On skepticism

So how do you really know the fish are happy?

The ancient Chinese philosopher Zhuangzi once told the story of having fallen asleep and dreaming he was a butterfly. Upon awakening, in that first moment when dreams and reality seem to merge, he recalled being unsure about whether he was, indeed, a man waking from a dream, or, instead, a butterfly dreaming it was a man. The skeptical paradox, loosely termed, is that any resolution of this uncertainty might be yet a further dream stage. The situation that results is reminiscent of what Prospero says in the “Tempest”:


We are such stuff
As dreams are made on; and our little life
Is rounded with a sleep.

There is surely nothing wrong with such dreams, but these examples raise the possibility that I might be dreaming even when thinking I am awake. René Descartes, in his first “Meditation,” does not find this completely convincing. He writes that waking experience is not completely like dreaming experience, but he goes on to argue that in any case, whether or not our senses deceive us, whether we are mad or sane, whether we are dreaming or awake, mathematics persists.

For example, consider the arithmetical proposition that 1 + 2 = 3. We can build an addition machine, say a microcomputer, into which we feed some initial input, call this “0,” upon which the computer program outputs some unique result, which we can safely call “1,” indicating that one operation has been performed on the initial input. If we now take that output and feed it back into our microcomputer, the new output, call it “2,” will be unique in the sense that now a second operation has been performed. Under these conditions, it seems fair to say that 0 + 1 + 1 = 2. Next we could build a macro that combines this whole process, namely the process of adding 2. If we feed 1 into the macro, it will output a unique value, which we call “3.” In this way we affirm that 1 + 2 = 3.

Descartes then argues that we might be deceived even about this equation under the circumstances that some malign being has controlled every experience we have had during our lives, including every sensory input. Then all that we know might be a staged illusion, and our every belief would be open to doubt. This would be a hyperbolic doubt. Now it seems that no belief is justified, which is the view of a radical skeptic.

More recently, skepticism has been as much about what the world is as about what we know. The American philosopher Saul Kripke in 1982 formulated a skeptical paradox about what there is. To reconstruct his paradox, we can return to the macro described earlier. By feeding outputs back into the macro as further inputs, if we begin with 0, the computer produces the series 2, 4, 6, … Say that, unbeknown to a student, the teacher alters the macro to function just as it always did until September 10, 2007, but after this date and forever thereafter, the second loop is eliminated so that the macro adds only 1. If the time factor seems unclear, another reconstruction would be that on the first 10,000 operations, the macro functions as the student anticipates, but on the very next operation, and thereafter, it switches to adding 1, in which case the student would anticipate the series of outputs to be 2, 4, 6, …, 10000, 10002 and so on. But in reality, the series would be 2, 4, 6, …, 10000, 10001, 10002 and so on. These are entirely different series. Even if the student gained access to the program, recognized the problem and corrected it, this is still no guarantee that the macro would continue to function as he anticipates. It might, at some juncture, miss a step, in which case the output series diverges.

Drawing on Kripke, one might then propose a solution to the skeptical paradox. Given the situation regarding the macro that misses a step, if no continuation of that series can be ruled out, then belief in any possible continuation is justified, in a special sense connected to that possibility. This solution in one respect is not so much different from the original problem Descartes posed: In the original case, no belief is justified; in the other, all beliefs are justified. In both cases, then, possible worlds become indistinct from the actual world. A more promising approach is to make additional assumptions explicit within a framework, in our case, to assume that the output series is, indeed, the anticipated one.

Let us return once more to Zhuangzi, who told another story, this one about crossing a bridge with a skeptically minded friend. Looking down into the stream below that bridge, Zhuangzi remarks on the happiness of the fish there. When his friend asks him how he knows the fish are happy, Zhuangzi replies, “How do you know that I do not know the happiness of the fish?”

These examples suggest that neither skepticism nor its solution necessarily enjoys a privileged position in philosophy. Indeed, the consequences of skepticism and its solution are beyond belief. Instead, we need a better understanding of our world and of what certain knowledge is. After all, as Ludwig Wittgenstein pointed out in a 1939 lecture, even given the lack of a logical guarantee regarding the persistence of the numeric series 1, 2, 3, ..., it is not like a bridge will fall down.

Frankel, in investigating the Justified True Belief account of knowledge, raised some questions with Link, a lecturer in the philosophy department, who introduced his student to Saul Kripke’s skeptical paradox. They anticipate that their continuing conversation about skepticism can be expanded and formalized for philosophical presentation. This article appeared in the Tufts Journal in May 2007.