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What is the difference in the role assigned to mathematics in economic theory for these two statements

What is the difference in the role assigned to mathematics in economic theory for these two statements

Jevons: “It is clear that Economics, if it is to be a science at all, must be a mathematical science.”

Marshall: “Use mathematics as shorthand language, rather than as an engine of inquiry.”

What is the difference in the role assigned to mathematics in economic theory for these two statements? What is the significance of the difference for understanding the requirements of economic theory, and the role of mathematics in them?

? Be sure to think about the two terms “mathematical science” and “engine of inquiry”: for example, is mathematics necessarily the engine of inquiry in a mathematical science? If so, does this mean that, for Marshall, economics is not a mathematical science? If it’s not, what kind of a science is it, for Marshall? This is just one way to do it, but be sure to think about the two terms in some way or another. ?

NOTE: The point of the essay is not to work through the details of the different views; nor to judge each, on its own, or in relation to the other, and to other lines in economic thought: are they right or wrong? The point is to think through the ways in which it defines what economic theory should be, what it should include and exclude, and how it should study what needs to be studied.

PS: The two quotes are to get started, be sure to read other relevant passages (e.g., the whole section from which the Jevons quote is taken). Here is the rest of what Marshall says in his letter to A.L. Bowley:

“(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can\’t succeed in 4, burn 3. This I do often.”

Requirements: 4 pages 

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What is the difference in the role assigned to mathematics in economic theory for these two statements

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