The article considers the problem of the conflict of norms in philosophical thinking within the framework of one paradigm. The subject of analysis is the styles of thinking in modern analytic philosophy in the treatment of the thesis of Aristotelian essentialism, a doctrine about necessary and contingent properties for objects. The conflict between the anti-metaphysical treatment of essentialism by Willard Quine and the revival of metaphysics of essentialism by Saul Kripke is investigated. The two approaches are compared within the framework of one paradigm of analytic philosophy on the basis of Quine's objections to quantifier modal logic and the admissibility of this logic in the concept of naming by Kripke. It is shown that Quine adopts normative guidelines within the framework of Russell's thesis "logic is the essence of philosophy", while Kripke's normative guidelines are based on recognizing the importance of pre-theoretical thinking inherent in the intuition of an ordinary person. The development of Kripke's new naming theory results in a revision of a significant number of traditional concepts, among which the justification for a priori necessary assertions stands out. Two ways of assessing the conflict of norms in analytic philosophy are considered. The first, belonging to Jaakko Hintikka, a prominent representative of the analytical trend, rejects the idea of the importance of pretheoretical thinking not explicated by logic. Hintikka believes that the refusal to use the logical apparatus when interpreting philosophical theses speaks of the weakness of the position of Kripke, who is known as the author of important logical ideas. The second, belonging to Richard Rorty, a prominent opponent of the analytical school, is based on the insignificance of addressing universal human intuition for philosophy. Rorty's position is motivated by the total criticism of the paradigm of analytic philosophy, while Hintikka's position is motivated by criticism of the norm of philosophical thinking within the framework of one paradigm. The article concludes that the history of rejection and revival in the analytic philosophy of Aristotelian essentialism is a change in the concept of normativity as a kind of a prescription of what can be done and what cannot be done there. As a consequence, the change of norms with the transition from one paradigm to another is inevitable. A view is suggested that it would be natural to regard the change in norms as a process within the framework of one paradigm, that is, a process within the framework of the normal (according to Thomas Kuhn) period of the development of science.