Validity, Invalidity, and Logical Form

When we say that an argument is valid we are saying something about its logical form. To put it epigrammatically, validity is a matter of form. We are saying that its form is such that no (actual or possible) argument of that form has true premises and a false conclusion. Validity is necessarily truth preserving. I just used the expression, 'its form.' But since an argument can have two or more forms, a better formulation is this:

1. An argument is valid iff it instantiates a valid argument-form.

Given (1), some will be tempted by

2. An argument is invalid iff it instantiates an invalid argument-form.

 

But (2) is false. After all, every (noncircular) argument instantiates an invalid form. 'Some cameras are digital devices; therefore, some digital devices are cameras,' which is obviously valid, instantiates the invalid form p therefore q. Similarly, every valid syllogism has the invalid form p, q, therefore r. Consider this argument:

3. Zeno is famous for his paradoxes of motion
4. Zeno is a Stoic
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5. Some Stoic is famous for his paradoxes of motion.

Is this argument valid?  The argument  is plainly valid inasmuch as it instantiates a valid form. The problem with the argument, of course, is that it is unsound: if (3) is true, then (4) is false, and if (4) is true, then (3) is false. For (3) to be true, 'Zeno' must refer to Zeno of Elea, but for (4) to be true, 'Zeno' must refer to Zeno of Citium. And of course neither can refer to my late cat, Zeno (may peace be upon him).

Now consider this argument:

6. If God created something, then God created everything
7. God created everything
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8. God created something.

This instantiates the formal fallacy of affirming the consequent. Is the argument therefore invalid? No! For it also instantiates a valid form:

Everything is such that: Fx
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Something is such that: Fx.