The following is a valid argument:

1. Pittacus is a good man

2. Pittacus is a wise man

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3. Some wise man is a good man.

That this argument is valid I take to be a datum, a given, a non-negotiable point. The question is whether traditional formal logic (TFL) is equipped to account for the validity of this argument. As I have already shown, it is quite easy to explain the validity of arguments like the above in modern predicate logic (MPL). In MPL, the logical form of the above argument is

Wp

---

(Ex)(Wx & Gx).

In order to evaluate the argument within TFL, it must be put into syllogistic form, otherwise the rules of the syllogism cannot be applied to it. Thus,

Every Pittacus is a wise man

Some Pittacus is a good man

-----

Some wise man is a good man.

This has the form:

Every P is a W

Some P is a G

-----

Some W is a G.

It is easy to prove that this form is valid by using a Venn diagram (not to be confused with an Euler diagram), or by applying the syllogistic rules. You will notice that I have rigged the argument so that those who deny that universal propositions have existential import will be satisfied that it is valid. Note also that the Venn diagram test would not work if the argument were given the following form:

Every P is a W

Every P is a G

-----

Some W is a G.

You can verify for yourself that if you diagram the premises you will not thereby have diagrammed the conclusion.

But is it logically acceptable to attach a quantifier to a singular term? How could a proper name have a sign of logical quantity prefixed to it? 'Pittacus' denotes or names exactly one individual. 'Every Pittacus' denotes the very same individual. So we should expect 'Every Pittacus is wise' and 'Pittacus is wise' to exhibit the same logical behavior. But they behave differently under negation.

The negation of 'Pittacus is wise' is 'Pittacus is not wise.' So, given that 'Pittacus' and 'every Pittacus' denote the same individual, we should expect that the negation of 'Every Pittacus is wise' will be 'Every Pittacus is not wise.' But that is not the negation (contradictory) of 'Every Pittacus is wise'; it is its *contrary*. So 'Pittacus is wise' and 'Every Pittacus is wise' behave differently under negation, which shows that their logical form is different. My argument can be put as follows:

a. Genuinely singular sentences have contradictories but not contraries.

b. Sentences like 'Every Pittacus is wise' have both contradictories and contraries.

Therefore

c. Sentences like 'Every Pittacus is wise' are not genuinely singular.

d. 'Pittacus is wise' is genuinely singular.

Therefore

e. The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL.

MPL 1, TFL 0.

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