Often an argument is valid, but it is still not clear why it is valid. It is not clear how the conclusion follows from the premises. Arguments are like pathways between premises and conclusions, and some of these pathways are more complicated than others. Yet even the simplest arguments reveal hidden complexities when examined closely. For example, there is no question that the following argument is valid:

(1) Harriet is in New York with her son.

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(2) Harriet’s son is in New York.

It is not possible for the premise to be true and the conclusion false. If asked why this conclusion follows from the premise, it would be natural to reply that:

You cannot be someplace with somebody unless that person is there, too.

This is not something we usually spell out, but it is the principle that takes us from the premise to the conclusion.

One thing to notice about this principle is that it is quite general—that is, it does not depend on any special features of the people or places involved. It is also true that if Benjamin is in St. Louis with his daughter, then Benjamin’s daughter is in St. Louis. Although the references have changed, the general pattern that lies behind this inference will seem obvious to anyone who understands the words used to formulate it. For this reason, principles of this kind are basically linguistic in character.

If we look at arguments as they occur in everyday life, we will discover that almost all of them turn on unstated linguistic principles. To cite just one more example: Alice is taller than her husband, so there is at least one woman who is taller than at least one man. This inference relies on the principles that hus- bands are men and wives are women. We do not usually state these linguistic principles, for to do so will often violate the rule of Quantity. (Try to imagine a context in which you would come right out and say, “Husbands, you know, are men.” Unless you were speaking to someone just learning the language, this would be a peculiar remark.) Nonetheless, even if it would usually be pe- culiar to come right out and state such linguistic principles, our arguments still typically presuppose them.


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