6. (8 marks) Translate the following argument into formal logical notation using

Question

6. (8 marks) Translate the following argument into formal logical notation using the scheme of abbreviation provided below. State whether or not the argument is valid and give a few words of justification for your answer. The domain is the set of all people, and Turing is an element of the domain. In the predicate definitions, "is" stands for "is/was". I(x): is intelligent. C(x): r is creative. B(x): x is a brilliant computer scientist. P(a): r can pass the Turing test. W(x): x wrote On computable numbers, with an application to the entscheidungsproblem. Anyone who can pass the Turing test is intelligent. No one is a brilliant computer scientist unless he is creative Turing wrote On computable numbers, with an application to the entscheidungsproblem. No one who can't pass the Turing test is creative. No one but a brilliant computer scientist could have written On computable numbers, with an application to the entscheidungsproblem .:. Turing is intelligent.

Explanation / Answer

1) Anyone who P(x) is I(x) - Turing test is a test for intelligence in a computer, requiring that a human being should be unable to distinguish the machine from another human being by using the replies to questions put to both. It doesn't test the intelligence of person. so invalid.

2) No one is B(x) unless he is C(x): This statement can be true because to become a computer scientist one should know how to build algorithms and solve real life problems using computer, which requires a lot of creativity. Because algorithm design needs to a person to be creative. Valid

3) Turing W(x): Yes, valid. Because anyone can wrote on computational numbers.

4) No one who P(x)' is I(x).: Invalid. Turing test is for computers, not humans.

5) No one but B(x) could have W(x): A person need not to be a computer scientist to write alogorithms on computational number, acomputer programmer can also do the same. One need to be a great scientist for that.

Therefore, Turing is I(x).

THANK YOU.

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