Why You Failed Your Logic Test

An interesting parallel’s struck me between nonexistent things and the dead: you can say anything you want about them. At least in United States law it’s not possible to libel the dead, since they can’t be hurt by any loss of reputation. That parallel doesn’t lead me anywhere obviously interesting, but I’ll take it anyway. At least it lets me start this discussion without too closely recapitulating the previous essay. The important thing is that at least in a logic class, if I say, “all the coins in this purse are my property”, as Lewis Carroll suggested, I’m asserting something I say is true without claiming that there are any coins in there. Further, I could also just as easily said “all the coins in this purse are not my property” and made as true a statement, as long as there aren’t any coins there.

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What We Can Say About Nonexistent Things

The modern interpretation of what we mean by a statement like “all unicorns are one-horned animals” is that we aren’t making the assertion that any unicorns exist. If any did happen to exist, sure, they’d be one-horned animals, if our proposition is true, but we’re reserving judgement about whether they do exist. If we don’t like the way the natural-language interpretation of the proposition leads us, we might be satisfied by saying it’s equivalent to saying, “there are no non-one-horned animals which are unicorns”, and that doesn’t feel quite like it claims unicorns exist. You might not even come away feeling there ought to be non-one-horned animals from that sentence alone.

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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.

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