For reasoning we have to use propositions. A declarative statement which may be true
or false but not both is called a proposition. According to Aristotle there could be only two
possibilities – a proposition could be either true or false and there could not be any third
possibility. This is correct so far as mathematics and other exact sciences are concerned. For
instance, the statement a = b can be either true or false. Similarly, any physical or chemical
theory can be either true or false. However, in statistical or social sciences it is sometimes
not possible to divide all statements into two mutually exclusive classes. Some statements
may be, for instance, undecided.
Deductive logic in which every statement is regarded as true or false and there is no
other possibility, is called Aristotlian Logic. Logic in which there is scope for a third or fourth
possibility is called non-Aristotelian.