Varia

There are two approaches to the semantics of second-order logic. They differ on the interpretation of the phrase “for every set of objects.” Does this have some fixed meaning to which we can refer, or do we need to consider the variety of meanings the phrase might have? In the first case (which will be called standard semantics), we are taking for granted certain mathematical concepts. In the second case (which will be called general semantics), much less is being taken for granted. In this case, to be considered valid, a sentence will need to be true under all the allowable meanings of the phrase “for every set of objects.”

Second-order and Higher-order Logic

Contemporary definitions are of two main sorts. One distinctively modern, conventionalist, sort of definition focuses on art's institutional features, emphasizing the way art changes over time, modern works that appear to break radically with all traditional art, and the relational properties of artworks that depend on works' relations to art history, art genres, etc. The less conventionalist sort of contemporary definition makes use of a broader, more traditional concept of aesthetic properties that includes more than art-relational ones, and focuses on art's pan-cultural and trans-historical characteristics.

Thomas Adajian, The Definition of Art, Stanford Encyclopedia of Philosophy