• Michael
    15.6k
    And to repeat my earlier question yet again, do you believe that this statement is true?

    London is the capital city of England and/or I was born in Leeds.
  • creativesoul
    11.9k
    Smith believes Jones owns a Ford. Smith believes that the statement 'Jones owns a Ford' is true. Smith believes the disjunction 'Jones owns a Ford or Brown is in Barcelona' follows from the statement 'Jones owns a Ford'.

    Now from here, you and Gettier want to say that Smith believes that the disjunction 'Jones owns a Ford or Brown is in Barcelona' is true.

    Is that right?
  • creativesoul
    11.9k
    p1. ((p) is true)
    p2. ((p v q) follows from (p))
    p3. ((p v q) is true if either (p) or (q) is true)
    C1. ((p v q) is true because (p))(from p1,p3)

    Elegance
  • Michael
    15.6k
    Smith believes that Jones owns a Ford. Smith believes that the statement 'Jones owns a Ford' is true. Smith believes the disjunction 'Jones owns a Ford or Brown is in Barcelona' follows from the statement 'Jones owns a Ford'.

    Now from here, you and Gettier want to say that Smith believes that the disjunction 'Jones owns a Ford or Brown is in Barcelona' is true.

    Is that right?
    creativesoul

    Yes. But Gettier doesn't just want to say it. He does say it. It's one of those premises that it doesn't make sense to refute, like "Jones was renting a Ford".
  • Michael
    15.6k
    p1. ((p) is true)
    p2. ((p v q) follows from (p))
    p3. ((p v q) is true if either (p) or (q) is true)
    C1. ((p v q) is true because (p))(from p1,p3)

    Elegance
    creativesoul

    C2. p ∨ q is true (from C1)
  • creativesoul
    11.9k
    Rational people do not believe statements unless they know what they mean. Knowing what a disjunction means is to know what makes them true. You and Gettier leave that part of Smith's thought/belief process sorely neglected.
  • creativesoul
    11.9k
    p1. ((p) is true)
    p2. ((p v q) follows from (p))
    p3. ((p v q) is true if either (p) or (q) is true)
    C1. ((p v q) is true because (p))(from p1,p3)
  • Michael
    15.6k


    C2. p ∨ q is true (from C1)
  • creativesoul
    11.9k
    Your report of Smith's thought/belief process is utterly inadequate.
  • creativesoul
    11.9k
    Rational people do not believe statements unless they know what they mean. Knowing what a disjunction means is to know what makes them true. You and Gettier leave that part of Smith's thought/belief process sorely neglected.
  • creativesoul
    11.9k
    Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))

    Salva veritate
  • Michael
    15.6k
    Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))creativesoul

    How many times am I going to explain this? I'm not saying that they're equivalent. This is just a strawman.

    I'm saying that the latter entails the former.

    Salva veritate

    Why do you keep saying this? It has no bearing on our discussion.
  • creativesoul
    11.9k
    p1. ((p) is true)
    p2. ((p v q) follows from (p))
    p3. ((p v q) is true if either (p) or (q) is true)
    C1. ((p v q) is true because (p))(from p1,p3)

    There are no problems with this formula. Imagine any disjunction arrived at by virtue of deducing it from believing P. Fill it out.
  • creativesoul
    11.9k
    Your logic and/or some of the rules are wrong. Brace yourself. I've dissolved disjunction problems...
  • Michael
    15.6k
    There are no problems with this formula. Imagine any disjunction arrived at by virtue of deducing it from believing P. Fill it out.creativesoul

    I'm not saying that there are problems. I'm saying that it's incomplete, which is why I am filling it out:

    C2. p ∨ q is true (from C1)
  • Michael
    15.6k
    Your logic and/or some of the rules are wrong.creativesoul

    No, yours are. You've said "False premisses and valid form cannot yield true conclusions". And of the following you've said "Can't get to 3 from 1 and 2. Can't get to 6 from 4 and 5":

    1. p
    2. p ⊨ p ∨ q
    3. p ∨ q

    4. Socrates is a man
    5. If Socrates is a man then Socrates is mortal
    6. Therefore, Socrates is mortal

    You're just wrong on all accounts.
  • creativesoul
    11.9k
    Salva veritate

    Why do you keep saying this? It has no bearing on our discussion.

