If-then arguments posit
logical sequences that sometimes include objects of the mind. For example, a
counterfactual argument proposes a
hypothetical or
subjunctive possibility which
could or
would be true, but
might not be false.
Conditional sequences involving subjunctives use
intensional language, which is studied by
modal logic, whereas
classical logic studies the
extensional language of
necessary and
sufficient conditions. In general, a logical
antecedent is a sufficient condition, and a logical
consequent is a necessary condition (or the
contingency) in a
logical conditional. But logical conditionals accounting only for necessity and sufficiency do not always reflect every day if-then reasoning, and for this reason they are sometimes known as
material conditionals. In contrast,
indicative conditionals, sometimes known as non-material conditionals, attempt to describe if-then reasoning involving hypotheticals, fictions, or counterfactuals.
Truth tables for if-then statements identify four unique combinations of premises and conclusions: true premises and true conclusions; false premises and true conclusions; true premises and false conclusions; false premises and false conclusions.
Strict conditionals assign a positive
truth-value to every case except the case of a true premise and a false conclusion. This is sometimes regarded as counterintuitive, but makes more sense when false conditions are understood as objects of the mind.
False antecedent A false antecedent is a premise known to be false, fictional, imaginary, or unnecessary. In a conditional sequence, a false antecedent may be the basis for any consequence, true or false. The subjects of
literature are sometimes false antecedents. Examples include the contents of false documents, the origins of
stand-alone phenomena, or the implications of
loaded words. Moreover, artificial sources, personalities, events, and histories. False antecedents are sometimes referred to as "
nothing", or "
nonexistent", whereas nonexistent referents are not referred to.
Art and
acting often portray scenarios without any antecedent other than an artist's imagination. For example, mythical heroes, legendary creatures, gods and goddesses.
False consequent A false consequent, in contrast, is a conclusion known to be false, fictional, imaginary, or insufficient. In a conditional statement, a fictional conclusion is known as a
non sequitur, which literally means
out of sequence. A conclusion that is out of sequence is not contingent on any premises that precede it, and it does not follow from them, so such a sequence is not conditional. A conditional sequence is a connected series of statements. A false consequent cannot follow from true premises in a connected sequence. But, on the other hand, a false consequent can follow from a false antecedent. As an example, the name of a
team, a
genre, or a
nation is a collective term applied
ex post facto to a group of distinct individuals. None of the individuals on a sports team is the team itself, nor is any musical chord a genre, nor any person America. The name is an identity for a collection that is connected by consensus or
reference, but not by sequence. A different name could equally follow, but it would have different
social or
political significance. ==Philosophy==