On Jul 2, 2014, at 6:12 AM, Edwina Taborsky <[email protected]> wrote:
> Sung wrote: > > "Mathematics is a species of the sign according to Peirce. (070114-1) >> All signs are arbitrary according to Saussure. Therefore, >> mathematics is arbitrary." > > This is invalid for two reasons: > > First, it is logically invalid. The error is called 'the fallacy of four > terms'. A valid syllogism must have exactly three unambiguous categorical > terms. But the term 'mathematics' as outlined above is ambiguous. Mathematics > is both a process and a producer of models. The specific model chosen may be > 'arbitrary' in the sense that it is symbolic, but the process used within > that mathematical reasoning is not arbitrary. There are two meanings of > mathematics in the syllogism above. > > Second, it is only symbolic signs that are arbitrary, in the sense that their > models are assigned by an external agent; iconic and indexical semiosic > relations are not arbitrary. Saussure's semiology applies only to symbols, > therefore, there are also TWO meanings of the term 'sign' in the above > syllogism. One could easily also add that Saussure just gets signs mangled in general. <grin> Thus a lot of the post-structuralist critique of Saussure which (at least for Derrida) goes rather in the direction of Peirce. I’ve long thought the surprise of how mathematical physics was is a bit of a counterpart as well. Again, easily explainable up to a point within Peirce’s semiotics and perhaps his ontology. Although of course Peirce’s ontology is rather more controversial than his semiotics. The question ends up being the place of the icon and the index in signs and in mathematics in particular. Contrary some I don’t think Peirce’s scholastic realism means we need be full throated platonists about mathematical entities the way some are. It seems that far too many mathematicians - especially those more naive on the philosophical background - provide a false dichotomy in discussions. Of course physicists are even worse, so no one take this as a critique of mathematicians - and physicists are rather apt to simply mix foundations in incoherent ways sometimes talking like a realist, sometimes an instrumentalist and sometimes an empiricist with regards to foundations. I find it rather rare a mathematician inconsistently pretends to be say an intuitionalist and then a platonist. But again it’s been an awfully long time since I’ve discussed any of this with physicists or mathematicians. So perhaps things have changed.
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