Logical truth and logical properties

If a sentence can be seen to be true simply because of its syntax, independently of the particular names and predicates it contains, we can say it is formally or logically true.

We already know that some necessary truths cannot be identified by their form as true. For, as we saw, every true identity statement is necessary. But these truths cannot be seen to be true simply by looking at their syntax. They are necessary but not logically true. Some identity statements—say, “Mars is the Evening Star”—are

false; some, like “The Morning Star is Venus,” are true. But there is no guarantee that you will know which such sentences are true and which false just because you both understand the language and know that they have the syntactic property of being identity state­ments between names.

As I have already said, logicians have concentrated on systems of logic, such as sentential or predicate logic, that identify valid argu­ments because of the presence of certain words such as “and” and “all.” We can say that these logics examine the logical properties of such words.

But in recent years a great deal of new work in logic has focused on the logical properties of other words: epistemic logic, for exam­ple, looks at the logical properties of “know,” and modal logic stud­ies the logical properties of “necessary” and “possible.” Thus, we can have modal sentential logic, which includes these words along with sentential variables, negation, and the connectives; and modal pred­icate logic, where we add variables for names and predicates as well. Possible-world semantics is, of course, particularly useful for modal logic, but we shall also be using possible-world semantics in the next chapter to examine some issues about the necessity of laws of nature. (You might have thought that “necessary” and “possible” were logical constants, that they could be defined simply by looking at their role in arguments. But the existence of different kinds of necessity—including the kind we shall look at in the next chapter— means that modal logic is not all you need to explain the idea of necessity.)

Recent formal logic has increased our understanding of validity, necessity, and logical truth. But the interest of these questions is not

simply that we want to make valid arguments or find logical truths.

So far I have suggested three reasons why philosophers have been interested in language:

a) because it is their primary tool,

b) because, unlike thoughts and ideas, it is public, and

c) because it is the medium in which we express truths.

But many of the ideas that we have discussed in this chapter will come up in later chapters, and some of them came up when we were discussing philosophy of mind and epistemology. That brings me to the last reason I want to suggest: that philosophers have found again and again that starting with questions about language can lead to new insights in every area of the subject.

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