Aspect Shifting, multiple carving and productive ambiguity in representation

 Giauqinto’s notion of “Aspect Shifting” (2007), which Atsoshi Shimojima develops in (2015), which can probably be traced back to Wittgenstein, is just Danielle Macbeth’s “multiple analysis” (2005), which she takes from Gottlöb Frege and which is central to my account of analysis, but I took mostly from Dummett, and is also Emily Grossholz’s “productive ambiguity” (2007) which itself was originally coined by Earle Brown in 1986, and Joo Shin’s “multiple carving” from (2002). Not only are they (extensionally and intensionally) equivalent, they also aim for the same philosophical function: to solve the so-called paradox of analysis, i.e., how can the conclusions (of valid deductive arguments) or solutions of constructive problems be at the same time new information, and contained in the premises or problems. Short version of the answer: because there is some sort of ambiguity in the way we represent the given information so that when you see them or analyze them in a certain way, it is clear that they are fully determined by the premises or whatever information is given at the beginning of the problem, but not that they contain the conclusion or solution; and then when you see them in another way, when you focus on a different aspect or analyze it in a different way,  it is clear that they contain the conclusion, or solution even if this shift makes it no more clear that the representation is determined by the premises or whatever is given in the problem.

Thus conceived, aspect shifting is just a limit case of a transformational analysis in the sense of Beaney, i.e., the intermediate step that allows the transition from premises to conclusion.


In Euclid I, for example, you can easily see that the three straight lines in the conclusion form a triangle, but you need to notice their relation to the circles to notice that they are also their radius. This shift in the interpretation of the lines is what allows us to infer that the triangle is equilateral. 

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