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Friday, September 7, 2007

Logical Links

Introduction to Philosophy (PHIL 2003)

3 comments:

  1. Subject: God Does Exist

    WHAT A GREAT ANALOGY OF GOD FOR THOSE WHO DON'T KNOW, BY ROBIN WILLIAMS NO LESS.
    This is one of the best explanations of why God allows pain and suffering that I have seen. It's an explanation other people will understand.

    A man went to a barbershop to have his hair cut and his beard trimmed. As the barber began to work, they began to have a good conversation. They talked about so many things and various subjects.

    When they eventually touched on the subject of God, the barber
    said: "I don't believe that God exists."

    "Why do you say that?" asked the customer.
    "Well, you just have to go out in the street to realize that God doesn't exist. Tell me, if God exists, would there be so many sick people? Would there be abandoned children? If God existed, there would be neither suffering nor pain. I can't imagine loving a God who would allow all of these things."

    The customer thought for a moment, but didn't respond because he didn't want to start an argument. The barber finished his job and the customer left the shop.
    Just after he left the barbershop, he saw a man in the street with long, stringy, dirty hair and an untrimmed beard. He looked dirty and un-kept.

    The customer turned back and entered the barber shop again and he said to the barber: "You know what? Barbers do not exist."

    "How can you say that?" asked the surprised barber. "I am here, and I am a barber. And I just worked on you!"

    "No!" the customer exclaimed. "Barbers don't exist because if they did, there would be no people with dirty long hair and untrimmed beards, like that man outside."

    "Ah, but barbers DO exist! What happens is, people do not come to me."

    "Exactly!"- affirmed the customer.
    "That's the point! God, too, DOES exist! What happens, is, people don't go to Him and do not look for Him. That's why there's so much pain and suffering in the world."

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  2. if you follow that, there can be no contradictions

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  3. What is an argument?

    An argument is a set of statements, one or more of which are purported to provide support or evidence for another statement. The prior are called premises, the latter the conclusion.

    Obviously, arguments can be good or bad. (I.e. the premises may not always support what they are purported to support.)

    Examples of arguments:


    1. All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.

    2. Since all birds have wings and penguins are birds, penguins have wings.

    3. The sky is dark and filled with clouds. It's probably going to rain.

    4. If the princess kisses the frog, then it will turn into a prince. She did kiss the frog. So, it turned into a prince.

    5. Wars should never be fought because they cause suffering.


    Note premise indicators (because, since, on account of, for, for the reason that, etc. - these terms indicate that a reason or evidence is being offered) and conclusion indicators (therefore, so, thus, hence, etc. - these terms indicate that an inference is being made.)

    Examples of non-arguments:


    1. Chocolate ice cream is tasty. It's my favorite. (Loose set of statements, simple assertion)

    2. If the Cubs win the pennant, then I'll be a happy camper. (Simple conditional statement: no conclusion is drawn)

    3. One must do several things in order to build a house. First one must raise the funds to build it. Second, one must hire someone to design the house. Then one must hire builders. The house must also be assessed by the state, etc. (Description; the first sentence is not really supported, but rather illustrated, by the following sentences.)

    4. Since yesterday, I haven't been feeling very well. ("Since" in this sense is not a premise indicator, but rather an indication of time.)


    To determine whether an argument is being offered, ask yourself whether any of the statements in the passage offer evidence or support for some main claim (rather than, for example, merely illustrating a main point as in example 3 above).


    Deductive Arguments - the conclusion is logically implied by the premises (or, the conclusion follows by definition).


    Examples of deductive arguments:

    Disjunctive Syllogism - Either John stole the money or Jane did. Jane didn't steal the money. So, John did.


    Hypothetical Syllogism - If the stock goes up, then it will split soon thereafter. If the stock splits, then the company will build fifty new stores. So, if the stock goes up, then the company will build fifty new stores.

