Editing Propositional calculus (section)

== Arguments ==
{{Main article|Argument}}
An [[argument]] is defined as a [[2|pair]] of things, namely a set of sentences, called the '''premises''',{{refn|group=lower-alpha|The set of premises may be the [[empty set]];<ref name="BostockIntermediate" /><ref name=":35" /> an argument from an empty set of premises is ''valid'' if, and only if, the conclusion is a [[Tautology (logic)|tautology]].<ref name="BostockIntermediate" /><ref name=":35" />}} and a sentence, called the '''conclusion'''.<ref name=":35"/><ref name=":21" /><ref name="BostockIntermediate" /> The conclusion is claimed to ''follow from'' the premises,<ref name="BostockIntermediate" /> and the premises are claimed to ''support'' the conclusion.<ref name=":21" />

=== Example argument ===
The following is an example of an argument within the scope of propositional logic:

:'''Premise 1:''' ''If'' it's raining, ''then'' it's cloudy.
:'''Premise 2:''' It's raining.
:'''Conclusion:''' It's cloudy.

The [[logical form]] of this argument is known as [[modus ponens]],<ref name=":13" /> which is a [[Classical logic|classically]] [[Validity (logic)|valid]] form.<ref name="ms14"/> So, in classical logic, the argument is ''valid'', although it may or may not be ''[[Soundness|sound]]'', depending on the [[Meteorology|meteorological]] facts in a given context. This '''example argument''' will be reused when explaining {{section link||Formalization}}.

=== Validity and soundness ===
{{Main article|Validity (logic)|Soundness}}
An argument is '''valid''' if, and only if, it is ''necessary'' that, if all its premises are true, its conclusion is true.<ref name=":35" /><ref name="ms15"/><ref name=":36"/> Alternatively, an argument is valid if, and only if, it is ''impossible'' for all the premises to be true while the conclusion is false.<ref name=":36" /><ref name=":35" />

Validity is contrasted with ''soundness''.<ref name=":36" /> An argument is '''sound''' if, and only if, it is valid and all its premises are true.<ref name=":35" /><ref name=":36" /> Otherwise, it is ''unsound''.<ref name=":36" />

Logic, in general, aims to precisely specify valid arguments.<ref name=":21" /> This is done by defining a valid argument as one in which its conclusion is a [[logical consequence]] of its premises,<ref name=":21" /> which, when this is understood as ''semantic consequence'', means that there is no ''case'' in which the premises are true but the conclusion is not true<ref name=":21" /> – see {{section link||Semantics}} below.