I have an exam in the course about higher order logic. I was looking for answer of the question "Explain the advantage and disadvantage of using Hilbert system". The disadvantage in the meaning of why it is hard to apply. Thanks.
From a practical point of view, the disadvantages of a Hilbert System are
From a theoretical point of view, the advantages of a Hilbert System are
The relation between a Hilbert system and a natural deduction system is similar to the relation between machine language and a high level programming language. Of course you can build a high level programming language on top of machine language, and similarly you can prove metatheorems about Hilbert systems which allow you to use some of the more convenient proof techniques from natural deduction systems also with Hilbert systems.