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You're calling this under the fried egg test, essentially. In my words, these are "terms that imply certain social knowledge that could not be derived from any of the constituents, nor from their combination." The question is if the combination of the words cake, of, soap implies any knowledge of meaning that could not be derived from the constituents. That soap is not eaten would imply that cake employs a definition other than the primary. Essentially it is a pragmatic assessment of the word senses at the level of semantic comprehension, which is common to sort ambiguity, e.g. "tree tunk" versus "elephant trunk" versus "trunk of a car", none of which are idiomatic. The question then becomes whether or not eating soap is social knowlege at a linguist and/or cultural level as opposed to common knowledge. Unless you want to add "cake of" everything that can't be eaten, unless there is another combination for cake of soap that might make as much sense (something easy from a soap opera?), unless you argue that one might make a cake cake from soap that isn't intended for consumption, and unless some other rule, none that I see, might apply, I would propose deletion. DAVilla17:06, 22 January 2007 (UTC)Reply
This has come up before. I don't know where we stand on it now, but the conclusion I remember from before (the fried egg test, as you say) was that it's idiomatic unless all the senses of the part work for the idiom as a whole. E.g., megapenny is not a really big penny and megastar is not a million celebrities. Both fried egg and boiled egg refer to particular kinds of eggs fried or boiled in particular ways, as has been discussed at length.
However, this can be taken too far, as practically any sentence is idiomatic under this analysis. (E.g., which meaning of for did I mean). One could argue that in this case the meaning of for is determined by English grammar and the surrounding words. This may help. Is any ambigious sentence idiomatic in the sense above? No, because by definition all meanings work. But there are clearly still pitfalls.
The real reason for "idiomatic" in CFI (as I recall, from editing CFI at the time) is the "and want to know what it means" clause of the general rule. This is inherently subjective, which is why there's a fair bit of further explanation in CFI. In cases like fried egg, most native speakers have the same picture (e.g., not a scrambled egg), but a non-native wouldn't, and this is important to us. As DAVilla points out, few people would mistake a cake of soap for something you could eat, because you don't eat soap (but what about Beavis and urinal cakes?). By contrast, sunny-side up and scrambled eggs could both be considered fried, but fried generally means the former. With that in mind, the rule would seem to be "It's idiomatic unless all meanings of the parts not disallowed by the context will work." Still subjective, but a little sharper.
I'm of two minds on this, but what tips the balance for me is cake of soap being used differently from bar of soap. Personally I'd like to know the difference. Intuitively there is one, but I'm not sure exactly what it is. If it's just the difference between bar (in any sense appropriate to soap) and cake (ditto), then I don't see a need. If there's some subtlety peculiar to soap and not other substances, then keep. tentative Keep. -dmh17:25, 23 January 2007 (UTC)Reply
Keep, I think the "cake" in "cake of soap" has a different meaning from the "cake" in a "cake of silver", "cake of ice", "cake of wax" etc. Even if it doesn't, I'd like that to be clarified for me, since it seems to be more common that all the other non-food "cakes" combined. Kappa03:49, 24 January 2007 (UTC)Reply
That might do the trick. In cake of soap, if cake = slab or bar in different cases then those are different senses, and the latter meaning would not be apparent from the summation. DAVilla05:15, 2 February 2007 (UTC)Reply
Delete. Sum of parts. A cake can mean any mass of compressed substance – the OED shows that as well as soap, people have talked about cakes of wax, coagulated blood, tobacco, clay, dried paint.... As usual, instead of adding more collocations that no-one will ever search for, we should be thinking about defining cake in a better way. Widsith16:29, 25 January 2007 (UTC)Reply
keep, very much. I thought this was some fancy food, which proves it's something people are likely to "run across and want to know what it means". -- Liliana•21:46, 23 April 2012 (UTC)Reply
Feels a bit redundant to me. You can also find "cake of meal", "cake of oats", "cake of sand", etc. It's anything in that kind of compact mass, or cake. Equinox◑22:21, 23 April 2012 (UTC)Reply
Delete. If you know the components' meanings, you know the whole's. If this is kept, combine the senses, which are truly one.—msh210℠ (talk) 21:49, 24 April 2012 (UTC)Reply
Im reading a poem with that phrase "a cake of soap" in the stanza. I never thought it was an actual cake. My first instinct was that was all that was left of her, like the residue or film on your skin left from soap. I did not take it literally. Just sharing my thought and not sure if that is even correct. — This comment was unsigned.
