It’s Time for the ‘Conditionals’ Argument to Die

Christian Tarsney

April 21, 2012

It’s that time of year again! The TOC is just around the corner, with all that that entails, and hopefully if you’re heading to Kentucky next weekend, your prep is progressing well, and you’ve got visions of plastic ponies dancing in your head.

I’m writing this article to express one simple wish for this year’s TOC. I have just the one (apart from the success of my debaters, and an absence of bloodshed), and I think it’s a pretty reasonable: I would like it to be that no round at the tournament to be won on the claim that “challenging assumptions of the resolution proves it true.” I’m not picky about how this wish gets fulfilled. I’d be more than happy if debaters simply stopped reading the argument. But I’d be equally thrilled if their opponents just beat the living hell out of it when it’s run. And I’d be reasonably satisfied if judges were to decide that the argument is just too insanely, bizarrely wrong to be voted on, regardless of circumstance.

It’s odd that I’d feel this way about an argument—in general, I have no beef with arguments that are absurd, even arguments that are blatantly wrong, because they force debaters to master a skill that’s difficult and worth having—namely, the skill of clearly and concisely justifying the obvious. But the conditionals argument is worse than ordinary debate nonsense: not only is it wrong, it’s really badly, crazily (and indisputably) wrong. And not only do debaters have a hard time explaining why it’s wrong, a good number of them (and their coaches, and their judges) are actually convinced that it’s right (or mostly right, or almost right). For whatever reason, it hasn’t generated the same burning hatred that (much less deserving) stupid arguments often do, and my hope in this article is to rectify that. I’ve had conversations about this argument with a bunch of people, including some very smart people who seemed to think the argument makes sense, so my hope is to spell out clearly enough the primary ways in which it goes wrong that there will no longer be any ambiguity regarding its status.

The conditionals argument, or “conditional logic” as it’s come to be called, is really, truly, not something about which there’s room for legitimate disagreement—it’s just wrong, plain and simple, in more ways than one. I’ve written at some length in order to be as clear as possible about why that is, so don’t feel obligated to read past the point where you’re convinced. But in case you’re not, I’ve tried to be reasonably thorough in spelling out a couple of mildly thorny background issues.

For those who don’t know, the argument as debaters have run it over the last year and a half goes as follows: (a) Whatever argument the negative is running doesn’t prove the resolution false on its own terms, but rather “challenges an assumption of the resolution.” (b) Statements like the resolution which make such “assumptions” should read as tacit conditionals—i.e., what they actually assert is “If [assumption], then [remaining propositional content of resolution].” (c) For all conditionals (i.e., all “if…then” statements), if the antecedent of the conditional (the “if” part) is false, then the conditional as a whole is true. These three claims in combination, then, mean that by refuting an “assumption” of the resolution, the negative has actually proved it true—wonder of wonders, but hey, it’s “logic”!

There are three things wrong with this argument: First, (b) is false. Second, (c) is completely ridiculous, and made plausible only by a blatant misreading of a fairly banal feature of logical formalism. And third, nine hundred and ninety-nine times out of any given thousand the argument gets run, (a) is false too.

Let’s take the last point first: There is a legitimate distinction between what a sentence asserts and what it simply takes for granted. Linguists refer to the latter category of semantic content as “presupposition.” The cases of presupposition most of us are familiar with are seemingly unanswerable questions like “Have you stopped bearing your wife?”, which take a (hopeful) falsity for granted such that either a “yes” or a “no” answer seems to imply it. What marks cases of presupposition, intuitively, is that the sentence makes sense only given the truth of the presupposition. Of course, it can’t merely be that the sentence would be false if the presupposition were false—then the entire semantic content of a sentence would count as presupposition, i.e. every sentence would “presuppose” its own truth, which obviates any useful distinction between assertion and presupposition. There is not, as far as I can see, any other useful distinction of this sort to be drawn, so what debaters have in mind by “assumption” must be presupposition.

Now, the most common use of the conditionals argument is as an offensive preempt to moral skepticism, and in that instance it requires the claim that the resolution “assumes”…well, debaters will say “assumes the existence of morality.” That can’t possibly be right, because it’s not clear that “morality” itself would be counted among the things that exist by even the strongest moral ontology. But let’s say, the resolution assumes the existence of moral facts, or moral properties, or that at least some things are morally right and some other things morally wrong, or that at least some positively worded moral utterances are true.

Does a typical debate resolution assume (read: presuppose) anything like this? I can’t imagine how one could think that it does. Suppose the resolution says something of the form: “a ought to x.” Does this fail to make sense if there are no true “ought” statements, in the same way that “John stopped beating his wife” ceases to make sense if it turns out John never beat his wife? Pretty obviously not. There’s nothing senseless about predicating properties which nothing possesses—merely something false. The sentence “Puff is a magic dragon who lived by the sea” does not assume that there is at least one magic dragon—it asserts (or at least implies) it. Similarly, the sentence “It is morally permissible for a to x” does not take for granted, as a condition of its intelligibility, that at least one agent is morally permitted to do at least one thing—it asserts the existence of a particular moral permission. (A small minority of moral-skeptical arguments, in debate and in academic philosophy, suggest that there is no sense at all to be made of moral language. But sentences don’t “presuppose” that the terms which compose them are coherent and meaningful in any sense which might license adding those coherence claims, as assumptions, to the semantic content of the sentence. There’s more that could be said here, but these arguments are rare enough that it’s not worth trying to unravel.)

