2

there is a point in a paper by Irene Heim related to problems with presuppositions in complex sentences that I do not properly get. The article is the following: https://onlinelibrary.wiley.com/doi/10.1002/9780470758335.ch10

In particular, I do not understand why the following should be the correct clause for the context updating operation determined by a quantifier:

c + Everyxi,A, Β = {(g, w) in c such that : for every a, if(g i/a ,w) belongs to c+A,then(g i/a ,w) in c+A+B}

In particular, I do not understand the role of the sequence function "g" that maps integers to objects of a domain and why the condition Heim gives should have intuitive appeal and relate to truth-conditional readings of the universal quantifier Edit:

I write how I have understood the notion of g succession, in order to see if I have the right concept in mind when looking at the paper:

In predicate logic, in order to give truth condition to quantfied sentences with respect to n interpretation structure M, we use succession in the following way. I write v for the valutation function that, with respect to a structure M and a succession s, gives a truth value to a formula.

v(M,s) gives truth to ∀xiA iff for all the successions s[i/a], differing from s for the i-th element they assign to i, v(M,s[i/a]) gives truth to A.

An equivalent formulation should be:

v(M,s) gives truth to ∀xiA iff for all the elements d of the domain of M, the succession s[i/a], differing from s for the i-th element they assign to i, v(M,s[i/a]) gives truth to A.

Now, in the context of the paper, what should be the CCP of, for instance, ∀xiFxi?

I think it should be:

{<g,w>in c such that for all elements e in D, g(e) is F in w}

Improve this question
3
  • 1
    The g and g i/a is nothing special to the presupposition paper, this is just the ordinary truth-functional semantics of quantifiers. If you don't understand sequence functions in general, I would suggest starting with a good book on predicate logic/asking a question about the general mechanism of quantifier evaluation before going at advanced applications like in the paper. Otherwise, if you understand what g and g i/a are for in general but not in this particular context, can you specify more precisely what it is that throws you off?
    – Natalie Clarius
    Apr 29, 2021 at 23:00
  • I tried to understand how should the clauses for simple quantifier formulas be formulated and added a part in which I present how I understand the concept of succession for FOL. I think that understanding how to apply the CCP model on simple quantification cases could help me understand the quantificational "For all x such that Fx then Gx"
    – PwNzDust
    Apr 30, 2021 at 9:17
  • Your understanding is correct, but the phenomenon the paper is interested in is the particular case of sentences like (7), where the F(xi) part is of the form A(xi) -> B(xi) with B containing a possessive pronoun whose antecedent is in A. That's where presuppositions arise, and that's why the more complicated definition is needed.
    – Natalie Clarius
    May 1, 2021 at 1:33

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.