This was a question posed to us in a lecture.

I have been thinking about it for ages.

Can I say that since all argument are instances of this invalid form p => q, the statement is true?

  • 2
    This is correct, if your argument has a single premiss (instantiating p). Otherwise, you might want to add more variables on the left of the arrow, and consider their conjunction (if conjunction is available). – J Marcos Jan 31 '15 at 18:16
  • "the statement" refers to which statement? "p => q?" "Every argument is an instance of an invalid argument form?" – James Kingsbery Feb 9 '15 at 21:57


An argument can instantiate several argument forms. For example, the argument

The sun is shining
If the sun is shining, it doesn't rain
Therefore, it doesn't rain

instantiates the (valid) form

p, p->q => q

but it also instantiates the (invalid) forms

p, r => q

p, p->r => q

p, r->q => q

For an argument to be formally valid, it doesn't have to instantiate only valid forms. This, in fact, seems impossible. It is enough for the argument to instantiate one valid form, for it to be formally valid. And that's how the above argument, in the example, is valid.

  • 1
    Well said, well explained. 10/10 – Yellow Skies Feb 2 '15 at 4:45
  • i just wanted to add that it most certainly can rain while the sun is shining --> rainbows – yamm Feb 4 '15 at 8:32

Maybe I am not assessing the problem correctly, but it seems to be a clear No.

If you can show just one example that fails to support the universally quantified statement »Every argument is an instance of an invalid argument form.«, you have proven its falsity. Further, I consider the modus ponens ponendo to be a valid (i.e. non-invalid) argument form. Thus, if I can find just one argument that can successfully carry the MPP's form, I have proven the falsity of the statement »Every argument is an instance of an invalid argument form.«

The following argument is indeed successfully carrying the MPP's form and thusly proves the falsity of the above statement:

»If I am a bachelor, I am not married. I am a bachelor. Thus: I am not married.«

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