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               Meaning, Reference & Modality.  Assignment 3
                           Andreas van Cranenburgh, 0440949
                              Tuesday, November 24, 2009

Exercise 1

Both hold. If phi can be repeated twice and produce an output assignment,
then it shows that phi does not prohibit outputs as is the case when
phi |/= phi, which occurs when phi binds a variable in such a way that
free occurrences of it in phi no longer hold. But if phi ^ phi is satisfiable,
this cannot be the case.

If that is not the case then phi must be idempotent, so that
after uttering it twice it can be uttered for a third time.

Although perhaps a self-referential sentence could be imagined like this:

  "I have not said this sentence twice"

.. which could be truthfully uttered twice, yet not a third time. However,
such a sentence does not seem possible in dynamic predicate logic.


Exercise 2

A structural difference between these examples and the ones in the paper is
that in these examples the dimes are existentially quantified, whereas the
donkeys are universally quantified. The parking meter is satisfied with only 
one dime.

We can give these sentences an intuitively correct interpretation by adding a
definition for the implication, instead of defining it in terms of
conjunction and negation:

[[phi -> psi]] = { <g, h> | h = g & if there is a k: <h, k> in [[phi]]
                       then there is a j: <k, j> in [[psi]] }

(the difference being that k is existentially quantified instead of
universally, as in the standard donkey sentence interpretation)

This solution also works for example (4) because only the definition of
implication is affected, not that of the quantifiers.


Exercise 3

It is consistent yet not coherent. It is consistent because it might be the
case that we do not know who Alfred is. Suppose we are in a state with the
following possibilities (Coreference & Modality, p. 10):

 - i: a denotes d, I(P) = {}
 - i': a denotes d', I(P) = {d}

Both possibilities remain after the first two conjuncts, but after the third
only the first remains. Since there is still a possibility left, the
conjunction is consistent.

However it is not coherent, because there is no state which supports this
conjunction. To see this, notice that to make the second conjunct true in some
state, this state should always have a possibility where I(P) is non-empty
(someone has done it). In this possibility, `a' will refer to some object not
in I(P), whereas x will have been assigned some object in I(P). But then,
after the third conjunct, this possibility has to go, and thus the sequence is
not coherent.


Exercise 4

These views are consistent. Just as Kripke argues that it is not
a priori known that Hesperus is Phosphorus (epistemic), while it is necessary
that they are equal (ontological).
Perhaps these views can be made consistent by letting the different modal
operators rangs over two different indices of worlds, in a 2-dimensional
semantics.  Horizontally would be the ontological distinctions, vertically the
epistemic. The operator M affects only the rows, the box and diamond
affect the columns. Names are rigid in each row, but non-rigid in the columns.


Exercise 5

The examples are handled by conceptual covers, which specify a way of
identifying individuals in a world. Ralph has two different conceptions of
Ortcutt, which is why he has the paradoxical beliefs. Ralph's beliefs do not
have to be inconsistent, as long as there are two different conceptual covers
in operation. This also goes for the speaker, since the conceptual covers
are selected pragmatically, if they are available and needed.


Exercise 6

1. The last translation is redundant because the first conjunct can be seen
as an instance of the principle LIn:  x_n = y_n -> []x_n = y_n
Also, a conceptual cover by definition has to specify an unique way of 
identifying each individual in a domain.

2. A conceptual cover with the non-rigid concept "lambda w [Ortcutt]w" to
cross-identify Orcutt. This means that whatever the world, Ortcutt refers to
Ortcutt in that world.
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