I think the issue might be that I’m interpreting circular reasoning as something stronger than you; ie, in the pernicious sense which explains why “The idea that circular reasoning is bad is widespread”.
I suspect that according to your interpretation all valid deductive reasoning is circular in some way, circularity thus being necessary for valid deductive reasoning. In this regard, circularity would be a desirable attribute.
In contrast, my interpretation is one in which in the process of affirming a belief, one presupposes something that would require to have already affirmed the same belief; what is sometimes called “begging the question”.
In this context, I don’t regard A |- A (circular in your sense, but not in mine) as problematic, as it just involves inferring something that has already been affirmed.
I think the issue might be that I’m interpreting circular reasoning as something stronger than you; ie, in the pernicious sense which explains why “The idea that circular reasoning is bad is widespread”.
I suspect that according to your interpretation all valid deductive reasoning is circular in some way, circularity thus being necessary for valid deductive reasoning. In this regard, circularity would be a desirable attribute.
In contrast, my interpretation is one in which in the process of affirming a belief, one presupposes something that would require to have already affirmed the same belief; what is sometimes called “begging the question”.
In this context, I don’t regard A |- A (circular in your sense, but not in mine) as problematic, as it just involves inferring something that has already been affirmed.