The two paradoxes of analysis

The two paradoxes of analysis can be illustrated and distinguished by considering the following propositions These sentences, one will recall, reveal the first paradox of analysis: (1) To be an instance of knowledge is to be an instance of justified true belief not essentially grounded in any falsehood (2) To be an instance of knowledge is to be an instance of knowledge These sentences reveal the second paradox of analysis: (3) A correct analysis is given by saying that to be a brother is to be a male sibling (4) A correct analysis is given by saying that to be a brother is to be a brother The two paradoxes must be clearly distinguished If one has a correct analysis in which the analysans and analysandum can be substituted salva veritate in all contexts, then, according to Ackerman, the first paradox does not arise, but the second one does Consider: Ackerman takes it to be the case that concept of a brother and the concept of a male sibling are substitutable salva veritate in all contexts and, hence, are the same concept. Thus, according to Ackerman, there is no paradox here: (1**) To be a brother is to be a male sibling (2**) To be a brother is to be a brother But there is one here: (3) A correct analysis is given by saying that to be a brother is to be a male sibling (4) A correct analysis is given by saying that to be a brother is to be a brother Keep in mind, these paradoxes of analysis seem to rest on the assumption that analysis is a relation wholly between concepts, rather than one between entities of other sorts, such as linguistic expressions and the assumption that in a correct analysis, analysans and analysandum will be the same concept these are very plausible assumptions, consider: when providing an analysis, one is concerned with concepts, those mental tools that one relies on to organize and, thus, to make sense of the world, rather than the arbitrary signs (scribbles or noises) that one makes when organizing the world

Why would our thinking about the world, and our making sense of it via thought, have anything to do with how we talk about it? Nevertheless, Ackerman thinks that to solve the second paradox, one must reject the first assumption above (just like, in order to solve the first paradox, she thinks one must reject the second assumption) So, in some cases, a correct analysis is not only about the relevant concepts, but the language used to express them Consequently, heres one proposal for what is being expressed by (3) above (5) A correct analysis is given by saying that the verbal expression x is a brother has the same meaning as the verbal expression x is a male sibling and the concept of being a brother is identical with the concept of being a male sibling But this proposal is not going to work, if the concept of being a brother just is the concept of being a male sibling, (5) just introduces a new case of the original paradox: (6) A correct analysis is given by saying that the verbal expression x is a brother has the same meaning as the verbal expression x is a male sibling and the concept of being a brother is identical with the concept of being a brother Ackerman points out, though, that the problem with (5) and (6) does not show that every proposal on which analysis is partly about concepts, partly about language must fail. Indeed, she thinking the following is the correct account of what is being expressed by the analysis given in (3) (3) A correct analysis is given by saying that to be a brother is to be a male sibling (7) A correct analysis is given by saying that the verbal expression x is a brother expresses the same concept as is expressed by the conjunction of the verbal expression x is a male when used to express the concept of being a male and x is a sibling when used to express the concept of being a sibling (7) pairs each constituent concept in the analysans separately with the verbal expression that expresses it, so (7) cannot be paraphrased as a conjunction that leads to the problems of (5) According to Ackerman, then, (7) shows the correct way in which an analysis is partly about words and partly about concepts and so reveals how one can go about resolving the second paradox of analysis