(This is a parody of that : An account of McTaggart's argument against time)
We begin our argument by distinguishing two ways in which possible worlds can be described. First, possible worlds can be described according to their possession of properties like being actual, being merely possible. (These properties are now referred at as “A properties.”) We call the series of worlds ordered by these properties “the A series.” But we say that possible worlds can also be ordered by two-place relations like being merely possible considered from, actual considered from, etc. (These relations are now called “B relations.”) We call the series of worlds ordered by these relations “the B series.”
We begin our argument by distinguishing two ways in which possible worlds can be described. First, possible worlds can be described according to their possession of properties like being actual, being merely possible. (These properties are now referred at as “A properties.”) We call the series of worlds ordered by these properties “the A series.” But we say that possible worlds can also be ordered by two-place relations like being merely possible considered from, actual considered from, etc. (These relations are now called “B relations.”) We call the series of worlds ordered by these relations “the B series.”
We claim that the B series alone does not properly permits one world to be distinguished as actual. I.e., we are saying that the A series is essential to modal distinctions. Our reason for this is that reality is essential to modal distinction, and the B series without the A series does not involve genuine reality (since B series worlds are equally possible, whereas A series propositions assign a world as the real one).
We also claim that the A series is inherently contradictory. For the different A properties are incompatible with one another. (No world can be both actual and merely possible.) Nevertheless, we insist, each world in the A series must possess all of the different A properties. (Since a possible world is from itself actual.)
One response to our argument that we anticipate involves claiming that it's not true of any world, w, that w is both actual and merely possible. Rather, the objection goes, we must say that w is merely possible from the actual world, and is actual from itself. But this objection fails, according to us, because the additional points of view that are invoked in order to explain w's possession of the incompatible A properties must themselves possess all of the same A properties (as must any further modal points of view invoked on account of these additional points of view, and so on ad infinitum). Thus, according to us, we never resolve the original contradiction inherent in the A series, but, instead, merely generate an infinite regress of more and more contradictions.
Since, according to us, the supposition that there is an A series leads to contradiction, and since there can be no modal distinction without an A series, we conclude that modal distinction itself, including both the A series and the B series, is to be rejected.
Needless to say, despite arguments such as ours, many philosophers will remained convinced of the pertinence of modal distinctions (for it certainly seems like there is a modal characteristic of the world). But a number of philosophers might be convinced by at least one part of our argument, namely, the part about the contradiction inherent in the A series. That is, some philosophers might be persuaded by us that the A series is not the case, even though they won't go so far as to deny the reality of modal distinction itself. These philosophers will accept the view (soon to be called “Lewisian modal realism”) that the B series is all there is to modalities. According to Lewisian modal realism, there are no genuine, unanalyzable A properties, and all talk that appears to be about A properties is really reducible to talk about B relations. For example, when we say that the world where Jesus is a girl has the property of being merely possible, all we really mean is that this world is not the world at which we are speaking. On this view, there is no sense in which it is true to say that one world is the real one, and any appearance to the contrary is merely a result of the way we humans happen to perceive our world.
The opponents of The Lewisian modal realism accept the view (often referred to as “Actualism”) that there are genuine properties such as being actual, being merely possible, etc.; that facts about these A properties are not in any way reducible to facts about B relations. According to Actualism, the reality of our world is indeniable and absolute, and not merely some mind-dependent phenomenon.
The Actualist might be happy to concede our claim that there can be no modal distinction without an A series, but the typical Actualist will want to reject the part of our argument that says that the A series is inherently contradictory. For the typical Actualist will deny our claim that each world in the A series must possess all of the different A properties. That is, she will deny that it is true of any world, w, that w is actual and merely possible. Instead, she will insist, the closest thing to this that can be true of a world, w, is (for example) that w might have been actual, and is merely possible, where the difference of modality in this claim is not to be analyzed away (just as the apparent references to the putative A properties actuality and mere possibility are not to be analyzed away in favor of reference to B relations).
Thus the standard Actualist response to our argument involves the notion that we must “take modalities seriously,” in the sense that there is a fundamental distinction between (for example) saying that x is F and saying that x might have been F. The thesis can be put this way.
Taking Modality Seriously: The verbal modality of ordinary language (expressions like ‘it is the case that’, ‘it might have been the case that’) must be taken as primitive and unanalyzable.
In virtue of her commitment to Taking Modality Seriously, the Actualist will say that no world ever possesses all of the different A properties. Thus, according to the Actualist, there is no contradiction in the A series — i.e., no contradiction in saying of a world, w, that w is actual, and might have been merely possible — and, hence, no contradiction to be passed along the different worlds at which w is actual and might have been actual.
In effect, then, the typical Actualist makes exactly the move in response to our argument that we anticipated, and explicitly rejected. Not surprisingly, then, many Lewisian will feel that the Actualist response fails.
