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Thread: 4 very easy arguments. Are they valid?

  1. Top | #51
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    Quote Originally Posted by Speakpigeon View Post
    Quote Originally Posted by fast View Post
    Quote Originally Posted by Speakpigeon View Post
    So, we have two statements, "Joe is not an elephant", and "Joe is an elephant", each of which is either true or false, but two statements that cannot be true at the same time so that their conjunction is necessarily false by the definition of the conjunction. But we do have the conjunction, and so it is a statement, and we know it's false because it is necessarily false.

    What we don't know is which statement is true and which is false. I guess we agree so far.

    Now, do you think there has ever been any human being who would have known which of these two statements is true and which is false?

    How do you solve that? Anybody knows?
    EB
    I’m not convinced that the new sentence created with the conjunction has a truth value. The sheer fact the inclusion creates a contradiction lends credence to the idea that no true proposition has been expressed.
    OK, I'm good with that.

    And you're good with Aristotle against the Dogmatics. Good job!

    But you do realise this means the conjunction is not a statement, right?

    Me, I would say it is, which means, against fast, that a statement needs not have a truth value.

    Ah, conundrums.
    EB
    Where there is no proposition, there is no statement. The utterance of a sentence where there is no proposition is not the utterance of a statement, so yes, if a contradiction has no expressed proposition, the sentence uttered is not a statement. All statements necessarily express propositions—as opposed to sentences.

  2. Top | #52
    Veteran Member Treedbear's Avatar
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    Quote Originally Posted by Angra Mainyu View Post
    Quote Originally Posted by Treedbear View Post

    In that case I just don't understand the value of syllogisms when they allow you to create a paradox by simply inserting a contradictory premise into an argument for no other purpose. That seems to be the sole purpose of P2". I can see the value of creating sorites ("a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion.") But I don't see that happening here. They're simply unconnected arguments.

    They do not allow you to "create paradoxes". It is not a paradox that from some premises, a contradiction follows. The reason I'm doing this is to try to help reduce some of the confusion caused by Speakpigeon in the other thread. It seems to me there might be room for some progress here, but I would like to know where you are, so I would like to ask you two questions:

    1. Do you realize why A1, A2, and A3 are valid?
    2. Do you realize why A4 is valid?
    I realize that A1, A2, and A3 are valid. The reason is that none of them, taken by itself, contains a contradiction.

    I would say that A4 is not valid because it appears to me that two or more premises contradict each other. In particular P1 and P2".
    A4:

    P1: Joe is either a squid or a giraffe.
    P1’: A giraffe is not an elephant.
    P1’’: An elephant is not a squid.
    P2’’: Joe is an elephant.
    C’’’: Joe is not an elephant, and Joe is an elephant.
    The fact that these premises are valid when they appear in A1, A2, and A3 has no bearing on whether A4 is valid.

    Sorry, but I haven't read any of Speakpigeon's other post, so I guess that means I've missed the point you're making. Also, sorry for taking so long to respond. I don't usually have internet access on weekends. I visit the forum during work hours to provide some sanity to my days, and I rely on an hour or so after work to address the more thought-provoking posts.
    Last edited by Treedbear; 02-12-2019 at 12:51 AM.

  3. Top | #53
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    Quote Originally Posted by Treedbear
    I realize that A1, A2, and A3 are valid. The reason is that none of them, taken by itself, contains a contradiction.
    That is not why they are valid. In fact, whether they contain a contradiction is not related to validity. The reason that they are valid is that the premises entail the conclusion.


    Another (perhaps more direct) example:

    Q1: A is either an X or a Y.
    Q2: A is not an X.
    C(Q1,Q2): A is a Y.

    That is clearly valid, because C(Q1,Q2) follows from Q1 and Q2.

    Q1: A is either an X or a Y.
    Q2: A is not an X.
    Q3: A is not a Y.
    C(Q1,Q2): A is a Y.
    C(Q1,Q2,Q3): A is a Y, and A is not a Y.

    That is clearly valid, because C(Q1,Q2, Q3) follows from Q3 and C(Q1,Q2), and in turn C(Q1,Q2) follows from Q1 and Q2.

