EHMCC + everything else?

    I've read some of your other posts and you seem to know something about math and logic. Are you simply rebelling against rationality as we know it?

    EDIT: Consider the definition I quoted: "The analysis, without regard to meaning or context,.....". Do you interpret this to mean "all possible worlds"? If so, we first replace "all possible worlds" with this fragment, remove the word "science" and any mention of "empirical" from your definition followed by some reference to valid reasoning from premises to a conclusion and "your" definition is spot on!
     
    Last edited: Jun 5, 2009
  14. Jun 5, 2009 #13

    tgt

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    I've just made a very naive definition with the view point of someone in 400BC would have. Would it be wrong to say that at that time science = maths? But obviously the word science and maths would have had different meanings as well at that time. Certainly the definition of science would be very different to the definition we would have now.
     
  15. Jun 5, 2009 #14
    You just contradicted yourself again. The great thinkers of ancient Greece were not naive. They were brilliant. They just didn't have the level of knowledge (or the technology) we have. Earlier you indicated they would be closer to "indisputable truths" than we are.

    I'm still interested in your answer to my direct question to you: Do you consider your reference to "all possible worlds" to be equivalent to "..without regard to meaning or context,..." ?
     
  16. Jun 5, 2009 #15

    honestrosewater

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    The objection that non-empirical sciences do not exist seemed to be precluded by the OP's qualification "deductive (as opposed to empirical) science". I think a more general definition of a science along the lines of a systematic investigation and description, perhaps with certain requirements concerning, e.g., consistency, precision, or repetition, would be acceptable. Of course, empirical sciences still use deductive reasoning, so the distinction between deductive and empirical sciences could use clarification.

    Logic does investigate and describe classes of all possible worlds using deductive methods, though I'm not sure this covers everything it does. A possible world is an abstract object. It doesn't have to be interpreted as or modeled by any physical object. I don't see what the problem is. Logic also involves the creation of theories and models and the study of their relationships. All the same can be said of math, so I don't see how logic could be considered the (one and only) science of all possible worlds. Math seems to include logic more than logic includes math, especially if you only consider the deductive parts of logic.

    Still, any definition that short is not likely to be helpful because of a lack of precision or comprehensiveness. The field of logic is the study of logical objects in logical ways. As a human endeavor, what count as logical objects or logical ways are not static or precisely predefined.

    What is the purpose of this definition anyway?
     
  17. Jun 6, 2009 #16

    tgt

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    They are so not naive that they killed someone because that someone discovered that irrational numbers come up naturally in mathematics!

    I didn't indicate at all that they would be closer to "indisputable truths" than we are. I said it comparing to the other knowledge at the time.

    I'd say all possible worlds with respect to the intuition of this world. One example would be that things either is or is not. No in betweens or anything. Hence it's not as broad as some modern definitions. This would probably be what the ancients thought all possible worlds to mean.
     
  18. Jun 6, 2009 #17

    tgt

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  19. Jun 6, 2009 #18

    honestrosewater

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    Depends on how I defined them and what criteria I was using to categorize them. I don't know all of the options, so I'm not sure which, if any, I would prefer. Are you attempting a partition? Do you know whether it is possible?

    I don't even know what I would try to categorize. Trying to categorize human activities looks way too complicated. Trying to categorize general objects doesn't seem to get anywhere since there can be more than one way to interpret the 'same' object. Perhaps I would try to interpret the fields as computers.

    Mathematical logic is not considered metamathematics by everyone. This thread has already shown that these things are not agreed upon.
     
  20. Jun 6, 2009 #19
    Yeah, it really depends on what you're focusing on. If by "mathematical logic" you mean the study of the kinds of structures found in logic by mathematical means for their own sake (like model theory), then that's a branch of mathematics. Otoh, if we study the structures because they model valid inferences, then we're doing logic.
     
  21. Jun 6, 2009 #20
    There are a number of logics for a number of 'worlds'. Modal logic, with its possibility and necessity operators has its particular applications. Ditto for quantum logic(s). These logics have a different structure than 'classical logic'. I already described the special structure of modal logic in another thread in response to a post of yours. Quantum logic has a different structure altogether. (I may be wrong, but I believe (P^notP) is true is some versions).

    If you mean logic in a very general way, I agree (maybe). But just what is this very general logic? I believe the definition I quoted in post 3 of this thread is as good as any. It seems that this very general logic should be definable, otherwise it's not..well, very logical is it?
     
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