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Image: It is already nonsense to deduce language universals from an idiosyncracy of English, no matter how surprising it is. It gains the distinction of blatant nonsense by the fact that there is a very simple explanation for the performance of the children (and adults) in this case: when you change '{verb}er of X' to X-{verb}er, you remove regular pluralization, if any, from X. In fact, there is even a simpler rule: If there is a simpler word which is very very close to X both semantically and phonologically (e.g rat to rats), use it instead of X. This rule does not require any modification of words. Of course, children may be using some mixture of these rules, potentially with other rules, and the mixture can vary between children. There may be cases when this rule does not work.

O Senor Don Gato was a cat.
On a high red roof Don Gato sat.
He was there to read a letter,
where the reading light was better,
'Twas a love-note for Don Gato!

"I adore you," wrote the ladycat,
who was fluffy white, and nice and fat.
There was not a sweeter kitty,
in the country or the city
and she said she'd wed Don Gato!

O Senor Don Gato jumped with glee!
He fell off the roof and broke his knee,
broke his ribs and all his whiskers,
and his little solar plexus
"Ay Caramba!!" cried Don Gato.

All the doctors they came on the run,
just to see if something could be done.
And they held a consultation,
about how to save their patient,
how to save Senor Don Gato.

But in spite of everything they tried,
poor Senor Don Gato up and died.
No, it wasn't very merry,
going to the cemetary,
for the ending of Don Gato.

But as the the funeral passed the market square,
such a smell of fish was in the air,
though the burial was plated,
he became reanimated,
he came back to life, Don Gato!