Deductive reasoning

Faulty generalization A faulty generalization is a conclusion about all or many instances of a phenomenon that has been reached on the basis of just one or just a few instances of that phenomenon.[1] It is an example of jumping to conclusions. For example, we may generalize about all people, or all members of a group, based on what we know about just one or just a few people. If we meet an angry person from a given country X, we may suspect that most people in country X are often angry. If we see only white swans, we may suspect that all swans are white. Faulty generalizations may lead to further incorrect conclusions. Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises. Logic[edit] The proportion Q of the sample has attribute A. Therefore, the proportion Q of the population has attribute A. Inductive fallacies[edit] Hasty generalization[edit] Examples[edit] Hasty generalization usually shows the pattern See also[edit]

The Science of Improv Through his studies of the brain "on jazz," music-loving otolaryngologist Charles Limb aims to unravel the mind's secrets of creativity. By Nick Zagorski | Photo by Keith Weller David Kane had never played keyboard quite like this. Sure, the 53-year-old musician and composer had experienced his share of cramped recording studios and poorly tuned pianos during his 37-year career. "Physically, it wasn't too uncomfortable," he jokes today, "but for my creative space, it was horrible." Three-dimensional surface projection of activations and deactivations associated with improvisation during jazz. "How do the legends, musicians like John Coltrane, get up on stage and improvise music for an hour or sometimes more?" Answering those questions appears daunting, as creativity may be the most enigmatic component of the human brain. "During improv, the brain deactivates the area involved in self-censoring, while cranking up the region linked with self-expression," Limb explains.

Reason Reason is the capacity for consciously making sense of things, establishing and verifying facts, applying logic, and changing or justifying practices, institutions, and beliefs based on new or existing information.[1] It is closely associated with such characteristically human activities as philosophy, science, language, mathematics, and art and is normally considered to be a distinguishing ability possessed by humans.[2] Reason, or an aspect of it, is sometimes referred to as rationality. Using reason, or reasoning, can also be described more plainly as providing good, or the best, reasons. For example, when evaluating a moral decision, "morality is, at the very least, the effort to guide one's conduct by reason—that is, doing what there are the best reasons for doing—while giving equal [and impartial] weight to the interests of all those affected by what one does."[7] Etymology and related words[edit] Philosophical history[edit] Classical philosophy[edit] The critique of reason[edit]

Jumping to conclusions Jumping to conclusions (officially the jumping conclusion bias, often abbreviated as JTC, and also referred to as the inference-observation confusion[1]) is a psychological term referring to a communication obstacle where one "judge[s] or decide[s] something without having all the facts; to reach unwarranted conclusions".[2][3] In other words, "when I fail to distinguish between what I observed first hand from what I have only inferred or assumed".[1] Because it involves making decisions without having enough information to be sure that one is right, this can give rise to bad or rash decisions. Subtypes[edit] Three commonly recognized subtypes are as follows:[4][5] Mind reading – Where there is a sense of access to special knowledge of the intentions or thoughts of others. Information[edit] Jumping to conclusions is a form of cognitive distortion. It is easy for interviewers to jump to conclusions, often resulting in a "costly hiring error due to false inference". Comedy[edit]

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Gravity Attraction of masses and energy In physics, gravity (from Latin gravitas 'weight'[1]) is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles.[2] However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light. On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Definitions History Ancient world In the ancient Middle East, gravity was a topic of fierce debate. Specifics

Irrelevant conclusion Irrelevant conclusion should not be confused with formal fallacy, an argument whose conclusion does not follow from its premises. Overview[edit] Ignoratio elenchi is one of the fallacies identified by Aristotle in his Organon. In a broader sense he asserted that all fallacies are a form of ignoratio elenchi.[3][4] Ignoratio Elenchi, according to Aristotle, is a fallacy which arises from "ignorance of the nature of refutation". ● Example 1: A and B are debating as to whether criticizing indirectly has any merit in general. A: There is no point in people ranting on social media about politics; the president is not going to read it anyway. B: But it is their social media. A: Well, I do not keep up with it anyway. ● Example 2: A and B are debating about the law. A: Does the law allow me to do that? B: The law should allow you to do that because this and that. B missed the point. Etymology[edit] The phrase ignoratio elenchi is from Latin, meaning 'an ignoring of a refutation'. See also[edit]

Top-down and bottom-up design Top-down and bottom-up are both strategies of information processing and knowledge ordering, used in a variety of fields including software, humanistic and scientific theories (see systemics), and management and organization. In practice, they can be seen as a style of thinking and teaching. A top-down approach (also known as stepwise design and in some cases used as a synonym of decomposition) is essentially the breaking down of a system to gain insight into its compositional sub-systems. In a top-down approach an overview of the system is formulated, specifying but not detailing any first-level subsystems. A bottom-up approach is the piecing together of systems to give rise to more complex systems, thus making the original systems sub-systems of the emergent system. Product design and development[edit] During the design and development of new products, designers and engineers rely on both a bottom-up and top-down approach. Computer science[edit] Software development[edit] Parsing[edit]

Argument In a typical deductive argument, the premises are meant to provide a guarantee of the truth of the conclusion, while in an inductive argument, they are thought to provide reasons supporting the conclusion's probable truth.[6] The standards for evaluating non-deductive arguments may rest on different or additional criteria than truth, for example, the persuasiveness of so-called "indispensability claims" in transcendental arguments,[7] the quality of hypotheses in retroduction, or even the disclosure of new possibilities for thinking and acting.[8] Formal and informal arguments[edit] Informal arguments as studied in informal logic, are presented in ordinary language and are intended for everyday discourse. Conversely, formal arguments are studied in formal logic (historically called symbolic logic, more commonly referred to as mathematical logic today) and are expressed in a formal language. Standard argument types[edit] Deductive arguments[edit] Validity[edit] For example: Soundness[edit]

Statistical inference Process of using data analysis Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term inference is sometimes used instead to mean "make a prediction, by evaluating an already trained model";[2] in this context inferring properties of the model is referred to as training or learning (rather than inference), and using a model for prediction is referred to as inference (instead of prediction); see also predictive inference. The conclusion of a statistical inference is a statistical proposition.[6] Some common forms of statistical proposition are the following: Models and assumptions [edit] Any statistical inference requires some assumptions. Degree of models/assumptions Statisticians distinguish between three levels of modeling assumptions; Importance of valid models/assumptions is smooth.