Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

The Two-Fold Sense of ‘The Actual World’

A correspondent poses the following difficulty:

. . . compare two possible worlds W1 and W2. What makes them different worlds? Their constituent substances and events – that’s how we identify a world. Let’s say that W1 and W2 are distinct possible worlds, and add that A, the actual world, is in fact W1. [. . .] And then we seem to have a problem: It turns out that W1 = A, but W1 ≠ W2. But if we say that A could have been W2, then it seems that W1 could have been W2 – but that’s impossible, given the necessity of identity. What to do, what to do . . . .

Think about how you would respond to this before proceeding.

I believe that the above is a pseudoproblem engendered by a failure to distinguish between 'A' used as a proper name or Kripkean rigid designator, and 'A' used as a definite description. Although there is and can be only one actual world, every world is possibly such that it is actual. Suppose that 'A' names, i.e., rigidly designates, our world, the world that happens to be actual. Then from the fact that other worlds could have been actual, it does not follow that any of these other worlds could have been identical to A. What follows is merely that they could have been actual.   'The actual world' is ambiguous.  It could be used as a substitute for the rigid designator 'A,' or it could be used as a definite description that is satisfied by whichever world happens to be actual.  The following is a consistent set of propositions:

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Bill Vallicella

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6 responses to “The Two-Fold Sense of ‘The Actual World’”

  1. Mike Avatar
    Mike

    If ‘the actual world’ is a rigid designator of our world, the world that happens to be actual, then the answer is in the negative: the actual world is not necessarily actual since it could have been non-actual.
    I’m a little confused. You seem to use ‘actual’ as a property and predicate it of our world in ‘the actual world is actual’. But the question concerns identity claims, right? On the one hand, taken as the ‘is’ of predication, if ‘the actual world’ is a rigid designator, then whatever is true here, for example that it is raining, is true at W2. So, it is true at W2 that it is raining in the actual world. This works the way ‘here’ does in the expression ‘it is true in China that it is raining here’ (in the southwest, U.S.). On the other hand, taken as the ‘is’ of identity, and still using ‘the actual world’ rigidly, it’s true as well at W2 that (using ‘@’ as a name for our world) @ is the actual world. Both expressions pick out our world, neither picks out W2. On yet a third hand, it is true that ‘actual’ has both a shifty and non-shifty sense, as Lewis puts it. In the non-shifty sense it’s true that ‘I could have been faster than I actually am’, but in the shifty sense, (if ‘@’ names our world), then @ might not have been the actual world. We let ‘the actual world’ shift reference from world to world.

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  2. David Brightly Avatar
    David Brightly

    Bill,
    Do we not have a problem of logical priority here? If the apparatus of possible worlds exists to explain what we mean by modal terms, does it make sense to apply ‘possible’ and ‘necessary’ to propositions concerning such worlds as wholes? To do this would appear to require another level of possible-world making and a regress looms. Surely our talk of A, W1, W2, etc, must eschew modal terms altogether?

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  3. Bill Vallicella Avatar
    Bill Vallicella

    David,
    It doesn’t exist to explain what we mean by modal terms, otherwise the explanations would be circular. For example, p is possible =df p is true in some but not all possible worlds. The apparatus of possible worlds is an extensional representation of modal relationships for the purposes of aiding our thinking about modal relationships. For example, everything necessary is possible, but not conversely. That is a rock-bottom modal truth that cannot be disputed. In possible worlds talk: For any x, if x exists in every world, then it exists in some world. The modal truth gets represented in terms of a quantificational truth. But you have to quantify over possible worlds.
    The aim is not to reduce the modal to the nonmodal.

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  4. Bill Vallicella Avatar
    Bill Vallicella

    Mike,
    The point is that ‘the actual world’ is ambiguous. It could be used as a stand-in for your ‘@’ which rigidly designates our world. Used that way, ‘The actual world is actual’ is contingently true. Or ‘the actual world’ could be used as a nonrigid definite description which picks out whichever world happens to be actual in the same way that ‘the president of the U. S.’ (construed as a nonrigid definite description) picks out whomever is the current office-holder, and is in that sense referentially ‘shifty.’ Used in the second way, ‘The actual world is actual’ is necessarily true.
    Suppose @ = W1. My correspondent rightly thinks that if @ = W1, then necessarily @ = W1. And he rightly thinks that necessarily W1 is not (identically) W2. But then he is puzzled how W2 could be actual given that @ = W1. His problem is a psuedoproblem sired by a failure to realize that ‘the actual world’ is ambiguous as explained above.
    The Lewis example is pertinent: ‘I could have been faster than I actually am’ is true if it means that there is a possible world in which I run faster than I run in @. But it is false if it means that there is a possible world W in which I run faster than I run in W.

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  5. Mike Avatar
    Mike

    The point is that ‘the actual world’ is ambiguous. It could be used as a stand-in for your ‘@’ which rigidly designates our world. Used that way, ‘The actual world is actual’ is contingently true.
    Well, it’s not obviously contingent. It depends on whether the second occurence of ‘actual’ is shifty. Let’s assume that you have in mind this proposition,
    1. the actual world = @
    That’s necessary, under your assumption that ‘the actual world’ is rigid, since ‘@’ is not shifty (or, at least, not easily read as shifty). But I agree we want to be able to truly say that,
    2. @ might not have been actual.
    This is the case when ‘actual’ is shifty in its second occurrence. I don’t think you disagree with that. I agree that this is the natural reading of (2). So, two points in relation to your post. First, the proposition expressed by ‘the actual world is actual’ is not obviously an identity claim. Once we understand it as an identity claim, your position depends on how we read both the first and second occurrences of ‘actual’. That’s what I had in mind.

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  6. Bill Vallicella Avatar
    Bill Vallicella

    I don’t follow you. We agree that necessarily @ = @. Presumably we also agree that actuality is an absolute, not a world-relative, property. Although every world W has the property of being actual-at-W, only one world has the property of being actual simpliciter. So, letting ‘actual’ express this property of absolutte actuality, it follows that ‘@ is actual’ is contingently true, if true. If it were necessarily true, then @ would be the only possible world, which would amount to modal Spinozism.
    ‘The actual world is actual,’ as I see it, does not express an identity claim but makes a predication: it predicates the absolute property of actuality of the referent of ‘the actual world.’ But the latter expression is ambiguous as between ‘@’ and ‘the unique W such that W has the property of being actual.’
    I suspect we are just looking at the matter from different angles.

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