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Prove or Disprove 1. The set of all undecidable propositions within a formal system is enumerable....

Prove or Disprove

1. The set of all undecidable propositions within a formal system is enumerable.

2. The set of all undecidable propositions within a formal system is decidable.

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Answer #1

1. The set of all undecidable propositions within a formal system is enumerable.

Ans: Undecidable propositions are those type of propositions which cannot be predicted, i.e. which are not binary in nature. These type of propositions will have more than 2 interpretations, where we have multiple internal and external decidability. So the set of all undecidable porpositions in any system (be it a formal system) cannot be enumerable

2. The set of all undecidable propositions within a formal system is decidable.

Ans: Similar is the case when it comes to find whether set of all undecidable propositions within a formal system will be decidable or not. It could be possible with some of the undecidable propositions to have a system with a decidable feature, but with n number of undecidable propositions, its not possible to have a formal system to be decidable.

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