In chapter 4 of Articulating Reasons, Brandom argues that singular terms must exhibit a certain sort of inferential behavior, namely symmetric. He argues that asymmetric substitution inferences for terms are impossible. I will present that argument in detail soon in another post, but I wanted to comment on an odd thing about the conclusion. Assuming the argument works, we find that if the language has certain expressive resources, namely either a conditional or a negation, then terms must lisence symmetric substitution. That is a fairly minimal condition, but it is still a non-trivial condition. If we have an impoverished langauge without either of those bits of logical vocabulary, the argument doesn’t get off the ground. Why does Brandom try to draw the stronger conclusion that singular terms must behave symmetrically with respect to substitution? Is there supposed to be something about inferentially articulated languages that require them to have at least one of those bits of logical vocabulary? Based on what he says in chapter 1, there doesn’t seem to be any such requirement. Is there some further condition that for any language that would be used by a group, that language must have such logical vocabulary? Again, there is no indication from any of the chapters in Articulating Reasons that there is such a condition. I’m not sure why the expresively impoverished langauges drop out of the picture. One guess is that for any inferentially articulated language, it is always possible to enrich it to include conditionals. Then the argument in ch. 4 would apply. However, this seems to leave open the possibility that in adding such vocabulary the singular terms are changed such that they act symmetrically rather than asymmetrically. Were this the case, then new conditional/negation-free conclusions could be drawn, meaning the conditional/negation were not actually conservative over the previous inferences. If the claim from the first chapter, that conditional/negation are conservative over any field (Brandom keeps calling collections of material inferences “fields”; I don’t know why, nor do I know why they aren’t just sets.) of material inferences is correct, then the result from ch. 4 would be that singular terms must behave symmetrically. Offhand, I don’t know what exactly the status of the conservativity claim is. This line of thought might call it into question, or, if it is solidly established, it might go a ways towards explaining why Brandom draws the conclusion that he does.

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