In a paper published in 1975, Robert Jeroslow introduced the concept of an experimental logic as a generalization of ordinary formal systems such that theoremhood is a Π 2 0 -property (or in practice Δ 2 0 ) rather than Σ 1 0 . These systems can be viewed as (rather crude) representations of axiomatic theories evolving stepwise over time. Similar ideas can be found in papers by Putnam (1965) and McCarthy and Shapiro (1987).The topic of the present article is a discussion of a suggestion by Allen Hazen, that these experimental logics might provide an illuminating way of representing "the human mathematical mind". This is done in the context of the well-known Lucas-Penrose thesis. Though we agree that Jeroslow's model has some merit in this context, and that the Lucas-Penrose arguments certainly are less than persuasive, some semi-technical doubts are raised concerning the alleged impact of experimental logics on the question of knowable self-consistency.

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We claim that a notion of rhetic acts can fulfil a useful function in speech act theory. Austin’s examples of rhetic acts are saying that something is so and so, telling someone to do something, and asking whether something is so or so. Though this certainly sounds as if he is talking about the illocutionary acts of asserting, giving directions, and asking questions, we explain why the acts Austin mentions are not illocutionary after all. In short, illocutionary acts are acts that commit the participants in a conversation to various things. The illocutionary force of an utterance is determined by what it commits the interlocutors to. Our suggestion is that what looks like illocutionary force in the cases mentioned by Austin is really the contributions grammatical moods make to the literal meaning of utterances. We argue that this contribution is not part of what characterizes illocutionary acts as such. The semantic contribution of mood already characterizes those speech acts that Austin uses to exemplify rhetic acts. These rhetic acts are not committing in the way that illocutionary acts essentially are. So there must be a sense in which such rhetic acts are not illocutionary ones. In the final section, we suggest that the varieties of rhetic acts indicated by Austin fit neatly into a standard linguistic theoretical framework of conversational scoreboards.