Everyone is female... Therefore ... ?

Discussion in 'General Philosophy' started by Speakpigeon, Aug 21, 2019.

?

Do you personally think this argument is logically valid?

Poll closed Oct 21, 2019.
  1. Yes, the argument is valid.

    0 vote(s)
    0.0%
  2. No, the argument is not valid.

    33.3%
  3. I don't know.

    33.3%
  4. The argument doesn't make sense.

    33.3%
  1. Speakpigeon Valued Senior Member

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    1,123
    Here is an interesting logical argument:

    Everyone is female;
    Therefore, any siblings are sisters.​

    Do you personally think this argument is logically valid?
    Thank you to cast a vote before posting any comment.
    EB
     
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  3. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    I think everyone is originally female (conception) and males are just a mutation in the womb.
     
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  5. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    Logically valid? No, at least not in the syntactic sense of requiring a form such that it is impossible for the premises to be true yet the conclusion false. The form here, after all, is simply P, therefore C.

    Any validity here is due to the semantics of the extra-logical terms, i.e. the meaning of the words rather than the logical form. Had you just asked whether it was valid, however, rather than specifically “logically valid”, then I would have said yes.



    Interestingly this also an example of an enthymeme... a logical argument in which one or more premises are not explicitly stated.
    In this case the argument, with premise unhidden, might be inferred as being:

    All siblings that are female are sisters.
    Everyone is female.
    Therefore any siblings are sisters.

    This now has syntactic validity:
    P.Q = R
    Q
    Therefore P = R
    (Or something like that... I’m sure there’s a more formal way to express it.)

    So it could be argued that, since in this expanded form the argument is valid, so the enthymeme, the 2-line argument, is itself syntactically valid. But in this case I’m not sure that holds, as the inferred additional premise is reliant upon the semantics of the extra-logical terms for its inference, i.e. it is the semantic connections between “female”, “sister”, and “sibling” that allow the inference, not any syntax.
     
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  7. Speakpigeon Valued Senior Member

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    1,123
    OK, that's an proper reply for once.
    Assessing the validity of an enthymeme will always require that you infer the unstated premise and you can only do that from context or from the argument as expressed.
    The only condition seems to be that the missing premise should be not only easy to guess but really obvious to the target audience, and it will be obvious essentially if you happen to believe the missing premise true, as is the case here since you just go back to definitions.
    The semantics is only there to help you find the missing premise. Once you have it, the semantic plays no part in assessing the validity of the complete argument, as indeed you demonstrate yourself by using mute letters to formalise the argument completed.
    However, you may have different ways to complete the argument. My own was as follow:

    For all x, Sister(x) implies Female(x);
    For all y, Sibling(y) implies either Sister(y) or Brother(y);
    For all z, Female(z);
    Therefore, for any a, Sibling(a) implies Sister(a).​

    And if you don't call that logical validity, I don't know what kind of validity you would have in mind.
    The distinction is between formally valid and valid simpliciter. Mathematicians are guilty, again, of using the term "validity" when they are in fact talking about formal validity, which can get the self-appointed experts confused.
    So, the argument is valid but not formally valid. Can you agree on that?
    EB
     
  8. James R Just this guy, you know? Staff Member

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    37,193
    Let John and Betty be siblings. We deduce:

    John is female (P3).
    Betty is female (P3).
    John is either a sister or a brother (P2).
    Betty is either a sister or a brother (P2).

    Now we're stuck. There's no way to deduce that John is a sister, and there's no way to establish that Betty is a sister, based on the given premises.

    In other words, the presented logical argument does not validly lead to the given conclusion. Note also that P1 is redundant, given P3.
     
