I actually think what you are going for is closer to JL Austin’s notion of an illocutionary act than anything in Wittgenstein, though as you say, it is an analysis of a particular token of the type (“believing in”), not an analysis of the type. Quoting Wikipedia:
(1) for the performance of which I must make it clear to some other person that the act is performed (Austin speaks of the ‘securing of uptake’), and
(2) the performance of which involves the production of what Austin calls ‘conventional consequences’ as, e.g., rights, commitments, or obligations (Austin 1975, 116f., 121, 139).”
Your model of “believing in” is essentially an unpacking of the “conventional consequences” produced by using the locution in various contexts. I think it is a good unpacking, too!
I do think that some of the contrasts you draw (belief vs. believing in) would work equally well (and with more generality) as contrasts between beliefs and illocutionary acts, though.
I actually think what you are going for is closer to JL Austin’s notion of an illocutionary act than anything in Wittgenstein, though as you say, it is an analysis of a particular token of the type (“believing in”), not an analysis of the type. Quoting Wikipedia:
“According to Austin’s original exposition in How to Do Things With Words, an illocutionary act is an act:
(1) for the performance of which I must make it clear to some other person that the act is performed (Austin speaks of the ‘securing of uptake’), and
(2) the performance of which involves the production of what Austin calls ‘conventional consequences’ as, e.g., rights, commitments, or obligations (Austin 1975, 116f., 121, 139).”
Your model of “believing in” is essentially an unpacking of the “conventional consequences” produced by using the locution in various contexts. I think it is a good unpacking, too!
I do think that some of the contrasts you draw (belief vs. believing in) would work equally well (and with more generality) as contrasts between beliefs and illocutionary acts, though.