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Syllogism, ,truth value of statements

  1. Jul 9, 2005 #1

    dx2

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    suppose

    all humans r mortal
    socrates is a human
    therefore,socrates is a mortal .........(conclusion)
    assuming the premises r true.

    what exactly is the statement "the premises r true" supposed to mean?
    or what is the meaning of truth?

    how does the conclusion follow from the premises,how can we be definitly sure.
    i suppose its about how mind places things in categories ,but this is too vague.
    i need something definite
    all help will be appreciated.
     
  2. jcsd
  3. Jul 9, 2005 #2
    Are you interested in the semantics of logical deduction? Or more about the nature of truth?

    For logic, there are many sites online that cover the basics... I'll scrounge around and post one here.
     
  4. Jul 10, 2005 #3

    honestrosewater

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    For syllogistic logic, http://www.philosophypages.com/lg/index.htm is good.
    It can mean two things:
    1) The premises are true in the real world;
    2) The premises have been assigned the value 'true'.
    Consider these arguments:

    A) All humans are mortal.
    Socrates is human.
    Therefore, Socrates is mortal.


    B) All pigs can fly.
    Socrates is a pig.
    Therefore, Socrates can fly.


    Notice that (A) and (B) share the same form, but the premises in (B) are not true in the real world, while the premises in (A) are true in real world. Logic is really only concerned with the form of arguments. Form, real world truth, and the distinction between them is precisely defined; You can see http://www.iep.utm.edu/v/val-snd.htm for an explanation. It so happens that if you assign 'true' to the premises in (A) and (B), the rules of syllogistic logic will force you to also assign 'true' to their conclusions. This is how you know for sure whether the conclusion follows from the premises- you just follow the rules of whichever logic you're using.
    If you have more questions that the links above don't answer, just ask. :)
     
  5. Jul 10, 2005 #4

    dx2

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    all men r mortals
    socrates is a man
    therefore socrates is mortal

    the conclusion appears to be so trivial,its already implicit in the premise,and "socrates is a man" this already implies that socrates is whatever a man is.

    so what is the point of expressing arguments in this form,i dont consider this to be reasoning at all.what have i reasoned? all i have done is describe whatever i already assumed in a new form.these r just tricks of the language.
    why r these laws considered so fundamental? i cant seem to understand. all books seem to explain everything else but this.
     
  6. Jul 10, 2005 #5

    honestrosewater

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    Well, first, it's a very simple example. A slightly more complex argument would be:
    If all birds having wings is sufficient for no pigs being able to fly, then Socrates is not human.
    Some pigs have wings and Socrates is human.
    Therefore, all birds have wings and some pigs can fly.

    But this isn't even the tip of the iceberg; Most logic isn't done in English but in some formal language.
    One point of formally analyzing arguments is to determine which arguments are valid according to which rules. You might note the importance of logic to mathematics, computer science, law, science, and philosophy; It plays a crucial role in them all.
    What do you consider reasoning? Can you give an example?
    Which laws do you mean?
     
  7. Jul 10, 2005 #6

    dx2

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    i dont know,i am not sure myself,about any of the questions i asked,i have reached a level where i can no longer understand what i am thinking about,atleast not coherently,but my agony cannot be interpretted in words,how hard may i try,all explanations lack just one thing,

    i will try please help if u can,i would really appreciate that..
    first is regarding:
    all A is B
    all B is C
    there fore all A is C

    first question,,"what is meant by all A is B?"
    my thoughts: A is a set,by set i mean a collection of object and by object i mean anything that can be interpreted by the sense,and so the collection can be about anything. similarly is B. and all A is B what does this mean?
    (1) all members of A are members of B,that is A and B r the same,and by same i mean
    how do u describe same?
    (2) it may also mean that there is a 1-1 correspondance between the members of A and B ,and how to interpret the correspondance is upto us.

    similarly we can interpret the meaning of all B is C


    But maybe i have understood ,how "A is C" then follows,but i need something more precise.i need to understand this in such a way so as to be rid of all doubt,and maths doest help,because i read in maths that these r the rules of inference,no one explains why the rules work,but u have to mould everything to work in accordance to the rules,so math is jus a manipulation of symbols according to some predefined rules.?(abstractly)

    by fundamental i meant the laws of modus pones and its type
    why r they supposed to be the fundamental of everything logical
    or why can every logical argument be thought of having originated from these laws.
    i dont know if u understand what i am trying to ask
    if u have anydoubt please ask,i will be happy to assist u in any way possible.
     
    Last edited: Jul 10, 2005
  8. Jul 11, 2005 #7
    I think thats a great example on your first reply, honestrosewater.

    Truth is relative to the physical world and is subject to perception and belief.
     
  9. Jul 11, 2005 #8

    honestrosewater

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    Okay, first of all, the reason for starting from scratch and building up the whole system very carefully is to avoid the confusion you're experiencing. Logic is just like math in this way, and I think it would help you very much to think of logic as being done just as math is done. You start with a clean slate and introduce your basic, undefined terms. Everything else that you introduce is precisely defined; If you're ever confused about what exactly something is or means, you can just read the definitions. So be sure that you're starting with a clean slate and not mixing in poorly defined terms or concepts along the way.
    You don't have to interpret these things- you define them. For instance, you may start with "collections" and "objects". Take "collection" and "object" as undefined terms. You also have a relationship: "membership". Take "membership" as undefined. You can then start to build some rules and define other relationships, pick out special kinds of objects, etc. Again, just for example, you might say:
    For every object x and every collection C, either x is a member of C or x is not a member of C.
    For every object x and every collection C, it is never the case that x is both a member of C and not a member of C.
    For any collections C and D, if every member of C is also a member of D, then C is a "subcollection" of D.
    For any collections C and D, if C is a subcollection of D and D is a subcollection of C, then C and D are "equal".
    And so on. That's how you need to approach the subject- that's how the subject is approached. So if you want to know what it means for two collections to be equal, you just read the definition.
    Now, back to your example:
    All A is B.
    All B is C.
    Therefore, all A is C.

    This is stated in syllogisitc logic. A, B, and C are called categorical terms. "All A is B" is a categorical proposition. "All A is B. All B is C. Therefore, all A is C." is a categorical syllogism. You can read all about these- their definitions and the relations between them- in the link I gave, http://www.philosophypages.com/lg/index.htm, starting with "Categorical Propositions". It answers the questions you've asked, and there's no point in me repeating it here.
    BTW, you can state the same thing in other logics, you just state it differently.
    It's more complex, but, yes, a part of math is the manipulation of symbols according to predefined rules.
    They aren't, and they can't. It takes a while to explain, but I gave an overview of the process of building a logic here, if you want to check it out.
     
  10. Jul 12, 2005 #9

    honestrosewater

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    Oh, BTW, there are some so-called fundamental laws or principles. They're 'fundamental' in that it makes a big difference whether you accept or deny them; Obviously, in logic, they aren't universal or absolute truths, since you can choose to accept or deny them. (Though there is a related dispute over fundamental logical truths in philosophy.) These laws go by various names, usually the law or principle of noncontradiction, the law or principle of the excluded middle, and the law or principle of bivalence. You can read more about them at http://www.earlham.edu/~peters/courses/logsys/pnc-pem.htm. And there may be some other 'fundamental' laws that I forgot.
     
  11. Jul 12, 2005 #10

    dx2

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    yes that has helped,and i remain grateful.
     
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