  9. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    9,558
    I fully agree that the full argument is logically valid, but the enthymeme is not. The missing premise must be supplied for the argument to be logically valid, as you asked. Logical validity must rely solely on the form of the logic. And from the form alone of the enthymeme you can not claim it logically valid.
    The enthymeme is a relatively powerful rhetorical device, helping reinforce ideas almost subconsciously through getting the audience to infer that which makes the argument logically valid. But the inference (in this case at least) relies on semantics, not logic itself.
    I have no issue with a full argument able to be logically valid (not that this is judgement on yours, though). The issue then is whether the enthymeme can be said to be logically valid simply because one can add a premise to make it so.
    Or in this case, logical validity or just validity, and since you asked whether the argument was logically valid...?
    I’m fairly sure they know what they’re talking about, and the context of the language they’re using. They undoubtedly use the term “validity” as a convenient short-form of anything like “formal validity” or “syntactical validity” etc. Because they all know what they mean when they use it.
    Just accept that that is what they mean, and move on.
    It is not logically valid, which is the question you originally asked. Can we agree on that?
     
    Last edited: Aug 22, 2019
  10. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    9,558
    Indeed. Good spot.

    To put his argument into simpler language:
    P1: all sisters are female
    P2: all siblings are either sisters or brothers
    P3: everyone is female
    C: all siblings are sisters

    Unfortunately it suffers from an undistributed middle, in that P1 says that while all sisters are female, it says nothing about brothers. So why can’t brothers be female (ignoring semantics)? You would have to exclude that possibility for it to be a logically valid argument.
    And as you say, without distributing fully (I.e. both brothers and sisters) you end up with P1 becoming redundant in the light of P3.
     
  11. Speakpigeon Valued Senior Member

    Messages:
    1,123
    You're correct. My bad.
    The first premise should read "For all x, Brother(x) implies not Female(x)".
    Thanks.
    EB
     
  12. Speakpigeon Valued Senior Member

    Messages:
    1,123
    No, because when we say that the enthymeme is valid, we do mean logically valid.
    And what else coud it be? Its validity is only that which is inherited from that of the complete argument, which is itself logically valid.
    We all agree that the enthymeme is not formally valid. Why is that a problem to talk of logical validity in this case as long as we keep the necessary distinction between formal and not formal?
    EB
     
  13. Jeeves Valued Senior Member

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    5,028
    What argument?
     
  14. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

    Messages:
    9,558
    Not as written, though, and the "correct" full logical argument must be inferred, with no guarantee of it being inferred correctly. Thus at best, as said, we could say that the full argument intended might be logically valid. You yourself have adequately demonstrated that an inferred missing premise can lead to an invalid argument.
    No, the validity of the enthymeme that you wrote was valid due to its semantics, not becuase of the complete argument - again you are reminded that you proposed a complete argument that was not formally valid.
    Semantically it is known that sisters are the only female siblings. The words mean the same thing in this context. The enthymeme relies on this semantic relationship to be valid as written, and thus it is semantically valid, not valid by form. And when we talk of logical validity we talk of the form, not semantics.
    If it is not formally valid then it is not logically valid, as validity in logic is about the form. Logic is formal. Enthymemes are generally only considered valid due to the combination of logical and extralogical, and if that extralogical element is the semantics then it can be said to be semantically valid (i.e. a missing premise can be supplied due to the semantics of the content that would make the expanded argument logically valid).
    Your example is one that can be said to be semantically valid, but since you asked whether the enthymeme was logically valid, the answer is a quite simple "no".
     
  15. Speakpigeon Valued Senior Member

    Messages:
    1,123
    As so we disagree.
    In the literature, the opposite of semantically valid is syntactically valid, not logically valid as you claim here.
    I don't know of any source saying that a semantically valid argument is not, or even may not be, logically valid.
    So, unless you can provide any authoritative source, there's no issue to our disagreement.
    EB
     
  16. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Dictionaries define validity (not "formal validity") in the context of logic as follows:

    Valid
    4. Logic
    a. Containing premises from which the conclusion may logically be derived: a valid argument.
    b. Correctly inferred or deduced from a premise: a valid conclusion.​

