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Extra info for Avicenna's Treatise on Logic, Part One of Danesh-Name Alai: A concise philosophical Encyclopaedia and Autobiography (Pt. 1)
Indeed, it seems that Hilbertian instrumentalism stands to benefit from such a comparison; for it shows a sensitivity to Frege's Problem and the Dilution Problem and the workings of an Equivalency Thesis that is lacking in Field's account. The ultima:te purpose of Field's instrumentalism is to show that we can account for the applicability of mathematics to empirical concerns without having to count it as true, and hence (according to Field's reasoning) without having to grant an ontology of abstract objects with the attendant well-known epistemological difficulties.
NOTES I In the same vein, though more recently, Kitcher writes, ... Hilbert divides grammatical sentences into those which have truth-values and those which do not, assigning sentences which express finitary propositions to the former class and ideal statements to the latter class. Ideal statements would be regarded as meaningless marks which are manipulated to facilitate our reasoning about finitary matters. The position is just that of a simple instrumentalist philosophy of science ... (Kitcher , p.
10 For this reason, we will often refer to Hilbert's instrumentalism as the "Metamathematical Replacement Strategy" (or, more briefly, the "Replacement Strategy"). 17 Actually, there is the potential for some confusion here. , what we have been calling propositions. Similarly, what we are calling inferences are not judgements of the truthpreservingness of shifts from one proposition (or set of propositions) to another, but rather the shifts themselves. This said, our present description of Frege's position should be seen merely as an attempt to state his views in the terminology that has already been established in this essay.