Detached Ideas

In commemoration of Apple surpassing Microsoft in market capitalization last week, here is Steve Jobs on Apple’s choice not to support Flash on the IPad:

–Paul

Sherry Turkle is the Abby Rockefeller Mauze Professor of the Social Studies of Science and Technology at MIT, and is the director of the MIT Initiative on Tech­nology and Self. She earned her doctorate in sociology and per­son­ality psychology from Harvard University, and is a licensed clinical psycho­logist. She writes about the “subjective side” of the relationship between people and technology.

I first read The Second Self: Computers and the Human Spirit nearly twenty years ago, and have used it in var­ious courses. Turkle describes how children often em­ploy computers as evocative objects — “things to think with” — which assist them in understanding their own capacities and limi­tations. The sense of self that emerges in children who have grown up with computers, for instance, can be quite different from that of children who have grown up, say, with animals and pets. Instead of the traditional Aristotelian notion of being a “rational animal”, the experience of such children can lead them to formulate a new genus and specific difference, to conceive of themselves as “feeling machines.” This sort of radical change in our understanding of who we are, it seems to me, could have pro­found consequences for our culture. It is important that we consider the pos­si­bility that technology might induce deep change.

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Peter Smith, of Logic Matters, has noticed a new Stanford Encyclopedia of Philosophy entry, Set Theory: Constructive and Intuitionistic ZF.  Constructive and intuitionistic set theories result from the rejection of the law of excluded middle, and effectively restrict set theoretical ontology to poten­tially infinite sets:

The shift from classical to intuitionistic logic, as well as the requirement of predicativity, reflects a conflict between the classical and the constructive view of the universe of sets. This also relates to the time-honoured distinction between actual and potential infinity. According to one view often associated to classical set theory, our mathematical activity can be seen as a gradual disclosure of properties of the universe of sets, whose existence is independent of us. This tenet is bound up with the assumed validity of classical logic on that universe. Brouwer abandoned classical logic and embarked on an ambitious programme to renovate the whole mathematical landscape. He denounced that classical logic had wrongly been extrapolated from the mathematics of finite sets, had been made independent from mathematics, and illicitly applied to infinite totalities.

In a constructive context, where the rejection of classical logic meets the requirement of predicativity, the universe is an open concept, a universe “in fieri”. This coheres with the constructive rejection of actual infinity (Dummett 2000, Fletcher 2007). Intuitionism stressed the dependency of mathematical objects on the thinking subject. Following this line of thought, predicativity appears as a natural and fundamental component of the constructive view. If we construct mathematical objects, then resorting to impredicative definitions would produce an undesirable form of circularity. We can thus view the universe of constructive sets as built up in stages by our own mathematical activity and thus open-ended. [SEP]

This article might interest our BA Seminar students, as well as students in Programming Languages who have recently encountered Curry-Howard Isomorphism — the correspondence between intuitionistic logic and CL_K.

–Paul