Missives from a fly bottle
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Last revised 31 August 2017
What’s a logical paradox?


This was written in 2009. It explains the notion of a logical paradox in a way that comes very naturally to me. The conclusion drawn at the end is probably the most important thing for me (“We are blinder than we can imagine in matters of straightforward logical reasoning”) but I find that it is rarely emphasized by others.
5. Descartes’s dream

The 17th-century French philosopher René Descartes was in his study one day, working quietly at his desk, when he began to wonder if he was just dreaming of being in his study and working at his desk.

He was both bemused and startled to find that he had no way of ruling out that his current experience was just a dream!

He wasn’t the first person to be startled in this way, since this strange notion of not knowing whether you are dreaming or awake has been entertained throughout history and may be found in many cultures.

As far back as the 4th century B.C., the Chinese sage Zhuangzi is said to have dreamt that he was a butterfly and then to have wondered if he was actually a butterfly dreaming he was a man. Likewise, in Plato’s dialogue, Theaetetus, we find Socrates wondering how a man could tell whether he was awake or merely dreaming and Theaetetus confessing to having no answer.

With the advent of modern science, such questions began to attract more attention and the issue is now acknowledged as a classic epistemological difficulty.

These days, the difficulty is raised in terms of a mad scientist who has supposedly kidnapped you and is toying with your brain, while keeping it alive in a vat. A neurochemical genius, he feeds you the illusion of having a normal life, while, in reality, you are just a brain in a vat in his laboratory on Mars.

How do you know this is not your situation?

Amazingly, according to some, you don’t. There is no way to tell. For all that you know, you really are a brain in a vat in a laboratory on Mars.

Needless to say, most people find this completely absurd and refuse even to contemplate the possibility! But the trouble is that the reasoning which generates the possibility is very compelling.

After all, if you were a brain in a vat, with your nerve endings rightly stimulated, your overall sensory experience would be indistinguishable from reality. You wouldn’t be able to tell the difference, so far as anyone knows. The reasoning here is straightforward, being just a modern extension of the familiar illusion of dreaming.

So, like it or not, we have a compelling piece of reasoning that generates an unbelievable conclusion. What do we do?

Some people just swallow the conclusion, as mentioned. They take comfort in the thought that it doesn’t matter that they cannot tell. Perhaps I’m a brain in a vat in a laboratory on Mars; perhaps I’m not. Who cares? Life still “goes on” for me in exactly the same way. Others insist there must be a flaw in the reasoning but no one has yet managed to uncover a convincing one. Descartes himself certainly tried!

Most people are just befuddled at the whole thing and decline to entertain it for more than a few minutes, preferring generously to leave it to the philosophers.

So this is another case where it is unclear if the unbelievable conclusion should be swallowed, or if the compelling reasoning should be faulted. Frankly, nobody can see through the thing.

In other words, we have a logical paradox, although this one is often called an epistemological difficulty, or a sceptical problem. The label doesn’t really matter. More important is the idea of a compelling piece of reasoning that culminates in an unbelievable conclusion, with no obvious way of defusing the tension, and we certainly have that here.

Those who take paradoxes seriously will usually go to great lengths to defuse such a tension, since one can always learn something in the process. In this case, for example, the paradox suggests that we do not understand the relation between mind and body very well, and it is likely that only a proper understanding of these notions will let us defuse the paradox.

For our purposes, we can leave Descartes in his meditations and take away a more general lesson from the examples that have been considered so far.