HOME

TheInfoList



OR:

In
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...
, logical form of a statement is a precisely-specified
semantic Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
version of that statement in a
formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A fo ...
. Informally, the logical form attempts to formalize a possibly
ambiguous Ambiguity is the type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement ...
statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal
formal language In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of sym ...
, the meaning of a logical form can be determined unambiguously from
syntax In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituenc ...
alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language. The logical form of an
argument An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialecti ...
is called the argument form of the argument.


History

The importance of the concept of form to logic was already recognized in ancient times.
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
, in the ''
Prior Analytics The ''Prior Analytics'' ( grc-gre, Ἀναλυτικὰ Πρότερα; la, Analytica Priora) is a work by Aristotle on reasoning, known as his syllogistic, composed around 350 BCE. Being one of the six extant Aristotelian writings on logic a ...
'', was probably the first to employ variable letters to represent valid inferences. Therefore,
Jan Łukasiewicz Jan Łukasiewicz (; 21 December 1878 – 13 February 1956) was a Polish logician and philosopher who is best known for Polish notation and Łukasiewicz logic His work centred on philosophical logic, mathematical logic and history of logic. ...
claims that the introduction of variables was "one of Aristotle's greatest inventions." According to the followers of Aristotle like Ammonius, only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms. The concrete terms ''man'', ''mortal'', and so forth are analogous to the substitution values of the schematic placeholders ''A'', ''B'', ''C'', which were called the "matter" (Greek ''hyle'', Latin ''materia'') of the argument. The term "logical form" itself was introduced by
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, a ...
in 1914, in the context of his program to formalize natural language and reasoning, which he called
philosophical logic Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical ...
. Russell wrote: "Some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure."preprint
/ref>


Example of argument form

To demonstrate the important notion of the ''form'' of an argument, substitute letters for similar items throughout the sentences in the original argument. ;Original argument :All humans are mortal. :Socrates is human. :Therefore, Socrates is mortal. ;Argument form :All ''H'' are ''M''. :''S'' is ''H''. :Therefore, ''S'' is ''M''. All that has been done in the ''argument form'' is to put ''H'' for ''human'' and ''humans'', ''M'' for ''mortal'', and ''S'' for ''Socrates''. What results is the ''form'' of the original argument. Moreover, each individual sentence of the ''argument form'' is the ''sentence form'' of its respective sentence in the original argument.


Importance of argument form

Attention is given to argument and sentence form, because ''form'' is what makes an argument valid or cogent. All logical form arguments are either inductive or deductive. Inductive logical forms include inductive generalization, statistical arguments, causal argument, and arguments from analogy. Common deductive argument forms are
hypothetical syllogism In classical logic, a hypothetical syllogism is a valid argument form, a syllogism with a conditional statement for one or both of its premises. An example in English: :If I do not wake up, then I cannot go to work. :If I cannot go to work, then ...
,
categorical syllogism A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...
, argument by definition, argument based on mathematics, argument from definition. The most reliable forms of logic are
modus ponens In propositional logic, ''modus ponens'' (; MP), also known as ''modus ponendo ponens'' (Latin for "method of putting by placing") or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference ...
,
modus tollens In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens' ...
, and chain arguments because if the premises of the argument are true, then the conclusion necessarily follows. Two invalid argument forms are
affirming the consequent Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dar ...
and
denying the antecedent Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form: :If ''P'', then ''Q''. :Therefore, if not ...
. ;Affirming the consequent :All dogs are animals. :Coco is an animal. :Therefore, Coco is a dog. ;Denying the antecedent :All cats are animals. :Missy is not a cat. :Therefore, Missy is not an animal. A logical
argument An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialecti ...
, seen as an
ordered set In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary r ...
of sentences, has a logical form that derives from the form of its constituent sentences; the logical form of an argument is sometimes called argument form. Some authors only define logical form with respect to whole arguments, as the schemata or inferential structure of the argument. In
argumentation theory Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory, incl ...
or
informal logic Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements). However, the precise definition of "informal logic" is a matter of some dispute. Ralph H. ...
, an argument form is sometimes seen as a broader notion than the logical form. It consists of stripping out all spurious grammatical features from the sentence (such as gender, and passive forms), and replacing all the expressions specific to ''the subject matter'' of the argument by
schematic variable In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instance, in the sentence :''Let A and B be two sen ...
s. Thus, for example, the expression "all A's are B's" shows the logical form which is common to the sentences "all men are mortals," "all cats are carnivores," "all Greeks are philosophers," and so on.


