Note on Wolterstorff
For those who might be interested in the idea by Nicholas Wolterstorff, I think I should point out that my brief summary of his theory was slightly inaccurate. (I used the phrase "illocutionary acts", whereas he speaks of "illocutionary actions".) His idea is to extend the notion of illocutionary acts (which are acts of "asking", "commanding" etc. through spoken or written locutionary acts) to include the possibility of non-verbal actions that might therefore be understood as speech.
"Locutionary acts are acts of uttering or inscribing words. Il-locutionary acts are acts performed by way of locutionary acts, acts such as asking, asserting, commanding, promising, and so forth. Once illocutionary acts are thus distinguished from locutionary acts, then it immediately occurs to one that though of course such actions as asking, asserting, commanding and promising, can be performed by way of uttering or inscribing sentences, they can be performed in many other ways as well. One can say something by producing a blaze, or smoke, or a sequence of light flashes. Even more interesting: one can tell somebody something by deputizing someone else to speak on one's behalf. In short, contemporary speech-action theory opens up the possibility of a whole new way of thinking about God speaking: perhaps the attribution of speech to God by Jews, Christians, and Muslims, should be understood as the attribution to God of illocutionary actions, leaving it open how God performs those actions - maybe by bringing about the sounds or characters of natural language, maybe not."
(Wolterstorff, Divine Discourse, p. 13)*
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* The citation from Wolterstorff appears here in accordance with the Permissions Policy of Cambridge University Press.