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, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements.
In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement.
More serious attempts to study such statement operators such as "and", "or" and "if...
then..." were conducted by the Stoic philosophers in the late 3rd century BCE.
These are, of course, cornerstones of classical propositional logic.
There is some evidence that Aristotle, or at least his successor at the Lyceum, Theophrastus (d.
is that branch of truth-functional propositional logic that assumes that there are are only two possible truth-values a statement (whether simple or complex) can have: (1) truth, and (2) falsity, and that every statement is either true or false but not both.
Whether a statement formed using this operator is true or false does not depend entirely on the truth or falsity of the statement to which the operator is applied.
Since most of their original works -- if indeed, many writings were even produced -- are lost, we cannot make many definite claims about exactly who first made investigations into what areas of propositional logic, but we do know from the writings of Sextus Empiricus that Diodorus Cronus and his pupil Philo had engaged in a protracted debate about whether the truth of a conditional statement depends entirely on it not being the case that its antecedent (if-clause) is true while its consequent (then-clause) is false, or whether it requires some sort of stronger connection between the antecedent and consequent -- a debate that continues to have relevance for modern discussion of conditionals.
The Stoic philosopher Chrysippus (roughly 280-205 BCE) perhaps did the most in advancing Stoic propositional logic, by marking out a number of different ways of forming complex premises for arguments, and for each, listing valid inference schemata.
For example, both of the following statements are true: Here, the first example is true but the second example is false.
Hence, the truth or falsity of a statement using the operator "necessarily" does not depend entirely on the truth or falsity of the statement modified.
(For more information on these alternative forms of propositional logic, consult Section VIII below.) The serious study of logic as an independent discipline began with the work of Aristotle (384-322 BCE).