An extraction of an argument from Richards and some words about it

I doubt this will count as a comment paper, but I did the work and thought I may as well share it!

Richards runs an argument of this sort against a possible-worlds semantics, which seems to be the more popular flavor of the 'unstructured proposition theory':

1. According to a possible-worlds semantics, the truth of a valid arguments premises ensures that of its conclusions, and the worlds in which all its premises are true are exactly the world in which all the premises and the conclusion are true.
2. Therefore valid arguments are logical truths. (from 1)
3. Valid arguments are not logical truths.
4. Therefore possible-worlds semantics is false. (from 1 - 3)

I hope that that is structured OK. I really cannot tell!

Richard gives an example with the argument:

Barbers shave only those who do not shave themselves; the barber Jones shaved all the men who attacked Lionel; hence, Jones didn't attack Lionel

which is clearly valid. This of course means that the truth of the premise ensures the truth of the conclusion. This means that the worlds where the premises are true are the worlds where the premises are true and the conclusion is true.

This also means that the intension of:

Barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel

is the intension of:

Barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel, and Jones didn't attack Lionel.

But then that means that it is a truth of logic that:

Whoever believes that (barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel), believes that (barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel, and Jones didn't attack Lionel).

And as Richard points out, this doesn't seem to be a truth, let alone a logical one.

It seems that the unstructured proposition theorist casts too wide a net. They may go on to offer a more restricted interpretation, but it fails as well. It seems that generally unstructured proposition theories have a heck of a time with deduction.