Identity and Possible Individuals. Counterfactual Properties. Transworld Identity. Overlap. Haecceitism. Worldbound Individuals. Counterpart Theory. Grammar.
COUNTERFACTUALS
AND
POSSIBLE
WORLDS
Nigel Shardlow
Third Year Dissertation B.A. Honours in Philosophy University of Manchester
I c
Contents
Counterfactuals and Possible Worlds.
CONTENTS Unit 0 0.1 0.2
0.3 0.2.1
0.3.2 0.3.3
Page Introduction The Nature of the Problem Terminological Excursus Motivations for a Positive Account Strengthening the Antecedent Transitivity Contraposition
1 1 3 5
6 6 7
The Analysis of Counterfactuals An Intuitive basis for a Theory Cotenability Possible Worlds Robert Stalnaker David Lewis Similarity
8 8 9 10 10 15 17
Identity and Possible Individuals Counterfactual Properties Transworld Identity Overlap Haecceitism Worldbound Individuals
21 21
Counterpart Theory Grammar Conventions Formal Grammar Semantics CTS5 Models Assignments, denotation and Truth Formal Semantics
35 35 35
4.1 4.2
Possible Worlds Commitment to worlds What worlds could be
40 40 44
5
Conclusion
46
1.1
1.2 1.3 1.3.1
1.3.2 1.3.3
2 2.1
2.2 2.2.1 2.2.2 2.3
3 3.1 3.1.1 3.1.2
3.2 3.2.1
3.2.2 3.2.3 4
Page
.1
23 24 26 31
36 37 37 38 38
Contents
0
Introduction We are apt to talk of circumstances and things which are, in a sense, not.
Profumo didn't make Prime Minister, but we still talk about what would have happened if he had. James Dean is dead, but we still make guesses about what he would look like, if he were alive today. In the first case we talk directly of a possible but nonactual state of affairs; in the second we ascribe properties to a possible but nonactual individual. Both examples involve a particular sort of conditional sentence, the counterfactual conditional The search for the correct analysis of counterfactual conditionals
B are given as follows [ 1973.49]. A
>
B is true at i if f either (i)
There is no A-world accessible from i
(ii)
There is an A-world k accessible from i such that, for any world j, if j (1. k then A
=>
or
B is true at j.
This version of the semantics no longer assumes that there is some closest , these worlds can be identified with sets of linguistic entities of some kind, such as maximally consistent sets of propositions. It needs to be emphasised that the 'language' out of which the Linguistic modal realist constructs his worlds need not be a language such as you or I speak. It can be a construction out of pure sets, or abstract propositions. The stock objection to Genuine modal realism is epistemological: how do we acquire our modal knowledge if possible worlds are spatiotemporally isolated from our own? Since the Genuine modal realist thinks that worlds are concrete, it's not even clear that he can argue that we acquire our modal knowledge in the same· way we acquire mathematical knowledge. Mathematical objects are at least abstract. s The stock objection to Linguistic modal realism is that
it is circular
insofar as it must take modality as primitive in its definition of consistency: A consistent set of sentences is a set the members of which could all be true together. I
think that the debate between these versions of modal realism is an empty
one.
In
the
earlier
chapters
of
this
dissertation
I
have
examined
counterfactuals, counterparts, and formal modal semantics, all of which involve the use of the concept of a possible world, without once declaring my allegiance to either of the two main brands of realism. I was able to do this because possible worlds play a definite role in the study of each of those topics, and they can play that
rOle,
and shed light on those subjects,
irrespective of
whether we can provide an answer to the quest ion of what they are.
Page 45
Chapter 4
5
Conclusion
The following summary remarks can serve as a conclusion to this investigation: Possible worlds semantics has yielded genuine insights into the logical properties
of
counterfactual
conditionals,
both
as
they
are
used
in
ordinary language, and as they are used in decision theory, probability theory and other scientific fields. These insights have been achieved by separating
issues
concerning
the
general
logical
properties
of
counterfactuals from issues concerning the evaluation of counterfactuals in specific contexts. The semantical analysis of counterfactuals has shed no light on the problem of law,
which was
for a
long time seen as the one and only
problem of counterfactual conditionals, although it has generated a new primitive,
similarity
