Logic Many Thanks to Wikipedia, the free encyclopedia, for this educational opportunity. Much of this page can be found with links at Wikipedia Logic (from As a Traditionally, logic is studied as a branch of Nature of logic Form is central to logic. It complicates exposition that ’formal’ in "formal logic" is commonly used in an ambiguous manner. Symbolic language is just one kind of formal logic, and is distinguished from another kind of formal logic, traditional
Consistency, soundness, and completeness Among the valuable properties that formal systems can have are:
Not all systems achieve all three virtues. The work of Rival conceptions of logic Logic arose (see below) from a concern with correctness of By contrast Deductive and inductive reasoning
The task of providing this definition may be approached in various ways, some less formal than others; some of these definitions may use History of logic Main article: Many cultures have employed intricate systems of reasoning and asked questions about logic or propounded logical paradoxes. For example, in Gongsun Long (ca. 325-25 BC) proposed the paradox "One and one cannot become two, since neither becomes two."The first sustained work on the subject of logic which has survived was that of However in India, innovations in the scholastic school, called Topics in logic Throughout history, there has been interest in distinguishing good from bad arguments, and so logic has been studied in some more or less familiar form. Consideration of the different types of logic explains that logic is not studied in a vacuum. While logic often seems to provide its own motivations, the subject develops most healthily when the reason for our interest is made clear. Syllogistic logic Main article: The Aristotle’s body of work on logic, with the constituting the first explicit work in formal logic, introducing the syllogistic. The parts of syllogistic, also known by the name Prior Analyticsterm logic, were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.Aristotle’s work was regarded in classical times and from medieval times in Europe and the Middle East as the very picture of a fully worked out system. It was not alone: the Predicate logic Main article: Logic as it is studied today is a very different subject to that studied before, and the principal difference is the innovation of predicate logic. Whereas Aristotelian syllogistic logic specified the forms that the relevant part of the involved judgements took, predicate logic allows sentences to be analysed into subject and argument in several different ways, thus allowing predicate logic to solve the The development of predicate logic is usually attributed to Modal logic Main article: In languages, The logical study of modality dates back to Deduction and reasoning Main article: The motivation for the study of logic in ancient times was clear, as we have described: it is so that we may learn to distinguish good from bad arguments, and so become more effective in argument and oratory, and perhaps also, to become a better person.
This motivation is still alive, although it no longer takes centre stage in the picture of logic; typically Mathematical logic Main article: Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.
The earliest use of mathematics and The boldest attempt to apply logic to mathematics was undoubtedly the Both the statement of Hilbert’s program and its refutation by Gödel depended upon their work establishing the second area of mathematical logic, the application of mathematics to logic in the form of If
Philosophical logic Main article:
Logic and the philosophy of language are closely related. Philosophy of language has to do with the study of how our language engages and interacts with our thinking. Logic has an immediate impact on other areas of study. Studying logic and the relationship between logic and ordinary speech can help a person better structure their own arguments and critique the arguments of others. Many popular arguments are filled with errors because so many people are untrained in logic and unaware of how to correctly formulate an argument. Logic and computation Main article: Logic cut to the heart of computer science as it emerged as a discipline: In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with Section F.3 on
Many fundamental logical formalisms are essential to section I.2 on artificial intelligence, for example Argumentation theory
Controversies in logic Just as we have seen there is disagreement over what logic is about, so there is disagreement about what logical truths there are. Bivalence and the law of the excluded middle Main article: The logics discussed above are all "
Logics such as Implication: strict or material? Main article: It is obvious that the notion of implication formalised in classical logic does not comfortably translate into natural language by means of "if... then...", due to a number of problems called the The first class of paradoxes involves counterfactuals, such as "If the moon is made of green cheese, then 2+2=5", which are puzzling because natural language does not support the The second class of paradoxes involves redundant premises, falsely suggesting that we know the succedent because of the antecedent: thus "if that man gets elected, granny will die" is materially true if granny happens to be in the last stages of a terminal illness, regardless of the man’s election prospects. Such sentences violate the Tolerating the impossible Main article: Closely related to questions arising from the paradoxes of implication comes the radical suggestion that logic ought to tolerate Is logic empirical? Main article: What is the Another paper by the same name by |

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