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, where the conclusion of a deductive argument is certain given the premises are correct; 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 are 20 balls—either black...

The Novum Organum, fully Novum Organum, sive Indicia Vera de Interpretatione Naturae ("New organon, or true directions concerning the interpretation of nature") or Instaurationis Magnae, Pars II ("Part II of The Great Instauration"), is a philosophical work by Francis Bacon, written in Latin and published in 1620. The title is a reference to Aristotle's work Organon, which was his treatise on logic and syllogism. In Novum Organum, Bacon details a new system of logic he believes to be superior to the old ways of syllogism. This is now known as the Baconian method. For Bacon, finding the essence of a thing was a simple process of reduction, and the use of inductive reasoning. In finding the cause of a 'phenomenal nature' such as heat, one must list all of the situations where heat is found. Then another list should be drawn up, listing situations that are similar to those of the first list except for the lack of heat. A third table lists situations where heat can vary. The 'form nature', or cause, of heat must be that which is common to all instances in the first table, is lacking from all...

A Treatise of Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects (1739–40) is a book by Scottish philosopher David Hume, considered by many to be Hume's most important work and one of the most influential works in the history of philosophy. The Treatise is a classic statement of philosophical empiricism, scepticism, and naturalism. In the introduction Hume presents the idea of placing all science and philosophy on a novel foundation: namely, an empirical investigation into human nature. Impressed by Isaac Newton's achievements in the physical sciences, Hume sought to introduce the same experimental method of reasoning into the study of human psychology, with the aim of discovering the "extent and force of human understanding". Against the philosophical rationalists, Hume argues that the passions, rather than reason, cause human behaviour. He introduces the famous problem of induction, arguing that inductive reasoning and our beliefs regarding cause and effect cannot be justified by reason; instead, our faith in induction and causation is caused by mental habit and custom. Hume defends...

The Taft equation is a linear free energy relationship (LFER) used in physical organic chemistry in the study of reaction mechanisms and in the development of quantitative structure–activity relationships for organic compounds. It was developed by Robert W. Taft in 1952 as a modification to the Hammett equation. While the Hammett equation accounts for how field, inductive, and resonance effects influence reaction rates, the Taft equation also describes the steric effects of a substituent. The Taft equation is written as: log ⁡ ( k s k ...

Inductively coupled plasma atomic emission spectroscopy (ICP-AES), also referred to as inductively coupled plasma optical emission spectroscopy (ICP-OES), is an analytical technique used for the detection of chemical elements. It is a type of emission spectroscopy that uses the inductively coupled plasma to produce excited atoms and ions that emit electromagnetic radiation at wavelengths characteristic of a particular element. The plasma is a high temperature source of ionised source gas (often argon). The plasma is sustained and maintained by inductive coupling from electrical coils at megahertz frequencies. The source temperature is in the range from 6000 to 10,000 K. The intensity of the emissions from various wavelengths of light are proportional to the concentrations of the elements within the sample. Mechanism The ICP-AES is composed of two parts: the ICP and the optical spectrometer. The ICP torch consists of 3 concentric quartz glass tubes. The output or "work" coil of the radio frequency (RF) generator surrounds part of this quartz torch. Argon gas is typically used to create the plasma. The ICPs have two...

Elementa harmonica is a treatise on the subject of musical scales by Aristoxenus, of which considerable amounts are extant. The work dates to the second half of the 4th century BC. It is the oldest substantially surviving work written on the subject of music theory. Title The work is generally known as Aristoxenou Harmonika Stoicheia or Elements of Harmonics. It is also known by the shorter title The Elements, rendering Greek Στοιχεία. The Work Historical context Aristoxenus's work departs from prior studies in which music was studied only in relation to an understanding of the kosmos. The study of music in the Pythagorean school c.500 had focused on the mathematical nature of harmonia. Aristotle, whose Peripatetic school Aristoxenus belonged to, addressed the subject in his work On the Soul. Aristoxenus opposed the position of the Pythagoreans; he favoured an intellectual treatment of the subject in Aristotelian terms, i.e. by applying the exercise of inductive logic with attention to empirical evidence...

First formulated by David Hume, the problem of induction questions our reasons for believing that the future will resemble the past, or more broadly it questions predictions about unobserved things based on previous observations. This inference from the observed to the unobserved is known as "inductive inferences", and Hume, while acknowledging that everyone does and must make such inferences, argued that there is no non-circular way to justify them, thereby undermining one of the Enlightenment pillars of rationality.While David Hume is credited with raising the issue in Western analytic philosophy in the 18th century, the Pyrrhonist school of Hellenistic philosophy and the Cārvāka school of ancient Indian philosophy had expressed skepticism about inductive justification long prior to that. The traditional inductivist view is that all claimed empirical laws, either in everyday life or through the scientific method, can be justified through...

Explanatory power is the ability of a hypothesis or theory to explain the subject matter effectively to which it pertains. Its opposite is explanatory impotence. In the past, various criteria or measures for explanatory power have been proposed. In particular, one hypothesis, theory, or explanation can be said to have more explanatory power than another about the same subject matter If more facts or observations are accounted for; If it changes more "surprising facts" into "a matter of course" (following Peirce); If more details of causal relations are provided, leading to a high accuracy and precision of the description; If it offers greater predictive power (if it offers more details about what should be expected to be seen and not seen); If it depends less on authorities and more on observations; If it makes fewer assumptions; If it is more falsifiable (more testable by observation or experiment, according to Popper). If it can be used to compress encoded observations into fewer bits (Solomonoff's theory of inductive inference) Recently, David Deutsch proposed that theorists...