What rule of grammar, or etymological history, makes "prophe-cy" (noun) become "prophe-sy" (verb)? What causes the C to become an S when the word usage changes?
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According to the Oxford English Dictionary, the differentiation between prophecy and prophesy as noun and verb, respectively, happened more or less arbitrarily; before circa 1700, both variants were used for both noun and verb each:
The reason why this pair exists, while either c or s was chosen for both forms in other Greek words, is most probably confusion about which Greek word they were derived from. Normally, Greek -tia results in English -cy/cie, while Greek -sis results in English -sy/se/sis (both through French). This development is probably related to two facts:
But a more common way of forming a word with a similar meaning from the same verb stem (phê-) in Greek would be prophêsis (cf. haerêsis => heresy); from this, the French derivation would result in -sie, -se, or -sis (though -sis is rather modern, as it is the exact Latin transcription of the Greek word). Prophêsis did not exist in classical Greek, because their only word for prophecy and the action of prophesying was not derived directly from the verbal stem, but from the noun prophêtes as above. But ignorance of this fact is probably what led people to spell -s- sometimes.
Perhaps certain writers thought the s was closer to the Greek and preferred it, especially in the verb, because they though it was -t- in the Greek noun and -s- in the Greek verb (which is not true). Or perhaps the differentiation developed for even more arbitrary reasons.
These guidelines are applicable in British English:
In American English, only prophecy (verb), prophesy (noun), advise (verb), and advice (noun) follow this guideline, with licence and practise being considered British spellings.
No rule whatever. It just is. The OED says