NationMaster - Encyclopedia: Logical argument

In logic, an argument is a set of statements, consisting of a number of premises, a number of inferences, and a conclusion, which is said to have the following property: if the premises are true, then the conclusion must be true or highly likely to be true. An argument is thus an attempt to demonstrate that the truth of the conclusion follows from the truth of the premises, and the role of the inferences is to illustrate why this connection exists. Logic (from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. ... In discourse, a premise (also premiss in British usage) is a claim which is part of a reason or objection. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ... A conclusion can have various specific meanings depending on the context. ... A common dictionary definition of truth is agreement with fact or reality.[1] There is no single definition of truth about which the majority of philosophers agree. ...

An argument proceeds from premises to inferences to conclusion by employing a particular form of reasoning. If the reasoning is deductive, then the argument attempts to show that the conclusion follows necessarily from the premises. If the reasoning is inductive, the argument may show only that the conclusion is highly likely to be true if the premises are true. Other forms of reasoning are also used, with corresponding variations in the precise sense in which the conclusion follows from the premise. Reasoning is the act of using reason to derive a conclusion from certain premises. ... Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ...

Logical arguments are extremely important in philosophy, science and other disciplines concerned with knowledge and truth. The philosopher Socrates about to take poison hemlock as ordered by the court. ... Part of a scientific laboratory at the University of Cologne. ...

Validity, soundness and effectiveness

A valid argument is one for which it is the case that if the premises are true then the conclusion must be true or highly likely to be true. Even if an argument is valid, however, its conclusion may not be true, because a valid argument need not have true premises. A sound argument is a valid argument that does have true premises, and is thus an argument with a conclusion that is true or highly likely to be true. In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. ... (This article discusses the soundess notion of informal logic. ...

Clearly it is very desirable to ensure that the arguments we employ in science and other disciplines are sound. It is, however, very often a matter of debate whether or not particular arguments are actually sound, often because their validity is in dispute.

Arguments can be invalid for a variety of reasons. There are well-established patterns of reasoning that arguments may follow which render them invalid; these patterns are known as logical fallacies. It has been suggested that this article or section be merged into Fallacy. ...

Even if an argument is sound (and hence also valid), an argument may still fail in its primary task of persuading us of the truth of its conclusion. Such an argument is then sound, but ineffective. An argument may fail to be effective because it is not scrutinizable, in the sense that it is not open to public examination. This may be because the argument is too long or too complex, because the terms occurring in it are obscure, or because the reasoning it employs is not well understood. The validity and soundness of an argument are logical properties of it, known as semantic properties. Effectiveness, on the other hand, is not a logical notion but a practical concern. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

Formal arguments and mathematical arguments

In mathematics, an argument can often be formalized by writing each of its statements in a formal language such as first-order Peano Arithmetic. A formalized argument should have the following properties: Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... In mathematics, logic, and computer science, a formal language is a language that is defined by precise mathematical or machine processable formulas. ... First-order logic (FOL) is a universal language in symbolic science, and is in use everyday by mathematicians, philosophers, linguists, computer scientists and practitioners of artificial intelligence. ... In mathematics, the Peano axioms (or Peano postulates) are a set of second-order axioms proposed by Giuseppe Peano which determine the theory of arithmetic. ...

Checking the validity of a formal argument is thus a straightforward matter, since the presence of these three properties is easily verified.

Most arguments used in mathematics are not formal in quite so strict a sense. Strictly formal proofs of all but the most trivial assertions are extremely tedious to construct and often so long as to be hard to follow without assistance from a computer. Automated theorem proving is sometimes used to overcome these problems. Automated theorem proving (ATP) or automated deduction, currently the most well-developed subfield of automated reasoning (AR), is the proving of mathematical theorems by a computer program. ...

In general mathematical practice arguments are formal insofar as they are formalizable in theory; this is sometimes expressed by saying that mathematical arguments are rigorous. Mathematicians are happy to make a single inference that would, if formalized, amount to a long chain of inferences, because they are confident that the formal chain could be constructed if required.

Nevertheless, one advantage of formalizing arguments is the possibility of constructing a theory of valid mathematical arguments such as proof theory. Proof theory investigates the class of valid arguments in mathematics as a whole, and hence elucidates what kinds of statements can occur as conclusions to sound mathematical arguments. Gödel's incompleteness theorems are proof-theoretic results which show the surprising fact that not all true mathematical statements can occur as the conclusion of formalized, sound mathematical arguments. In effect, not all true statements of mathematics are provable. Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ... In mathematical logic, GÃ¶dels incompleteness theorems, proved by Kurt GÃ¶del in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. ...

