1. Lecture 6 Modality: Possible worlds
Dr. Donnchadh O’Conaill
9/2/2017
Metaphysics University of Helsinki

2. 1. Introduction
Modal notions: Necessity, possibility, contingency, impossibility
Different strengths relative to different contexts:
Physical: proposition p is necessary, possible etc. given the laws of nature, physical nature of the world, etc.
Logical: p is necessary etc. given the laws of logic, i.e., p doesn’t entail a contradiction
Metaphysical: different entities can exist together, or exclude each other

3. Different kinds of modality
De dicto modality: modality applied to whole propositions – ‘Necessarily, p is true’ or ‘Possibly, p is true’
De re modality: modality applied to objects – e.g., I am necessarily a person, contingently a lecturer
These kinds of modality can come apart:
‘Necessarily, the number of planets = 8’
‘The number of planets is necessarily 8’
(1) is de dicto, and is false; (2) is de re, and true

4. 2. Challenges to modality
(i) Do we have a clear grasp of modal notions?
Empiricists: experience reveals what is the case, not what could be or is necessarily
“the only necessity is verbal necessity” (Loux 2006, 155) e.g., bachelors are necessarily male by definition
(ii) Non-extensionality of modal discourse
Extensional discourse: substitution of co-referring terms does not change truth-value of sentences
Non-extensional: substitution changes truth-values…

5. (3) ‘There is water in the cup’ is extensional
Substitute ‘H2O’ for ‘water’:
(4) ‘There is H2O in the cup’ – same truth-value as (3) – but now consider:
(5) John thinks that there is water in the cup
After ‘thinks’, this is a non-extensional context: same substitution gives us
(6) ‘John thinks that there is H2O in the cup’
But John may not think any such thing! He may be ignorant of the chemical make-up of water

6. Modal discourse is non-extensional
Suppose George is the tallest person in the room – now consider the following:
(7) George is male
(8) Necessarily, George is male
(7) would remain true if we substitute for ‘George’ the co-referring expression ‘the tallest person in the room’
But (8) would become false: even if the tallest person is the room is male, this is not a necessary truth

7. Importance of extensional discourse
Extensional contexts are governed by clear rules of inference: “where language is extensional, we have logics that make clear precisely which sentences follow from any set if sentences” Loux, 156
So in principle we know what we are committed to by accepting any set of sentences
Worry is that non-extensional contexts are not governed by such rules: we have no clear grasp of what we are committed to

8. 3. Possible worlds
“I think there is an infinity of possible ways in which to create the world, according to the different designs which God could form, and that each possible world depends on certain principal designs or purposes of God […] certain laws of the general order of this possible universe” (Leibniz 1956, 333)
Without reference to God: “ways, complete or total ways, things might have been” (Loux 159)

9. Different ways things might have been can determine the truth of modal claims:
“we take the different ways things could be to constitute the truth makers for our pre-philosophical modal beliefs” Loux 159
E.g., a necessary truth is one which would have been true no matter how things had turned out
Possible truth: one which would have been true had things gone a certain way

10. Proposition can be true in one possible world but false in another:
‘Elvis is alive’ is true given some ways things might have been, false in others
This gives us a way to understand modal concepts
“in possible world semantics, the modal operators are interpreted as quantifiers over possible worlds” (Menzel 2013, § 1.2)
Necessarily true: true in all possible worlds
Possibly true: true in some possible world

11. Possible world and de re modal truths
Different possible worlds can include different objects
Often thought that the same object can exist in more than one possible world: e.g., I exist in this world but I would have existed had I become a pilot
Necessity de re: x is necessarily F – i.e., in every possible world containing x, x is F
This is necessary even though x itself is not
Possibility de re: x is possibly F – in some possible world, x exists and is F

12. 4. Possible worlds nominalism
Austere nominalist: talk about a property is talk about a set of concrete particulars
Problem: different predicates can be satisfied by same class of particulars – e.g., ‘human’, ‘featherless biped’
But the class of humans in any possible world is different from class of featherless bipeds in any possible world
e.g., a possible world with feathered humans?
Properties as sets of particulars from across all possible worlds

13. Nominalist accounts of modality
Proposition: a set of possible worlds
“like global properties that partition worlds rather than their inhabitants into sets” Loux, 165
Necessary truth: a set of possible worlds which contains every possible world
Possibly true: a set of possible worlds contains at least one possible world
‘It is possible that Elvis is alive’ – the set of possible worlds in which Elvis is alive contains at least one member

14. Necessarily false: a set of possible worlds which contains no members, i.e., is empty
E.g., ‘All bachelors are married’ would be false no matter how things turned out
How about de re modality?
x is necessarily F: x belongs to the set of F-objects in every possible world where x exists
x is possibly F: x belongs to the set of F-objects in at least one world in which x exists

15. Next week: the metaphysics of possible worlds…

16. Works cited
Leibniz, G. W. F. (1956) Philosophical Papers and Letters (trans. Loemker, L. E.) Dordrecht: Reidel
Menzel, C. (2013) ‘Possible Worlds’, Stanford Encyclopedia of Philosophy