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# Topic: Constructivist logic

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 Intuitionistic logic - Wikipedia, the free encyclopedia Intuitionistic logic, or constructivist logic, is the symbolic logic system originally developed by Arend Heyting to provide a formal basis for Brouwer's programme of intuitionism. The syntax of formulæ of intuitionistic logic is similar to propositional logic or first-order logic. In classical propositional logic, it is possible to take one of conjunction, disjunction, or implication as primitive, and define the other two in terms of it together with negation, such as in Łukasiewicz's three axioms of propositional logic. en.wikipedia.org /wiki/Intuitionistic_logic   (1117 words)

 Constructivism (mathematics) - Wikipedia, the free encyclopedia Constructivist mathematics uses constructivist logic, which is essentially a removal of the law of the excluded middle from classical logic. This is not to say that the law of the excluded middle is denied entirely; special cases of the law will be provable as theorems. Thus to Brouwer, one cannot say "either Goldbach's conjecture is true, or it is not." And while the conjecture may one day be solved, the argument applies to similar unsolved problems; to Brouwer, the law of the excluded middle was tantamount to assuming that every mathematical problem has a solution. en.wikipedia.org /wiki/Mathematical_constructivism   (1331 words)

 Paul Lorenzen - Wikipedia, the free encyclopedia Lorenzen came 1962 to University of Erlangen (South Germany) and founded the school of constructivist philosophy there. He developed, Constructivist logic, Constructivist type theory and Constructivist analysis. Paul Lorenzen: Normative Logic and Ethics, Mannheim/Zürich 1969 en.wikipedia.org /wiki/Paul_Lorenzen   (417 words)

 Introduction   (Site not responding. Last check: 2007-10-31) Constructivists claim that it is impossible to describe the nature of actors independently from a particular historical context. Constructivists claim that it is this cycle that recurs through time in world politics and it is this cycle that is the foundation of constructivist explanations of phenomena in world politics. Constructivists answer this question by arguing that the logic of anarchy at the heart of realist treatments is not set in stone. www.udel.edu /poscir/mjhoff/Constr.htm   (6834 words)

 Frege and Language [Internet Encyclopedia of Philosophy] In a logically perfect language – as Frege conceived of it – the vagueness of predicates could be eliminated through their arrangement in an axiomatic system, through logical analysis, as well as informal elucidations and clarification of the primitive terms by way of examples. For Frege, the logician's main goal in her struggle with language is to "separate the logical from the psychological;" that is, the logician's main goal in her struggle with language is to isolate the logically relevant aspects of grammar and meaning from those that are not. As "Boole's Logical Calculus and the Concept-Script", in Frege 1979: 9-46. www.iep.utm.edu /f/freg-lan.htm   (15446 words)

 IfP, Center for International Relations/Peace and Conflict Studies, TAP 34A A much-stated criticism of constructivist foreign policy theory is the fact that an actor is frequently confronted with many value-based expectations of behavior, with the result that a distinction between relevant and irrelevant expectations of behavior is made difficult or becomes arbitrary. Constructivist authors conclude from this that a logic of appropriateness is at work in international society whose yardstick is provided to a considerable degree by the norms of international law (see, for example, Franck 1990; Kratochwil 1989). For constructivists, however, it is less significant whether or not an expectation of behavior is recognized as "law" because even norms whose legal character is disputed but whose expectations of behavior are recognized as a yardstick of appropriate behavior in international society display a high degree of commonality. www.uni-tuebingen.de /uni/spi/taps/tap34a.htm   (17709 words)

 [No title] They feel that constructivists who don't recognize classical mathematics as legitimate have serious philosophical delusions which cause them to work in very restricted areas of mathematics, but that their view of those areas is the same as that of the classical mathematician, once the definitions are understood correctly. Constructivists understand Bishop's claim that nothing is true unless and until it has been proved as saying that we cannot assert that something is true until it has been proved. Constructivists are often accused of confusing epistemology and ontology. www.math.fau.edu /Richman/Docs/intrview.html   (9565 words)