Logical arguments in science

In ordinary, philosophical and scientific argumentation abductive arguments and arguments by analogy are also commonly used. Arguments can be valid or invalid, although how arguments are determined to be in either of these two categories can often itself be an object of much discussion. Informally one should expect that a valid argument should be compelling in the sense that it is capable of convincing someone about the truth of the conclusion. However, such a criterion for validity is inadequate or even misleading since it depends more on the skill of the person constructing the argument to manipulate the person who is being convinced and less on the objective truth or undeniability of the argument itself. It has been suggested that Abductive validation be merged into this article or section. ... Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ...

Less subjective criteria for validity of arguments are often clearly desirable, and in some cases we should even expect an argument to be rigorous, that is, to adhere to precise rules of validity. This is the case for arguments used in mathematical proofs. Note that a rigorous proof does not have to be a formal proof. For the medical term see rigor (medicine) Rigour (American English: rigor) has a number of meanings in relation to intellectual life and discourse. ... ...

In ordinary language, people refer to the logic of an argument or use terminology that suggests that an argument is based on inference rules of formal logic. Though arguments do use inferences that are indisputably purely logical (such as syllogisms), other kinds of inferences are almost always used in practical arguments. For example, arguments commonly deal with causality, probability and statistics or even specialized areas such as economics. In these cases, rather than to the well-defined principles of pure logic as explicitly set out and agreed upon in an academic, professional or other strictly understood context, logic in everyday usage almost always refers to something the reader or audience of the argument believe they perceive in the argument, and which drives them inexorably towards some conclusion, something perhaps ill-defined in their own minds (as opposed to putting the emphasis on examining by what criteria they actually accept this apparently compelling force as correct, which is how the formal rules of pure logic are constructed). And yet this feeling of inexorable conviction is also the foundation of those begrudgingly somewhat unsatisfying definitions we give of "logic"; in that we who are driven to construct these most conscientious, circumspect and clear definitions were initially drawn to do so by a similar belief that we recognized some intrinsic logic or compelling rational force in the world- even in the most everyday arguments, although such a view may have been naive, and is in any case incapable of being tested in any objective and/or universally satisfying fashion. In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ... Logic (from ancient Greek λόγος (logos), meaning reason) is the study of arguments. ... It has been suggested that this article be split into multiple articles accessible from a disambiguation page. ... Probability is the likelihood that something is the case or will happen. ... A graph of a normal bell curve showing statistics used in educational assessment and comparing various grading methods. ... This article needs additional references or sources for verification. ...

Theories of arguments

Theories of arguments are closely related to theories of informal logic. Ideally, a theory of argument should provide some mechanism for explaining validity of arguments. Informal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial (technical) or formal language (see formal logic). ...

One natural approach would follow the mathematical paradigm and attempt to define validity in terms of semantics of the assertions in the argument. Though such an approach is appealing in its simplicity, the obstacles to proceeding this way are very difficult for anything other than purely logical arguments. Among other problems, we need to interpret not only entire sentences, but also components of sentences, for example noun phrases such as The present value of government revenue for the next twelve years. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

One major difficulty of pursuing this approach is that determining an appropriate semantic domain is not an easy task, raising numerous thorny ontological issues. It also raises the discouraging prospect of having to work out acceptable semantic theories before being able to say anything useful about understanding and evaluating arguments. For this reason the purely semantic approach is usually replaced with other approaches that are more easily applicable to practical discourse. This article is about the philosophical meaning of ontology. ...

For arguments regarding topics such as probability, economics or physics, some of the semantic problems can be conveniently shoved under the rug if we can avail ourselves of a model of the phenomenon under discussion. In this case, we can establish a limited semantic interpretation using the terms of the model and the validity of the argument is reduced to that of the abstract model. This kind of reduction is used in the natural sciences generally, and would be particularly helpful in arguing about social issues if the parties can agree on a model. Unfortunately, this prior reduction seldom occurs, with the result that arguments about social policy rarely have a satisfactory resolution. An abstract model (or conceptual model) is a theoretical construct that represents something, with a set of variables and a set of logical and quantitative relationships between them. ...

Another approach is to develop a theory of argument pragmatics, at least in certain cases where argument and social interaction are closely related. This is most useful when the goal of logical argument is to establish a mutually satisfactory resolution of a difference of opinion between individuals. In linguistics and semiotics, pragmatics is concerned with bridging the explanatory gap between sentence meaning and speakers meaning. ...

