McDowell thinks that speakers, when they are uttering a sentence intentionally, in fact, are expressing a thought which the sentence is used for communication. In McDowell's view, we must take speaker’s linguistic behavior as a performance of a speech act with a specific content (various thoughts) and specific type (such as expressing a thought, asking a question, and so on). McDowell defends a modest theory of meaning and argues that an interpreter or a theorist should be seen as a person who has and has had a prior grasp of a language. But, Dummett believes that a theory of meaning should not take for granted some piece of a language or presuppose having some primitive concepts of that language by a speaker. A theory of meaning, as Dummett says, must explain all primitive concepts which primitive terms of the language in question express, and describe what it is to have these concepts by a speaker. McDowell by criticizing this view insists that, this approach to meaning falls in the mere behaviorism and then, Dummett is forced to explain meaning in reductive and non-intentional (behavioral) terms. McDowell urges that giving this behavioral account of meaning attacks our intuitive and common sense view that language and meaning are normative and rational. Thus, giving an immodest theory of meaning, in McDowell's view, is impossible. In this essay, after describing McDowell's and Dummett's views on workings of a theory of meaning, I will describe McDowell's argument against possibility of giving an immodest theory of meaning and eventually, I'm going to evaluate the plausibility of the argument.