Study how language and linguistics reinforce cultural divisions by examining how language is used to include or exclude certain groups. For instance, assess how literacy tests ostracize non-English speakers from civic engagement or how standardized language tests exclude non-English speakers from higher education. Alternatively, you could explore how particular words (such as the word “freshmen”) have contributed to division between genders and how gender-specific language (such as gendered articles in certain languages) reinforce gender stereotypes.
Fundamental contributions to the sociology of mathematical knowledge have been made by Sal Restivo and David Bloor . Restivo draws upon the work of scholars such as Oswald Spengler (The Decline of the West, 1918), Raymond L. Wilder and Lesley A. White, as well as contemporary sociologists of knowledge and science studies scholars. David Bloor draws upon Ludwig Wittgenstein and other contemporary thinkers. They both claim that mathematical knowledge is socially constructed and has irreducible contingent and historical factors woven into it. More recently Paul Ernest has proposed a social constructivist account of mathematical knowledge, drawing on the works of both of these sociologists.
Of the three basic kinds of complex idea, relations are the easiest to understand. The mind can consider any idea as it stands in relation to any other. By observing the similarities and differences, the mind derives further ideas, ideas of relation. For instance, we might compare our simple ideas of two patches of color and notice that one is of a different size than the other, thereby getting the idea of bigger and the idea of smaller. Or else, we might compare our ideas of two people and get the ideas of father and son. Our ideas of cause and effect, which Locke examines at length in chapter xxvi, are produced by noticing that qualities and substances begin to exist and that they receive their existence from the operation of some other being. We call a "cause" whatever produces any simple of complex idea to come into existence, and an "effect" whatever is produced. Our ideas of moral relations, which Locke turns to in chapter xxviii, are produced by comparing our voluntary actions to some law. It is Locke's third and final category of relational ideas, ideas of identity and diversity, that is of great importance to the history of philosophy. This is the topic of Chapter xxvii. It is in the context of this discussion that Locke presents his theory of personal identity, that is, his theory of what makes us the same person over time. According to Locke, remaining the same person has nothing to do with remaining the same substance, either physical or mental. Instead, personal identity has only to do with consciousness: it is by the consciousness of one's present thoughts and actions that the self is conceived, and it is through the continuous link of memory that the self is extended back to past consciousness. Locke's argument for this claim rests on his idea of identity, which is defined in terms of a comparison between something presently existing and the existence of that thing at an earlier time. This notion of identity stems from the basic principle that no two things of the same kind can exist in the same place at the same time, as well as the extension of this principle that, therefore, no two things can have the same beginning and neither can any thing have two beginnings. Things retain their identity, then, as long as they do not become essentially altered because once something is essentially altered, it has a new beginning as a new thing. In other words, identity is retained through continuous history. Of course, to remain essentially unaltered has a different meaning for different ideas. Locke separates the idea of a substance, the idea of an organism, and the idea of a person. The identity of these three types of idea is determined by different criteria. The identity of a material substance consists merely in its matter; a mass of atoms retains its identity as long as the number of atoms remains the same. The identity of living organisms cannot be tied to matter because both plants and animals are continuously losing and gaining matter and yet retain their identity. The idea of a living organism is of a living system, not of a mass of matter, and therefore it is only the living system that must remain intact for the identity to remain the same. Locke chooses the word "man" to refer to that aspect of the human being that denotes him as a type of animal. With this definition of man, Locke is able to claim that the identity of man, because it is just a particular instance of animal, is tied to body and shape. That other aspect of the human being, the human as a thinking, rational thing, Locke calls "person." The identity of person rests entirely in consciousness. A person is defined as a thinking thing, and thought, as we have seen, is inseparable from consciousness (remember Transparency of the Mental). It is, therefore, in consciousness alone that identity must exist.