    It bears on the discussion by virtue of pointing out that the two are not equivalent.

    Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))

    The former neglects the other deduction. The latter exhausts the former, but not the other way around. The latter is utterly inadequate for representing the necessary thought/belief process required for believing Q when Q is a disjunction arrived at from believing P.
  • creativesoul
    11.9k
    There you go again using simple beliefs and statements thereof...

    Irrelevant.

    Use a disjunction. Apply my formula. Show a problem with the result.
  • Michael
    15.6k
    It bears on the discussion by virtue of pointing out that the two are not equivalent.

    Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))

    The former neglects the other deduction. The latter exhausts the former, but not the other way around. The latter is utterly inadequate for representing the necessary thought/belief process required for believing Q when Q is a disjunction arrived at from believing P.
    creativesoul

    But I'm not saying that they're equivalent. I'm saying that the latter entails the former.

    If I believe that Donald Trump is the President because he won the popular vote then I believe that Donald Trump is the President.

    So if I believe that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford then I believe that Jones owns a Ford or Brown is in Barcelona.
  • Michael
    15.6k
    I did use a disjunction:

    1. p
    2. p ⊨ p ∨ q
    3. p ∨ q

    I swear you're just being wilfully ignorant now. But then you've repeatedly shown that you don't understand basic logic, so perhaps it isn't wilful.
  • creativesoul
    11.9k
    1. p
    2. p ⊨ p ∨ q
    3. p ∨ q

    4. Socrates is a man
    5. If Socrates is a man then Socrates is mortal
    6. Therefore, Socrates is mortal

    There's something missing. Do you not notice?

    "All men are mortal" is missing from the latter. p v q is true because p is missing from the former.
  • creativesoul
    11.9k
    Use a disjunction and put the argument in English terms... long form.
  • Michael
    15.6k
    There's something missing. Do you not notice?creativesoul

    There isn't. They're valid. It's modus ponens.
  • creativesoul
    11.9k
    :-O

    I've little to no reason to continue this discussion. You deny a clearly missing premiss, and are attempting to brow beat me with man-made rules that do not take proper account of actual thought/belief processes...
  • Michael
    15.6k
    I did use a disjunction:

    1. p
    2. p ⊨ p ∨ q
    3. p ∨ q

    And in English

    1. London is the capital city of England
    2. If London is the capital city of England then by entailment London is the capital city of England and/or I was born in Leeds
    3. Therefore, London is the capital city of England and/or I was born in Leeds
  • Michael
    15.6k
    I've little to no reason to continue this discussion. You deny a clearly missing premisscreativesoul

    Because there isn't one. Just look up modus ponens:

    If something is F, it is G.
    a is F.
    Therefore, a is G.

    If Socrates is a man then he is mortal
    Socrates is a man
    Therefore, Socrates is mortal
  • creativesoul
    11.9k
    Rational people do not believe statements unless they know what they mean. Knowing what a disjunction means is to know what makes them true. You and Gettier leave that part of Smith's thought/belief process sorely neglected.
  • Michael
    15.6k
    Smith knows what "Jones owns a Ford or Brown is in Barcelona" means. That's how he knows that it follows from "Jones owns a Ford". Your arguments just don't make any sense.

    I believe that London is the capital city of England, and so I believe that "London is the capital city of England or pigs can fly" is true.

    Smith believes that Jones owns a Ford, and so he believes that "Jones owns a Ford or Brown is in Barcelona" is true.
  • creativesoul
    11.9k
    I agree that Smith knows what the disjunction means.

    Knowing what a disjunction means requires knowing what makes it true.
  • Michael
    15.6k
    I agree Smith knows what the disjunction means.

    Knowing what a disjunction means requires knowing what makes it true.
    creativesoul

    Yes, and he believes it to be true. And it's true. So he has a true belief.
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