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Inductive Reasoning
Inductive reasoning refers to a variety of method of reasoning, methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike Deductive reasoning, ''deductive'' reasoning (such as mathematical induction), where the conclusion is ''certain'', given the premises are correct, inductive reasoning produces conclusions that are at best ''probable'', given the evidence provided. Types The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded. Inductive generalization A generalization (more accurately, an ''inductive generalization'') proceeds from premises about a Sample (statistics), sample to a conclusion about the statistical population, population. The observation obtained from this sample is projected onto the broader population. : The proportion Q of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for mathematical proof, proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for n = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case n = k, ''then'' it must also hold for the next case n = k + 1. These two steps establish that the statement holds for every natural number n. The base case does not necessarily begin with n = 0, but often with n = 1, and possibly with any fixed natural number n = N, establishing the trut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Sense
Common sense () is "knowledge, judgement, and taste which is more or less universal and which is held more or less without reflection or argument". As such, it is often considered to represent the basic level of sound practical judgement or knowledge of basic facts that any adult human being ought to possess. It is "common" in the sense of being shared by nearly all people. Relevant terms from other languages used in such discussions include the aforementioned Latin, itself translating Ancient Greek ('), and French '. However, these are not straightforward translations in all contexts, and in English different shades of meaning have developed. In philosophical and scientific contexts, since the Age of Enlightenment the term "common sense" has been used for rhetorical effect both approvingly and disapprovingly. On the one hand it has been a standard for good taste, good sense, and source of scientific and logical axioms. On the other hand it has been equated to conventional wisdom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Defeasible Reasoning
In philosophy of logic, defeasible reasoning is a kind of provisional 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 con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Bacon
Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626) was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England under King James I. Bacon argued for the importance of natural philosophy, guided by the scientific method, and his works remained influential throughout the Scientific Revolution. Bacon has been called the father of empiricism. He argued for the possibility of scientific knowledge based only upon inductive reasoning and careful observation of events in nature. He believed that science could be achieved by the use of a sceptical and methodical approach whereby scientists aim to avoid misleading themselves. Although his most specific proposals about such a method, the Baconian method, did not have long-lasting influence, the general idea of the importance and possibility of a sceptical methodology makes Bacon one of the later founders of the scientific method. His portion of the method based in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eliminative Induction
The Baconian method is the investigative method developed by Francis Bacon, one of the founders of modern science, and thus a first formulation of a modern scientific method. The method was put forward in Bacon's book ''Novum Organum'' (1620), or 'New Method', to replace the old methods put forward in Aristotle's ''Organon''. It influenced the early modern rejection of medieval Aristotelianism. Description in the ''Novum Organum'' Bacon's view of induction Bacon's method is an example of the application of inductive reasoning. However, Bacon's method of induction is much more complex than the essential inductive process of making generalisations from observations. Bacon's method begins with description of the requirements for making the careful, systematic observations necessary to produce quality facts. He then proceeds to use induction, the ability to generalise from a set of facts to one or more axioms. However, he stresses the necessity of not generalising beyond what the fac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Method
The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and medieval world. The scientific method involves careful observation coupled with rigorous skepticism, because Philosophy of science#Observation inseparable from theory, cognitive assumptions can distort the interpretation of the Perception#Process and terminology, observation. Scientific inquiry includes creating a testable hypothesis through inductive reasoning, testing it through experiments and statistical analysis, and adjusting or discarding the hypothesis based on the results. Although procedures vary across Branches of science, fields, the underlying #Process, process is often similar. In more detail: the scientific method involves making conjectures (hypothetical explanations), predicting the logical consequences of hypothesis, then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Science
Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, and the ultimate purpose and meaning of science as a human endeavour. Philosophy of science focuses on metaphysical, epistemic and semantic aspects of scientific practice, and overlaps with metaphysics, ontology, logic, and epistemology, for example, when it explores the relationship between science and the concept of truth. Philosophy of science is both a theoretical and empirical discipline, relying on philosophical theorising as well as meta-studies of scientific practice. Ethical issues such as bioethics and scientific misconduct are often considered ethics or science studies rather than the philosophy of science. Many of the central problems concerned with the philosophy of science lack contemporary consensus, including whether ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argument Form
In logic, the logical form of a statement is a precisely specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language. The logical form of an argument is called the argument form of the argument. History The importance of the concept of form to logic was already recognized in ancient times. Aristotle, in the '' Prior Analytics'', was one of the first people to employ variable letters to represent valid inferences. Therefore, Jan Łukasiewicz claims that the introduction of variables was "one of Aristotle's greatest inventions." A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Proposition
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the ''subject term'') are included in another (the ''predicate term''). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called ''A'', ''E'', ''I'', and ''O''). If, abstractly, the subject category is named ''S'' and the predicate category is named ''P'', the four standard forms are: * All ''S'' are ''P''. (''A'' form) * No ''S'' are ''P''. (''E'' form) * Some ''S'' are ''P''. (''I'' form) * Some ''S'' are not ''P''. (''O'' form) A large number of sentences may be translated into one of these canonical forms while retaining all or most of the original meaning of the sentence. Greek inves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cherry-picked
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of pointing to individual cases or data that seem to confirm a particular position while ignoring a significant portion of related and similar cases or data that may contradict that position. Cherry picking may be committed intentionally or unintentionally. The term is based on the perceived process of harvesting fruit, such as cherries. The picker would be expected to select only the ripest and healthiest fruits. An observer who sees only the selected fruit may thus wrongly conclude that most, or even all, of the tree's fruit is in a likewise good condition. This can also give a false impression of the quality of the fruit (since it is only a sample and is not a representative sample). A concept sometimes confused with cherry picking is the idea of gathering only the fruit that is easy to harvest, while ignoring other fruit that is higher up on the tree and thus more difficult to obtain (see ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Case-based Reasoning
Case-based reasoning (CBR), broadly construed, is the process of solving new problems based on the solutions of similar past problems. In everyday life, an auto mechanic who fixes an engine by recalling another car that exhibited similar symptoms is using case-based reasoning. A lawyer who advocates a particular outcome in a trial based on legal precedents or a judge who creates case law is using case-based reasoning. So, too, an engineer copying working elements of nature (practicing biomimicry) is treating nature as a database of solutions to problems. Case-based reasoning is a prominent type of analogy solution making. It has been argued that case-based reasoning is not only a powerful method for computer reasoning, but also a pervasive behavior in everyday human problem solving; or, more radically, that all reasoning is based on past cases personally experienced. This view is related to prototype theory, which is most deeply explored in cognitive science. Process Case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
