I use single quotation marks to mention an expression. So whereas Boston is a North American city, ‘Boston’ is the name of a North American city. I use double quotation marks to quote what another person said. For example, Quine said that quotation “… has a certain anomalous feature …” (Quine, 1940, 26). I use corner quotation marks when I need to use a variable or subscript within a quoted expression. So ‘˹the bank1 is open˺’ and ‘˹the bank2 is open˺’ refer to disambiguations of ‘the bank is open’.
I also use corner quotes for substitutional quantification. In particular ‘(∏φ) ˹φ˺ in English means that φ’ asserts that for every English sentence φ, writing φ (not ‘φ’!) in quotation marks, followed by ‘in English means that’, followed by φ without quotations marks results in a truth. In particular, it asserts that ‘snow is white’ in English means that snow is white, that ‘grass is green’ in English means that grass is green, … and so on.
The passage just quoted from Quine continues “A quotation is not a description, but a hieroglyph; it designates its object not by describing it in terms of other objects, but by picturing it” (Quine, 1940, 26). Though I mostly follow Quine’s recommendations for the usage of quotation marks I cannot agree with this: in fact I take quotation as a paradigmatic example of descriptive, rather than depictive, representation. I think this presupposition is defensible, but also dispensable, so I won’t defend it here.