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Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's twovolume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truthandconsequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) 

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...) 

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11page 1936 Tarski consequencedefinition paper is based on a monistic fixeduniverse framework?like Begriffsschrift and Principia Mathematica. Monistic fixeduniverse frameworks, common in preWWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multipleuniverse framework?like the 1931 Gödel incompleteness paper. A pluralistic multipleuniverse framework recognizes multiple (...) 

John Venn and Charles L. Dodgson (Lewis Carroll) created systems of logic diagrams capable of representing classes (sets) and their relations in the form of propositions. Each is a proof method for syllogisms, and Carroll's is a sound and complete system. For a large number of sets, Carroll diagrams are easier to draw because of their selfsimilarity and algorithmic construction. This regularity makes it easier to locate and thereby to erase cells corresponding with classes destroyed by the premises of an (...) 



This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premiseconclusion arguments. The premises and conclusion of an argument have information content (they ?say? something), and they have subject matter (they are ?about? something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an informationprocessing procedure exhibiting a stepbystep deduction of the conclusion from the premiseset. Invalidity is established by (...) 

We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semiclassical negations”. Each of these negations deals only with one of the (...) 

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...) 

Brown, Frank Markham: Boolean Reasoning: The Logic of Boolean Equations. Second edition, New York: Dover, 2003; i–xii, 291 pp. USD$16.95. ISBN: 0486427854. 





In his influential Laws of Thought , the mathematician George Boole presented a formulation of logic using algebraic expressions and manipulations. His widow, Mary Everest Boole, undertook an ambitious project of disseminating his ideas by introducing lay audiences to the law of pulsation, a prescription for correct reasoning that incorporates two of his fundamental insights. Contemporary scholarship presents a fragmented picture of Mary Boole, regarding her largely as a source of information on the religiopsychological impetus for her husband's contributions to (...) 

This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes nonspecialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s twovolume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...) 