Argumentative dialogue

Arguments as discussed in the preceding paragraphs are static, such as one might find in a textbook or research article. They serve as a published record of justification for an assertion. Arguments can also be interactive, in which the proposer and the interlocutor have a more symmetrical relationship. The premises are discussed, as well the validity of the intermediate inferences. For example, consider the following exchange, illustrated by the No true Scotsman fallacy: It has been suggested that this article or section be merged with Special Pleading . ...

In this dialogue, the proposer first offers a premise, the premise is challenged by the interlocutor, and finally the proposer offers a modification of the premise. This exchange could be part of a larger discussion, for example a murder trial, in which the defendant is a Scotsman, and it had been established earlier that the murderer was eating sugared porridge when he or she committed the murder.

In argumentative dialogue, the rules of interaction may be negotiated by the parties to the dialogue, although in many cases the rules are already determined by social mores. In the most symmetrical case, argumentative dialogue can be regarded as a process of discovery more than one of justification of a conclusion. Ideally, the goal of argumentative dialogue is for participants to arrive jointly at a conclusion by mutually accepted inferences. In some cases however, the validity of the conclusion is secondary. For example; emotional outlet, scoring points with an audience, wearing down an opponent or lowering the sale price of an item may instead be the actual goals of the dialogue. Walton distinguishes several types of argumentative dialogue which illustrate these various goals:

Van Eemeren and Grootendorst identify various stages of argumentative dialogue. These stages can be regarded as an argument protocol. In a somewhat loose interpretation, the stages are as follows:

Van Eemeren and Grootendorst provide a detailed list of rules that must be applied at each stage of the protocol. Moreover, in the account of argumentation given by these authors, there are specified roles of protagonist and antagonist in the protocol which are determined by the conditions which set up the need for argument. Argumentation theory, or argumentation, is the science of effective civil debate or dialogue and the effective propagation thereof, using rules of inference and logic, as applied in the real world setting. ...

Many cases of argument are highly unsymmetrical, although in some sense they are dialogues. A particularly important case of this is political argument. A political argument is an instance of a logical argument applied to politics. ...

Much of the recent work on argument theory has considered argumentation as an integral part of language and perhaps the most important function of language (Grice, Searle, Austin, Popper). This tendency has removed argumentation theory away from the realm of pure formal logic. Herbert Paul Grice (1913 - 1988), usually publishing under the name Paul Grice, was a British educated philosopher of language, who spent the last two decades of his career in the U.S. // Life Born and raised in the United Kingdom, Grice was educated first at Clifton College and then at... Searle is a surname, and may refer to John Rogers Searle (1932â€“ ), American philosopher, famous for work on consciousness Charles Edward Searle, British academic; Vice-Chancellor of Cambridge University in 1888-89. ... John Langshaw Austin (March 28, 1911 - February 8, 1960) was a philosopher of language, who developed much of the current theory of speech acts. ... Popper may refer to: A popping dancer. ...

One of the original contributors to this trend is the philosopher Chaim Perelman, who together with Lucie Olbrechts-Tyteca, introduced the French term La nouvelle rhetorique in 1958 to describe an approach to argument which is not reduced to application of formal rules of inference. Perelman's view of argumentation is much closer to a juridical one, in which rules for presenting evidence and rebuttals play an important role. Though this would apparently invalidate semantic concepts of truth, this approach seems useful in situations in which the possibility of reasoning within some commonly accepted model does not exist or this possibility has broken down because of ideological conflict. Retaining the notion enunciated in the introduction to this article that logic usually refers to the structure of argument, we can regard the logic of rhetoric as a set of protocols for argumentation. ChaÃ¯m Perelman (May 20, 1912 â€“ January 22, 1984), a Polish-born philosopher of law, who studied, taught, and lived most of his life in Brussels. ...

Other theories

In recent decades one of the more influential discussions of philosophical arguments is that by Nicholas Rescher in his book The Strife of Systems. Rescher models philosophical problems on what he calls aporia or an aporetic cluster: a set of statements, each of which has initial plausibility but which are jointly inconsistent. The only way to solve the problem, then, is to reject one of the statements. If this is correct, it constrains how philosophical arguments are formulated. Nicholas Rescher (born July 15, 1928 in Hagen, Germany) is an American philosopher, affiliated for many years with the University of Pittsburgh, where he is currently University Professor of Philosophy and Chairman of the Center for the Philosophy of Science. ... Aporia (Greek: : impasse; lack of resources; puzzlement; embarassment ) denotes, in philosophy, a philosophical puzzle or state of puzzlement, and, in rhetoric, a rhetorically useful expression of doubt. ...

