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.