View Poll Results: Do you think all these arguments are valid, only some are, or none of them?

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  • All these arguments are valid

    1 16.67%
  • Only some of these arguments are valid

    1 16.67%
  • None of these argument is valid

    3 50.00%
  • I don't know

    1 16.67%
  • These arguments don't make sense.

    0 0%
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Thread: All; therefore some?

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    Contributor Speakpigeon's Avatar
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    All; therefore some?

    Ah, here is a very interesting piece of logic. I give the general form of the argument first, and then three straightforward applications of the general form.

    All A's are/have F;
    Therefore, some A is/has F.
    All angels have wings;
    Therefore, some angel has wings.

    All politicians are liars;
    Therefore, some politician is a liar.

    All imaginary beings have serious existential problems;
    Therefore, some imaginary being has serious existential problems.
    Thank you to say whether you think all these arguments are valid, or only some, or none.

    Thank you to cast your vote before posting any comment.
    EB

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    Quote Originally Posted by Speakpigeon View Post
    Ah, here is a very interesting piece of logic. I give the general form of the argument first, and then three straightforward applications of the general form.

    All A's are/have F;
    Therefore, some A is/has F.
    All angels have wings;
    Therefore, some angel has wings.

    All politicians are liars;
    Therefore, some politician is a liar.

    All imaginary beings have serious existential problems;
    Therefore, some imaginary being has serious existential problems.
    Thank you to say whether you think all these arguments are valid, or only some, or none.

    Thank you to cast your vote before posting any comment.
    EB
    It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.

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    Super Moderator Bronzeage's Avatar
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    A redundant statement is not an argument just because it includes the word "therefore".

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    Contributor Speakpigeon's Avatar
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    Thanks to posters who have cast their vote.
    EB

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    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by Jokodo View Post
    It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.
    Can you justify this?
    EB

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    Quote Originally Posted by Speakpigeon View Post
    Quote Originally Posted by Jokodo View Post
    It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.
    Can you justify this?
    EB
    It's how we have defined ALL to operate, in order to achieve full equivalence between ALL and NOT ANY NOT. It is intuitively clear that ALL A P implies NOT ANY A NOT P. Except for this particular corner case where there are no As, the reverse is also clearly true. We lack however clear intuitions for what should be the truth value of ALL A said of an empty set A. Defining it in such a way that it's always true allows for a simple, mechanic check: ALL A ARE P is false if and only if there is at least one A that isn't P. This leads to an overall more elegant and consistent system.

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    Even if we treat ALL A as always carrying an existential presupposition as an integral party of its meaning, it doesn't become false of an empty set - it gets an undefined truth value, requiring a trivalent logic. It's what being a presupposition means: the negation of a statement does not imply the negation of the its presuppositions. In order for "the king of France is bald" to be either true or false in most modern implementations of logic, there has to be a French king.

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    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by Jokodo View Post
    Quote Originally Posted by Speakpigeon View Post
    Quote Originally Posted by Jokodo View Post
    It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.
    Can you justify this?
    EB
    It's how we have defined ALL to operate, in order to achieve full equivalence between ALL and NOT ANY NOT. It is intuitively clear that ALL A P implies NOT ANY A NOT P. Except for this particular corner case where there are no As, the reverse is also clearly true. We lack however clear intuitions for what should be the truth value of ALL A said of an empty set A. Defining it in such a way that it's always true allows for a simple, mechanic check: ALL A ARE P is false if and only if there is at least one A that isn't P. This leads to an overall more elegant and consistent system.
    No, I mean, can you justify that "all" and "some" are used in English only in the way that you imply here?
    EB

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    However most analyses would posit that the existential presupposition is a pragmatic import: people don't generally have a habit of making specific claims of nonexistent entities, so the moment we hear someone talk of ALL As, we conclude they believe in the existence of As and evaluate the rest of their claim under that assumption - even though it is not something they ever claimed explicitly.

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    Quote Originally Posted by Speakpigeon View Post
    Quote Originally Posted by Jokodo View Post

    It's how we have defined ALL to operate, in order to achieve full equivalence between ALL and NOT ANY NOT. It is intuitively clear that ALL A P implies NOT ANY A NOT P. Except for this particular corner case where there are no As, the reverse is also clearly true. We lack however clear intuitions for what should be the truth value of ALL A said of an empty set A. Defining it in such a way that it's always true allows for a simple, mechanic check: ALL A ARE P is false if and only if there is at least one A that isn't P. This leads to an overall more elegant and consistent system.
    No, I mean, can you justify that "all" and "some" are used in English only in the way that you imply here?
    EB
    I cannot justify something I never claimed. You asked about logic and implication, not about any and all ways English speakers use a particular word. I believe I bade clear I'm taking about the concept and not the word by using all caps.

    There is an argument to be made that the pure semantics of the English word is indeed very much parallel to the abstract concept and any meanings beyond that it customarily receives is in the domain of pragmatics, for a quick sketch of which I refer you to my last post - but it's not an argument I made in the post you replied to.

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