A syllogism is usually in the following form:

1. Anything that is a six legged creature is an insect. (i.e. All six legged creatures are insects)

2. A fly is a six legged creature

3. Therefore, a fly is an insect.

The sentence "x is an insect" can be broken down into its subject, x, and a predicate, "is an insect." We say that the sentence is a statement form, since it becomes a statement once we fill in x. Here is how we shall write it symbolically: The subject is already represented by the symbol x, called a term here, and we use the symbol P for the predicate "is a six legged creature." We then write Px for the statement form. (It is normal to write the predicate before the term; this is related to the convention of writing function names before variables.) Similarly, if we use Q to represent the predicate "is an insect" then Qx stands for "x is an insect." We can then write the statement "If x is a six legged creature then x is is an insect" as PxàQx. To write our whole statement, "For all x, if x is an insect then x is a six legged creature" symbolically, we need symbols for "For all x." We use the symbol "∀" to stand for the words "for all" or "for every." Thus, we can write our complete statement as ∀x[Px→Qx].

Let’s now translate the syllogism into symbolic logic:

· The statement "A fly is a six legged creature" uses the predicate P to make a statement about a particular six legged creature, the fly.

· Let’s use the letter f to stand for the fly. (We shall always use small letters for terms and big letters for predicates.)

· Then Pf is the statement "A fly is a six legged creature." Similarly, Qf is the statement "A fly is an insect." The argument now looks like this:

1. ∀x[Px→Qx] For all x, if x is an insect then x is a six legged creature

2. Pf A fly is a six legged creature

3. ∴ Qf A fly is an insect