• unenlightened
    740
    One last time.

    It does not conclude what you say its conclusion is, because it does not assert what you claim its premise is, and that is how "if" functions. Your 'interpretation' is flat wrong.
  • Sapientia
    2.1k
    One last time.

    It does not conclude what you say its conclusion is, because it does not assert what you claim its premise is, and that is how "if" functions. Your 'interpretation' is flat wrong.
    unenlightened

    Again, I'm not talking about any assertion. A premise isn't the same as an assertion, and a premise need not be asserted. If discussing validity, i.e. whether B follows A, then A is the premise and B is the conclusion. If you say "If A then B" then it makes perfect sense to talk about B as the conclusion, and to question whether it follows.

    Thanks for the condescension, but I think that it is you who is mistaken, and who does not seem to understand what I am saying.
  • unenlightened
    740
    it makes perfect senseSapientia

    It makes perfect sense, If you bracket off the 'if'. But the 'conclusion' is not the conclusion of an argument that is being made. If you will look back a page or two, you will see the confusion that results from talking about a conclusion to an argument that has not been made. The validity of a conditional argument can very well be discussed, but for god's sake analyse it as a condition and a conditional conclusion. and not a premise and a conclusion.
  • jamalrob
    1k
    "If A then B" appears to be a conditional statement, not an argument. A is the antecedent and B is the consequent (not the premise and conclusion). Un seems obviously right to me.
  • Sapientia
    2.1k
    "If A then B" appears to be a conditional statement, not an argument. A is the antecedent and B is the consequent (not the premise and conclusion).jamalrob

    Yes! Antecedent and consequent. You have done a better job at clearing this up for me than unenlightened has, just by using those terms. That is the correct terminology, and that is actually what I was trying to convey. There is obviously a similarity in the meaning of those words. I was just using the wrong terminology. Just as a conclusion is supposed to follow a premise, the consequent is supposed to follow the antecedent. The latter is supposed to be a logical consequence or implication of the former.

    But cannot also a conditional statement be an argument? I get that it can be a statement, an assertion, a premise as part of an argument, and that it's conditional, but I see no reason why it cannot also be an argument.

    If the Bible is true, then God exists.

    That certainly looks like an argument to me, and one with which it does indeed, as I said, make perfect sense to discuss the validity of. Un's criticism about me not understanding the "if" misses the mark, I think. I do understand that. He should give me some credit.

    Un seems obviously right to me.jamalrob

    Well, I wasn't entirely disagreeing with him, and was actually agreeing with some of the criticism he was directing at me.
  • Wosret
    1.1k
    It's not really antecedent and consequent as that does imply that the latter must follow from the former, but "conditional" basically means "contingent", so this isn't the case. A conditional statement is true if the conclusion is true, it need in no way follow logically from the hypothesis.

    For instance "if I don't eat this sandwich, then my dog will explode", the conclusion doesn't follow from the hypothesis, but that doesn't mean that it isn't true. It's true if my dog explodes, even if it had absolutely nothing to do with my sandwich eating.
  • Sapientia
    2.1k
    In any case, with implication, such as material implication, "antecedent" and "consequent" are the correct terms to use. Otherwise encyclopaedias on the topic have got it wrong.
  • Wosret
    1.1k
    The important thing is that the "then" doesn't mean "therefore" suggesting a logical connection, but simply "also", so that one doesn't require any logical, empirical or causal relationship from one to the other.

    Consequent means "following as a result or effect", and is thus misleading, as you went on to suggest there must then be a logical connection.

    I don't care what other people believe, being wrong is their inalienable right.
  • Sapientia
    2.1k
    Whether there is or isn't a logical connection, that is its purpose, function or meaning. How can it not be? And if you say otherwise, then I think that you have not understood. We're talking about material implication. If A, then B. That is stating a logical connection between A and B.

    A conditional statement is true if the conclusion is true, it need in no way follow logically from the hypothesis.

    For instance "if I don't eat this sandwich, then my dog will explode", the conclusion doesn't follow from the hypothesis, but that doesn't mean that it isn't true. It's true if my dog explodes, even if it had absolutely nothing to do with my sandwich eating.
    Wosret

    That's bringing soundness into it, but I was just talking about validity. If the conclusion doesn't follow, then it's invalid. I said nothing of truth or falsity.
  • unenlightened
    740
    p1. If the dog has exploded, my work is done.
    p2. The dog has exploded.
    c1. My work is done.

    ...

    p3. If my premises are true, my conclusion is true. (My argument is valid.)
    p4. My premises are true. (It is true that my argument is valid, and it is true that it is true.)
    c2. My conclusion is true. (Ain't that the truth!)
  • Agustino
    4.2k
    So much unenlightenment! >:)
  • Mongrel
    1.5k
    We're talking about material implication. If A, then B. That is stating a logical connection between A and B.Sapientia

    Don't think so.

    If you're in North America, you're an asshole.

    There's nothing about being in North America that causes asshole-hood, so we're just looking at incidence, not consequence. There's an association, but the cause of both could be a third entity.

