Introduction to Philosophy/Logic/Building More Complicated Formulas
- 'I need a hammer and nails or a screwdriver and screws.'
Though we know what is meant by the above statement, it is technically ambiguous - imagine saying it to a not very bright apprentice. In this case no harm would be done and the apprentice might fetch an unnecessary tool. One could think of other situations where such ambiguity could be lethal.
In propositional calculus we use brackets to prevent any ambiguity:
- 'I need (a hammer and nails) or (a screwdriver and screws).'
This is just like the usual mathematical use of brackets: you evaluate the contents first.
We don't use brackets around ¬ symbols -- it binds tightly onto whatever is following it.