A synonym for "science of science" is the back-formed term "logology" (Christopher Kasparek, "Prus' Pharaoh: the Creation of a Historical Novel", The Polish Review, vol. XXXIX, no. 1, 1994, note 3, pp. 45–46; Stefan Zamecki, Komentarze do naukoznawczych poglądów Williama Whewella (1794–1866): studium historyczno-metodologiczne [Commentaries to the Logological Views of William Whewell (1794–1866): A Historical-Methodological Study], Warsaw, Polish Academy of Sciences, 2012, ISBN978-83-86062-09-6, [English-language] summary, pp. 741–43). The term "logology" provides convenient grammatical variants not available with the earlier terms, "science of science" and "sociology of science": i.e., "logologist", "to logologize", "logological", "logologically".
