University:
Boston University
Course:
CAS PH 630 | American Philosophy
Academic year:

2023
Views:

407

Pages:

15
Author:

Melina Hobbs

Wittgenstein’s and Turing’s point To say what a formal system of logic is, we cannot just write down another formal system. We have to get at this conceptually, philosophically. We must clarify what a system of logic (or “definite method”) is by looking at what it is used for. Their answer: Logic is used by human beings who speak, act, calculate and converse in an embodied social world (words are constantly embedded in evolving forms of life). Sieg (2006) Most importantly in the given intellectual context [the move from arithmetically motivated calculations to general symbolic processes that underlie them] has to be carried out programmatically by human beings: the Entscheidungsproblem had to be solved by us in a mechanical way; it was the normative demand of radical intersubjectivity between humans that motivated the step from axiomatic to formal systems. And the next step, from formal systems to their uses by embodied human beings. Wittgenstein, RPP I §1096 (MS 135, 1947) Turing’s “Machines”. These machines are humans who calculate. And one might express what he says also in the form of games. And the interesting games would be such as brought one via certain rules to nonsensical instructions... One has received the order “Go on in the same way” when this makes no sense, say because one has got into a circle. For that order makes sense only in certain positions. (Wittgenstein knows that Turing’s proof turns on constructing a tautological machine that is circular, ending in nonsense (“Do What You Do”) (Floyd 2012).) The Stored Program Computer Concept Turing (1936) constructs the Universal Machine that does the work of all machines, including itself. It can operate on its own commands. • One cannot diagonalize out of the class of computable functions: the Universal Machine gives us a robust “absolute” parameter for what counts as a step in a computation, not dependent upon any particular language or system of logic (Gödel: “a miracle”). • Turing’s Universal Machine is responsible for the ubiquity of computational processing in our world, and its indefinite extent of application and ability to compress what is definable. • The Universal Machine shows that there are no ultimate, general dichotomies between hardware, data, and software. Turing, Lecture to the London Mathematical Society (1947) The Masters [i.e., mathematicians] are liable to get replaced because as soon as any technique becomes at all stereotyped it becomes possible to devise a system of instruction tables which will enable the electronic computer to do it for itself. It may happen however that the masters will refuse to do this. They may be unwilling to let their jobs be stolen from them in this way. In that case they would surround the whole of their work with mystery and make excuses, couched in well-chosen gibberish, whenever any dangerous suggestions were made. I think that a reaction of this kind is a very real danger. What is a Turing Machine? What is a Turing Machine? Turing 1936, The Universal Machine Wittgenstein: Turing’s “Machines”: these are humans who calculate. Turing (1936): “We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions.” What is a Turing Machine? A Slave to the System Emil Posts’s “Workers” (1936) What is a Turing Machine? Who “sees” the tape? What is a Turing Machine? Wolfram, A New Kind of Science What is a Turing Machine? (A “Computor”) Blythe House London What is a Turing Machine? Bletchley Park: The Collosus What is a Turing Machine? Turing and Wittgenstein in Conversation • 1937 Discussions in the Cambridge Botanical Gardens. • 1939 Turing, working at Bletchley, still teaches at Cambridge, attends Wittgenstein’s lectures on the foundations of math. • 1942 Turing writes about types and phraseology, thanking Wittgenstein. • 1942-44 Turing makes his “Notes on Notations”. • 1948 The Manchester “Baby”: 1st electronic stored-program computer; Turing notes that it can “surprise” him. 1st programming manual for the Mark II (1950). Strachey: 1st computer-generated music (BBC, “God Save the Queen”). • 1950 Turing publishes his “Imitation Game”.