The “Opposite Day” Argument (A Reductio of Putnam’s Argument)

By Jon Cogburn

One of the benefits of being a philosophy professor is that there's never any trouble with playing Opposite Day with your kids. This is the game where the world has been transformed such that English (insert your language here) is now an idiolect where every sentence means "the opposite" of what it does in English. Most kids will play this at the lexical level, trying to come up with antonyms, e.g. "Look down at the ground!" instead of "Look up that the sky!" But this is a mug's game, at the level of your kids' art. Most words don't have "opposites." What's "the opposite" of bird? Cold-blooded invertabrate mammal who lacks feathers, wings, and beak?

But if you're a professor of analytic philosophy you've had your nose rubbed in so much Frege, Russell, and Quine that all you have to do is go sentential. Instead of saying "You mustn't look at that cold-blooded invertabrate mammal who lacks feathers, wings, and beak" all you have to say is "It is not the case that you should look at that bird." Sentential negation FTW.

Unfortunately though, if you've taken enough philosophy, then you start to notice a systematic problem with Opposite Day. At some point one of the players will invariably get flustered and say something to the effect of "O.K. It's not Opposite Day anymore." But of course, if it's Opposite Day, then the sentence that it is not the case that it is Opposite Day merely means that it is Opposite Day. Note that "It is not Opposite Day" is pragmatically analytic in the same way that "I am here" is. It is true whether it is Opposite Day or not. If it's not Opposite Day and you utter it, you are uttering something true. If it is Opposite Day, then (given what Opposite Day does to meanings) you are also uttering something true.

And of course "It is Opposite Day" is always false for the same reason. If it's not Opposite Day, the sentence is clearly false. But if it is Opposite Day, then the sentence means what we mean in non-Opposite Day English when we say "It's not the case that it's Opposite Day."

This causes a range of practical and philosophical difficulties. How does one get out of the game? Perhaps one could say "It is Opposite Day." But since "it" refers to the context of utterance, you've just uttered something false (remember, on Opposite Day, the assertion that it is Opposite Day means the same as saying that it is not the case that it is Opposite Day). Luckily though, temporal deixis gets us out of this. Consider "Thirty Seconds from now, it will be Opposite Day." This sentence works both to flip you to Opposite Day and to flip you out of Opposite Day.

Philosophically, the sentence "It is Opposite Day" functions suspiciously like "I am a Brain in a Vat." If it really were Opposite Day, then the vast majority of us are going around uttering falsehoods, and we don't even know it! Likewise (supposedly)* if the world is a Matrix and we are all just envatted brains being fed a simulacrum reality, then most of what we think we know is also false. And, if** Hilary Putnam is correct, the sentence "I am a brain in a vat" is just as pragmatically self defeating as "It is Opposite Day." If you're not a brain in a vat, you are saying something false. If you are a brain in a vat, you are also saying something false, because in the idiolect of English spoken in the vat, the words "brain" and "vat" don't refer to actual brains in vats, but rather to the fantastic images of vats and brains fed to you by your matrixy overlords. Note that Putnam's Brain in a Vat argument is, in a sense, like our children's strategies for speaking the Opposite Day idiolect. It's lexical. On the other hand, the Opposite Day argument is sentential. Moreover, it does not rely on an overstrong causal account of reference, as Putnam's does.***

So we seem to have a refutation of skepticism that doesn't rely on the causal theory of reference of individual terms! Again if radical skepticism were true, then it would be Opposite Day. So if it is not Opposite Day, then radical skepticism is false. In this manner, the skeptical argument can be rendered:

1. If I know that P, then I know that it is not Opposite Day
2. I do not know that it is not Opposite Day
3. Thus, I do not know that P.

This is by analogy to the standard (this from Lance Hickey):

1. If I know that P, then I know that I am not a brain in a vat
2. I do not know that I am not a brain in a vat
3. Thus, I do not know that P.

Now consider Hickey's version of Putnam's argument:

1. Assume we are brains in a vat
2. If we are brains in a vat, then “brain” does not refer to brain, and “vat” does not refer to vat (via Causal Constraint)
3. If “brain in a vat” does not refer to brains in a vat, then “we are brains in a vat” is false
4. Thus, if we are brains in a vat, then the sentence “We are brains in a vat” is false (1,2,3)

But our reformulated Putnamian Argument is the following:

1. Assume it is Opposite Day
2. If it is Opposite Day, then “It is Opposite Day” means that it is not Opposite Day
3. If “It is Opposite Day” means that it is not Opposite Day, then “It is Opposite Day” is false
4. Thus, if it is Opposite Day, then the sentence “It is Opposite Day” is false (1,2,3)

According to Hickey, in reference to Putnam's argument:

Putnam adds that “we are brains in a vat” is necessarily false, since whenever we assume it is true we can deduce its contradictory. The argument is valid and its soundness seems to depend on the truth of (3), assuming (CC) is true.

But our argument's (3) is not lexical, and so does not assume that a Causal Constraint is true! So we seem to have a much stronger anti-skeptical argument. We know it is not Opposite Day. That is, we know that it is not the case that what most human beings are asserting is false. Radical skepticism is false. Q.E.D. You're welcome, history of philosophy.**** 

[Notes:

*Mark Silcox and I disagree! See our "Against Brain-in-a-Vatism" Also see my essay in Silcox's (ed.) forthcoming Experience Machines: The Philosophy of Virtual Worlds, where I try to show what happens when we consider Putnam's argument against brains in vats along the lines of a Graham Priest style inclosure paradox. Interesting stuff happens once you make the connection.

**Big if! See Lance Hickey's Internet Encyclopedia of Philosophy article on the brain in a vat as well as my article in Silcox's anthology.

***The moral of Putnam and Kripke's attacks on the description theory of reference isn't that we never secure reference with descriptions (where by "secure reference" I just mean that we would correctly determine that reference had failed if the description were found to be false). It's that we don't always secure reference with descriptions. Weirdly, late Putnam himself pointed this out to a generation of philosophers of language who had misread him. Read his discussion of phlogiston in Words in Life. But, as far as I know, he never realized that this admission is fatal to his anti-skeptical argument.

****Seriously, I don't know what the above shows. Maybe it shows that the focus on causal theories in Putnamian and Davidsonian anti-skeptical arguments is misplaced. On the other hand, the demonstrative "it" in "It is Opposite Day" works in many respects in the same way that causal theorists argue that reference is secured for seemingly non-indexical terms like "brain" and "vat" so there is a connection. On the assumption that there are no obvious howlers in the above, it might be be worthwhile to reread Hickey's article closely, seeing the extent to which one can mine analogues to various takes on Putnam's argument.]