Logical form

 

From Wikipedia, the free encyclopedia

 

This is one of a collection of articles which has a direct, or indirect relevance for the development of the UDP. Blogger Ref http://www.p2pfoundation.net/Universal_Debating_Project

 

 

Jump to: navigation, search

This article is about the term as used in logic. For the linguistics term, see Logical Form

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 sciences 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.^[1]
The logical form of an argument is called the argument form or test form of the argument.

Contents

 [hide] 

• 1 History
• 2 Example of argument form
• 3 Importance of argument form
• 4 See also
• 5 References
• 6 Further reading
• 7 External links

History[edit]

The importance of the concept of form to logic was already recognized in ancient times. Aristotle, in the Prior Analytics, was probably the first to employ variable letters to represent valid inferences. Therefore, Łukasiewicz 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, 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" itself 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 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." ^[2][3]

Example of argument form[edit]

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.^[4]

Importance of argument form[edit]

Attention is given to argument and sentence form, because form is what makes an argument valid 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.^[5] Some authors only define logical form with respect to whole arguments, as the schemata or inferential structure of the argument.^[6] In argumentation theory or informal logic, an argument form is sometimes seen as a broader notion than the logical form.^[7]
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[edit]

• Argument map
• Fallacy

• Logical fallacy
• Informal fallacy

• Categorial grammar
• Sense and reference
• Analytic proposition
• List of invalid argument forms
• List of valid argument forms
• Synthetic proposition

References[edit]

1. Jump up ^ The Cambridge Dictionary of Philosophy, CUP 1999, pp. 511-512
2. Jump up ^ Russell, Bertrand. 1914(1993). Our Knowledge of the External World: as a field for scientific method in philosophy. New York: Routledge. p. 53
3. Jump up ^ Ernie Lepore, Kirk Ludwig (2002). "What is logical form?". In Gerhard Preyer, Georg Peter. Logical form and language. Clarendon Press. p. 54. ISBN 978-0-19-924555-0.  preprint
4. Jump up ^ Hurley, Patrick J. (1988). A concise introduction to logic. Belmont, Calif.: Wadsworth Pub. Co. ISBN 0-534-08928-3. 
5. Jump up ^ J. C. Beall (2009). Logic: the Basics. Taylor & Francis. p. 18. ISBN 978-0-415-77498-7. 
6. Jump up ^ Paul Tomassi (1999). Logic. Routledge. p. 386. ISBN 978-0-415-16696-6. 
7. Jump up ^ Robert C. Pinto (2001). Argument, inference and dialectic: collected papers on informal logic. Springer. p. 84. ISBN 978-0-7923-7005-5. 

Further reading[edit]

• Richard Mark Sainsbury (2001). Logical forms: an introduction to philosophical logic. Wiley-Blackwell. ISBN 978-0-631-21679-7. 
• Gerhard Preyer, Georg Peter, ed. (2002). Logical form and language. Clarendon Press. ISBN 978-0-19-924555-0. 
• Gila Sher (1991). The bounds of logic: a generalized viewpoint. MIT Press. ISBN 978-0-262-19311-5. 

External links[edit]

• Logical form at PhilPapers
• Logical Form entry by Paul Pietroski in the Stanford Encyclopedia of Philosophy
• Logical form at the Indiana Philosophy Ontology Project
• Beaney, Michael, "Analysis", The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.)
• IEP, Validity and Soundness

[show] v t e Philosophy of language Philosophers Plato (Cratylus) Gorgias Confucius Xunzi Aristotle Stoics Pyrrhonists Scholasticism Ibn Rushd Ibn Khaldun Thomas Hobbes Gottfried Wilhelm Leibniz Johann Herder Ludwig Noire Wilhelm von Humboldt Fritz Mauthner Paul Ricœur Ferdinand de Saussure Gottlob Frege Franz Boas Paul Tillich Edward Sapir Leonard Bloomfield Zhuangzi Henri Bergson Lev Vygotsky Ludwig Wittgenstein Philosophical Investigations Tractatus Logico-Philosophicus Bertrand Russell Rudolf Carnap Jacques Derrida Of Grammatology Limited Inc Benjamin Lee Whorf Gustav Bergmann J. L. Austin Noam Chomsky Hans-Georg Gadamer Saul Kripke A. J. Ayer G. E. M. Anscombe Jaakko Hintikka Michael Dummett Donald Davidson Paul Grice Gilbert Ryle P. F. Strawson Willard Van Orman Quine Hilary Putnam David Lewis John Searle Joxe Azurmendi Scott Soames Stephen Yablo John Hawthorne Stephen Neale Theories Causal theory of reference Contrast theory of meaning Contrastivism Conventionalism Cratylism Deconstruction Descriptivist theory of names Direct reference theory Dramatism Expressivism Linguistic determinism Logical atomism Logical positivism Mediated reference theory Nominalism Non-cognitivism Phallogocentrism Quietism Relevance theory Semantic externalism Semantic holism Structuralism Supposition theory Symbiosism Theological noncognitivism Theory of descriptions Verification theory Concepts Ambiguity Linguistic relativity Meaning Language Truth-bearer Proposition Use–mention distinction Concept Categories Set Class Intension Logical form Metalanguage Mental representation Principle of compositionality Property Sign Sense and reference Speech act Symbol Entity Sentence Statement more... Related articles Analytic philosophy Philosophy of information Philosophical logic Linguistics Pragmatics Rhetoric Semantics Formal semantics Semiotics Category Task Force Discussion

[show] v t e Logic Outline History Fields Argumentation theory Axiology Critical thinking Logic in computer science Mathematical logic Metalogic Metamathematics Non-classical logic Philosophical logic Philosophy of logic Set theory Foundations Abduction Analytic and synthetic propositions Antinomy A priori and a posteriori Deduction Definition Description Induction Inference Logical form Logical consequence Logical truth Name Necessity and sufficiency Meaning Paradox Possible world Presupposition Probability Reason Reasoning Reference Semantics Statement Strict implication Substitution Syntax Truth Validity Lists topics Mathematical logic Boolean algebra Set theory other Logicians Rules of inference Paradoxes Fallacies Logic symbols Portal Category WikiProject (talk) changes

Retrieved from "http://en.wikipedia.org/w/index.php?title=Logical_form&oldid=586819800"

Categories:

• Abstraction
• Analytic philosophy
• Philosophy of language
• Concepts in logic
• Logical truth
• Arguments