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  1. #21
    Occasional Member Evan's Avatar
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    Quote Originally Posted by SolitaryWalker View Post
    If the argument is deductively valid, then IF the premises are true, the conclusion is necessarily true. A deductively valid argument is false if and only if the premises are false, as by definition, all truth-preserving premises in a deductively valid argument entail a truthful conclusion.
    I assume you mean that the conclusion of a deductively valid argument can only be false if some non-zero subset of the premises are false.

    I agree.

    But that doesn't mean the conclusion can't be true if some of the premises are false.

    For example:
    Evan is a person.
    2+2=4
    Green is not a color.
    Therefore
    Evan is a person.

    Just because a premise is false doesn't mean the conclusion is false.

    The premises of any deductive argument always entail a set of propositions.

    The conclusion of any deductive argument always entails some subset (possibly including the whole set) of those propositions.

    If a premise is false, it means some of the entailed propositions are false. If you just avoid those and pick out others that are true as your conclusion, you have an argument where some premise is false and the conclusion is true.

    So, is provoker a hamster? No.
    Are all hamsters members of typeC? No.

    Is every single entailment of those two premises false? Not necessarily. There are plenty of true ones. Like provoker being a member of typeC.

  2. #22
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by reason View Post
    EvanHowever, this reminds me of people who say they have solved the problem of induction, because swans are by definition white, and if we ever found a "black swan," it wouldn't really be a swan at all..

    I never said such a thing. My post was not at all concerned with induction. All I maintained was that the argument you have cited is not an instance of a deductively valid argument that contains false premise (s) and a true conclusion.

    The person who once induced the false conclusion that all swans are white and later discovers a black swan and claims it is not a swan is making an equivocation fallacy. Feather color is not the defining feature of the swan, hence, by definition it could be either black or white. If the same person in question claims that a black swan is not a swan at all, he subtly changes the definition of the swan. Or simply, he uses the same word to describe two different phenomena. (1) A creature that is defined by its bodily features and (2) a creature that must be necessarily white.

    That error was yours, not mine. You've used the term provoker as a human being (if you have asserted that the conclusion of your argument is true) and you've used it to define a creature that is a hamster.

    If you did not commit the fallacy of equivocation, your argument has a false conclusion. If your argument has a true conclusion (as it is indeed true that there is a human being who is a member of this message board), then your argument is guilty of the aforementioned fallacy as one of your premises defines provoker as something other than a human being.


    [QUOTE=Evan;842149]I assume you mean that the conclusion of a deductively valid argument can only be false if some non-zero subset of the premises are false.

    I agree.

    Quote Originally Posted by Evan View Post
    But that doesn't mean the conclusion can't be true if some of the premises are false..
    The conclusion of a valid argument can be true if some of the premises are false. An argument with contradictory premises is the only example of a deductively valid argument that contains false premise (s) and a true conclusion. Most arguments with false premises and a true conclusion are deductively invalid.

    There are valid arguments containing false premises and a true conclusion. It looks like you've cited another example of such an argument. It is the kind of a reasoning process where one of the premises is identical to the conclusion. (Hence, now we know the contradictory premise and the circular reasoning argument forms can have a true conclusion with some false premises).

    Bottom line is, the argument cited by reason wasn't one of those reasoning chains where there is a true conclusion following from false premises.


    Quote Originally Posted by Evan View Post
    For example:
    Evan is a person.
    2+2=4
    Green is not a color.
    Therefore
    Evan is a person...
    I think that here, you have unintentionally informed me of something that I overlooked. Namely that the circular reasoning argument is an instance of a deductively valid argument where the conclusion may be true, yet some of the premises may be false. Although, it appears as if you were trying to prove that some arguments (whether valid or invalid) can have false premise(s) and a true conclusion.

    Quote Originally Posted by Evan View Post
    Granted, circular reasoning, although containing an informal logic fallacy (question begging) is devoid of formal logical fallacies, hence it is necessarily valid. ...
    It's valid, circular reasoning arguments always are.

