A Quick Note on the “It’s Meaningless” Solution to the Liar Paradox

In an earlier post, I discuss one good reason to reject the solution to the Liar paradox that says that it’s meaningless: it means calling some other sentences, like “This sentence is in Japanese” and “This sentence has five words” meaningless, though they seem to be obviously meaningful.

Anyone who defends this solution has to bite the bullet on these sentences. It’s a tough bullet to bite, but at first it doesn’t seem implausible. Maybe those sentences only seem to be meaningful, though they aren’t really.

I came across three sentences today that convince me that rejecting all self-referential sentences is, in fact, utterly ridiculous. I found them in Tim Urban’s newest amazing article on Elon Musks’ newest mind-blowing venture, Neuralink. (By the way: go read it. Now. Elon Musk is turning humanity into the Starchild from the end of 2001 and you’re reading about loopy sentences? Get out of here!)

Here are the three sentences:

That’s why we still communicate using technology Bok invented, it’s why I’m typing this sentence at about a 20th of the speed that I’m thinking it, and it’s why brain-related ailments still leave so many lives badly impaired or lost altogether.

And

Right now, your eyes are making a specific set of horizontal movements that allow you to read this sentence.

And

None of this stuff will take any effort or thought—we’ll all get very good at it and it’ll feel as automatic and subconscious as moving your eyes to read this sentence does to you now.

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Vagueness: The Sorites Paradox

Imagine we have 0 grains of sand. Do we have a heap of sand? Of course not! Well, what if we add one grain? We obviously still do not have a heap. Okay, what if we add one more? One more after that?

No matter how many grains of sand we have, adding just one more will never turn a non-heap into a heap. This is called the “tolerance principle,” and it is the defining feature of vague properties. It says that a small enough change can never alter the applicability of a vague property.

Say you have a red shirt. Change the frequency by an imperceptible amount. Obviously, the shirt is still red. Take someone who is sober. One ml of beer will not make that person drunk.

A problem appears when we compound these small increments. Here’s a version of the argument:

1) 0 grains of sand is not a heap (premise)

2) 1 grain of sand is not a heap (by #1 & tolerance principle)

3) 2 grains of sand is not a heap (by #2 & tolerance principle)

10001) 10000 grains of sand is not a heap (by #10000 & tolerance principle)

Welcome to the sorites paradox (“sorites” = “heap” in Greek), the argument that allows us to prove that a 90-year-old woman is a child, a blade of grass is red, and Danny DeVito is tall. It was invented by Eubilides sometime in the 4th century BCE, when he also invented the Liar and a few other paradoxes.…

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Do Abstract Objects Exist?

Real?

Do numbers “exist”? What about properties? I know my red apple exists, but does “redness” itself exist?

The existence of abstract objects seems, at first, like a deep metaphysical question. In fact, it’s a question of the pragmatics of language.

A couple of quick definitions. The view that abstract objects do exist is called “Platonism.” The view that they don’t is “nominalism.” Those who think they do exist, but only in the mind, are “conceptualists.”

Let’s take the case of numbers. A typical nominalist argument says that while you may bump into two apples somewhere along your travels, you’re never going to bump into “2.” There is no such thing independent of our descriptions of states of affairs. And that’s all abstract objects are – descriptions. They exist only in language.

The conceptualist replies: the fact that they exist even just as descriptions demonstrates that they do exist – in the mind. Abstract objects are mental fictions, and as such, they exist.

The Platonist’s retort: how do you explain that we all come up with the same mental fictions? When you and I speak of “the number of apples here,” we’re not talking about two different fictions that each of us came up with and which we happened to give the same name to. We’re speaking about the same thing: the number 2!

The Platonist may add that science corroborates the existence of numbers. Science predicts reality, and it does so through the use of numbers. This verifies the fact that numbers aren’t just some arbitrary or socially conditioned way of interpreting the world.…

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