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.

Consider the myriad coloured squares below and these two obvious facts about them:

The *first* square looks red.

Colourwise, any two*adjacent* squares look the same.

Colourwise, any two

These two facts generate a paradox since they allow us to “deduce” that the

All the same, the deduction is as follows:

The first square looks red.This reasoning is extremely simple, but it must also be completely flawed, since the bottom line cannot possibly be swallowed. This was known to the ancient Greeks, who knew this paradox well, but, to this day, despite no shortage of suggestions, no one has given a satisfactory account of the “flaw” in the reasoning!

But any two adjacent squares look the same.

Ergo, the second square looks red.

But any two adjacent squares look the same.

Ergo, the third square looks red.

But any two adjacent squares look the same.

Ergo, the fourth square looks red.

But ....Ergo, the last square looks red.

.

.

The ancient Greeks themselves discussed the paradox in terms of a heap of sand, or sometimes wheat.

A lone grain of sand, they observed, is obviously not a heap of sand. But, equally obviously, adding

Repeated reasoning then “proves” that you can

It also illustrates our point well since, with our coloured squares, it was only the outrageous conclusion (“The last square looks red”) that made us question the reasoning. If the conclusion had seemed

Indeed, people unfamiliar with this paradox employ this sort of reasoning all the time, perfectly convinced of their logic!

For example, in the oft-heated abortion debate, “pro-lifers” often argue that if it is impermissible to abort a foetus one hundred days after conception (when everyone agrees that the foetus is recognizably human), then it must be impermissible 99 days after conception too.

After all,

Repeated reasoning then “proves” that the foetus cannot permissibly be aborted even

We cannot blame them for seeing no flaw in this logic, since even those who know there is a flaw cannot say what it is.

This case should worry us though, for how many others like it exist that we have no inkling of? In the present case, we are lucky enough to have realized that the given

But might there be other cases where it hasn’t yet dawned upon us that a certain style of reasoning is flawed, even though we employ it all the time, perfectly

Unfortunately, by its very nature, we have no real way of knowing. But there is reason to suspect that the phenomenon is more widespread than we might think. Let’s consider another famous case where the same danger proves to arise.

Achilles & the tortoise

The surprise exam

Newcomb’s problem

Newcomb’s problem (sassy version)

Seeing and being

Logic test!

Philosophers say the strangest things

Favourite puzzles

Books on consciousness

Philosophy videos

Phinteresting

Philosopher biographies

Philosopher birthdays

Draft

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