X: I have discovered that tomatoes were grown in Ireland in the Neolithic.
Y: That is highly unlikely. The seeds and leaf remains that form almost the entire base of your assertions belong to turnips. Just check out these pictures for comparison.
X: Professor Y subscribes to an earlier Kuhnian paradigm than myself. Therefore his work is incommensurable with mine, and he is by definition unable to criticise me. I remain convinced that tomatoes were grown in Ireland in the Neolithic.
What a great argument! And it works not just in archaeology either:
"The public and media has called my cabinet reshuffle pointless windowdressing. But they all subscribe to an earlier Kuhnian paradigm so their criticism is naturally wildly off the mark."
"No, I didn't do my homework. Homework is part of an earlier Kuhnian paradigm and of course incommensurable with me playing video games all night."
"Yes officer, I'm sure to you it does look like we sold old scraps of pork and chicken as beef. But that's just because you subscribe to an earlier Kuhnian paradigm you see; to me it's actually all prime beef and perfectly legal, I promise."