    The Malankovitch Cycle resulted in an attraction of the world's assholes to North America.
  • Agustino
    4.2k
    Here's my issue with your points once again:

    1. All men are animals
    2. If Socrates is a man, then Socrates is an animal.

    So you're trying to say that if all men are animals, then the conditional (2) is always true. There's a bit of sophistry in this to be honest. A conditional is false only if the consequent is false given the antecedent. If someone grants (1), then whether Socrates is a man or not has no bearing on the truth of (2). The whole question is whether or not Socrates is an animal follows from Socrates is a man, and given (1) it does, as we already know from the traditional 3 premise argument (we couldn't draw its conclusion otherwise). But the reason why I say it's a sophistry, is that it doesn't tell us anything about how things actually are. It doesn't actually tell us if Socrates is a man or an animal. Socrates could be a man and an animal, or he could be an animal, or he could be neither - what couldn't be the case is that Socrates is a man and yet isn't an animal. And the fact is that (2) is a specific example of the general clause covered by (1). You could replace Socrates with a variable, and then you'd get an identical statement with (1). (2) is just a specific instance of (1) in other words.
  • unenlightened
    740
    But the reason why I say it's a sophistry, is that it doesn't tell us anything about how things actually are. It doesn't actually tell us if Socrates is a man or an animal.Agustino

    Yes, that is correct; a conditional does not say how things are, but only that if they are thus then they are so. After all, it is equally the case that if Zeus is a man then Zeus is an animal (given 1.).
    But of course we know Zeus is not a man. But if you look back a few posts, it is still the case that conditional premises can function in logical arguments.

    It might be that 2. is true even though 1. is false. For instance it might be the case that:

    3. all men except Buddha and Jesus are animals.

    In which case 2. follows from 3 and 1. is false.

    Now if 1. can be false and 2. true, I think you have to admit that they do not say the same thing, or that one is contained in or an instance of the other.


    It is the nature of argument that a conclusion must always say the same or less than the sum of its premises, and it is au contraire sophistry and necessarily illogical to demand that more should be said.
  • Agustino
    4.2k
    In which case 2. follows from 3 and 1. is false.unenlightened
    Does it? Wouldn't 2. have to say "If Socrates is a man, and Socrates isn't Buddha or Jesus, then Socrates is an animal?" If so, then my criticism is still valid.

    Personally unenlightened, I would be very surprised if there can be non-tautologous and non-circular one premise arguments. They must all be reducible, in principle, to:
    A
    Therefore A

    Otherwise I fail to see how they could follow;

    A
    Therefore B

    Only follows if B is in some way related to A, and the only way it can be related to A must be defined through A itself, and thus B must be contained within A (be a particular instance of it). I am a man of faith, and I have faith in common sense.
  • unenlightened
    740
    Well if you want to be so picky, I can modify 3. instead of 2. as you do, thusly:

    4. All men except Buddha and Jesus, who have no other monikers particularly Greek ones, are animals.

    Happy now?
  • Agustino
    4.2k
    4. All men except Buddha and Jesus, who have no other monikers particularly Greek ones, are animals.unenlightened
    No, because 2. would have to say "If Socrates is a man, and Socrates isn't Buddha or Jesus, and he has no other monikers particularly greek ones, then Socrates is an animal"

    It is not defined in 2. whether Socrates is a Greek, whether he isn't Buddha or Jesus, and whatever other conditions you put in 1. And neither is such a thing defined in 1. And it must be defined somewhere for the conclusion to follow. So either you put it as additional premises, or you put it within the conditional. This is necessary - I fail to see how this could be otherwise.
  • Benkei
    381
    If you say "If A then B" then it makes perfect sense to talk about B as the conclusion, and to question whether it follows.Sapientia

    A conditional claim such as "If A then B" has a premiss, which is that A implies B. If A is true (this would be a separate premiss), we could conclude that B is true. You can only conclude B once you have the additional premiss that A is true but the sentence "if A then B" does not state A is true and therefore no conclusion can be made from it.

    p1. If A then B
    p2. A
    C. therefore B
  • Benkei
    381
    Does it? Wouldn't 2. have to say "If Socrates is a man, and Socrates isn't Buddha or Jesus, then Socrates is an animal?" If so, then my criticism is still valid.

    Personally unenlightened, I would be very surprised if there can be non-tautologous and non-circular one premise arguments. They must all be reducible, in principle, to:
    A
    Therefore A

    Otherwise I fail to see how they could follow;

    A
    Therefore B

    Only follows if B is in some way related to A, and the only way it can be related to A must be defined through A itself, and thus B must be contained within A (be a particular instance of it). I am a man of faith, and I have faith in common sense.
    Agustino

    And again: earlier reply
  • Sapientia
    2.1k
    Don't think so.

    If you're in North America, you're an asshole.

    There's nothing about being in North America that causes asshole-hood, so we're just looking at incidence, not consequence. There's an association, but the cause of both could be a third entity.

    The Malankovitch Cycle resulted in an attraction of the world's assholes to North America.
    Mongrel

    It isn't about causation, but it is about a logical connection - whether that is explicated by incidence, causation, or otherwise. And it is nevertheless about consequence, but not if you're just using that as a synonym for "cause". It is saying that if you are in North America, then you are an asshole. That is the consequence of being in North America - whatever the reason. It could be to do with genetics, the environment, the culture, or a coincidence, but logically, in this limited respect, that doesn't make a difference. And there is no way around that one. If that conditional statement is true, then it is logically impossible to simultaneously be in North America and not be an asshole.

    The consequent is true as a result or consequence of the antecedent being true - the latter of which, in your example, would mean being in North America. It is called the consequent for a reason.
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