What are the components of a proof?Sentences that are shown to be soundStatements in natural languageNecessary, possible, and contingent truthsPremises, derivations, conclusion

The components of a proof typically include:

1. Premises: These are the statements or facts that are assumed to be true at the beginning of the proof. They form the basis on which the argument is built.

2. Derivations: These are the logical steps that are taken to move from the premises to the conclusion. They are based on rules of inference, which are accepted logical techniques for deriving one statement from another.

3. Conclusion: This is the final statement that is proven to be true based on the premises and derivations. It is the end result of the proof.

In addition to these, a proof may also involve necessary, possible, and contingent truths. A necessary truth is a statement that must be true in all possible circumstances, a possible truth is a statement that is true in some possible circumstances, and a contingent truth is a statement that is true in the actual world but not necessarily in all possible worlds.

Finally, proofs are often expressed in natural language, but they can also be formalized using symbolic logic. In either case, the sentences used in the proof must be shown to be sound, meaning that they are both logically valid (i.e., the conclusion follows necessarily from the premises) and the premises are true.