PHIL3212: Contemporary Metaphysics
Week 12: Ways and Possible Worlds and Propositions
Possible worlds
1. It is popular to account for modality in terms of possible worlds:
a. It is possible that Graham passes iff in some possible world Graham passes
b. It is necessary that Graham passes iff in every possible world Graham passes
2. What is a possible world? Here is Lewis:
I believe that there are possible worlds other than the one we happen to inhabit. If an
argument is wanted, it is this. It is uncontroversially true that things might be otherwise
than they are. I believe, and so do you, that things could have been different in countless
ways. But what does this mean? Ordinary language permits the paraphrase: there are
many ways things could have been besides the way they actually are. On the fact of it, this
sentence is an existential quantification. Is says that there exist many entities of a certain
description, to wit ‘ways things could have been’. I believe that things could have been
different in countless ways; I believe permissible paraphrases of what I believe; taking the
paraphrase at its face value, I therefore believe in the existence of entities that might be
called ‘ways things could have been’. I prefer to call them ‘possible worlds’.
3. So according to Lewis possible worlds are, by definition, ways things could have been.
So they are ways. So they are properties, according to what we have been doing.
4. If they are properties then they are not particulars, as Lewis takes them to be (he takes
them to be particulars, of the same kind as our actual world).
5. Properties of what? Plausibly, the world. This is what Stalnaker thinks.
Propositions
6. It is often thought that there are such things as propositions.
7. Why? To explain various phenomena. Such as:
a. If I assert something using ‘snow is white’ and a French speaker asserts something
using ‘la neige est blanche’ then there is some thing that we both assert. That thing is a
proposition.
8. Some standard claims:
a.
b.
c.
d.
e.
Propositions are the meanings of declarative sentences (relative to contexts)
Propositions are the primary objects of belief
Propositions are the primary bearers of truth
Propositions are the primary bearers of possibility and necessity
Propositions are the primary relata of entailment
9. What is a proposition? Some or all of the following are often claimed:
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a. They are particulars
b. They are abstract
c. They have structure.
i. If you understand what I mean by ‘San Francisco’, what I mean by ‘is hilly’, and
the structure with which I am using the sentence, then you are thereby in a position
to understand what I mean by ‘San Francisco is hilly’; this is explained if that
which I mean by ‘San Francisco is hilly’ (the proposition that San Francisco is
hilly) is a structured thing having as constituents that which I mean by ‘San
Francisco’ and that which I mean by ‘is hilly’.
d. According to the Russellian view of propoitions, the proposition that San Francisco is
hilly has San Francisco (the city) as a constituent, and also the property of being hilly.
e. They have modes of presentation.
i. This allows the Russellian view to explain why it seems true that Lois believes that
Superman is strong but false that Lois believes that Clark Kent is strong, even
though the proposition that Superman is strong is the proposition that Clark Kent is
strong.
f. They are sets of possible worlds.
Propositions are ways
10. Here are three reasons to think that the proposition that cows eat grass is a way:
a. “As it happens, cows eat grass, but things might not have been that way.” Here I have
used ‘that way’ unproblematically to refer to that which I mean by ‘cows eat grass’
(the proposition that cows eat grass). I could not do this unproblematically unless that
thing is a way. Try it: “I saw Hilary Clinton last night; I love that way.”
b. “Cows eat grass – that is the way things are.” Here I have used ‘that’
unproblematically to refer to that which I mean by ‘Cows eat grass’ (the proposition
that cows eat grass), and to say of this thing that it is the way things are. I could not do
this unproblematically unless that thing is a way. Try it: “I saw Hilary Clinton last
night; that is the way I most admire.”
c. “How are things in Australia? In Australia, cows eat grass.” Here I have used ‘cows eat
grass’ unproblematically to specify how things are in Australia; that is, to specify the
way things are in Australia. I could not do this unproblematically unless that which I
mean by ‘cows eat grass’ (the proposition that cows eat grass) is a way. Try it: “How
does John walk? John walks in the park.”
11. A similar trio of arguments can be given for any proposition. So:
Propositions are ways
(For all p: if p is a proposition then p is a way)
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12. Here is some evidence that propositions are not ways, at least not always:
a. If I tell you that John believes that San Francisco is hilly, then it would be problematic
for you to respond by asking, “John believes how?”
b. If the proposition that I mean by ‘that San Francisco is hilly’ were a way, then we
would expect to be able to form an echo question by replacing ‘that San Francisco is
hilly’ by ‘how’. After all, there are many cases in which we can do this kind of thing:
John walks like a duck; John walks how? John eats as if he is starving; John eats how?
John swims like Mary; John swims how?
13. Perhaps the reason it is problematic in the case of ‘John believes how?’ is that on its
natural interpretation this expresses a question about the way in which John believes, and
not about which way it is that is the object of his belief – this is problematic because the
expression that ‘how’ replaces is used to specify the latter and not the former.
Propositions are properties
14. I have just argued that propositions are ways. I have also argued that ways are properties.
Putting these together we get:
Propositions are properties
(For all p: if p is a proposition then p is a property)
15. If propositions are properties, then what are they properties of? I can think of two answers:
a. They are 1-place properties of the world (or worlds, if there is more than one).
b. They are 0-place properties, such that when they are instantiated there is no thing by
which they are instantiated. This idea is not obviously absurd – it is, for example,
common practice in predicate calculus to think of sentence letters as 0-place predicate
letters, denoting 0-place properties (i.e. truth values).
