Formal logic needs to translate natural language
arguments into a formal language, like first-order logic, to
assess whether they are valid. In this example, the letter
"c" represents Carmen while the letters "M" and "T" stand
for "Mexican" and "teacher". The symbol " ∧ " has the
meaning of "and".
new formal systems have been proposed.
There are disagreements about what makes a
formal system a logic.[22] For example, it has
been suggested that only logically complete
systems, like first-order logic, qualify as
logics. For such reasons, some theorists deny
that higher-order logics are logics in the strict
sense.[23]
When understood in a wide sense, logic
encompasses both formal and informal logic.[24] Informal logic uses non-formal criteria and standards to
analyze and assess the correctness of arguments. Its main focus is on everyday discourse.[25] Its
development was prompted by difficulties in applying the insights of formal logic to natural language
arguments.[26] In this regard, it considers problems that formal logic on its own is unable to address.[27]
Both provide criteria for assessing the correctness of arguments and distinguishing them from
fallacies.[28]
Many characterizations of informal logic have been suggested but there is no general agreement on its
precise definition.[29] The most literal approach sees the terms "formal" and "informal" as applying to the
language used to express arguments. On this view, informal logic studies arguments that are in informal
or natural language.[30] Formal logic can only examine them indirectly by translating them first into a
formal language while informal logic investigates them in their original form.[31] On this view, the
argument "Birds fly. Tweety is a bird. Therefore, Tweety flies." belongs to natural language and is
examined by informal logic. But the formal translation "(1) ; (2)
; (3) " is studied by formal logic.[32] The study of natural language
arguments comes with various difficulties. For example, natural language expressions are often
ambiguous, vague, and context-dependent.[33] Another approach defines informal logic in a wide sense as
the normative study of the standards, criteria, and procedures of argumentation. In this sense, it includes
questions about the role of rationality, critical thinking, and the psychology of argumentation.[34]
Another characterization identifies informal logic with the study of non-deductive arguments. In this way,
it contrasts with deductive reasoning examined by formal logic.[35] Non-deductive arguments make their
conclusion probable but do not ensure that it is true. An example is the inductive argument from the
empirical observation that "all ravens I have seen so far are black" to the conclusion "all ravens are
black".[36]
A further approach is to define informal logic as the study of informal fallacies.[37] Informal fallacies are
incorrect arguments in which errors are present in the content and the context of the argument.[38] A false
dilemma, for example, involves an error of content by excluding viable options. This is the case in the
fallacy "you are either with us or against us; you are not with us; therefore, you are against us".[39] Some
theorists state that formal logic studies the general form of arguments while informal logic studies
particular instances of arguments. Another approach is to hold that formal logic only considers the role of
Informal logic