Random content

Standard Notation

Important: This symbolism was created for optimal viewing on Internet Explorer 7.0. Other browsers or other versions of IE might introduce errors.

Standard notation is simply the notation I use throughout this website in essays - usually on topics in philosophical logic - where brevity requires symbolic abbreviation. I put all my definitions on this page to avoid repetition. More complex topics in second order logic, set theory and elementary analysis obviously require fuller and more rigorous definitions, which are provided in the context of the individual essays.

Basic Symbols

1. The letters “p, q,  r…” stand for propositions.

2. The letters “a, b, c…” stand for individuals.

3. The letters “F, G, H…” stand for properties.

4. The letters “x, y, z…” stand for individual variables.

5. “(x)(Fx)” means “everything that is F” or “Everything is F”

6. “¬p” means “It is not the case that p”

7. “¬(x)(Fx)” means “It is not the case that everything that is F…” or “It is not the case that everything is F”

8. “(x)Fx” means “¬(x)¬(Fx)”

It is assumed that propositional symbols can be mapped on to the truth values T and F.

Truth Functional Connectives

1. “p & q” means “p and q”

2. “p V q” means “p or q”

3. “p  q” means  “if p then q”

4. “p ≡ q” means “p if and only if q”

The meanings of the right side of each of these definitions are truth functional.