Getting This Existence Thing Straight

Midway through “What Lewis Carroll Says Exists That I Don’t” I put forth an example of claiming a property belongs to something which clearly doesn’t exist. The problem — and Carroll was writing this bit, in Symbolic Logic, at a time when it hadn’t reached the current conclusion — is about logical propositions. If you assert it to be true that, “All (something) have (a given property)”, are you making the assertion that the thing exists? Carroll gave the example of “All the sovereigns in that purse are made of gold” and “all the sovereigns in that purse are my property”, leading to the conclusion, “some of my property is made of gold”, and pointing out that if you put that syllogism up to anyone and asked if she thought you were asserting there were sovereigns in that purse, she’d say of course. Carroll has got the way normal people talk in normal conversations on his side here. Put that syllogism before anyone and point out that nowhere is it asserted that there are any coins in the purse and you’ll get a vaguely annoyed response, like when the last chapter of a murder cozy legalistically parses all the alibis until nothing makes sense.

I put forth a contrary example, though, that you could say “all unicorns are one-horned animals” and get no disagreement from anyone, even though pretty much everyone would agree that unicorns don’t exist. And, quite properly, BunnyHugger protested that I was playing with existential import without addressing it. I certainly was. Carroll was working around the issue also. But he’d interpret my assertion that “all unicorns are one-horned animals” as making two assertions: “all unicorns are one-horned animals” and “at least one unicorn exists”. And again, for normal conversational English, that’s probably the reading we would take. (For a rare case in claiming what someone now safely dead would have said in a modern situation I can be pretty certain: Carroll wrote to friends about precisely this form of an argument, although about different specific subjects, and the specific subjects don’t matter at all in evaluating the logical soundness.)

Let me turn my unicorn proposition around: “there are no non-one-horned animals that are unicorns.” Is that true? Well, if we’re agreed there aren’t unicorns, then certainly it’s true. Is it different from my original statement? Well, if there are any unicorns, and the original proposition’s true, then the turned-around one is also true. If there are any unicorns, and the turned-around proposition’s true, then the original one is too (if the animals don’t have one horn, they’re not unicorns; if they are unicorns, they’ve got one horn). There might be some one-horned animals that aren’t unicorns, but we don’t make much claim about them one way or another. How about if the turned-around proposition is false, that there’s a non-one-horned animal that is a unicorn? (How? Carroll and any four-year-old would give the answer immediately.) But then the original proposition, that all unicorns have one horn, is false. Pretty quickly we can go from the original being false, and there being a unicorn without one horn, to the turned-around version, and no non-one-horned animals being unicorns being false.

It seems like the original and the turned-around propositions make the same claim; they’re both true or both false together. But the original feels like it’s asserting an existence, and the turned-around feels like it’s making no such thing, and this is probably why the argument about whether existence is implied was such a good one and went on for so long. Both points of view make sense.