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Thus, one aspect of thisgeneral theme (T7) is the erroneous attempts by SS to simplify IUTch (cf. (T3),(T4), (T5), (T6)) to such an extent that it leads to meaningless contradictions (assummarized in (Smm), (GLR1), (GLR2)).

On the other hand, (cf. the discussionof §8, §13 below), (T7) also refers to situations where the techniques introducedin IUTch actually do yield simplifications, relative to more naive approaches tovarious situations that arise in IUTch. Finally, (T9) proceeded relatively smoothly,in the sense that it consisted essentially of a straightforward exposition of thecontent of the multiradial algorithms of [IUTchIII], Theorem 3.11. That is to say,the position of SS with regard to (T9) was that they did not dispute the validityof these algorithms, but rather the non-triviality, or substantive content, of thesealgorithms, on account of their positions with regard to (T1), (T2), (T3), (T4),(T5), (T6).

§5. In some sense, it seems that the logical starting point of the differences inpoint of view between SS and HM (and hence of various fundamental misunder-standings of SS) may be understood as a consequence of the difference betweenthe following two approaches to considering histories of operations performed onmathematical objects in a given discussion of mathematics (cf. (T1)):

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