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Defining Logic

  1. Oct 12, 2003 #1

    Kerrie

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    For those of us who are still learning and understanding philosophy, can we differentiate logic in the most simple terms?
     
  2. jcsd
  3. Oct 13, 2003 #2
    Differentiate logic from what?
     
  4. Oct 13, 2003 #3
    The most practical and simplistic definition I've so far heard is, "logic makes things better"- Marylin Savant
     
  5. Oct 14, 2003 #4
    Kerrie, did you mean to "define" logic?
     
  6. Oct 14, 2003 #5

    FZ+

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    Formalised reasoning?
     
  7. Oct 14, 2003 #6

    Tom Mattson

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    A good working definition of logic is that it is the set of prescriptive (as opposed to descriptive) laws of reasoning.

    If I may do a little cut-and-paste job from my Logic Notes:

    [?] Is logic the study of the laws of thought?
    That’s too broad. There is plenty of thought that logic is not concerned with. For example, imagining two-headed goats is thought, but the logician does not care about that. We are interested in that particular subset of thought called reasoning

    [?]Ah, so logic is the study of the laws of reasoning then, right?
    Still too broad, and the root of the problem lies in the two uses of the word “law”. Laws can be either descriptive or prescriptive. A descriptive law is a statement of how something is done, as in the laws of nature. They cannot be broken or repealed. On the other hand, a prescriptive law is a statement of how something should be done, as in the laws set forth by a legislature. They can be broken and changed. The study of the descriptive laws of reason (how people do, in fact, reason) is not logic, but psychology. But the study of the prescriptive laws of reason (how people ought to reason) is logic.

    [?]So, we are interested in the latter—the prescriptive laws of reasoning.
    Correct. That will be our definition of logic throughout this study
     
  8. Oct 14, 2003 #7

    Kerrie

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    so who or what determines "should" be done? or how it should be done?
     
  9. Oct 15, 2003 #8

    Tom Mattson

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    Keeping to the simple example of a 2-valued logic (T and F), we have a variety of logical inferences that can always be trusted, as well as some that cannot be trusted. Logical forms can be shown to be either valid or invalid by Venn diagrams (in syllogistic logic) or truth tables (in propositional logic). That is, we can determine with certainty whether a logical form always leads from true premises to a true conclusion. If it does then it is valid, and if not then it is invalid.

    Note that establishing validity does not tell us whether or not the premises are actually true, it merely tells us that if the premises are true, then the conclusion is also true.

    From the Stanford Encyclopedia of Philosophy, in an article called Logical Form, we find the following discussion (color emphasis mine):

    There's a lot more there, but I think the question is answered with what I presented here. The validity of some reasoning and the invalidity of others is determined by philosophers and mathematicians (this is where philosophy and math overlap) who find such "impeccable inferrences".
     
  10. Oct 16, 2003 #9
    Philisophically speaking (ha I love the length of that word)

    Some one once said to me

    "There is a logic for everything and everything has a logic"

    "There is a science for everything and everything has a science"

    The logic I love the most is the logic of music, it is so infinite in it's application, the logic of a performer giving it all, the logic of the audience with tears in their eyes, the logic of rhythm and melodies, counterpoint, harmony, harmonics and discord.

    The logic of what is it? hmmm 72 notes ,just add humanity and wow what a outcome.

    I am sailing....I am sailing....home again ...cross the sea. I am sailing stormy waters to be near you to be free......(Rod Stewart)

    Ha ...i'm going to cry... and i can tell you if you look hard enough you'll find that response quite logical to.
     
  11. Oct 24, 2003 #10
    Are you one given to sesquipedalian extravagance?
     
  12. Oct 24, 2003 #11
    actuallymydictionaryhasbeencensoredhavingallwordsinexcessofonefootinlengthdeletedandsotomakeupforitijustaddafewlettersandalittleextrameaningandwellificanunderstanditthenIassumethatyoucantoo. And if you can't I would suggest you get a dictionary like mine that has been censored, having all words in excess of one foot deleted, and so to make up for it i.......
     
    Last edited by a moderator: Oct 24, 2003
  13. Nov 8, 2003 #12
    in particular:
    this is correct as long as one realizes that one of the premises is that ((A-->B)&A)-->B is true for all statements A and B. or you could say by definition of -->.
     
  14. Nov 8, 2003 #13
    I would say that it is deductive and inductive arguments from previously stated points that theorize the wrong of a system/design, which is not supposed to be based on emotion or whim but is often substituted for those purposes and principles.
     
  15. Nov 8, 2003 #14
    check out http://mathworld.wolfram.com/PropositionalCalculus.html. it gives some axiom schemata for formal logic. i guess most people would say that (11), modus ponens, is the most important one.

    these all seem like whims to me though they don't seem to be based on emotion. however, once you accept those axiom schemata which i could call whims, the theorems that follow from them are not of the whim variety.
     