    The fact that the conclusion is a contradiction is not relevant as to whether it is valid. But perhaps, you have other concept of validity in mind. If so, what do you understand as "valid"?


    Quote Originally Posted by Treedbear
    I would say that A4 is not valid because it appears to me that two or more premises contradict each other. In particular P1 and P2".
    A4:

    P1: Joe is either a squid or a giraffe.
    P1’: A giraffe is not an elephant.
    P1’’: An elephant is not a squid.
    P2’’: Joe is an elephant.
    C’’’: Joe is not an elephant, and Joe is an elephant.
    The fact that these premises are valid when they appear in A1, A2, and A3 has no bearing on whether A4 is valid.
    Premises are not the sort of thing that can be valid or invalid. Premises can be true or false. But arguments can be valid or invalid. Assuming that A1, A2, and A3 are valid, it follows at once that A4 is also valid, since the premises of A4 entail the conclusion (I already explained why in my previous reply to you, and in the hidden part of the OP).

    Quote Originally Posted by Treedbear
    Sorry, but I haven't read any of Speakpigeon's other post, so I guess that means I've missed the point you're making. Also, sorry for taking so long to respond. I don't usually have internet access on weekends. I visit the forum during work hours to provide some sanity to my days, and I rely on an hour or so after work to address the more thought-provoking posts.
    No problem.

  4. Top | #54
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    Quote Originally Posted by Lion IRC View Post
    :l

    Is this thread some kind of satirical send-up of transgenderism?
    Must be. After all, that's the only thing those damned atheists care about.
    Do human beings have free will? I can't decide.

  5. Top | #55
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    I have a question.

    If a valid deductive argument entails a contradiction, does that guarentee that a premise is false?

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    Quote Originally Posted by fast View Post
    I have a question.
    If a valid deductive argument entails a contradiction, does that guarentee that a premise is false?
    It guarantees that at least one premise is false, though it might be undetermined which one is so if we are talking about the formal argument and we have not determined the premises. For example, if you go by the argument:

    P1: A.
    P2: ¬A.
    C: A and ¬A,

    the argument is valid by its form, but we have not yet chosen what A is. Whatever A is, given that A is a statement, either A is false or ¬A is false. But as long as we have not chosen A, it is undetermined which one is false. Also, saying A="Joe is an elephant" is not enough to determine the premises, since "Joe" is just a name, and without further information, it is not determined whether Joe is an elephant, so determination will depend on context.

  7. Top | #57
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    And to follow up,

    No valid deductive argument with a contradictory conclusion can be sound.

  8. Top | #58
    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by fast View Post
    And to follow up,

    No valid deductive argument with a contradictory conclusion can be sound.
    Good point!
    EB

  9. Top | #59
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    Quote Originally Posted by Speakpigeon View Post
    Quote Originally Posted by fast View Post
    And to follow up,

    No valid deductive argument with a contradictory conclusion can be sound.
    Good point!
    EB
    Well, it helps to keep my intuition in check. I am comforted in knowing I can disregard unsoundness when assessing the validity of an argumemt. We can’t do that with just any ole use of “valid.”

    Contradiction in conclusion? No problem. It’s not like it’s leading anyone astray. When the big bad wolf tells little red riding hood that

    P1 the house is just over the next hill and
    P2 the house is not just over the next hill
    So
    C the house is both just over and not just over the next hill

    She’ll see the truth and know not to trust. If an argument is valid, we should trust that flow is such that the premises in fact lead just where it’s said they do, to the conclusion. Having an unsound argument doesn’t imply that the arguments form is faulty. In this case, it’s unsoundness isn’t a function of a lack of validity; the only thing else (the only thing, thanks to a particular definitional use) is that at least one premise is false.

    Edited to add:

    Bad wolfy

  10. Top | #60
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    Quote Originally Posted by fast View Post
    I have a question.

    If a valid deductive argument entails a contradiction, does that guarentee that a premise is false?
    Of course not.

    But the only way an argument is set up rationally is with true premises.

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