Logical form
Encyclopedia
In logic, the logical form of a sentence (or proposition
or statement
or truthbearer
) or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form. In an ideal logical language, the logical form can be determined from syntax
alone; formal languages used in formal science
s are examples of such languages. Logical form however should not be confused with the mere syntax used to represent it; there may be more than one string
that represents the same logical form in a given language.
The logical form of an argument
is called the argument form or test form of the argument
.
was probably the first to employ variable letters to represent valid inferences (in the Prior analytics
). (For which reason Łukasiewicz says that the introduction of variables was 'one of Aristotle's greatest inventions').
According to the followers of Aristotle (such as Ammonius
), only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms. The concrete terms man, mortal, etc., 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" was introduced by Bertrand Russell
in 1914, in the context of his program to formalize natural language and reasoning, which he called philosophical logic
. Russell wrote: "Some kind of knowledge of logical forms, though with most people it is not explicit, is involved in 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."
Original argument
Argument Form
All we have 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.
or cogent. Some examples of valid argument forms are modus ponens
, modus tollens
, disjunctive syllogism
, hypothetical syllogism
and dilemma
. Two invalid argument forms are affirming the consequent
and denying the antecedent
.
A logical argument
, seen as an ordered set
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
or informal logic
, 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 variables. 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.
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
or statement
Statement
Statement may refer to:* A kind of expression in language *Statement , declarative sentence that is either true or false*Statement , the smallest standalone element of an imperative programming language...
or truthbearer
Truthbearer
Truth-bearer is a term used to designate entities that are either true or false and nothing else. The thesis that some things are true while others are false raises the question of the nature of these things. Since there is divergence of opinion on the matter, the term truthbearer is used to be...
) or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form. In an ideal logical language, the logical form can be determined from syntax
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
alone; formal languages used in formal science
Formal science
The formal sciences are the branches of knowledge that are concerned with formal systems, such as logic, mathematics, theoretical computer science, information theory, systems theory, decision theory, statistics, and some aspects of linguistics....
s are examples of such languages. Logical form however should not be confused with the mere syntax used to represent it; there may be more than one string
String (computer science)
In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set or alphabet....
that represents the same logical form in a given language.
The logical form of an argument
Argument
In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...
is called the argument form or test form of the argument
Argument
In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...
.
History
That the concept of form is fundamental to logic was already recognized in ancient times. AristotleAristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
was probably the first to employ variable letters to represent valid inferences (in the Prior analytics
Prior Analytics
The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....
). (For which reason Łukasiewicz says that the introduction of variables was 'one of Aristotle's greatest inventions').
According to the followers of Aristotle (such as Ammonius
Ammonius Hermiae
Ammonius Hermiae was a Greek philosopher, and the son of the Neoplatonist philosophers Hermias and Aedesia. He was a pupil of Proclus in Athens, and taught at Alexandria for most of his life, writing commentaries on Plato, Aristotle, and other philosophers....
), only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms. The concrete terms man, mortal, etc., 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" was introduced by Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
in 1914, in the context of his program to formalize natural language and reasoning, which he called philosophical logic
Philosophical logic
Philosophical logic is a term introduced by Bertrand Russell to represent his idea that the workings of natural language and thought can only be adequately represented by an artificial language; essentially it was his formalization program for the natural language...
. Russell wrote: "Some kind of knowledge of logical forms, though with most people it is not explicit, is involved in 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."
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 we have 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 validValidity
In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is valid....
or cogent. Some examples of valid argument forms are modus ponens
Modus ponens
In classical logic, modus ponendo ponens or implication elimination is a valid, simple argument form. It is related to another valid form of argument, modus tollens. Both Modus Ponens and Modus Tollens can be mistakenly used when proving arguments...
, modus tollens
Modus tollens
In classical logic, modus tollens has the following argument form:- Formal notation :...
, disjunctive syllogism
Disjunctive syllogism
A disjunctive syllogism, also known as disjunction-elimination and or-elimination , and historically known as modus tollendo ponens,, is a classically valid, simple argument form:where \vdash represents the logical assertion....
, hypothetical syllogism
Hypothetical syllogism
In logic, a hypothetical syllogism has two uses. In propositional logic it expresses one of the rules of inference, while in the history of logic, it is a short-hand for the theory of consequence.-Propositional logic:...
and dilemma
Dilemma
A dilemma |proposition]]") is a problem offering two possibilities, neither of which is practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable...
. Two invalid argument forms are affirming the consequent
Affirming the consequent
Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form:#If P, then Q.#Q.#Therefore, P....
and denying the antecedent
Denying the antecedent
Denying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the form:The name denying the antecedent derives from the premise "not P", which denies the "if" clause of the conditional premise....
.
A logical argument
Argument
In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...
, seen as an ordered set
Ordered set
In order theory in mathematics, a set with a binary relation R on its elements that is reflexive , antisymmetric and transitive is described as a partially ordered set or poset...
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
Argumentation theory, or argumentation, is the interdisciplinary study of how humans should, can, and do reach conclusions through logical reasoning, that is, claims based, soundly or not, on premises. It includes the arts and sciences of civil debate, dialogue, conversation, and persuasion...
or informal logic
Informal logic
Informal logic, intuitively, refers to the principles of logic and logical thought outside of a formal setting. However, perhaps because of the informal in the title, the precise definition of informal logic is matters of some dispute. Ralph H. Johnson and J...
, 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 variables. 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.
See also
- Argument map
- FallacyFallacyIn logic and rhetoric, a fallacy is usually an incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor , or take advantage of social relationships between people...
- Logical fallacy
- Informal fallacyInformal fallacyAn informal fallacy is an argument whose stated premises fail to support their proposed conclusion. The deviation in an informal fallacy often stems from a flaw in the path of reasoning that links the premises to the conclusion...
- Categorial grammarCategorial grammarCategorial grammar is a term used for a family of formalisms in natural language syntax motivated by the principle of compositionality and organized according to the view that syntactic constituents should generally combine as functions or according to a function-argument relationship...
- Sense and referenceSense and referenceSinn and bedeutung are usually translated, respectively, as sense and reference. Two different aspects of some terms' meanings, a term's reference is the object that the term refers to, while the term's sense is the way that the term refers to that object.Sinn and bedeutung were introduced by...
- Analytic proposition
- logical formLogical formIn logic, the logical form of a sentence or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form...
- List of invalid argument forms
- List of valid argument forms
- Synthetic proposition