References

Robert Audi (born November 1941) is a philosopher working on ethics, especially intuitionism, at the University of Notre Dame, where he holds a joint appointment in the philosophy department and in business ethics. ... John Langshaw Austin (March 28, 1911 â€“ February 8, 1960) was a philosopher of language, who developed much of the current theory and terminology of speech acts. ... Vincent F. Hendricks is a philosopher and logician. ... Yuri I. Manin. ... ChaÃ¯m Perelman (May 20, 1912 â€“ January 22, 1984), a Polish-born philosopher of law, who studied, taught, and lived most of his life in Brussels. ... Jules TuPac Henri PoincarÃ© (April 29, 1854 â€“ July 17, 1912) (IPA: [][1]) was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ... Sir Karl Raimund Popper, CH, FRS (July 28, 1902 â€“ September 17, 1994), was an Austrian and British philosopher and a professor at the London School of Economics. ... L. (Lizzie) Susan Stebbing (1885-1943) was a British philosopher. ... There are very few or no other articles that link to this one. ... Attacking Faulty Reasoning is a textbook on logical fallacies by T. Edward Damer that has been used for many years in a number of college courses on logic, critical thinking, argumentation, and philosophy. ...

See also

Categories: Cleanup from March 2007 | Philosophical terminology | Arguments Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ... Boolean logic is a complete system for logical operations. ... It has been suggested that Abductive validation be merged into this article or section. ... Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ... An Argument map is a visual representation of the structure of an argument in informal logic. ... Wikipedia does not yet have an article with this exact name. ... Look up fallacy in Wiktionary, the free dictionary. ... In Philosophical logic, an informal fallacy is a pattern of reasoning which is false due to the falsity of one or more of its premises. ... In philosophy, the term logical fallacy properly refers to a formal fallacy : a flaw in the structure of a deductive argument which renders the argument invalid. ... Argumentation theory, or argumentation, embraces the arts and sciences of civil debate, dialogue, conversation, and persuasion. ... Practical arguments are a logical structure used to determine the validity or dependencies of a claim. ... Image File history File links Portal. ... Logic (from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. ... For other uses, see Reason (disambiguation). ... The history of logic documents the development of logic as it occurs in various rival cultures and traditions in history. ... Philosophical logic is the application of formal logical techniques to problems that concern philosophers. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... The metalogic of a system of logic is the formal proof supporting its soundness. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Reasoning is the act of using reason to derive a conclusion from certain premises. ... Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). ... Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ... It has been suggested that Abductive validation be merged into this article or section. ... Informal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial (technical) or formal language (see formal logic). ... This article is about the word proposition as it is used in logic, philosophy, and linguistics. ... Inference is the act or process of deriving a conclusion based solely on what one already knows. ... In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. ... An argument is cogent if and only if the truth of the arguments premises would render the truth of the conclusion probable (i. ... Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ... are you kiddin ? i was lookin for it for hours ... Look up fallacy in Wiktionary, the free dictionary. ... A syllogism (Greek: â€” conclusion, inference), usually the categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... Syntax in logic is a systematic statement of the rules governing the properly formed formulas (WFFs) of a logical system. ... The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so conscientious logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. ... In logic, WFF is an abbreviation for well-formed formula. ... An axiom is a sentence or proposition that is not proved or demonstrated and is considered as obvious or as an initial necessary consensus for a theory building or acceptation. ... Look up theorem in Wiktionary, the free dictionary. ... In mathematical logic, a formal system is consistent if it does not contain a contradiction, or, more precisely, for no proposition Ï† are both Ï† and Â¬Ï† provable. ... (This article discusses the soundess notion of informal logic. ... In mathematical logic, a theory is complete, if it contains either or as a theorem for every sentence in its language. ... A logical system or theory is decidable if the set of all well-formed formulas valid in the system is decidable. ... In logic and mathematics, a formal system consists of two components, a formal language plus a set of inference rules or transformation rules. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... Recursion theory, or computability theory, is a branch of mathematical logic dealing with generalizations of the notion of computable function, and with related notions such as Turing degrees and effective descriptive set theory. ... Zeroth-order logic is a term in popular use among practitioners for the subject matter otherwise known as boolean functions, monadic predicate logic, propositional calculus, or sentential calculus. ... In mathematics, a finitary boolean function is a function of the form f : Bk â†’ B, where B = {0, 1} is a boolean domain and where k is a nonnegative integer. ... In logic, the monadic predicate calculus is the fragment of predicate calculus in which all predicate letters are monadic (that is, they take only one argument), and there are no function letters. ... In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows to establish that certain formulas are theorems of the formal system. ... In logic, a logical connective is a syntactic operation on sentences, or the symbol for such an operation, that corresponds to a logical operation on the logical values of those sentences. ... Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ... First-order logic (FOL) is a universal language in symbolic science, and is in use everyday by mathematicians, philosophers, linguists, computer scientists and practitioners of artificial intelligence. ... ... In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ... In mathematical logic, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. ... In philosophical logic, a modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. ... Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. ... Michaels the greatest boyfriend in the whole wide world, and Id love to call him in a phonebooth sometime. ... In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. ... doxastic logic is a modal logic that is concerned with reasoning about beliefs. ... Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. ... Introduced by Giorgi Japaridze in 2003, Computability logic is a research programme and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of truth. ... Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. ... In mathematical logic, linear logic is a type of substructural logic that denies the structural rules of weakening and contraction. ... Relevance logic, also called relevant logic, is any of a family of non-classical substructural logics that impose certain restrictions on implication. ... A non-monotonic logic is a formal logic whose consequence relation is not monotonic. ... A paraconsistent logic is a logical system that attempts to deal nontrivially with contradictions. ... Dialetheism is a paraconsistent logic typified by its tolerance of at least some contradictions. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... Look up paradox in Wiktionary, the free dictionary. ... Antinomy (Greek anti-, against, plus nomos, law) is a term used in logic and epistemology, which, loosely, means a paradox or unresolvable contradiction. ... Is logic empirical? is the title of two articles that discuss the radical concept, that the empirical facts about quantum phenomena may provide grounds for revising classical logic. ... Aristotle (Greek: AristotÃ©lÄ“s) (384 BC â€“ 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... George Boole [], (November 2, 1815 â€“ December 8, 1864) was a British mathematician and philosopher. ... Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. ... Rudolf Carnap (May 18, 1891, Ronsdorf, Germany â€“ September 14, 1970, Santa Monica, California) was an influential philosopher who was active in central Europe before 1935 and in the United States thereafter. ... â€¹ The template below (Expand) is being considered for deletion. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar â€“ 26 July 1925, IPA: ) was a German mathematician who became a logician and philosopher. ... Gerhard Karl Erich Gentzen (November 24, 1909 â€“ August 4, 1945) was a German mathematician and logician. ... [...]I dont believe in natural science. ... David Hilbert (January 23, 1862, KÃ¶nigsberg, East Prussia â€“ February 14, 1943, GÃ¶ttingen, Germany) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. ... Saul Aaron Kripke (born in November, 1940, Long Beach, New York) is an American philosopher and logician now emeritus from Princeton and professor of philosophy at CUNY Graduate Center. ... Giuseppe Peano Giuseppe Peano (August 27, 1858 â€“ April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ... Charles Sanders Peirce (IPA: /pÉs/), (September 10, 1839 â€“ April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Hilary Whitehall Putnam (born July 31, 1926) is an American philosopher who has been a central figure in Western philosophy since the 1960s, especially in philosophy of mind, philosophy of language, and philosophy of science. ... For people named Quine, see Quine (surname). ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 â€“ 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a Norwegian mathematician. ... // Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland â€“ October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ... Alan Mathison Turing, OBE (23 June 1912 â€“ 7 June 1954) was an English mathematician, logician, and cryptographer. ... Alfred North Whitehead, OM (February 15, 1861 Ramsgate, Kent, England â€“ December 30, 1947 Cambridge, Massachusetts, USA) was an English-born mathematician who became a philosopher. ... For a more comprehensive list, see the List of logic topics. ... This is a list of topics in logic. ... A logician is a person, such as a philosopher or mathematician, whose topic of scholarly study is logic. ... This is a list of rules of inference. ... This is a list of mathematical logic topics, by Wikipedia page. ... This is a list of basic discrete mathematics topics, by Wikipedia page. ... Set theory Axiomatic set theory Naive set theory Zermelo set theory Zermelo-Fraenkel set theory Kripke-Platek set theory with urelements Simple theorems in the algebra of sets Axiom of choice Zorns lemma Empty set Cardinality Cardinal number Aleph number Aleph null Aleph one Beth number Ordinal number Well... This is a list of paradoxes, grouped thematically. ... This is a list of fallacies. ... In logic, a set of symbols is frequently used to express logical constructs. ...

Contents

Validity, soundness and effectiveness GA_googleFillSlot("encyclopedia_square");