# Quantifier clause in Heim's presupposition theory

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}

• 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? 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" 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. May 1, 2021 at 1:33