Linguistics Encyclopedia.pdf

Both of the premises of this argument could be true while the conclusion was false. Such
inductive arguments are central to the growth of scientific knowledge of the world. But
formal logic is not concerned with inductive arguments; it is concerned with deductive
validity, with arguments which meet the stricter standard of correctness described above
(see Skyrms, 1975, for a survey of work in inductive logic).
Logically valid arguments are often described as formally valid: if an argument is
valid, then any argument of the same form is valid. This means that logicians are not
concerned with arguments which depend upon the meanings of particular descriptive
terms, such as:
Peter is a bachelor, so Peter is unmarried.
Rather, they are concerned solely with arguments which are valid in virtue of their logical
or grammatical structure; they are concerned with features of structure that are signalled
by the presence of so-called logical words: connectives, like ‘not’, ‘and’, ‘or’,
‘if…then…’; quantifiers like ‘all’, ‘some’, and so on. We can represent the logical form
of an argument by replacing all the expressions in it other than logical words and
particles by variables, as in the example in the opening paragraph. The logical form of
the example in the present paragraph can be ex pressed:
a is F, so a is G.
We see that the argument is not logically valid because it shares this form with the
blatantly invalid
John is a husband, so John is a woman.
To explain why Peter’s being unmarried follows from his being a bachelor, we must
appeal to the meanings of particular non-logical words like ‘bachelor’ and ‘married’; it
cannot be explained solely by reference to the functioning of logical words.
I have described logic as concerned with the validity of arguments. It is sometimes
described as concerned with a particular body of truths, the logical truths. These are
statements whose truth depends solely upon the presence of logical words in them. For
example:
Either London is a city or it is not the case that London is a city.
This is claimed to be true by virtue of its logical form: any statement of the form
Either P or it is not the case that P.
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is true and is an illustration of the law of excluded middle, i.e., there is no third
intermediate possibility.