The doctrine of "conceptual relativism" has been defended by Hilary Putnam since the mid-1970s and has become a prominent part of his thought up to the present date, including the recent collection "Philosophy in an Age of Science" (2012). Putnam's conceptual relativism has been regarded as a cornerstone of his "internal realism" but which has survived his rejection of that position around 1990. I will describe Putnam's present position and his current defense of this doctrine which states that there may be non-trivial cases of cognitively equivalent descriptions of the same phenomena and which are (seemingly) contradictory. Equivalent descriptions occur in physical theories (waves vs. particles) and this is important to Putnam. Such physical theories involve words like "object" and "exist" and Putnam claims that these words have many different uses; sentences like "there exist three objects on the table" and "there exist seven objects on the table" may both describe the same phenomena concerning the objects on the table, if we, for instance, use ordinary counting of the objects in the first sentence and if we count mereological sums when we describe the number of objects in the second sentence. Putnam's critics say that he only uses a word like "exist" in a more or less inclusive way, and thus that he has just changed the meaning of the word. I will explain why Putnam rejects this critique, and I will also defend Putnam on important accounts, but I will also put forward some critique. In particular, I agree with Matti Eklund, who sees little or no difference between conceptual relativism and what Putnam calls conceptual pluralism; Putnam agrees that there may be different descriptions of a room, e.g., in terms of tables and chairs on the one hand and in terms of particles and fields on the other, and that it was an earlier mistake of his to include such an example as an instance of conceptual relativity, since 1) there is no apparent contradiction and 2) the descriptions are not cognitively equivalent. But once one has admitted this, it seems difficult to sustain an important notion of conceptual relativity, at least in Putnam's sense, since it is not clear to me that different "equivalent" descriptions in physical theories are of the same nature as in the example of different ways of counting objects on a table.