Counterfactuals, Possible Worlds, and my Mom

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A counterfactual is

a conditional statement whose antecedent is known (or, at least, believed) to be contrary to fact. Thus, for example, "If George W. Bush had been born in Idaho, then he would never have become President." Unlike material implications, counterfactuals are not made true by the falsity of their antecedents. Although they are not truth-functional statements, counterfactuals may be significant for the analysis of scientific hypotheses.[1]

The Philosopher J. L. Mackie, for instance, held that counterfactuals are condensed arguments; therefore, they cannot have truth values.[2] Arguments, it will be recalled, are sound (or not) or valid (or not). Only propositions, which can make up arguments, are assessed as true or false.

However, I have to confess. I believe counterfactuals are truth-functional, since I often accuse others (and get accused by others) for being wrong about my claims of hypothetical states of affairs. Sometimes it's about affairs of the past – e.g., if you had asked her on a date, she would have gone out with you – and sometimes it's about affairs of the future – e.g., if you ask her on a date, she will go out with you. The regular and effortless usage (along with communicative and predictive success) of these kinds of claims in ordinary discourse is what I think justifies my belief that counterfactuals are truth-functional. In this essay, I'll attempt to analyze counterfactuals by first placing them within the context of possible worlds, and then developing a single counterfactual to see what sense I can make of it. In the end, though I'll argue that counterfactuals can rightly be assessed as true or false, I won't be wholly convincing – admittedly, even to myself.

I

David Lewis is considered to have given the first robust account of counterfactuals by analyzing them in terms of the semantics of possible worlds. The truth is, I don't fully understand what this means. But I like what I've seen. Possible worlds are descriptions of the way things might be, and not every description of the various ways things might be (or might have been) can be stated in conjunction. Sometimes, it's "either/or" but not "both/and." (Sometimes this is called the hard "or" -- i.e., the "xor")

For example, it's not possible that I'm both (a) the biological son of Bill and Kay, *and* (b) the biological son of two other people (on the presumption that all sons have but two biological parents). These, (a) and (b), are two possible worlds cases that are not compatible with one another. One among those possible worlds is the so-dubbed actual world, the world in which Bill and Kay are my parents. I'll give this statement a short-hand index label.

(0:) Brint is the son of Bill and Kay.

However, some possible worlds are more similar than others. Intuitively, it seems more accurate to say that a possible world in which

(1:) Brint is the son of Bill and Vennie

has more comparative similarity to the the actual world, than a possible world in which

(2:) Brint is son of Cepheus and Myrtle.

(Let Cepheus and Myrtle be two arbitrary people who are non-relatives of my parents) In comparing the two statements, we would say that (1) is "closer to actuality" (to use the Lewis vocabulary.) To use a short-hand, we could say that (1) is closer to (0) than is (2).

In sum, given the full set of possible worlds, there will be one world in that set which is the actual world – i.e., is the world I am in when uttering the various statements. In a trivial sense, that possible world resembles the actual world more than any other; or, to say the same thing -- the actual world resembles itself more than any other of the worlds in the set of possible worlds. Or again, (0) is closest to (0). Also, there will be various worlds closer or farther away in terms of the attributes they share with the actual world. Indeed, there can be "ties" among this ordering of worlds. Recall (1), Brint is the son of Bill and Vennie, and now consider:

(3:) Brint is the son of Mike and Kay.

These two, (1) and (3), are equally close to the actual state of affairs. (Again, neither are actual states of affairs; Only Bill and Kay are rightly assessed as my parents.)

II

Now after that bit of review about possible worlds, maybe I'm finally in a position to examine a counterfactual. In the early '60s, my mother and father (again, Bill and Kay) met, married; and eventually bore myself and my younger brothers in the natural manner. So to construct a counterfactual, I'll posit this:

(4:) If Bill and Kay had never met, then Brint would not have been the son of Bill and Kay.

The thought behind (4) is that their meeting one another caused me to come into being, caused me to be the biological son of Bill and Kay. Again, they met and initiated a set of causes which eventually make (0) true. (I have to wonder if a chain of causes is a truth maker for a proposition. Is that right? I'm unclear on how truth is assessed for a proposition that represents a chain of causes over a temporal window. I'm guessing that I'm not the only clueless one about such matters.) So (4) presumes no meeting, counter to the historical facts of what happened in the early '60s; and (4) presumes no Brint, counter to the actual facts. (I'm here; I'm their son).

