Leaving mathematics as it is : Wittgenstein's later philosophy of mathematics
Wittgensteinâs later philosophy of mathematics has been widely interpreted to involve Wittgensteinâs making dogmatic requirements of what can and cannot be mathematics, as well as involving Wittgenstein dismissing whole areas (e.g. set theory) as not legitimate mathematics. Given that Wittgenstein promised to âleave mathematics as it isâ, Wittgenstein is left looking either hypocritical or confused. This thesis will argue that Wittgenstein can be read as true to his promise to âleave mathematics as it isâ and that Wittgenstein can be seen to present coherent, careful and non-dogmatic treatments of philosophical problems in relation to mathematics. If Wittgensteinâs conception of philosophy is understood in sufficient detail, then it is possible to lift the appearance of confusion and contradiction in his work on mathematics. Whilst apparently dogmatic and sweeping claims figure in Wittgensteinâs writing, they figure only as pictures to be compared against language-use and not as definitive accounts (which would claim exclusive right to correctness). Wittgenstein emphasises the importance of the applications of mathematics and he feels that our inclination to overlook the connections of mathematics
Dawson, Ryan
Leaving mathematics as it is : Wittgenstein's later philosophy of mathematics. Wittgensteinâs later philosophy of mathematics has been widely interpreted to involve Wittgensteinâs making dogmatic requirements of what can and cannot be mathematics, as well as involving Wittgenstein dismissing whole areas (e.g. set theory) as not legitimate mathematics. Given that Wittgenstein promised to âleave mathematics as it isâ, Wittgenstein is left looking either hypocritical or confused. This thesis will argue that Wittgenstein can be read as true to his promise to âleave mathematics as it isâ and that Wittgenstein can be seen to present coherent, careful and non-dogmatic treatments of philosophical problems in relation to mathematics. If Wittgensteinâs conception of philosophy is understood in sufficient detail, then it is possible to lift the appearance of confusion and contradiction in his work on mathematics. Whilst apparently dogmatic and sweeping claims figure in Wittgensteinâs writing, they figure only as pictures to be compared against language-use and not as definitive accounts (which would claim exclusive right to correctness). Wittgenstein emphasises the importance of the applications of mathematics and he feels that our inclination to overlook the connections of mathematics
mathematics wittgenstein_later philosophy_mathematics wittgenstein_later philosophy_mathematics widely interpret involve wittgenstein make dogmatic requirement mathematics well involve wittgenstein dismiss whole area set_theory legitimate mathematics given wittgenstein promise leave mathematics wittgenstein leave look either confuse argue_wittgenstein read true promise leave mathematics wittgenstein see present coherent careful non dogmatic treatment philosophical_problem relation mathematics wittgenstein_conception philosophy understood sufficient detail possible appearance confusion contradiction work mathematics whilst apparently dogmatic sweeping claim figure wittgenstein writing figure picture compare language_use definitive account would claim exclusive right correctness wittgenstein emphasise_importance application mathematics feel inclination overlook connection mathematics