Church thesis in english
way as to refer only to what can be done by means of effective methods. 1.3 The meaning of computable and computation in Turings thesis Turing introduced his machines with the intention of providing an idealized description of a certain human activity, the tedious one of numerical computation. 2.2.4 The weaker form of the thesis and hypercomputation A hypercomputer is any information-processing machine (notional or real) that is able to achieve more than Turings human rote-worker can in principle achieve (see the entry on computation in physical systems ). Whatever sequence the human computer is computing, a Turing machine can be constructed to compute the same sequence, Turing said (1936: 77). (1990: 26) These various"tions are typical of writing on the foundations of computer science and computational theories of mind. Turing proved that no such machine can be specified.
So, given his thesis that if an effective method exists then it can be carried out by one of his machines, it follows that there is no such method. The equivalence of the analyses bears only on the question of the extent of what is humanly computable, not on the question of whether the functions generatable by machines could extend beyond the functions generatable by human computers (even human computers who work forever and. The, church-Turing thesis (also known as, church's thesis, Church's conjecture and, turing's thesis ) is a statement about computers. That is, it can display any systematic pattern of responses to the environment whatsoever. When the Church-Turing thesis is expressed in terms of the replacement concept proposed by Turing, it is appropriate to refer to the thesis also as Turings thesis, and as Churchs thesis when expressed in terms of one or another of the formal replacements proposed. In reality the Church-Turing thesis does not entail that the brain (or the mind, or consciousness) can be modelled by a Turing machine program, not even in conjunction with the belief that the brain (or mind, or consciousness) is scientifically explicable, or rule-governed, or scientifically. However, this convergence is sometimes taken to be evidence for the maximality thesis. Turing did not show that his machines can solve any problem that can be solved by instructions, explicitly stated rules, or procedures (Gregory 1987 and nor did he prove that the universal Turing machine can compute any function that any computer, with any architecture, can.