Intuition in the context of Approximate

Positivism is a philosophical school that holds that all genuine knowledge is either true by definition or positive – meaning a posteriori facts derived by reason and logic from sensory experience. Other ways of knowing, such as intuition, introspection, or religious faith, are rejected or considered meaningless.

Although the positivist approach has been a recurrent theme in the history of Western thought, modern positivism was first articulated in the early 19th century by Auguste Comte. His school of sociological positivism holds that society, like the physical world, operates according to scientific laws. After Comte, positivist schools arose in logic, psychology, economics, historiography, and other fields of thought. Generally, positivists attempted to introduce scientific methods to their respective fields. Since the turn of the 20th century, positivism, although still popular, has declined under criticism within the social sciences by antipositivists and critical theorists, among others, for its alleged scientism, reductionism, overgeneralizations, and methodological limitations. Positivism also exerted an unusual influence on Kardecism.

Causality is an influence by which one event, process, state, or object (a cause) contributes to the production of another event, process, state, or object (an effect) where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason for the event or process.

In general, a process can have multiple causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Thus, the distinction between cause and effect either follows from or else provides the distinction between past and future. While the former viewpoint is more prevalent in physics, some writers have held that causality is metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such, it is a basic concept, and one might expect it to be more apt as an explanation of other concepts of progression than something to be explained by yet more fundamental ideas. The concept is like those of agency and efficacy. For this reason, a leap of intuition may be needed to grasp it. Accordingly, causality is implicit in the structure of ordinary language, as well as explicit in the language of scientific causal notation.

Transcendentalism is a philosophical, spiritual, and literary movement that developed in the late 1820s and 1830s in the New England region of the United States. A core belief is in the inherent goodness of people and nature, and while society and its institutions have corrupted the purity of the individual, people are at their best when truly "self-reliant" and independent. Transcendentalists saw divine experience inherent in the everyday. They thought of physical and spiritual phenomena as part of dynamic processes rather than as discrete entities.

Transcendentalism is one of the first philosophical currents that emerged in the United States; it is therefore a key early point in the history of American philosophy. Emphasizing subjective intuition over objective empiricism, its adherents believe that individuals are capable of generating completely original insights with little attention and deference to past transcendentalists. Its rise was a protest against the general state of intellectualism and spirituality at the time. The doctrine of the Unitarian church as taught at Harvard Divinity School was closely related.

Transcendental idealism is a philosophical system founded by German philosopher Immanuel Kant in the 18th century. Kant's epistemological program is found throughout his Critique of Pure Reason (1781). By transcendental (a term that deserves special clarification) Kant means that his philosophical approach to knowledge transcends mere consideration of sensory evidence and requires an understanding of the mind's innate modes of processing that sensory evidence.

In the "Transcendental Aesthetic" section of the Critique of Pure Reason, Kant outlines how space and time are pure forms of human intuition contributed by our own faculty of sensibility. Space and time do not have an existence "outside" of us, but are the "subjective" forms of our sensibility and hence the necessary a priori conditions under which the objects we encounter in our experience can appear to us at all. Kant describes time and space not only as "empirically real" but transcendentally ideal.

Vidya (Sanskrit: विद्या, IAST: vidyā) figures prominently in all texts pertaining to Indian philosophy – meaning science, learning, knowledge, and scholarship. Most importantly, it refers to valid knowledge, which cannot be contradicted, and true knowledge, which is the intuitively-gained knowledge of the self. Vidya is not mere intellectual knowledge, for the Vedas demand understanding.

Romanticism (also known as the Romantic movement or Romantic era) was an artistic and intellectual movement that originated in Europe towards the end of the 18th century. The purpose of the movement was to advocate for the importance of subjectivity, imagination, and appreciation of nature in society and culture in response to the Age of Enlightenment and the Industrial Revolution.

Romanticists rejected the social conventions of the time in favour of a moral outlook known as individualism. They argued that passion and intuition were crucial to understanding the world, and that beauty is more than merely an affair of form, but rather something that evokes a strong emotional response. With this philosophical foundation, the Romanticists elevated several key themes to which they were deeply committed: a reverence for nature and the supernatural, an idealization of the past as a nobler era, a fascination with the exotic and the mysterious, and a celebration of the heroic and the sublime.

Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the most general continuous functions, and their definition is the basis of topology.

Philosophical methodology encompasses the methods used to philosophize and the study of these methods. Methods of philosophy are procedures for conducting research, creating new theories, and selecting between competing theories. In addition to the description of methods, philosophical methodology also compares and evaluates them.

Philosophers have employed a great variety of methods. Methodological skepticism tries to find principles that cannot be doubted. The geometrical method deduces theorems from self-evident axioms. The phenomenological method describes first-person experience. Verificationists study the conditions of empirical verification of sentences to determine their meaning. Conceptual analysis decomposes concepts into fundamental constituents. Common-sense philosophers use widely held beliefs as their starting point of inquiry, whereas ordinary language philosophers extract philosophical insights from ordinary language. Intuition-based methods, like thought experiments, rely on non-inferential impressions. The method of reflective equilibrium seeks coherence among beliefs, while the pragmatist method assesses theories by their practical consequences. The transcendental method studies the conditions without which an entity could not exist. Experimental philosophers use empirical methods.

Authenticity is a concept of personality in the fields of psychology, existential psychotherapy, existentialist philosophy, and aesthetics. In existentialism, authenticity is the degree to which a person's actions are congruent with their values and desires, despite external pressures to social conformity. The conscious self comes to terms with the condition of Geworfenheit, of having been thrown into an absurd world (without values and meaning) not of their own making, thereby encountering external forces and influences different from and other than the Self. Authenticity has emerged as a central concept in contemporary models of well-being and the good life, serving as a foundational principle in many leading psychological frameworks. A person’s lack of authenticity is considered bad faith in dealing with other people and with one's self; thus, authenticity is in the instruction of the Oracle of Delphi: “Know thyself.” Concerning authenticity in art, the philosophers Jean Paul Sartre and Theodor Adorno held opposing views and opinions about jazz, a genre of American music; Sartre said that jazz is authentic and Adorno said that jazz is inauthentic. Many musical subcultures require artistic authenticity, lest the community consider an artist to be a poseur for lacking authenticity (creative, musical, or personal); artistic authenticity is integral to many genres of music, including but not limited to genres of rock (such as punk rock and heavy metal), club music (such as house and techno), and hip-hop.

In the 18th century, Romantic philosophers recommended intuition, emotion, and a connection to Nature as the necessary counterbalances to the intellectualism of the Age of Enlightenment. In the 20th century, Anglo–American preoccupations with authenticity centered on the writings of existentialist philosophers whose native tongue is not English; therefore, the faithful, true, and accurate translation of the term existentialism was much debated, to which end the philosopher Walter Kaufmann assembled a canon of existentialist philosophers. Kaufmann's canon includes the Dane Søren Kierkegaard (1813–1855), the German Martin Heidegger (1889–1976), and the Frenchman Jean-Paul Sartre (1905–1980). For these existentialists, the conscious Self comes to terms with existence (being and living) in an absurd, materialist world featuring external forces, e.g. Geworfenheit (Thrown-ness), and intellectual influences different from and other than the Self.