 Approaches to the Study of Foreign Policy Derived from International Relations Theories   (Site not responding. Last check: 2007-10-31) It is sometimes suggested that there is a huge gap between theories of international politics and theories of foreign policy such that any borrowing from theories of the former type in order to construct theories of the latter is deeply suspect (Waltz 1979, 1986). Of course, whether one of them is true or to what extent each of them is illuminating foreign policy behavior is another matter (and one that is beyond the scope of this chapter which will not be concerned with testing or otherwise evaluating the three theories that it presents and reconstructs). Constructivist analysis of German foreign policy would be hard pressed to predict, or to account for, what the appropriate course of action was in this situation. www.isanet.org /noarchive/rittberger.html   (3610 words)

 More on Mathematical Constructivism Constructivist mathematics uses constructivist logic, which closely identifies truth with proof. These views were forcefully expressed by David Hilbert in 1928, when he wrote in Die Grundlagen der Mathematik, "Taking the principle of excluded middle from the mathematician would be the same, say, as proscribing the telescope to the astronomer or to the boxer the use of his fists" [1]. (The law of excluded middle is not valid in constructivist logic.) Errett Bishop, in his 1967 work Foundations of Constructive Analysis, worked to dispel these fears by developing a great deal of traditional analysis in a constructive framework. www.artilifes.com /mathematical-constructivism.htm   (739 words)

 Re: What is /are The Logic(s) of Life?... and Adjointness is Fundamental in Categories and Topoi of Biological Systems 'Constructivist' in Logic and Fundamental Mathematics is not limited to either recursive, or algorithmic, or finitary proofs; it is exactly the opposite. Currently, famous logicians also say emphatically that only 'constructivist' logic provides for--- 'true entailment'--------------, and that the 'other' Logics, such as Boolean or predicative logic, finitary, etc., ----do NOT allow for 'true' Entailment----which is also Robert Rosen's main point and is well-made in his book on "Essays on Life..." C. I also wrote previously: "The logic of predicates, or predicative logic, is in essence also Boolean-based, and-- as Rashevsky himself showed in several articles published in BMB in the 50's-- it leads to equivalent results to those that are obtained by Sets and Relations for biological and societal organisms. www.panmere.com /rosen/mhout/msg01756.html   (1050 words)

 Topics in Logic: Extensions and Alternatives to Classical Logic Modal Logic (the logic of possibility and necessity; add sentential operators for 'it is necessary that' and 'it is possible that', where the latter can be defined as 'it is not necessary that it is not the case that'. Deontic Logic (logic of obligation: add sentential operators for 'it is obligatory that' and 'it is permissible that', where permissibility can be defined as 'not obligatory that not:' Again the main interest may be philosophical, in ethics. Paraconsistent Logic (logics that allow contradictions, sentences of the form P and ~P, to be true. www.trinity.edu /cbrown/topics_in_logic/modifications.html   (596 words)

 What is a Proposition? | Lambda the Ultimate In Aristotelian logic a proposition is a particular kind of sentence: one which affirms or denies a predicate of a subject. The so-called constructivists (who are the modern intuitionists and who generally wear the mantle only part time) have effectively shown that all modern mathematics, including measure theory(!) (but not logic itself) can be reconstructed without its aid. You could go for a fuzzy logic; you could again use [0,1] as your range, this time as a pragmatic bodge where you say TALL=0.8 to say that some-one is quite tall, conflating the issue of how tall with the issue of how sure we are that he is tall. lambda-the-ultimate.org /node/1239   (3726 words)

 The Sydney School: Mathematics, the Science of Structure: an Aristotelian realist philosophy of mathematics: Guide to ... So when the constructivist says that there exists a proof that can produce a given number he does not mean to say that the proof has actually been given, but that it could be given, by a being with an infinite amount of time and patience. If the social constructivist knows that in us `the function of cognition is adaptive and serves the organization of the experiential world' then it must be the case that our knowledge of the world involves the `discovery of ontological reality' - for there we have some. Russell's logicism remains popular among philosophers who would like to see mathematics as trivial - triviality being both a perfect excuse for not putting in the effort of finding out about it and a quick way of dismissing arguments based on the objectivity of mathematical truth. web.maths.unsw.edu.au /~jim/philmathschools.html   (4899 words)

