• Nicholas Ferreira
    78
    Bertrand Russell, on his "On Denoting", states that “the father of Charles II was executed” becomes
    It is not always false of x that x begat Charles II and that x was executed and that ‘if y begat Charles II, y is identical with x’ is always true of y”.
    This last sentence is logically expressed as ¬(∀x)[¬(Bx∧Ex∧(∀y)[By⊃(y=x)])], which is logically equivalent to (∃x)[Bx∧Ex∧(∀y)[By⊃(y=x)]]. But this sentence is false, since the third part of the conjunction ((∀y)[By⊃(y=x)]) is false. And (∀y)[By⊃(y=x)] is false because there is an y such that y begat Charles II and y≠x. In this case, y is the mother of Charles II, who begat him and wasn't executed.

    Is my analysis correct? For me, his 'translation' for "the father of Charles II was executed" doesn't have enough predicates to distinguish x from other things, and since there is more than one thing that begat Charles II, he would need to predicate another characteristic to confer uniqueness to x.
    A solution for this would be consider "It is not always false of x that x begat Charles II and that x was executed and that x was a man and that ‘if y begat Charles II and y was a man, y is identical with x’ is always true of y". That is ¬(∀x)[¬(Bx∧Ex∧Mx∧(∀y)[By∧My⊃(y=x)])]. This is true, because although there are more than one thing that begat Charles II, there is only one which begat him and that is a man.

    What do you think?

  • Snakes AliveAccepted Answer
    743
    'Begat' traditionally refers to paternity. 'Bore' refers to maternity.
  • Nicholas Ferreira
    78
    Oh, I thought it could be the case, but since english isn't my native language, I used a translator and thought that "begat" could be applied to both paternity and maternity. Thanks!
  • Terrapin Station
    13.8k
    The real "error" is why you'd think that “the father of Charles II was executed” would amount to anything like “It is not always false of x that x begat Charles II and that x was executed and that ‘if y begat Charles II, y is identical with x’ is always true of y” for anyone except for perhaps some lone extremely OCDish weirdo.
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