Colin McGinn on Paradoxical Paradoxes

The indented material is from Colin McGinn's blog. My responses are flush left and  in blue.

Paradoxes exist.

True.

Paradoxes belong either to the world or to our thought about the world.

True, if 'or' expresses exclusive disjunction.

They cannot belong to the world, because reality cannot be intrinsically paradoxical.

True.  And so one ought to conclude that paradoxes reside in our thought about the world. 

They cannot belong to our thought about the world, because then we would be able to alter our thought to avoid them (they cannot be intrinsic features of thought).

But surely we can alter our thought to avoid the paradoxes that reside in our thought about the world but not in the world. 

Therefore, paradoxes don’t exist.

Non sequitur. 

Therefore, paradoxes both exist and don’t exist.

Non sequitur. Although paradoxes do not exist in the world, in reality, they do exist in our thinking about the world, thinking that can be altered so as to avoid paradoxicality.

This is the paradox of paradoxes.

There is no such a paradox.  It seems to me that McGinn is equivocating on 'paradox.' His first three assertions are all true if 'paradox' means logical contradiction.  But for the fourth assertion to be true, McGinn cannot mean by 'paradox' logical contradiction. 

The Paradox of the Smashed Vase will help me make my point. 

Suppose you inadvertently knock over a priceless vase, smashing it to pieces. You say to the owner, "There's no real harm done; after all it's all still there." And then you support this outrageous claim by arguing:

1) There is nothing to the vase over and above the ceramic material that constitutes it.

2) When the vase is smashed, all the ceramic material that constitutes it remains in existence.

Therefore

3) The vase remains in existence after it is smashed.

"I don't owe you a penny!" (Adapted from Nicholas Rescher, Aporetics, U. of Pittsburgh Press, 2009, p. 91.)

This paradox arises from faulty thinking easily corrected. The mistake is to think that an artifact such as a vase is strictly and numerically identical to the matter that composes it. Not so: the arrangement or form of the matter must also be taken into consideration.  This response is structurally the same as the much more detailed response I make to Peter van Inwagen's denial of the existence of  artifacts.