 Untitled Document According to Alexandr Rodchenko, another forerunner of the soviet constructivist movement, the constructivist artists "were committed to quitting the studio and going into the factory, where the real body of life is made." This concept embodies one of the general facets of communism; everyone is equal and should maintain equal responsibilities. Generally the art that was produced during the constructivist movement can be characterized by saying that the essence of basic geometry was the most present factor. It is very true indeed when considering that late nineteenth century Victorian Logic and its influence on modern visual reasoning and the internet as we see it today, one must look back toward the very basic principles of geometry devised by the brilliant grandfathers of mathematics. www.duke.edu /~nsr3/essays/firstessaypage.htm   (1684 words)

 Contructivist Learning Theory Agreement on a constructivist theory of learning is not widespread due largely to what Derry (1996) terms "ethnocentrism within various constructivisms". In von Glasersfeld's (1995b) radical constructivist conception of learning, the teachers play the role of a "midwife in the birth of understanding" as opposed to being "mechanics of knowledge transfer". The following section outlines how a constructivist epistemology and theory of learning may be expressed as or translated into a wide variety of specific characteristics or principles of constructivist learning and teaching. www.cdli.ca /~elmurphy/emurphy/cle2b.html   (1460 words)

 Constructivism: Philosophical & Epistemological Foundations The meaning that is produced by these thought processes is external to the understander, and it is determined by the structure of the real world (p.28). In contrast, the constructivist view argues that knowledge and reality do not have an objective or absolute value or, at the least, that we have no way of knowing this reality. Von Glasersfeld (1995) indicates in relation to the concept of reality: "It is made up of the network of things and relationships that we rely on in our living, and on which, we believe, others rely on, too" (p.7). www.cdli.ca /~elmurphy/emurphy/cle2.html   (911 words)

 Valente/Dracula's Crypt. Chapter 1   (Site not responding. Last check: 2007-10-31) The expatriation of his parents was an ex-patriation for Stoker in another sense: it became a momentary disconnection from the settler heritage of security and privilege associated with his father's blood and a reconnection with the unsettled heritage of distress and flight associated with his mother's blood. Logically, if unexpectedly, Jerry seizes upon the ethnic stereotype lodged in this commentary as partial vindication of his own beleaguered initiative to live abroad: "'One thing John Sebright tells me, that there is less drunkenness in England than here'" (31-32). This recursive, constructivist logic, which Stoker will refine and recalibrate in Dracula, not only carries the unrealized potential to reconcile the divergent generic strains in The Primrose Path but also has the virtue of reconciling the novel's broadly political and narrowly personal agendas in a single stroke. www.press.uillinois.edu /epub/books/valente/ch1.html   (11478 words)

 SEP: Constructive Mathematics In order to describe the logic used by the intuitionist mathematician, it was necessary first to analyse the mathematical processes of the mind, from which analysis the logic could be extracted. Experience shows that the restriction to intuitionistic logic always forces mathematicians to work in a manner that, at least informally, can be described as algorithmic; so algorithmic mathematics appears to be equivalent to mathematics that uses only intuitionistic logic. Taking the logic as the primary characteristic of constructive mathematics, it does not reflect the primacy of mathematics over logic that was part of the belief of Brouwer, Heyting, Markov, Bishop, and other pioneers of constructivism. plato.stanford.edu /entries/mathematics-constructive   (6364 words)

