Argument terminology used in logic
argument is made up of a chain of simple arguments. This means that the conclusion of one argument acts
as a premise of later arguments. For a complex argument to be successful, each link of the chain has to be
successful.[43]
Arguments and inferences are either
correct or incorrect. If they are correct
then their premises support their
conclusion. In the incorrect case, this
support is missing. It can take
different forms corresponding to the
different types of reasoning.[62] The
strongest form of support corresponds
to deductive reasoning. But even
arguments that are not deductively
valid may still be good arguments
because their premises offer non-
deductive support to their conclusions.
For such cases, the term ampliative or
inductive reasoning is used.[63]
Deductive arguments are associated
with formal logic in contrast to the
relation between ampliative arguments and informal logic.[64]
A deductively valid argument is one whose premises guarantee the truth of its conclusion.[11] For
instance, the argument "(1) all frogs are amphibians; (2) no cats are amphibians; (3) therefore no cats are
frogs" is deductively valid. For deductive validity, it does not matter whether the premises or the
conclusion are actually true. So the argument "(1) all frogs are mammals; (2) no cats are mammals; (3)
therefore no cats are frogs" is also valid because the conclusion follows necessarily from the premises.[65]
According to an influential view by Alfred Tarski, deductive arguments have three essential features: (1)
they are formal, i.e. they depend only on the form of the premises and the conclusion; (2) they are a
priori, i.e. no sense experience is needed to determine whether they obtain; (3) they are modal, i.e. that
they hold by logical necessity for the given propositions, independent of any other circumstances.[66]
Because of the first feature, the focus on formality, deductive inference is usually identified with rules of
inference.[67] Rules of inference specify the form of the premises and the conclusion: how they have to be
structured for the inference to be valid. Arguments that do not follow any rule of inference are
deductively invalid.[68] The modus ponens is a prominent rule of inference. It has the form "p; if p, then
q; therefore q".[69] Knowing that it has just rained ( ) and that after rain the streets are wet ( ), one
can use modus ponens to deduce that the streets are wet ().[70]
The third feature can be expressed by stating that deductively valid inferences are truth-preserving: it is
impossible for the premises to be true and the conclusion to be false.[71] Because of this feature, it is often
asserted that deductive inferences are uninformative since the conclusion cannot arrive at new
information not already present in the premises.[72] But this point is not always accepted since it would
mean, for example, that most of mathematics is uninformative. A different characterization distinguishes
Deductive