The paper presents the results of the research of the term "intension" in analytical philosophy, psychology and linguistic pragmatics, develops and theoretically substantiates the concept of "intensional intersubjectivity", reveals its essence and features, classifies speech acts on the basis of intensional conditioning, makes a detailed analysis of speech acts of strict and non-strict conditioning on the material of works of Russian writers. The work is addressed to teachers, students, a wide range of readers who are interested in the issues of successful speech interaction.