 ACJ Special: Individual Differences or Social Pragmatics Specifically, we argue that constructivist researchers have tapped into qualitatively different social pragmatics.  Kenneth Gergen (1985) observed that, "Forms of discourse emerge, for one, as a response to certain practical problems encountered in human relationships" (p. Early constructivist research investigated how persuasive skills develop in childhood and early adolescence.  An early study by Clark and Delia (1976) served as a heuristic prototype for later studies. In summary, constructivist research has documented a massive complex of interrelated attributes (i.e., social cognition, person-centered communication indices, related skills, values, and social practices) that fit into a coherent pattern.  These relationships are broad enough, deep enough, and profound enough to constitute fundamentally different social pragmatics. www.acjournal.org /holdings/vol5/iss3/special/leichty.htm   (3921 words)

 [No title] Logical structure of sentences and arguments; elementary symbolic methods; applications. A second-semester course in symbolic logic: formal syntax and semantics, basic metatheory (soundness, completeness, compactness, and Lowenheim-Skolem theorems), and further topics in logic. Issues in philosophical logic and its applications, such as theories of meaning, logical paradoxes, epistemic logic, deontic logic, modal logic, existence, and identity. www.utexas.edu /student/registrar/gopherfiles/catalog/cat-ug/Ch08/LA.PHL.txt   (2455 words)

 In Science Constructivist theories of science have cleared a discursive and political space that the nationalistic right is only too eager to move into. But when science is joined to culture at the hip in the constructivist fashion, it also opens the door to the so-called "ethno-sciences" -- "Hindu science," "Islamic science," "third world women's science" -- wherein scientific rationality is subordinated to the "forms of life" of different communities. The BJP may be on the wrong side of the egalitarian ideals espoused by science critics, but it is by no means on the wrong side of their constructivist logic. www.geocities.com /indianfascism/fascism/in_science.htm   (2941 words)

 3050 Ending the Semester There are logics, such as intuitionist logic and constructivist logic, which deny some of the rules we have accepted. This logic includes a variable for time - t and propositions are true at time t0 or false at time t0. Fuzzy logic replaces the simple truth functions with two values T or F (or equivalently range {0,1}) with more general functions with range the whole interval [0,1]. www.math.yorku.ca /Courses/9697/Math2090/2090_whend.html   (1505 words)

 index_lnk_7.html "Constructivist mathematics" has a completely different meaning, which sometimes causes confusion at joint meetings of professional mathematicians and mathematics educators. These are the three ways in which the world may be said to be "inconsistent". Consistent logics can be developed that enable us to describe these inconsistent states of affairs; see e.g. www.unl.edu /tcweb/fowler/myGeometry/piagetGeomTchrs/Links/index_lnk_7.html   (579 words)

 Logic Analyzer - Information   (Site not responding. Last check: 2007-10-31) Logic is the College logic is a for presented as first course in traditional logic, logic is the of logic have included well. Unlike ordinary modal hybrid logic makes it temporal which use modal They also feature, model In, simplification conjunction conjunction, mathematical and type rbjpub cl tlc001.htm Category:Mathematical maths stub Bunched is a substructural that, like linear, has Bunched extended with separation. Inductive Inductive Generalizations constructivist constructivist, classical, logic and set paraconsistent paraconsistent, classical, and set Category:Mathematical noncommutative. www.freewebs.com /information24/logic-analyzer.html   (274 words)

 David - Note that this is exactly the law that is rejected by intuitionistic/constructivist logic. I myself prefer proof by induction because it's constructivist, so much so that sometimes you can derive algorithms from them. And I find nothing is wrong with straight application of the predicate, such as used in forming the basis of the induction. www.crazylife.org /~util/129635.html   (779 words)

 Topos Logic   (Site not responding. Last check: 2007-10-31) Popper invented many new Classical logic interpretations of statistical probability theory and was an expert defender of Classical logic. Anything proved using Intuitionist Logic, a weakened form of logic, is automatically proved in classical logic. From the abstract: "A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. home.earthlink.net /~enigl/TL.htm   (2174 words)

 constructivist - OneLook Dictionary Search We found 7 dictionaries with English definitions that include the word constructivist: Tip: Click on the first link on a line below to go directly to a page where "constructivist" is defined. Phrases that include constructivist: constructivist epistemology, constructivist logic, constructivist type theory www.onelook.com /?w=constructivist   (98 words)

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