George Berkeley (12 March 1685 – 14 January 1753), Bishop of Cloyne, was an Irish philosopher, and one of the three most famous British Empiricists (with John Locke and David Hume). He is best known for developing an early form of idealism, according to which the only things which exist are minds and the ideas which they perceive. The University of California, Berkeley, and the city that grew up around it were both named after him.
Contributions to philosophy
In An Essay towards a New Theory of Vision (1709) Berkeley set out an empirical theory of vision which challenged Descartes' account of distance vision, an account which requires geometrical calculations based on the disparity between images formed in two eyes set apart. The size of the retinal image of an object is smaller the further away that an object is, yet we do not perceive a similar change in the size of an object as it recedes - we perceive it as being of a constant size. Descartes had proposed that we constantly implicitly calculate the true size of the object by estimating its distance from us, and correcting for that - and proposed that we implicitly estimate the distance of an object by measuring the disparity of the retinal images in our two eyes. By contrast, Berkeley argued that we estimate the size of an object by using our past experience - by associating the image with what we know of the size of the object, and by our experience for example that distant things appear fainter than near things. He argued that the distance, magnitude, and shape of objects are properties which are directly perceived only by touch, so to ascribe these properties to things that we see, we must learn to associate ideas of sight and touch. This associative approach explained how distance vision can be achieved with only one eye, and the moon illusion, anomalies unexplained by the geometric account.
“It is indeed an opinion strangely prevailing amongst men, that houses, mountains, rivers […] have an existence natural or real, distinct from their being perceived by the understanding. […] For what are the forementioned objects but the things we perceive by sense, and what do we perceive besides our own ideas or sensations; and is it not plainly repugnant that any one of these or any combination of them should exist unperceived?”
Berkeley was a staunch defender of idealism, the view that reality comprises of only minds and their ideas. This committed him to immaterialism, the idea that material things independent from the mind do not exist. In his work Principles of Human Understanding, Berkeley lays out his argument for the non-existence of matter:
- We perceive objects (people, houses, mountains)
- We perceive only our own ideas and sensations
- Therefore, objects are ideas
In order to defend his viewpoint of idealism, Berkeley attempts to disprove materialism. He does this by attacking the doctrine of abstract ideas. Berkeley defines abstraction as follows:
- The mind is presented objects
- The mind can abstract (single out) properties from these objects
- The mind uses these abstract properties from individual objects to form a generalization of the object as a whole.
For example, the mind can perceive different cars. They may vary in size, color, shape, etc., but the mind can single out these properties to form the general idea of a car. Berkeley argues that this is a falsifying move. The mind abstracts existence from perception, and comes to believe that things can exist unperceived. Berkeley believes it is illogical to assume things can exist unperceived just because we can generalize objects from the properties of specific objects.
In short, Berkeleyan idealism is the viewpoint that only minds and their ideas exist. He attempts to prove this by building his own argument for immaterialism and attacking the doctrine of abstract ideas from materialism.
Berkeley and infinitesimals
"Thus Fluxions may be considered in sundry Lights and Shapes, which seem all equally difficult to conceive. And indeed, as it is impossible to conceive Velocity without time or space, without either finite length or finite Duration, [ ] it must seem above the powers of Men to comprehend even the first Fluxions. And if the first are incomprehensible, what shall we say of the second and third Fluxions, &c.? He who can conceive the beginning of a beginning, or the end of an end, somewhat before the first or after the last, may be perhaps sharpsighted enough to conceive these things. But most Men will, I believe, find it impossible to understand them in any sense whatever."
In 1734 Bishop Berkeley published a tract called The Analyst. In this, the new calculus of Newton and Leibniz was attacked and especially the concept of "fixed infinitesimal" set forth by Isaac Newton in the Principia and in an appendix to the Opticks. Since the concept of an infinitely small, and yet finite, quantity was still fairly muddled and confused, Berkeley, although not a mathematician by training, made an extremely effective attack. His arguments provoked controversy among mathematicians and led to the clarification of central ideas underlying the new theory. 
- George Berkeley (1710) A Treatise Concerning the Principles of Human Knowledge
- George Berkeley (1685—1753) Internet Encyclopedia of Philosophy
- George Berkeley (1734)THE ANALYST or, a discourse addressed to an Infidel Mathematician wherein it is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith