Quite so. It never does to read too much meaning into nursery rhymes, though what the Opies called "the happy guessers" persist in doing just that, so that there are any number of extravagent myths about them which circulate now as received wisdom, in spite of being completely groundless. There is always a risk that discussions of this kind may contribute overmuch to the huge bulk of material which must be examined before being once again discarded.

I remember This Old Man from the 1950s, too, under similar circumstances to Marje (though I wasn't born till '54). The Seeger references earlier may create confusion; while Q referred to a 1953 recording by Pete Seeger, my reference -which was ambiguous; my apologies for that- was to Ruth Crawford Seeger's book, American Folk Songs for Children (1948), which would have tied in nicely had it not emerged that my original guess was wrong by at least forty years. References in my earlier posts to a possible American source for this version should be disregarded in the light of my later comments.

I'm fairly sure that I also remember it sung on Listen with Mother in those days, though whether I learned it from radio or family I don't know. We may also have sung it at school, but my early childhood memories are not very coherent.

The term "Paddywhack" has been around a long while. I mentioned the dance tune of that name earlier on, and Dick has also referred to it; although that tune was current in the 18th century, it is unclear when that particular name was first applied to it; it has had others. As a slang term for a Large Irishman it was well-known; it can also refer to a rage (hence the still-used expression "getting into a right paddy"), and this would presumably be related to the reputation for fighting of which many people seem still to be quite proud (see any Disney film in which Ireland features for examples of that particular stereotype). There is also the nursery term for a slap already mentioned, which is clearly the sense in this song, as can be seen from the accompanying actions.