    Last edited: Nov 8, 2003
  16. Nov 9, 2003 #15
    Re: Re: Defining Logic

    Ok, I see what you mean by the whims of Modus Ponens, but all formal logic has to deal with some level of truth from that given someone. All logic has to be supplied and attributed to axiom schemata's, and axioms help provide information for theories, which in turn could form into laws.

    So in conclusion all logic, could be a form of mental projection of whim and and absolute immplicit reason without a(n) of option of a doubt in their mind? And for that matter wouldn't logic have to have a basis of rule or law with propositional statistics to support that idea?

    You could make a connection and say that logic is extremely parallel to faith, couldn't you in some cases?
     
    Last edited: Nov 9, 2003
  17. Nov 9, 2003 #16
    dictionary.com provides definitions of the word faith, of which, here are two:
    1. Confident belief in the truth, value, or trustworthiness of a person, idea, or thing.
    2. Belief that does not rest on logical proof or material evidence. See Synonyms at belief. See Synonyms at trust.

    axioms do not rest on logical proof but one could say they do rest on material evidence. one who would say they rest on material evidence wouldn't be having faith in those axioms as in the second sense of faith. the first sense of faith makes it seem as though whenever one is confident in the truth of something that faith is involved.

    just for fun, i was wondering what would happen if instead of adopting a definition of if/then, symbolized by A→B, and a definition of and, symbolized by A∧B, and then proving that modus ponens is a tautology, what would happen if we assume the definition of ∧ and that modus ponens is a tautology? would that force the definition of A→B?

    ok, one usually says that A→B is defined by this truth table:
    A B A→B
    T T T
    T F F
    F T T
    F F T.

    but let's leave it open:
    A B A→B
    T T ?
    T F ?
    F T ?
    F F ?

    two assumptions:
    A B A∧B
    T T T
    T F F
    F T F
    F F F

    and that modus ponens is a tautology:
    A B ((A→B)∧A)→B
    T T T
    T F T
    F T T
    F F T.

    using these assumptions, can we solve for the ?'s?

    let's put it together and keep track of the different ?'s with subscripts denoted ?_n:
    A B A→B (A→B)∧A ((A→B)∧A)→B
    T T ?_1 ?_5 T
    T F ?_2 ?_6 T
    F T ?_3 ?_7 T
    F F ?_4 ?_8 T

    by definition of ∧, we already know that ?_7=?_8=F since A is F in those two cases.

    from this truth table, we can derive this, substituting F for ?_7 and ?_8:
    C B C→B
    ?_5 T T
    ?_6 F T
    F T T
    F F T

    we also have this:
    A B A→B
    T T ?_1
    T F ?_2
    F T ?_3
    F F ?_4

    from the table before this, we get ?_3=?_4=T. (thus we can say that vacuous truth must be in place in order for modus ponens to operate, which is nice.)

    from the first table with subscripted question marks, we can turn to the 4th column for info. let me write down some statements:
    ?_5=T iff ?_1=T and
    ?_6=T iff ?_2=T.

    hence ?_5=?_1 and ?_6=?_2. let's repeat the original table including what we know and leaving ?_1 and ?_2 as they are for now:
    A B A→B (A→B)∧A ((A→B)∧A)→B
    T T ?_1 ?_1 T
    T F ?_2 ?_2 T
    F T T F T
    F F T F T.

    there are four possibilities now (a reduction from 28 possibilities):
    ?_1 ?_2
    T T
    T F
    F T
    F F

    i don't see anything wrong with any of these possibilities. i'm not seeing how ?_1 is forced to be T and ?_2 forced to be F... perhaps if we add the assumption that (A→B)→(¬B→¬A) is a tautology then that will force ?_1 to be T and ?_2 to be F...
     
    Last edited: Nov 9, 2003
  18. Nov 9, 2003 #17
    The best way I have found to describe logic -

    Think well and live in harmony with your thoughts.
    Think logically and live consistently. -MP Hall
     
  19. Nov 9, 2003 #18
    Logic attempts reduction of representation for given information.
     
  20. Nov 18, 2003 #19
    Logic cannot be defined.

    Logic to me may be utter rubbish to the insane man in the asylum. What the cheetah sees as logic may be foolish to what we humans believe.

    Hence, I'll say logic is relative. It varies from individual to individual. Why then do you want to define logic?

    But if you insist on defining logic, its simply a set of reasoning which we believe holds true in our context. Thats my opinion.
     
  21. Nov 21, 2003 #20
    I believe logic is something that you gain by daily experience.
     
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