"Conceptual analysis" is one of important analytic philosophers' tools in philosophical argumentations. In the process of analysis, we specify the elements or constituents of a concept on which basis we define the concept. With regard to conceptual analysis, a well-known paradox known as "the paradox of analysis" is proposed holding that a true conceptual analysis cannot be informative in the sense that it cannot enhances our previous knowledge about the concept. If true, our widespread focus on conceptual analysis on philosophical argument is implausible. In order to cash out the meaning of the paradox, we will first elucidate Moore's (1903) open question argument, we will argue that the argument entails the paradox of analysis. We will then argue that the paradox's claim is implausible, that is, true conceptual analysis can be informative. We will then consider, on the basis of our argument against the paradox of analysis, Church's (1956) account of intensional identities. Our argument, apart from showing the informativity of conceptual analysis, undermines any philosophical positions, like Moore's open question argument, presupposing the paradox of analysis.