Etymology
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natural (n.)

"person with a natural gift or talent," 1925, originally in prizefighting, from natural (adj.). But an older sense is almost opposite to this, "half-wit, idiot" (one "naturally deficient" in intellect), which was in use 16c. to 19c. In Middle English, the word as a noun meant "natural capacity, physical ability or power" (early 14c.), and it was common in sense "a native of a place" in Shakespeare's day. Also in 17c., "a mistress."

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natural (adj.)

c. 1300, naturel, "of one's inborn character; hereditary, innate, by birth or as if by birth;" early 14c. "of the world of nature (especially as opposed to man)," from Old French naturel "of nature, conforming to nature; by birth," and directly from Latin naturalis "by birth, according to nature," from natura "nature" (see nature).

Of events, features, etc., "existing in nature as a result of natural forces" (that is, not caused by accident, human agency, or divine intervention), late 14c. From late 14c. of properties, traits, qualities, "proper, suitable, appropriate to character or constitution;"  from late 15c. as "native, native-born." Also late 15c. as "not miraculous, in conformity with nature," hence "easy, free from affectation" (c. 1600). Of objects or substances, "not artificially cultivated or created, existing in nature" c. 1400. As a euphemism for "illegitimate, bastard" (of children), it is recorded from c. 1400, on the notion of blood kinship (but not legal status).

Natural science, that pertaining to physical nature, is from late 14c.;  natural history meaning more or less the same thing is from 1560s (see history).  Natural law "the expression of right reason or the dictate of religion inhering in nature and man and having ethically binding force as a rule of civil conduct" is from late 14c. Natural order "apparent order in nature" is from 1690s. Natural childbirth is attested by 1898. Natural life, usually in reference to the duration of life, is from mid-15c.; natural death, one without violence or accident, is from mid-15c. To die of natural causes is from 1570s.

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philosophy (n.)
Origin and meaning of philosophy

c. 1300, philosophie, "knowledge, learning, scholarship, scholarly works, body of knowledge," from Old French filosofie "philosophy, knowledge" (12c., Modern French philosophie) and directly from Latin philosophia, from Greek philosophia "love of knowledge, pursuit of wisdom; systematic investigation," from philo- "loving" (see philo-) + sophia "knowledge, wisdom," from sophis "wise, learned;" a word of unknown origin [Beekes]. With many spelling variants in Middle English (filozofie, phelosophie, etc.).

From mid-14c. as "the discipline of dealing in rational speculation or contemplation;" from late 14c. as "natural science," also "alchemy, occult knowledge;" in the Middle Ages the word was understood to embrace all speculative sciences. Meaning "system a person forms for conduct of life" is attested from 1771. The modern sense of "the body of highest truth, the science of the most fundamental matters" is from 1794.

Nec quicquam aliud est philosophia, si interpretari velis, praeter studium sapientiae; sapientia autem est rerum divinarum et humanarum causarumque quibus eae res continentur scientia. [Cicero, "De Officiis"]
[Philosophical problems] are, of course, not empirical problems; but they are solved through an insight into the workings of our language, and that in such a way that these workings are recognized — despite an urge to misunderstand them. The problems are solved, not through the contribution of new knowledge, rather through the arrangement of things long familiar. Philosophy is a struggle against the bewitchment (Verhexung) of our understanding by the resources of our language. [Ludwig Wittgenstein, "Philosophical Investigations," 1953]
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natural-born (adj.)

"so by nature, born so," 1580s, from natural (adj.) + born.

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physiology (n.)

1560s, "study and description of natural objects, natural philosophy" (a sense now obsolete), from French physiologie (16c.) or directly from Latin physiologia "natural science, study of nature," from Greek physiologia "natural science, inquiry into nature," from physios "nature" (see physio-) + logia "study" (see -logy). Meaning "science of the normal function of living things" is attested from 1610s. Related: Physiologic; physiologist.

The two words [physics/physiology] had once the same wide meaning of natural science or natural philosophy. They have now been narrowed & differentiated, physics retaining only the properties of matter & energy in inorganic nature, & physiology only the normal functions & phenomena of living beings. [Fowler, 1926]
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naturalism (n.)

1630s, "action based on natural instincts," from natural (adj.) + -ism. In philosophy, as a view of the world and humanity's relationship to it involving natural forces only (and excluding spiritualism and superstition), from 1750. As a tendency in art and literature, "conformity to nature or reality, but without slavish fidelity to it," from 1850.

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naive (adj.)

1650s, "natural, simple, unsophisticated, artless," from French naïve, fem. of naïf, from Old French naif "naive, natural, genuine; just born; foolish, innocent; unspoiled, unworked" (13c.), from Latin nativus "not artificial," also "native, rustic," literally "born, innate, natural" (see native (adj.)). In philosophy, "unreflecting, uncritical" (1895), used of non-philosophers. Related: Naively.

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mathematics (n.)

"the science of quantity; the abstract science which investigates the concepts of numerical and spatial relations," 1580s; see mathematic (the older form of the word in English, attested from late 14c.) + -ics. Originally one of three branches of Aristotelian theoretical science, along with first philosophy (or metaphysics) and physics (or natural philosophy).

Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. [Bertrand Russell, "A History of Western Philosophy"]
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philosophic (adj.)

"pertaining to philosophy," mid-15c., philosophik, from Old French filosofique (Modern French philosophique) and directly from Late Latin philosophicus, from Greek philosophikos, from philosophia "philosophy" (see philosophy).

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reductionism (n.)
1948, in philosophy, from reduction in specialized sense in philosophy (1914) + -ism. Related: Reductionist.
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