Expression of The Mathematical Objection as an Explicit Argument
Taking into consideration the Mathematical objection, we can be conclusive that unlike the human beings, no machine can distinguish between the unprovable formulae for the provable. Otherwise stated, if a mathematician happens to be confronted with a similar challenge, he or she would explore around and finally come up with new methods of proof. A matter of fact is that one key aspect that forms the foundation of creativity in mathematics is the envisaging up of innovative methods particularly for solving problems, proving theories, and so on. But are, in the human beings creative process, mathematicians at all times computable? If we can assume an unbounded supply of time, in, paper, and mathematicians? This question can be expressed in a number of ways. One is that the series of new approaches say …mi, mi…; the community of idealized mathematicians produce over time is a computable system in the sense of Turing.
By virtue of fashioning new methods when required, we can envisage the probability that the mathematicians can compute any desired figure of numerals that are of an incomputable sequence. If we suppose that the Turing machine is equivalent to the mind of a human being, H. Then the real moves show that the Turing machine cannot be equivalent to H. From this we can conclusively say that the Turing machine is not a human mind. Furthermore, considering this on the basis of a rationalistic attitude we can with ease conclude that the mind is not mechanical for the reasons that if the mind is actually a machine, then there would exist several theoretic questions that are undecidable for the mind and this contradicts the rationalistic attitude.
Turing’s Response to That Objection as an Explicit Argument.
Turing response to this objection by denying the rationalistic optimism and as a counter move stating that; ” it is established that there are limitations to the powers of any particular machine, it has only been stated, without any sort of proof, that no such limitations apply to the human intellect” (Turing 445). Through this rejoinder, Turing does not let the matter rest there but goes on to affirm that on only this basis “But I do not think [the Mathematical Objection] can be dismissed quite so lightly” (Turing 445). In the supposition that the Turing machine is equivalent to the human mind, Turing antidote to this assumption is that the human beings think in terms of a collection of minds or dynamically changing mind whereby each mind-stage is the same or rather equal to a different Turing machine. In other words, he makes use of a series of proof-producing machines that are increasingly powerful to put across his point. With this remarks, he summarizes that “…there might be men cleverer than any given machine, but then again there might be other machines cleverer again, and so on.” (Turing 445)
Whether Turing’s Response Is Adequate with an Explanation
The adequacy of Turing’s response can be viewed in two ways. The first is that it is inadequate if he intends to ascertain that machines can think. The obvious reason for terming it insufficient is that as per my understanding, his argument is comparable to a digit recognition test in a computer whereby scoring all the digit recognition tests does not mean that, that computer possess a vision equivalent to that of a human being. On the other hand, the evidence is way beyond sufficiency is Turing intended to presume that this shift of perspective could spark interest and help us think more precisely concerning the topic.
Turing, Alan M. “Computing machinery and intelligence.” Mind59.236 (1950): 433-460.