1. Lecture 7 Modality: Metaphysics of possible worlds
Dr. Donnchadh O’Conaill
14/2/2017
Metaphysics University of Helsinki

2. 1. Introduction
What are possible worlds? i.e., considering the metaphysics of modality
To what are we committed when we say, e.g., ‘Necessarily, p’ or ‘Possibly, p’?
Two options
Possibilism: other possible worlds are possible but not actual entities
Actualism: the only entities which exist are actual entities – we must find some way to accommodate possible worlds in the actual world

3. 2. Possibilism
Possible worlds nominalism is a reductive account of properties and modality in terms of sets of possible worlds:
“it had better be possible to understand what possible worlds are independently of any reference to the things that get explained in terms of them” (Loux )
So how do we understand possible worlds?
“It is uncontroversially true that things might be otherwise than they are. […] Ordinary language permits the paraphrase: there are many ways things could have been besides the way they actually are” (Lewis 1973, 84) …

4. “On the face of it, this sentence is an existential quantification
“On the face of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit ‘ways things could have been’” (Lewis 1973, 84)
What are these entities? Lewis: you know what the actual world is – a collection of concrete particulars
Possible worlds “are more things of that sort differing not in kind but only in what goes on in them” (Lewis 1973, 85) – i.e., collections of concrete particulars

5. Possibilism: entities exist which are possible but not actual
Just as real as the entities in the actual world, but not in the same spacetime
What is the actual world? Lewis: whichever world it is in which an utterance (such as this one) is made
The term ‘actual’ does not mark out anything ontologically distinctive: rather, it is an indexical, like ‘here’

6. Transworld individuals
‘It is possible that I didn’t study philosophy’: this is a true proposition
Does its truth mean that I exist (not teaching philosophy) in a different possible world?
Possibilist: no – rules out transworld individuals, individuals which exist in more than one possible world
Such individuals would be identical but have different properties in different world…

7. Indiscernibility of Identicals
Indiscernibility of Identicals: if a = b, then any property F had by a must be had by b, and vice-versa
Transworld individuals violate this principle
Suppose a exists in possible worlds W1 and W2 - a-in-W1will have properties which a-in-W2 lacks, and vice-versa – e.g., a studies philosophy in W1, not in W2
By the principle above, a-in-W1 cannot be identical with a-in-W2

8. 3. Problems with possibilism
Every individual is world-bound: an entity which exists in one possible world only
Problem: how could things have been different for me? Since I exist in just one possible world, I could not have existed in one of the other ‘ways things could have been’
Undermines the reason for possible worlds
Furthermore, every property I have is essential to me, i.e., a property I have at every world in which I exist

9. Counterpart theory
Lewis: can explain de re modality by counterpart relation, relation of similarity between numerically distinct entities in different possible worlds
“Your counterparts resemble you closely […] But they are not really you” (quoted in Loux, 171)
Essential property: had by me and by all my counterparts in other possible worlds
E.g., nothing could be my counterpart unless it was a person

10. Problems with counterpart theory
“counterpart theorists are not giving us an analysis of our notions of essence and accident: they are changing the subject” (Loux, 180)
I can feel relief or frustration that things didn’t go differently for me: this would make no sense on counterpart theory, since my feelings would be about someone else
Likewise, I might have not studied philosophy – isn’t this truth about me, rather than about some other person?

11. Problems with modality
Necessary proposition: for the possibilist, this is the set of all possible worlds
Problem: on this view all necessary truths are identical, since each is a set with the same members
Likewise with necessarily false propositions (‘Bachelors are married’, ‘Circles are square’)
And with properties instantiated by the same individuals: e.g., ‘having three sides’ and ‘having three angles’

12. 4. Actualism
Actualism: the only things which exist are actual, i.e., in this world
What are the other possible worlds?
Plantinga: start with states of affairs, e.g., my being a lecturer, Paris being in France
Abstract entities
Like Platonic universals, states of affairs are necessary: can exist but not obtain
My being a lecturer obtains; my being a superhero does not – but it does exist, i.e., it is part of the actual world

13. Actualism vs possibilism
“a possible world is a possible state of affairs”: complete, cannot have more or fewer parts (Plantinga 1976, 144)
Merely possible worlds exist in the actual world but do not obtain in this world
Actual world is obtaining state of affairs
“So A, the actual world, is an abstract object. It has no center of mass; it is neither a concrete object nor a mereological sum of concrete objects” (Plantinga 1976, 144)

14. An object is in a possible world = had this world been actual, the object would have existed
Objects in the actual world: those which exist, given that this state of affairs obtains
Essential vs accidental properties: entity x is necessarily F if for any possible world in which x exists, x would be F
But can individuals exist in more than one possible world?

15. 5. Transworld individuals
Actualists: there are transworld individuals
How about Leibniz’s Law? Distinguish:
world-indexed properties: e.g. being tall-in-W1, where W1 is a possible world
non-indexed properties: being tall
The properties things actually have are non-indexed: i.e., John is tall, but also has property of being short-in-W1 – had W1 been actual, John would (actually) have been short
No property that John both has in this world and lacks in W1

16. “How […] can a single thing be in several different worlds at once
“How […] can a single thing be in several different worlds at once?” (Loux, 181)
Plantinga: belief that there are transworld individuals is necessary for many common beliefs, e.g., “When I believe that things could have gone otherwise for me, I believe they could have gone otherwise for this very person” (181)
“to say I exist in possible worlds other than this world is just to say that there are possible worlds […] which are such that had any of them been actual, I would have existed” (182)

17. Explaining transworld identity
What makes objects which exist in different worlds identical across worlds?
Essential properties? No – each of us shares the essential property of being a person
Haecceity: individual essence, “a property such that the thing has it essentially and necessarily nothing other than the thing has it” (Loux, 182)
e.g., property of being identical with Elvis
Problem: do haecceities explain Transworld identity, or require it?

18. Next lecture: is time real?

19. Works cited
Lewis, D. K. (1973) ‘Possible Worlds’ in Counterfactuals. Cambridge MA: Harvard University Press.
Plantinga, A. (1976) ‘Actualism and Possible Worlds’ Theoria 42 (1-3):