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Logical Reasoning
Two kinds of logical reasoning are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or ''premise'', a conclusion or ''logical consequence'' and a rule or ''material conditional'' that implies the ''conclusion'' given the ''precondition'', one can explain the following. # Deductive reasoning determines whether the truth of a ''conclusion'' can be determined for that ''rule'', based solely on the truth of the premises. Example: "When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet." Mathematical logic and philosophical logic are commonly associated with this type of reasoning. # Inductive reasoning attempts to support a determination of the ''rule''. It hypothesizes a ''rule'' after numerous examples are taken to be a ''conclusion'' that follows from a ''precondition'' in terms of such a ''rule''. Example: "The grass got wet numerous times when it rained, therefore: the grass alway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argument Terminology Used In Logic (en)
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective. In logic, an argument is usually expressed not in natural language but in a symbolic formal language, and it can be defined as any group of propositions of which one is claimed to follow from the others through deductively valid inferences that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific fields such as mathematics and computer science. Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments. Deductive arguments can be valid, and the valid ones can be sound: in a valid argument, premisses necessitate the conclusion, even if one or more of the premises is false ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Informal Logic
Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements). However, the precise definition of "informal logic" is a matter of some dispute. Ralph H. Johnson and J. Anthony Blair define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation."Johnson, Ralph H., and Blair, J. Anthony (1987), "The Current State of Informal Logic", ''Informal Logic'', 9(2–3), 147–151. Johnson & Blair added "... in everyday discourse" but in (2000), modified their definition, and broadened the focus now to include the sorts of argument that occurs not just in everyday discourse but also disciplined inquiry—what Weinstein (1990) calls "stylized discourse." This definition reflects what had been implicit in their practice and what others were doing in their informal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word ''wikt:infer, infer'' means to "carry forward". Inference is theoretically traditionally divided into deductive reasoning, deduction and inductive reasoning, induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference Formal proof, deriving Logical consequence, logical conclusions from premises known or assumed to be truth, true, with the Rule of inference, laws of valid inference being studied in logic. Induction is inference from particular evidence to a Universal (metaphysics), universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing Abductive reasoning, abduction from induction. Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation stud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallacy
A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument which may appear stronger than it really is if the fallacy is not spotted. The term in the Western intellectual tradition was introduced in the Aristotelian '' De Sophisticis Elenchis''. Some fallacies may be committed intentionally to manipulate or persuade by deception. Others may be committed unintentionally because of human limitations such as carelessness, cognitive or social biases and ignorance, or, potentially, as the inevitable consequence of the limitations of language and understanding of language. This includes ignorance of the right reasoning standard, but also ignorance of relevant properties of the context. For instance, the soundness of legal arguments depends on the context in which the arguments are made. Fallacies are commonly divided into "formal" and "informal." A formal fallacy is a flaw in the structure of a deductive argument which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dialogical Logic
Dialogical logic (also known as the logic of dialogues) was conceived as a pragmatic approach to the semantics of logic that resorts to concepts of game theory such as "winning a play" and that of "winning strategy". Since dialogical logic was the first approach to the semantics of logic using notions stemming from game theory, game theoretical semantics (GTS) and dialogical logic are often conflated under the term ''game semantics''. However, as discussed below, though GTS and dialogical logic are both rooted in a game-theoretical perspective, in fact, they have quite different philosophical and logical background. Nowadays it has been extended to a general framework for the study of meaning, knowledge, and inference constituted during interaction. The new developments include cooperative dialogues and dialogues deploying a fully interpreted language (''dialogues with content''). Origins and further developments The philosopher and mathematician Paul Lorenzen (University of Erl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Thinking
Critical thinking is the analysis of available facts, evidence, observations, and arguments to form a judgement. The subject is complex; several different definitions exist, which generally include the rational, skeptical, and unbiased analysis or evaluation of factual evidence. Critical thinking is self-directed, self-disciplined, self- monitored, and self- corrective thinking. It presupposes assent to rigorous standards of excellence and mindful command of their use. It entails effective communication and problem-solving abilities as well as a commitment to overcome native egocentrism and sociocentrism. History The earliest records of critical thinking are the teachings of Socrates recorded by Plato. These included a part in Plato's early dialogues, where Socrates engages with one or more interlocutors on the issue of ethics such as question whether it was right for Socrates to escape from prison. The philosopher considered and reflected on this question and came to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argumentation Theory
Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory, includes the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural rules in both artificial and real-world settings. Argumentation includes various forms of dialogue such as deliberation and negotiation which are concerned with collaborative decision-making procedures. It also encompasses eristic dialog, the branch of social debate in which victory over an opponent is the primary goal, and didactic dialogue used for teaching. This discipline also studies the means by which people can express and rationally resolve or at least manage their disagreements. Argumentation is a daily occurrence, such as in public debate, science, and law. For example in law, in courts b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argument
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective. In logic, an argument is usually expressed not in natural language but in a symbolic formal language, and it can be defined as any group of propositions of which one is claimed to follow from the others through deductively valid inferences that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific fields such as mathematics and computer science. Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments. Deductive arguments can be valid, and the valid ones can be sound: in a valid argument, premisses necessitate the conclusion, even if one or more of the premises is false ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analogy
Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject (the analog, or source) to another (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, in which at least one of the premises, or the conclusion, is general rather than particular in nature. The term analogy can also refer to the relation between the source and the target themselves, which is often (though not always) a similarity, as in the biological notion of analogy. Analogy plays a significant role in problem solving, as well as decision making, argumentation, perception, generalization, memory, creativity, invention, prediction, emotion, explanation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-demonstrative Reasoning
In philosophical logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductively valid. It usually occurs when a rule is given, but there may be specific exceptions to the rule, or subclasses that are subject to a different rule. Defeasibility is found in literatures that are concerned with argument and the process of argument, or heuristic reasoning. Defeasible reasoning is a particular kind of non-demonstrative reasoning, where the reasoning does not produce a full, complete, or final demonstration of a claim, i.e., where fallibility and corrigibility of a conclusion are acknowledged. In other words, defeasible reasoning produces a contingent statement or claim. Defeasible reasoning is also a kind of ampliative reasoning because its conclusions reach beyond the pure meanings of the premises. Defeasible reasoning finds its fullest expression in jurisprudence, ethics and moral philosophy, epistemology, pragmatics and conversational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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