The second place the conditionals argument goes wrong has to do with its suggestion for how we handle presupposition. There are two general approaches to this question that I’m aware of: one is to simply write off sentences with false presuppositions as neither true nor false, for essentially the reason that we don’t want to answer “Have you stopped beating your wife?” in either the affirmative or the negative. The other is to pull the presuppositions out as conjuncts to the (explicitly) asserted semantic content of the sentence. This is, famously, Bertrand Russell’s proposed analysis of sentences involving non-referring definite descriptions. “The present king of France is bald” tries to make reference via a description to which nothing corresponds (namely, “the present king of France”), and Russell’s solution was to simply extract a existence and uniqueness claims and tack them onto the front of the sentence, yielding “There is someone who is the present king of France, and only one such person, and he is bald.” (The worry motivating Russell did not exactly concern presupposition in the linguist’s sense, but his problem can be assimilated to a general theory of presupposition.)

I don’t know what to point out about the analysis of presupposition other than that these are both prima facie plausible solutions, while no one I’m aware of proposes (generally) analyzing sentences which involve presupposition as conditionals. If I make a statement that carries questionable presuppositions, and this is pointed out to me, I might choose to reformulate my claim conditionally: “Well, all I really meant to say was that if John ever beat his wife, he no longer does.” But in so doing, I’m saying something quite a bit weaker (i.e., something that could more easily come out true) than my original assertion. A moral error theorist might assent to a claim like “If anything were morally wrong, kicking puppies would be,” but will certainly not assent to “Kicking puppies is morally wrong.”

Finally, putting aside those problems, what if debate resolutions really did have tacit conditional form? Is it right, as debaters have been asserting, that any “if…then” statement with a false antecedent is true? Well, let’s see: “If John McCain had won the 2008 presidential race, then he would have personally flown Air Force One to Neptune to negotiate a trade agreement with the Plutonians.” “If it rains today in Tucson, then Iran will halt its nuclear program.” “If I go to the store tomorrow [assume I won’t], I’ll buy two hundred packs of fruit roll-ups.” Conditionals…false antecedents…and yet, somehow, they all seem pretty false.

“But,” I hear you ask, “how come the Stanford Encyclopedia of Philosophy says that all conditionals with false antecedents are true?” In a nutshell, the answer is this: Logicians want to formalize certain bits of ordinary “natural languages” like English which seem to act as logical operators—for instance “and,” “or,” “not,” “if…then,” “if and only if,” “every,” “some,” “necessarily,” “possibly”…the list goes on. The first five are the ones which logicians usually pick out as “sentential connectives”—meaning, they connect sentences—and a desirable feature of sentential connectives, in formal logics, is that they be what’s called “truth-functional.” Truth-functionality requires, for a connective, that the truth value (true or false) of any sentence it governs be simply a function of the truth values of the parts which the connective holds together. So, if I have a formal conditional A → B, we’d like to read the ‘→’ such that simply knowing whether A and B are true will tell me whether the entire sentence is true.

It’s a sad fact of doing logic that no logical operator actually works, in English or other natural language, quite how we’d like it to work for logic, and there are cases which seem to show that no sentential connective in English is really quite truth-functional. For logicians, this fact can be noted and set aside, because their interest is in logical structure, not in a perfect mapping of ordinary language. But if you make the mistake of reading a logician talking about logic as a linguist talking about language, they’ll seem to be saying some pretty odd (and bizarrely wrong) things—none more so than that English conditionals have an accurate, truth-functional characterization.

The main reason they don’t is that, in ordinary English, most conditionals carry counterfactual content—saying “If A, then B,” asserts not merely (as in formal logics) that “Either not A, or else B, or both,” but rather “If A were to be the case then B would be the case.” Philosophers like to talk about counterfactuals in terms of “possible worlds,” so that the sentence “If John McCain had won in 08, he’d have flown Air Force One to Neptune,” turns out to mean something like “In the world most like ours except that John McCain wins the 08 election, he also pilots Air Force One to Neptune.” To know whether that’s true, given that he didn’t win the election in the real world (i.e. given a false antecedent), you need to know more than just whether he flew Air Force One to Neptune in the real world—i.e., the conditional has no truth-functional analysis.

Don’t worry if you find that all dense and boring—I won’t be the one to say you shouldn’t. But I will be the one to say you should never run the conditionals argument, and you should never lose to it. For all that I love about debate, the occasional success of this sort of argument should be cause for genuine worry about some of the downsides of debate pedagogy—namely that, in some instances, it teaches debaters (and judges) to defer to authority (“He’s got a card saying it, so I can’t answer the argument unless I’ve got a card too.”); to believe the ridiculous unthinkingly (all conditionals with false antecedents are true? really?); and to delude themselves about their grasp of arguments they don’t even begin to understand, for the purpose of either running them or voting on them. If you want to get the most out of your participation in debate, it’s important to recognize and avoid those risks, and rejecting the conditionals argument is a great place to start.