    Quote Originally Posted by Evan View Post
    Just because a premise is false doesn't mean the conclusion is false....
    No, it does not. As I have maintained, in contradictory arguments and now we know, in circular reasoning arguments, the conclusion may be true although the premise (s) are false.

    In the case of circular reasoning, at least one premise must be true. (As the conclusion is true and its identical to one of the premises.) In the argument of contradictory premises, there is one true premise by definition. It has the form of A, not A. Necessarily it is true that either A is true or not A is true.



    The premises of any deductive argument always entail a set of propositions.

    The conclusion of any deductive argument always entails some subset (possibly including the whole set) of those propositions.

    If a premise is false, it means some of the entailed propositions are false. If you just avoid those and pick out others that are true as your conclusion, you have an argument where some premise is false and the conclusion is true.

    Quote Originally Posted by Evan View Post
    So, is provoker a hamster? No.
    Are all hamsters members of typeC? No.

    Is every single entailment of those two premises false? Not necessarily. There are plenty of true ones. Like provoker being a member of typeC.
    These premises do not entail the conclusion that provoker(person named colin) is a member of typeC as the argument is invalid. They do, however, entail the false conclusion that there is a hamster member of the forum who has the name of provoker.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

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  3. #23
    Senior Member reason's Avatar
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    Quote Originally Posted by SolitaryWalker View Post
    However, the fact that you are utterly unresponsive to carefully constructed arguments and frequently neglect to support your views lead me to guess that your experience with formal logic is limited. Either that is the case or you are inordinately intellectually lazy or terribly obstinate.
    Oww, why must you cut so deep? My fragile NT ego cannot take such an assault.

    Oops! I mean ... it's not me who doesn't understand logic, but you! I bet you don't even know the difference between a disjunction and a conjunction, or know what the Sheffer Stroke is. It's so sad that an NT can't make one non-fallicious argument! I'd sure hate to be you.
    A criticism that can be brought against everything ought not to be brought against anything.

  4. #24
    Senior Member reason's Avatar
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    SolitaryWalker,

    To not define terms according to your preference is not to commit a fallacy.

    If I choose not to define "Provoker" as being, in part, a non-hamster, then that is my prerogative in a logical argument. (I wasn't really defining "Provoker" at all, but using it like a logical variable -- some interpretations of its meaning may lead to contradiction, but others will not.)

    If it turned out that Provoker was a girl (with an odd voice and a habit of confusing pronouns), then would you say "my concept of Provoker is, in part, a male, so it turns out that Provoker does not exist. Instead, this person like Provoker in every way except being female exists who I shall designate 'Provoker-1'"?

    In any case, this is all really besides the point; namely, false premises can have true consequences.
    A criticism that can be brought against everything ought not to be brought against anything.

  5. #25
    Senior Member matmos's Avatar
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    Quote Originally Posted by reason View Post
    In any case, this is all really besides the point; namely, false premises can have true consequences.
    If the fairies at the bottom of the garden blow you magic kisses.

  6. #26
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    Just thought this was kinda funny.

    The NF Idyllic - last thread posted in : What is your favourite Virtue?
    The NT Rationale - last thread posted in : Probability Relations and Induction

  7. #27
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by reason View Post
    If I choose not to define "Provoker" as being, in part, a non-hamster, then that is my prerogative in a logical argument..
    No, you did not. You have defined provoker as a hamster only. Your premise states that provoker is a hamster. It does not state that provoker is a hamster and a human being. If you truly have defined the premise as you say you did, your premise would state that provoker is a hamster and a human being, not only that provoker is a hamster. The inference that provoker is a hamster and a human being from the written statement that provoker is a hamster is illegitimate. It is purely psychological and not logical, as there is nothing in the premise stating that provoker is a human being.

