Argument
Universal Turing machine
Overview
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Or, in other words, a Turing machine that is capable of simulating any other specialized Turing machines.
Common sense might say that a universal machine is impossible, but Turing proves that it is possible. He suggested that we may compare a human in the process of computing a real number to a machine that is only capable of a finite number of conditions
q
1
,
q
2
,
…
,
q
R
{\displaystyle q_{1},q_{2},\dots ,q_{R}}
; which will be called "m-configurations". He then described the operation of such machine, as described below, and argued:
It is my contention that these operations include all those which are used in the computation of a number.
Turing introduced the idea of such a machine in 1936–1937.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Thus there arises a classification of modes of formation, or in the language commonly used by mathematicians, a classification of Functions. Any number, considered as formed from any other number, is called a function of it; and there are as many kinds of functions as there are modes of formation. The simple functions are by no means numerous, most functions being formed by the combination of several of the…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Universal Turing machine is.
227.] Finite Cognition, when it pre-supposes what is distinguished from it to be something already existing and confronting it,--to be the various facts of external nature or of consciousness--has, in the first place, (1) Formal identity or the abstraction of universality for the form of its action. Its activity therefore consists in analysing the given concrete object, isolating its differences, and giving them the…
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Universal Turing machine is.
Hence, in the conclusion of a syllogism we restrict a predicate to a certain object, after having thought it in the major in its whole extent under a certain condition. This complete quantity of the extent in relation to such a condition is called universality (universalitas). To this corresponds totality (universitas) of conditions in the synthesis of intuitions.
Immanuel Kant, The Critique of Pure Reason
States what Universal Turing machine is.
Related ideas
- Alan Turing
- Proof assistant
- John von Neumann
- Marvin Minsky
- Roger Penrose
- Turing machine
- Computer science
- Church–Turing thesis
- Algorithm
- Entscheidungsproblem
- Halting problem
- Matita
Place in the tradition
Part of Epiphenomenalism.