 Regarding the second premise, it remains to be shown that we need to take the step from the notion of a possible thought—which is abstracted from the notion of a possible mind that is capable of error and so of thinking something false—to the notion of an abstract proposition. Church attributed the discovery of the latter notion to both Bolzano and Frege (Church 1943a; 1956a,b). However, Church did not endorse Bolzano’s arguments so much as his conclusion. (For the argument, see  §3.3 of the entry on Bolzano.)  And as for Frege, Church simply reiterated his remarks about the objectivity, mind and language independence, and publicity of Gedanke, without telling us exactly why possible thoughts are not also objective, mind-and-language-independent, abstract and public. Perhaps the issue is that the existence of possible thoughts depends on the existence of possible minds, whereas propositions, such as that two and two are four, do not depend on the existence of possible minds, since, intuitively, they would be true if there were no minds at all. Arguably, then, the notion of an abstract proposition must be postulated by and so is an ontological commitment of a theory that can explain the foregoing intuition.