of a number

machadinho

Senior Member
Português do Brasil
Russell's own formal implementation of the Theory of Descriptions suggests a significant gap between surface syntax and logical form. But upon reflection it is clear the gap has little to do with descriptions per se. In order to characterize the logical forms of quantified sentences "every F is G" or "some F is G" in standard first-order logic we have to use formulae containing sentence connectives, no counterparts of which occur in the surface forms of the sentences. And when we turn to a sentence like "just two Fs are G", we have to use many more expressions that do not have counterparts in surface syntax, as well as repetitions of a number that do [have counterparts in surface syntax]:
(31) ∃x ∃y ((x≠y • Fx • Fy • Gx • Gy) • ∀z ((Fz • Gz) ⊃ (z=x V z=y))).
(Neale, Facing Facts, p108-9)​
Hi. What does of a number mean here?¹
(a) we have to use a number of repetitions (i.e, many repetitions)
(b) we have to use repetitions of that number in blue.
(c) we have to use as many repetitions as 2
(d) ?
Thanks a lot! :)
¹The formula (31) means "just two Fools are Goo", in contrast to a much simpler formula, ∃x(∀y(Fy ≡ y=x) • Gx), which means "the Fool is Goo".
 
  • Egmont

    Senior Member
    English - U.S.
    In addition to using expressions that do not have counterparts in surface syntax, we also have to use repetitions of expressions that do [have counterparts in surface syntax].

    Does that help?
     
    < Previous | Next >
    Top