    Modus Ponens - If the frog is really a prince, then he can be cured with a kiss from a princess. The frog is a prince. So, he can be cured with a kiss.

    Modus Tollens - If the frog is really a prince, then he can be cured with a kiss from a princess. The frog cannot be cured. So, it is not a prince.


    Contrast the last two valid forms with the following two invalid forms.


    Denying the Antecedent - If the Cubs win, then I'll be happy. The Cubs didn't win. So, I'm not happy.

    (Why is this a bad argument? I might be happy for some other reason. The Cubs' winning is a sufficient condition for my being happy, but it isn't necessary that the Cubs win in order for me to be happy.)

    Affirming the Consequent - If the Cubs win, then I'll by happy. I'm happy. Therefore, the Cubs won.

    (Think about the condition set up in the "if...then..." sentence: There might be other things that make me happy besides the Cubs' winning.)

    Something like these fallacies can be seen in the following dialogues:

    Pundit: If our candidate wins the election, then there will be more jobs.
    Voter: I'm not going to vote for your candidate.
    Pundit: So, you must not support more jobs!

    Such an inference is invalid since other candidates might create more jobs, too.

    Pundit: Anyone who supports morality is a Republican.
    Joe Blow is a Republican.
    So, obviously Joe Blow supports morality.

    This is invalid because Joe Blow might be a republican for some other reason.



    Don't confuse "if...then..." constructions with "if and only if" constructions. Compare:


    1. The frog can be cured by a kiss if and only if it is a prince.

    ( = If the frog can be cured by a kiss, then it is a prince, and if it is a prince, then it can be cured by a kiss.) This is called a biconditional statement.



    2. The frog can be cured by a kiss if it is a prince.

    ( = If it is a prince, the frog can be cured by a kiss.)



    3. The frog can be cured by a kiss only if it is a prince.

    ( = If the frog can be cured by a kiss, then it is a prince.)



    With a bit of reflection, you should be able to see that each of these statements generates different conditions regarding being a frog-prince and being curable via a kiss.


    When evaluating deductive arguments, use the following strategy:


    1. Determine the form of the argument. (That is, figure out what the premises are and how they are supposed to fit together to support the conclusion.) Don't worry about whether the premises are true or false.

    2. Is the form of the argument a valid form? That is, if all the premises were true, would they support the conclusion? (Or is the argument invalid, as in some of the examples above?) If the argument isn't valid, then STOP. An invalid argument is a bad argument.

    3. If the argument is valid, then ask, "Are all the premises true?" If they aren't, then STOP. An argument with false premises is a bad argument.

    4. If the argument is valid, and all its premises are true, then it is a good argument.



    Inductive Arguments - the conclusion is highly supported by the premises (although not 100%).

    Arguments which make predictions, generalizations (based on a sample), are based on cause and effect, the testimony of others, or analogies, or are probabilistic in some other way are inductive. The best way to distinguish inductive arguments from inductive arguments is to determine whether the conclusion is only highly likely to be true if the premises are true (inductive) or if the conclusion follows by definition from the premises (deductive).


    Examples of inductive arguments.



    1. The sun has risen every morning for millions of years. So, the sun will probably rise tomorrow.

    2. Everyone who comes to the pool wears flip-flops. The next person who comes will be wearing flip-flops.

    3. Jim jogs every day. He must be very healthy.

    4. Jan is very healthy. She probably exercises a lot.

    5. The President said that everything is under control. So, everything is under control.

    6. She is just like my mother. So, she probably nags people too much.

    Think about how in each of these arguments the conclusion is likely, although not certain.



    At some point in your education, you were probably told that inductive arguments move from the specific to the general, and that deductive arguments move from the general to the specific. Whoever told you that was either wrong or using the terms in a very different way. The best way to think about the distinction is in terms of probability: the conclusion of a deductive argument follows 100%, or not at all; whereas the conclusion of an inductive argument can be supported in varying degrees of strength by the premises (or evidence).

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