Logic as a Formal Deductive System

• Formal Deductive Systems
  • Language: A set of ``sentences": i.e. marks on paper.
  • Rules: How to generate new sentences from old ones.

• An essential feature of a formal system is that we make no reference to the meanings of the sentences.
• Example: Unary Numbers
  • Language: The single sentence {I}
  • Rule of concatenation:

    Given X is a sentence and Y is a sentence, infer that the concatenatation of X and Y is a sentence.