    Quote Originally Posted by reason View Post
    If it turned out that Provoker was a girl (with a really deep voice and a habit of confusing pronouns), then would you say "my concept of Provoker is, in part, a male, so it turns out that Provoker does not exist. Instead, this person like Provoker in every way except being female exists who I shall designate 'Provoker-1'"
    ..
    Again, with respect to however you define provoker, the onus is on you to prominently indicate this in the premise. Otherwise, the only legitimate inference regarding the definition of provoker is one that is explicitly stated in the argument and nothing else. All you have stated is that provoker is a hamster.

    Bottom line is, if in your argument, you use a word that is present in the premises and you attribute a different definition to the word than the one it had in the premises, you are indeed committing an equivocation fallacy.

    Quote Originally Posted by reason View Post
    In any case, this is all really besides the point; namely, false premises can have true consequences.
    Indeed, only in the case of contradictory premises and in circular reasoning. Not in the argument you have cited.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

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  8. #28
    Senior Member reason's Avatar
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    SolitaryWalker is clearly a hamster.
    A criticism that can be brought against everything ought not to be brought against anything.

  9. #29
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    Quote Originally Posted by reason View Post
    The conclusion of a deductive argument may be true even when the premises are false. For example,

    Every hamster is a member of TypologyCentral
    Provoker is a hamster
    Therefore,
    Provoker is a member of TypologyCentral

    The deductive relation between premises and conclusion is merely that if the premises are true, then the conclusion is also true.
    Basically, on this point I am with SolitaryWalker in thinking that while the conclusion of a deductive argument can be true whilst its premises false, it is not for the reason you concede, which is couched in the dubious example you have provided. Your example commits the fallacy of equivocation and a basic categorical error. It is comparable to the following:

    Every mouse is ESFJ
    Reason is a mouse
    Therefore,
    Reason is an ESFJ

    Here, the conclusion is true (for sake of argument we will assume you actually are ESFJ as it could be the case that that is a misnomer) but true only insofar as we take Reason to identify with the category human and not the category mouse (as we are in agreement that the premises are false). It follows, therefore, that if we take Reason to remain in the same category (mouse) as specified in the premises, then in it is impossible for the premises to be false and the conclusion true as you hoped would be accomplished by your example. On the contrary, the conclusion would also be false. It follows then that the only way to have false premises and a true conclusion, which can be deduced from those premises in the type of syllogism you are proposing, requires that you equivocate by taking Reason in the conclusion to apply to a different category than Reason in the premise. That is misleading and a logical fallacy--namely, equivocation. It follows, therefore, that this cannot be used as an example to support your initial claim.

    From the point of view of a logic textbook, to have a case where the premises are false and the conclusion is true requires a different kind of argumentnamely, an argument that contains contradictory premises. An argument that contains contradictory premises is automatically valid, since its premises cannot be true together, and thus we can never have a situation where all the premises are true (the premises can never be true at the same time), and the conclusion false. The following is an example:

    All snails are slimy. Some snail is not slimy. Thus, the President of the United States is a Democrat!

    Here, the argument is considered deductively valid as anything follows from a contradiction, and the conclusion is true, but it is very counterintuitive and I doubt it yields much utility outside of logic books.

  10. #30
    Senior Member reason's Avatar
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    Provoker,

    I understand SolitaryWalker's objection, but its just silly talk.

    In short, the claim is that my conclusion, "Provoker is a member of TypologyCentral," is not actually true, is because the "Provoker" in that proposition refers to a hamster. However, this merely follows from including "is a hamster" as a necessary property of being "Provoker," but obviously I would never have meant to imply that when presenting the argument.

    If John is a blacksmith and John is still John when he becomes a carpenter, then "is a blacksmith" was never a necessary property of being John. If the same is true of being Provoker and being a hamster, then these objections do not matter. In other words, the term "Provoker" just includes among its properties, "is either a human or a hamster."
    A criticism that can be brought against everything ought not to be brought against anything.

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