Perfection

Perfection is a state, variously, of completeness, flawlessness, or supreme excellence.

The term designates a range of diverse, if often kindred, concepts used in a variety of fields.

Term and concept The noun "perfection", the adjective "perfect", and the verb "to perfect" derive from the Latin verb "perficere" – "to finish" or "to bring to an end".Władysław Tatarkiewicz, "Perfection: the Term and the Concept", Dialectics and Humanism, vol. VI, no. 4 (autumn 1979), p. 5.

The ancient Greek word for "perfection" was "teleiotes".Władysław Tatarkiewicz, "Perfection: the Term and the Concept", Dialectics and Humanism, vol. VI, no. 4 (autumn 1979), p. 6.

The Greek polymath Aristotle (384–322 BCE) distinguished three concepts of perfection: 1. that which was complete – which contained all the requisite parts; 2. that which was so good that nothing of the kind could be better; 3. that which had attained its purpose.Władysław Tatarkiewicz, "Perfection: the Term and the Concept", Dialectics and Humanism, vol. VI, no. 4 (autumn 1979), p. 7.

The Polish philosopher Władysław Tatarkiewicz (1886 – 1980) notes that perfection is often confused with other qualities, such as "excellence". The German polymath Leibniz (1646–1716), who thought the world to be the best of all possible worlds, never called it perfect.Władysław Tatarkiewicz, "Perfection: the Term and the Concept", Dialectics and Humanism, vol. VI, no. 4 (autumn 1979), p. 9.

Paradox

The Franco-Italian scholar Joseph Juste Scaliger (1540–1609), the Italian polymath Lucilio Vanini (1585–1619), and (according to Vanini) the Greek philosopher Empedocles (ca. 494 – ca. 434 BCE) held that the greatest perfection was imperfection, for if the world were perfect, it could not be further perfected.Władysław Tatarkiewicz, "Paradoxes of perfection", Dialectics and Humanism, vol. VII, no. 1 (winter 1980), p. 77.

This idea accorded with the Baroque aesthetic of Vanini and the French polymath Marin Mersenne (1588–1648): the perfection of an art work occurs when the spectator complements the work with an act of contemplation.Władysław Tatarkiewicz, "Paradoxes of perfection", Dialectics and Humanism, vol. VII, no. 1 (winter 1980), p. 77.

Perfect numbers

The ancient Greeks called perfect numbers "teleioi". A variety of numbers have been called "perfect", for example the number 10 (a person's hands have 10 fingers).Władysław Tatarkiewicz, "Perfect Numbers", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 137.

Greek mathematicians regarded as "perfect" a number which equals the sum of its divisors that are smaller than itself, such as the number 6, because 1 + 2 + 3 = 6.Władysław Tatarkiewicz, "Perfect Numbers", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), pp. 137–138.

Euclid (fl. 300 BCE) gave a formula for (even) "perfect" numbers: Np = 2p−1 (2p − 1) where p and 2p − 1 are prime numbers.Władysław Tatarkiewicz, "Perfect Numbers", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 138.

After more than two millennia of study, it still is not known whether there exist infinitely many perfect numbers; or whether there are any odd ones.Władysław Tatarkiewicz, "Perfect Numbers", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 138.

Physics A number of fictitious physical entities are traditionally called "perfect":

A perfectly rigid body is one that supposedly is not deformed by forces applied to it.Władysław Tatarkiewicz, "Perfection in Physics and Chemistry", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 139.

A perfectly plastic body is one that is supposedly deformed indefinitely as a load is applied to it.Władysław Tatarkiewicz, "Perfection in Physics and Chemistry", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 139.

A perfectly black body would be one that absorbed, completely, radiation falling upon it.Władysław Tatarkiewicz, "Perfection in Physics and Chemistry", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 139.

A perfect fluid would be one that is incompressible and non-viscous.Władysław Tatarkiewicz, "Perfection in Physics and Chemistry", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 139.

A perfect gas would be one whose molecules did not interact with each other and had no volume of their own.Władysław Tatarkiewicz, "Perfection in Physics and Chemistry", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 139.

All these are fictitious ideals that do not exist in nature. They are useful insofar as they set physical extremes which nature can only approach asymptotically.Władysław Tatarkiewicz, "Perfection in Physics and Chemistry", Dialectics and Humanism, vol. VII, no. 2 (spring 1980), p. 139.

Ethics

The ancient Greek philosopher Plato (born ca. 428–423 BCE, died ca. 347 BCE) seldom used the term "perfection", but the concept of "the good", central to his philosophy, was tantamount to "perfection".Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 117.

