Logic Symbols

Philosophy of Language

Spring, 2000
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 Symbol font installed.)

symbol English equivalent interpretation

&
(sometimes Ù )

and

 P & Q is true if and only if P is true and Q is true

Ú

or (inclusive)

 P Ú Q is true if and only if at least one of P and Q are true

~
(sometimes Ø )

not

 ~P is true if and only if P is false

®
(sometimes É )

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 Ú ~(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: February 24, 2000.
Comments?  cbrown@trinity.edu.

Curtis Brown | Philosophy of Language | Philosophy Department | Trinity University