    If the enthymeme is valid, then its conclusion is logically derived.
    EB
     
  17. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    9,558
    Clearly.
    Logical validity is all about form. Hence the definition of logical validity: an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. I.e. irrespective of whatever semantics we apply to the terms.
    Syntax is likewise all about form. Hence with regard validity the two can be treated as synonymous.
    Semantic validity, however, relies on extra-logical elements - such as meaning - to bridge the gap from the given form and any validity we wish to assign to the argument. The enthymeme you posted is semantically valid, but is not logically valid as written, only in an expanded form, which must be inferred from the semantics.
    Show me one that says otherwise, or at least provide an actual rebuttal that is more than just "well, you can't prove otherwise".
    So you go to the most dumbed down place you can find for your definitions? Figures.
    No, only if an enthymeme is logically valid is its conclusion logically derived. It is ironic, given that we are talking about logic, that you think that if something that is logically valid can be considered valid then everything that is considered valid must be logically valid. I leave you to figure out the logical fallacy you're committing, here.
    In your example, the conclusion is semantically derived (along with some help from logic, of course). But logic alone can not get you to the validity of the conclusion from the premise given. That requires semantics. Hence the term semantic validity.
     
  18. Speakpigeon Valued Senior Member

    Messages:
    1,123
    So, in other words, you can't justify your position.
    My position is simple. An enthymeme or an informal argument is a logical argument. When it is valid, its validity is logical validity, not any other sort of validity.
    The fact that assessing its validity requires to take meaning into account doesn't change that fact. Instead, a logically valid argument will be either syntactically valid or semantically valid. I don't know of any source contradicting this view, and you clearly can't provide any.
    My view is justified by common sense: It's a logical argument, it's valid as a logical argument, it's validity therefore can only be logical validity.
    You, however, cannot justify your view.
    EB
     
  19. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    9,558
    On the contrary, I have justified my position. And it is a position you have not rebutted. I can't be held accountable for you simply ignoring the justification.

    You claim it is a logical argument, yet there is no logical form to the argument you posted that is valid. It relies on semantics for the inference of the missing premise that would make it logically valid, an inference that you more than amply demonstrated is not guaranteed to be correct.
    If your own inability to infer correctly does not demonstrate to you the weakness of your position then there is little further to be gained from engaging your ignorance.

    You have also posted numerous polls that you have claimed to be valid that are not in fact logically valid. This should also demonstrate to you the difference between logical validity and the more colloquial notion of validity that you seem to favour. You continue to confuse the two, to argue one as if it is the other.
    C'est la vie.

    Your "common sense" is nothing of the sort. An enthymeme is only questionably an argument in the first instance. And even if considered an argument it is clearly not explicitly logically valid, and only implicitly valid if one infers a missing premise that would enable the expanded argument to be considered so.

    If you can't comprehend that logical validity is about form then there's little point in you continuing with your polls about logical validity. But I'm guessing that won't stop you.

    Of course, if you amend the definition of logical validity so that you are correct, I guess you would end up being correct.
    Or if you continue to engage in your ironic fallaciousness, as highlighted earlier, well, that's what you will continue to do.
    Trough. Water. The rest is up to you.
     
  20. Speakpigeon Valued Senior Member

    Messages:
    1,123
    You're still not justifying your view. You're only repeating and there's no need for that since I already understood the first time round and your claim is just that, a claim. Everything you say here is irrelevant to whether a valid argument is or not a logically valid argument. There's no authoritative source to support your claim and your argument about semantic validity is irrelevant since that something is semantic doesn't preclude that it is logical, except perhaps in your own idiosyncratic perspective. OK, we can stop here, I think.
    EB
     
  21. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    Justification doesn't need authoratative support... it merely needs to be justification. Which has been provided. And repeated for you. It is fair enough that you don't agree with it, but given your inability to even recognise it as such, and your dismissal as irrelevant that which patently is not, seemingly just because it differs from your view, I agree that it probably is best you stop here.
     
  22. Speakpigeon Valued Senior Member

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    1,123
    Reminder...
    EB
     

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