Louis Cazamian develops Henri Bergson’s concise remarks, which show humour as a special sort of comical transposition of language. Cazamian stresses that humour is based on transposition, which is inevitably conscious, and he is concerned with the division of humour into four different species according to the modes of transposition. Cazamian focuses especially on the complexity of humour and its impact. Even if a certain view of the world and life, that is, a kind of “matter” of humour, is obviously suggested by the mechanism of transposition, that is, by the “form” of humour, it is impossible to determine any universal rule describing the relationship between matter and form. In that sense Cazamian emphasizes the indefinability of humour, and points to the indeterminability of the humorous effect. These arguments demonstrate the essential influence that many important themes of Bergson’s aesthetics and philosophy have had on Cazamian’s conception of humour, a conception that proves to be integrally Bergsonian.
We consider real valued functions $f$ defined on a subinterval $I$ of the positive real axis and prove that if all of $f$’s quantum differences are nonnegative then $f$ has a power series representation on $I$. Further, if the quantum differences have fixed sign on $I$ then $f$ is analytic on $I$.