It's very curious to me that people find a tension between the necessity of baptism and BoD, because they seem to make this argument based on the "plain" or "obvious" use of the word necessary precluding the possibility of the necessary item being supplied for.
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As an example, it is perfectly sensible to speak of hard work as being necessary to support one's family, and no one who says its necessary would, by saying so, intend to preclude the fact that someone born into a trust fund really doesn't need to work hard, since the property and finances have been supplied in another way. We could think of a million things that are truly necessary that can be supplied for. Point simply being that there's nothing "plain" or "obvious" about the word "necessary" radically excluding a supplication of effect; indeed, if we actually "go to the Church" (instead of "Churchmen", as happenby is wont to distinguish) we read that baptism is the instrumental cause of justification, which tells you everything you need to know. Instruments are metaphysically substitutable, while principals (in this case, Christ's passion) are not. Which is why the Old Testament Fathers, despite doing everything that was asked of them for justification, did not go immediately to Heaven-- because there was not yet a principal efficient cause of their justification.
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Anyways, the tension between the necessity of baptism and BoD is just a fabrication, both with regards to what the Church teaches and in regards to the very foundation (i.e., "ordinary" language and "plain" meanings) on which the case for a contradiction rests.