Logical form in modern logic

The fundamental difference between modern formal logic and traditional, or Aristotelian logic, lies in their differing analysis of the logical form of the sentences they treat: *On the traditional view, the form of the sentence consists of (1) a subject (e.g., "man") plus a sign of quantity ("all" or "some" or "no"); (2) the copula, which is of the form "is" or "is not"; (3) a predicate (e.g., "mortal"). Thus: "all men are mortal." The logical constants such as "all", "no," and so on, plus sentential connectives such as "and" and "or," were called
syncategorematic In logic and linguistics, an expression is syncategorematic if it lacks a denotation but can nonetheless affect the denotation of a larger expression which contains it. Syncategorematic expressions are contrasted with categorematic expressions, whi ...
terms (from the Greek ''kategorei'' – to predicate, and ''syn'' – together with). This is a fixed scheme, where each judgment has a specific quantity and copula, determining the logical form of the sentence. *The modern view is more complex, since a single judgement of Aristotle's system involves two or more logical connectives. For example, the sentence "All men are mortal" involves, in term logic, two non-logical terms "is a man" (here ''M'') and "is mortal" (here ''D''): the sentence is given by the judgement ''A(M,D)''. In
predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
, the sentence involves the same two non-logical concepts, here analyzed as m(x) and d(x), and the sentence is given by \forall x (m(x) \rightarrow d(x)), involving the logical connectives for
universal quantification In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other ...
and implication. The more complex modern view comes with more power. On the modern view, the fundamental form of a simple sentence is given by a recursive schema, like natural language and involving
logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...
s, which are joined by juxtaposition to other sentences, which in turn may have logical structure. Medieval logicians recognized the problem of multiple generality, where Aristotelian logic is unable to satisfactorily render such sentences as "some guys have all the luck," because both quantities "all" and "some" may be relevant in an inference, but the fixed scheme that Aristotle used allows only one to govern the inference. Just as linguists recognize recursive structure in natural languages, it appears that logic needs recursive structure.


Logical forms in natural language processing

In
semantic parsing Semantic parsing is the task of converting a natural language utterance to a logical form: a machine-understandable representation of its meaning. Semantic parsing can thus be understood as extracting the precise meaning of an utterance. Application ...
, statements in natural languages are converted into logical forms that represent their meanings.


See also

*
Argument map An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes the key components of the argument, traditionally called the '' conclusion'' and the ''premises'', also called ''con ...
*
Fallacy A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument which may appear stronger than it really is if the fallacy is not spotted. The term in the Western intellectual tradition was intr ...
:*
Logical fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic syst ...
:*
Informal fallacy Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Fall ...
*
Categorial grammar Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and seman ...
*
Sense and reference In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the ...
*
Analytic–synthetic distinction The analytic–synthetic distinction is a semantic distinction, used primarily in philosophy to distinguish between propositions (in particular, statements that are affirmative subject–predicate judgments) that are of two types: analytic propos ...
*
List of valid argument forms Of the many and varied argument forms that can possibly be constructed, only very few are valid argument forms. In order to evaluate these forms, statements are put into logical form. Logical form replaces any sentences or ideas with letters to re ...


References


Further reading

* * *


External links

* * *
Beaney, Michael, "Analysis", The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.)

IEP, Validity and Soundness
{{DEFAULTSORT:Logical Form Abstraction Analytic philosophy Philosophy of language Concepts in logic Logical truth Arguments