Notice that there is an event, a meeting, tied to (or not tied to) a relational fact, being a son. This tie worries me a bit. A simpler statement would be, “If the petroleum had exploded, then there would have been energy released.” That's two presumed events tied together. Or, “If the city hall were made of granite, then some building in town would be made of stone.” That's two presumed facts tied together. (4) is a bastardized version of event and fact; and even here it's of an event that wasn't, and of a fact that isn't.

III

Oddly enough, though (4) appears to be counterfactual, I suspect it probably isn't so. The antecedent could be true, and yet the consequent could be false – that is, it can be true that “Bill and Kay never met”, and still true that “Brint would have been the (biological) son of Bill and Kay.”

There is a possible state of affairs which barely departs from what actually happened in the early 60s. Suppose my father, being a good Hoosier, stayed to complete his degree at Indiana University. And that my mother, being a crazy-fast typist, stayed working at the newspaper office (also in Indiana). Now as is often the case, my father would have been a cash-strapped college student; and, would have taken that quick shot at earning easy money, as have done many college males: selling DNA at a local sperm bank. My mother, married at the time, would have wanted children, but obtained none from unproductive Mike. Thus, would she have simply made the choice to avail herself of a fertility clinic, the very one which good-ol' possible world Dad too regularly profited from – well, the rest falls out easily. The timing of the ovary release; the happenstance of that one special sperm cell – and here I would be, born even of the same womb, sired even by the same father. Thus, (4) does not seem appropriate as a counterfactual after all, since I could still be their biological son though they never met.

Now all counterfactual statements are hypothetical statements, and hypothetical statements are false just when the antecedent is true and the consequent is false. I was able to posit a true antecedent and false consequent without any contradictions appearing. So that's why I am thinking (4) probably isn't a counterfactual. But this introduces a confusion to me: What exactly am I claiming when I say, “That counterfactual is false.”?

First, suppose someone claims (wrongly) this to be a counterfactual:

(5:) If Bill and Kay had met, then Brint would have been the son of Bill and Kay.

Well, as a matter of history, they did meet (true antecedent) and I am their son (true consequent). Thus, at first glance, I could claim (5) is not counter to fact at all. It is a fact. A rebuttal might be that I've confused two things:

(5a:) Brint would have been the son of Bill and Kay
(5b:) Brint is the son of Bill and Kay

(5b) seems more straightforwardly true or false. But (5a) far less so; it seems to demand a context be filled before it's truth status can be assessed. Indeed, (5) itself could be read with a non-temporal “had” in the antecedent:

(5)* If Bill and Kay would have met, then Brint would have been the son of Bill and Kay.

And in this case the same worry appears for the antecedent of (5)* as it did for the consequent of (5a): a context seems demanded before a truth value can be assessed. Perhaps the undetermined truth status of “would”'s is why it has been claimed that counterfactuals are not truth-functional statements.

Second, somebody could argue more generally that I've misunderstood counterfactuals. (It's possible I've misunderstood them; I'll certainly grant that.) That a counterfactual is affirmed, doesn't exclude it from being possibly true. All I've done is given a consistent state of affairs that shows the antecedent is consistent with the state of affairs identified by the consequent. But the role of a counterfactual, so the argument runs, is to refer to a false state of affairs, not to show inconsistency between states of affairs. Perhaps there's merit to this charge against me; but, I would like to know what the object of such a reference would be – i.e., where are these so-called “false states of affairs”? Are they but abstractions within our own minds? Are they in some platonic realm of forms? Are they (false) ideas in the mind of God? I think there are problems all around here.

At this, then, I must conclude my analysis, for if I were to continue to think of counterfactuals, then it is possible that I would drive myself (and my readers) insane.


REFERENCES

[image] Jennifer Dixon "Best of All Possible Worlds" ICM 2006 Benoit Mandelbrot Fractal Art Contest

[1]Philosophical Dictionary

[2] "Counterfactual Theories of Causation" Standford Encyclopedia of Philosophy