Logic Symbols

Philosophy of Science

Some Logic Symbols

A fair number of our reading assignments have contained logical symbols.   Here are a few of these with translations.  (Won't display properly unless you have the Lucida Sans Unicode font installed.)

 symbol English equivalent interpretation & (sometimes ⋀ ) and P & Q is true if and only if P is true and Q is true ⋁ or (inclusive) P ⋁ Q is true if and only if at least one of P and Q are true ~ (sometimes ¬ ) not ~P is true if and only if P is false → (sometimes ⊃ ) if . . . then P → Q is true if and only if either P is false or Q is true (i.e. if P is true, so is Q; otherwise, if P is false, Q can be either) ∀x (sometimes (∀x), (x) ) for all x ∀x(x is a tree ⋁ ~(x is a tree) ) means that everything is either a tree or not a tree (literally:  for all x, either x is a tree or x is not a tree) ∃x (sometimes (∃x) ) there is an x such that ∃x(x is a tree) says that there is a tree (at least one; could be more than one).  Literally:  there is an x such that x is a tree.

 Last update: January 28, 2002 Curtis Brown | Philosophy of Science | Philosophy Department | Trinity University cbrown@trinity.edu