16. To fix the discussion, I will assume that there is such a thing as the world, that there is just
one of them, and that propositions are properties of the world.
17. By ‘property of the world’ I do not mean a property that the world actually has; I mean to
include properties that the world does not have but used to have, or will have, or might
have had, or might have, and so on. I mean any property such that the world is the kind of
that can have that property (whether or not it actually does).
If propositions are properties of the world, can we make the usual claims?
18. Propositions are particulars?
a. It seems that this would have to go: properties are not particulars.
19. Propositions are abstract?
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a. Many take properties to be abstract.
20. Propositions have structure?
a. Many take properties to have structure. If you understand what I mean by ‘loves’, what
I mean by ‘Mary’, and the structure with which I am using the verb phrase ‘loves
Mary’, you are thereby in a position to understand what I mean by ‘loves Mary’; this is
explained if that which I mean by ‘loves Mary’ (the property of loving Mary) is a
structured thing having as constituents that which I mean by ‘loves’ and that which I
mean by ‘Mary’.
21. Propositions are Russellian?
a. It seems plausible that properties are Russellian: that the 1-place property of loving
Mary, for example, is a structured property having as constituents the 2-place relation
of loving and the particular Mary.
22. Propositions have modes of presentation?
a. It seems plausible that properties have modes of presentation. Suppose that ‘royal red’
and ‘postbox red’ denote the same colour property. It is plausible that someone might
believe that a certain colour patch is royal red, but not believe that it is postbox red,
even though royal red is postbox red.
23. Propositions are sets of possible worlds?
a. I have proposed that possible worlds are properties of the world.
b. And that propositions are properties of the world.
c. Here is an idea: possible worlds are maximally specific properties of the world. That is,
they are maximally specific propositions.
d. Then we can take a proposition to be a set of possible worlds: any property p has a set
of maximally specific determinates, and we can identify p with that set of properties.
So what if propositions are properties?
24. Perhaps it reduces our ontological commitments.
25. More significantly, it collapses the study of propositions into the study of properties. In
particular, the study of: truth, assertion, and entailment.
Truth
26. What is truth? Or: what is it for something to be true? Some famous answers:
a.
b.
c.
d.
The correspondence theory
The coherence theory
The pragmatic theory
The deflationary theory
27. Here’s my hat to throw into the ring:
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Truth is instantiation
(For a proposition to be true is for it to be instantiated)
(If propositions are 1-place properties, then it is for it to be instantiated by the world; if
they are 0-place properties, then it is for it to be instantiated, simpliciter.)
28. Then the problem of figuring out the nature of truth is just the well-known problem of
figuring out the nature of instantiation. There is just one phenomenon here, not two.
Assertion
29. If truth is instantiation then it is natural to propose:
Assertion is predication
(To assert a proposition is to predicate it)
(If propositions are 1-place properties, then it is to predicate it of the world; if they are 0place properties, then it is to predicate it, simpliciter.)
30. Note that we sometimes use ‘true’ when predicating properties:
a. It is true of San Francisco that it is hilly
31. Here is a possibility:
a. We use sentences of the form ‘It is true of X that F’ to predicate properties of things –
in place of ‘X’ we use a referring term; in place of ‘F’ we use a property expression.
b. As a special case we have ‘It is true of the world that F’, which we shorten to ‘It is true
that F’.
c. The complement of ‘that’ is always a property expression.
Entailment
32. What should we say about propositional entailment?
33. We could say this:
a. For proposition p to entail proposition q is for it to not be possible for the world to
have p but not q.
34. More generally:
a. For property p to entail property q is for it to not be possible for something to have p
but not q.
35. But this gives us the paradoxes of entailment.
36. If propositions are properties then we can try the following:
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Entailment is determination
(For a proposition p to entail a proposition q is for p to be a determinate of q)
37. More generally:
For property p to entail property q is for p to be a determinate of q
38. We do get: that grass is green entails that grass is coloured. Why? Because the proposition
that grass is green is a determinate of the proposition that grass is coloured (it makes sense
to say, “Grass is coloured; more specifically, grass is green.”).
39. We do get: that 2 + 2 = 4 entails that 2 + 2 > 3. Why? Because the proposition that 2 + 2 =
4 is a determinate of the proposition that 2 + 2 > 3 (it makes sense to say, “2 + 2 > 3; more
specifically, 2 + 2 = 4.”).
40. We do get: that 2 + 2 = 5 entails that 2 + 2 > 3. Why? Because the proposition that 2 + 2 =
5 is a determinate of the proposition that 2 + 2 > 3 (it makes sense to say, “2 + 2 > 3; more
specifically, 2 + 2 = 5.”).
41. We do not get: that 2 + 2 = 5 entails that grass is green. Why not? Because the proposition
that 2 + 2 = 5 is not a determinate of the proposition that grass is green (it does not make
sense to say, “Grass is green; more specifically, 2 + 2 = 5.”).
42. We do not get: that grass is green entails that 2 + 2 = 4. Why not? Because the proposition
that grass is green is not a determinate of the proposition that 2 + 2 = 4 (it does not make
sense to say, “2 + 2 = 4; more specifically, grass is green.”).
43. The proposal respects the idea that for p to entail q there needs to be some kind of
connection between p and q.
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