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Inductive Fallacies
A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an example of jumping to conclusions. For example, one may generalize about all people or all members of a group, based on what one knows about just one or a few people: * If one meets a rude person from a given country X, one may suspect that most people in country X are rude. * If one sees only white swans, one may suspect that all swans are white. Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises, or one which is not justified by sufficient or unbiased evidence. Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions, yet only weakly buttress the conclusions, hence a faulty generalization is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Informal Fallacy
Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Fallacies, despite being incorrect, usually ''appear'' to be correct and thereby can seduce people into accepting and using them. These misleading appearances are often connected to various aspects of natural language, such as ambiguous or vague expressions, or the assumption of implicit premises instead of making them explicit. Traditionally, a great number of informal fallacies have been identified, including the fallacy of equivocation, the fallacy of amphiboly, the fallacies of composition and division, the false dilemma, the fallacy of begging the question, the ad hominem fallacy and the appeal to ignorance. There is no general agreement as to how the various fallacies are to be grouped into categories. One approach sometimes found in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Misleading Vividness
Anecdotal evidence is evidence based only on personal observation, collected in a casual or non-systematic manner. The term is sometimes used in a legal context to describe certain kinds of testimony which are uncorroborated by objective, independent evidence such as notarized documentation, photographs, audio-visual recordings, etc. When used in advertising or promotion of a product, service, or idea, anecdotal reports are often called a testimonial, which are highly regulated in some jurisdictions. When compared to other types of evidence, anecdotal evidence is generally regarded as limited in value due to a number of potential weaknesses, but may be considered within the scope of scientific method as some anecdotal evidence can be both empirical and verifiable, e.g. in the use of case studies in medicine. Other anecdotal evidence, however, does not qualify as scientific evidence, because its nature prevents it from being investigated by the scientific method. Where only one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secundum Quid
''Secundum quid'' (also called ''secundum quid et simpliciter'', meaning " hat is truein a certain respect and hat is trueabsolutely") is a type of informal fallacy that occurs when the arguer fails to recognize the difference between rules of thumb (''soft'' generalizations, heuristics that hold true ''as a general rule'' but leave room for exceptions) and categorical propositions, rules that hold true universally. Since it ignores the limits, or qualifications, of rules of thumb, this fallacy is also named ignoring qualifications. The expression misuse of a principle can be used as well. Example The arguer cites only the cases that support his point, conveniently omitting Bach, Beethoven, Brahms etc. Compare with: In popular culture The following quatrain can be attributed to C. H. Talbot: I talked in terms whose sense was hid, ''Dividendo, componendo et secundum quid''; Now ''secundum quid'' is a wise remark And it earned my reputation as a learned clerk. Types Inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Number
In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name ''square'' number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by ''n'' points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of ''n''; thus, square numbers are a type of figurate numbers (other examples being Cube (algebra), cube numbers and triangular numbers). Square numbers are non-negative. A non-negative integer is a square number when its square root is again an intege ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling (statistics)
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population in question. Sampling has lower costs and faster data collection than measuring the entire population and can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Survey
Survey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey data collection, such as questionnaire construction and methods for improving the number and accuracy of responses to surveys. Survey methodology targets instruments or procedures that ask one or more questions that may or may not be answered. Researchers carry out statistical surveys with a view towards making statistical inferences about the population being studied; such inferences depend strongly on the survey questions used. Polls about public opinion, public-health surveys, market-research surveys, government surveys and censuses all exemplify quantitative research that uses survey methodology to answer questions about a population. Although censuses do not include a "sample", they do include other aspects of survey methodology, li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Reasoning
Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' reasoning. If the premises are correct, the conclusion of a deductive argument is ''certain''; in contrast, the truth of the conclusion of an inductive argument is '' probable'', based upon the evidence given. Types The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. Inductive generalization A generalization (more accurately, an ''inductive generalization'') proceeds from a premise about a sample to a conclusion about the population. The observation obtained from this sample is projected onto the broader population. : The proportion Q of the sample has attribute A. : Therefore, the proportion Q of the population has attribute A. For example, say there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallacy Of Composition
The fallacy of composition is an informal fallacy that arises when one infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber, therefore the vehicle of which it is a part is also made of rubber." This is fallacious, because vehicles are made with a variety of parts, most of which are not made of rubber. The fallacy of composition can apply even when a fact is true of every proper part of a greater entity, though. A more complicated example might be: "No atoms are alive. Therefore, nothing made of atoms is alive." This is a statement most people would consider incorrect, due to emergence, where the whole possesses properties not present in any of the parts. This fallacy is related to the fallacy of hasty generalization, in which an unwarranted inference is made from a statement about a sample to a statement about the population from which it is drawn. The fallacy of compos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biased Sample
In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. Medical sources sometimes refer to sampling bias as ascertainment bias. Ascertainment bias has basically the same definition, but is still sometimes classified as a separate type of bias. Distinction from selection bias Sampling bias is usually classified as a subtype of selection bias, sometimes specifically termed sample selection bias, but some classify it as a separate type of bias. A distinction, albeit not universally accepted, of sampling bias is that it undermines the external validity of a test (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof By Example
In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. The structure, argument form and formal form of a proof by example generally proceeds as follows: Structure: :I know that ''X'' is such. :Therefore, anything related to ''X'' is also such. Argument form: :I know that ''x'', which is a member of group ''X'', has the property ''P''. :Therefore, all other elements of ''X'' must have the property ''P''. Formal form: :\exists x:P(x)\;\;\vdash\;\;\forall x:P(x) The following example demonstrates why this line of reasoning is a logical fallacy: : I've seen a person shoot someone dead. : Therefore, all people are murderers. In the common discourse, a proof by example can also be used to describe an attempt to establish a claim using statistically insignificant examples. In which case, the merit o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overwhelming Exception
An overwhelming exception is an informal fallacy of generalization. It is a generalization that is accurate, but comes with one or more qualifications which eliminate so many cases that what remains is much less impressive than the initial statement might have led one to believe. Examples * "Our foreign policy has always helped other countries, except of course when it is against our National Interest..." :The false implication is that their foreign policy always helps other countries. The rhetorical use of the fallacy can be used to comic effect, as in the below examples: * "All right, but apart from the sanitation, the medicine, education, wine, public order, irrigation, roads, a fresh water system, and public health... ''what have the Romans ever done for us!?''" – ''Monty Python's Life of Brian'' :The attempted implication (fallacious in this case) is that the Romans did nothing for them. *"Well, I promise the answer will always be ''yes.'' Unless ''no'' is required." – '' M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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