Logic Symbols

Philosophy of Science

Curtis Brown

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