Christianity embraced the ideal of perfection. Matthew 5:48 enjoined: "Be ye therefore perfect, even as your Father which is in heaven is perfect."Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 117.

Saint Augustine (354 – 430), a Roman North African, wrote that not only that man is properly termed perfect and without blemish who is already perfect, but also he who strives unreservedly after perfection.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 118.

Some Bible voices cast doubt on whether perfection is attainable by man. 1 John 1:8 says: "If we say that we have no sin, we deceive ourselves, and the truth is not in us."Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 118.

As early as the 5th century, two distinct views on perfection had emerged within the Church: that perfection was attainable by man on earth by his own powers; and, that it may come only by special divine grace.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 119.

The 14th century saw, with the Scotists, a shift in interest from moral to ontological perfection. The 15th century, particularly during the Italian Renaissance, saw a shift to artistic perfection.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 121.

The second half of the 16th century brought the Counter-Reformation, the Council of Trent, and heroic attempts to attain perfection through contemplation and mortification of the flesh.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 121.

The first half of the 17th century saw the beginnings of Jansenism and a growing belief in predestination and in the impossibility of perfection without divine grace.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 121.

The 18th century and the Enlightenment brought a sea change to the idea of moral perfection, from religious to secular. The perfect man was he who lived in harmony with nature.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 122.

The mid-18th century saw a brief retreat from the idea of perfection, when the French Encyclopédie entry on "Perfection" discussed only technological perfection – the optimal matching of human handiworks to the tasks set for them; no mention was made of moral, aesthetic, or ontological perfection.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 123.

The 18th century otherwise saw declarations about the coming perfection of man from Immanuel Kant (1724 – 1804) and Johann Gottfried von Herder (1744 – 1803).Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 123.

Other writers, of this and following periods, who expected perfection to come about via secular processes included David Hume, John Locke, David Hartley, Claude Adrien Helvétius, Jeremy Bentham, Charles Fourier, Francis Galton, Johann Gottlieb Fichte, Georg Wilhelm Friedrich Hegel, and the 19th-century positivists and evolutionists including the polymath Herbert Spencer.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 123.

From the 20th century, writes Tatarkiewicz, the goal has been not so much perfection as improvement aimed at attaining excellence.Władysław Tatarkiewicz, "Moral Perfection", Dialectics and Humanism, vol. VII, no. 3 (summer 1980), p. 124.

Aesthetics

In ancient Greece, the 6th-century BCE Pythagoreans held that perfection in beauty and art consisted in correct proportions and in a harmonious arrangement of parts. For Plato, in the 5th and 4th centuries BCE, beauty and perfection were one.Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), p. 145. The views of these Greeks dictated that, for every art, there was but one perfect form.Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), pp. 145–146.

There was also a common belief that certain proportions and shapes were perfect in themselves. Plato felt that the most perfect proportion was the ratio of the side to the diagonal of a square.Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), p. 146.

Aristotle (384–322 BCE) regarded the circle as the perfect, most beautiful form. Roman politician and orator Cicero (106 – 43 BCE) wrote: "Two forms are the most distinctive: of solids, the sphere ... and of plane figures, the circle..."Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), p. 146.

Renaissance aesthetics placed less emphasis than had classical aesthetics on the unity of things perfect. Italian courtier Baldassare Castiglione (1478 – 1529), in his Courtier, wrote of Leonardo, Andrea Mantegna, Raphael, Michelangelo, and Giorgione, that "each of them is unlike the others, but each is the most perfect in his style."Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), p. 147.

Perfection gradually came to be seen as but one of many admirable qualities. Italian Renaissance scholar Cesare Ripa (ca. 1555 – 1622), in his Iconologia, placed perfezione on an equal footing with grace (grazia), prettiness (venustà), and beauty (bellezza).Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), p. 147.

Still, Leibniz's pupil Christian Wolff (1679 – 1754) wrote in his Psychology that beauty consisted in perfection and that this was the reason why beauty was a source of pleasure. No such general aesthetic theory, explicitly naming perfection – writes Tatarkiewicz – had ever been formulated by any of perfection's devotees from Plato to Italian Renaissance architect Andrea Palladio (1508 – 1580).Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), p. 150.

Wolff's theory of beauty-as-perfection was elaborated by the school's chief aesthetician, Alexander Gottlieb Baumgarten (1714 – 1762). Gotthold Ephraim Lessing (1729 – 1781) considered both beauty and sublimity to be ideas of perfection.Władysław Tatarkiewicz, "Aesthetic Perfection", Dialectics and Humanism, vol. VII, no. 4 (autumn 1980), p. 150.