Editing George Berkeley (section)

==Contributions to philosophy<!--'Esse est percipi' redirects here-->==
{{Main|Subjective idealism}}
{{Blockquote|According to Berkeley there are only two kinds of things: spirits and ideas. Spirits are simple, active beings which produce and perceive ideas; ideas are passive beings which are produced and perceived.<ref>Bettcher T. M. ''Berkeley: A Guide for the Perplexed''. [[Continuum International Publishing Group|Continuum Publishing]], 2008. p. 14.</ref> }}

The use of the concepts of "spirit" and "idea" is central in Berkeley's philosophy. As used by him, these concepts are difficult to translate into modern terminology. His concept of "spirit" is close to the concept of "conscious subject" or of "mind", and the concept of "idea" is close to the concept of "sensation" or "state of mind" or "conscious experience".

Thus Berkeley denied the existence of matter as a [[metaphysics|metaphysical]] substance, but did not deny the existence of physical objects such as apples or mountains ("I do not argue against the existence of any one thing that we can apprehend, either by sense or reflection. That the things I see with mine eyes and touch with my hands do exist, really exist, I make not the least question. The only thing whose existence we deny, is that which philosophers call matter or corporeal substance. And in doing of this, there is no damage done to the rest of mankind, who, I dare say, will never miss it.", ''Principles'' #35). This basic claim of Berkeley's thought, his "idealism", is sometimes and somewhat derisively called "immaterialism" or, occasionally, [[subjective idealism]]. In ''Principles'' #3, he wrote, using a combination of Latin and English, ''esse is percipi'' (to be is to be perceived), most often if slightly inaccurately attributed to Berkeley as the pure Latin phrase '''''esse est percipi'''''<!--boldface per WP:R#PLA-->.<ref>Fogelin, Robert ''Berkeley and the Principles of Human Knowledge''. [[Routledge]], 2001. p. 27.</ref> The phrase appears associated with him in authoritative philosophical sources, e.g., "Berkeley holds that there are no such mind-independent things, that, in the famous phrase, ''esse est percipi (aut percipere)''—to be is to be perceived (or to perceive)."<ref name="SEP">Downing, Lisa, "[http://plato.stanford.edu/archives/spr2013/entries/berkeley/ George Berkeley]", The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), [[Edward N. Zalta]] (ed.). Retrieved 21 August 2013.</ref>

Hence, human knowledge is reduced to two elements: that of spirits and of ideas (''Principles'' #86). In contrast to ideas, a spirit cannot be perceived. A person's spirit, which perceives ideas, is to be comprehended intuitively by inward feeling or reflection (''Principles'' #89). For Berkeley, we have no direct 'idea' of spirits, albeit we have good reason to believe in the existence of other spirits, for their existence explains the purposeful regularities we find in experience<ref>Fogelin, Robert ''Berkeley and the Principles of Human Knowledge''. [[Routledge]], 2001. pp. 74–75.</ref> ("It is plain that we cannot know the existence of other spirits otherwise than by their operations, or the ideas by them excited in us", ''Dialogues'' #145). This is the solution that Berkeley offers to the [[problem of other minds]]. Finally, the order and purposefulness of the whole of our experience of the world and especially of nature overwhelms us into believing in the existence of an extremely powerful and intelligent spirit that causes that order. According to Berkeley, reflection on the attributes of that external spirit leads us to identify it with God. Thus a material thing such as an apple consists of a collection of ideas (shape, colour, taste, physical properties, etc.) which are caused in the spirits of humans by the spirit of God.

===Theology===
A convinced adherent of Christianity, Berkeley believed God to be present as an immediate [[Causality|cause]] of all our experiences.

{{blockquote|He did not evade the question of the external source of the diversity of the [[sense data]] at the disposal of the human individual. He strove simply to show that the causes of sensations could not be things, because what we called things, and considered without grounds to be something different from our sensations, were built up wholly from sensations. There must consequently be some other external source of the inexhaustible diversity of sensations. The source of our sensations, Berkeley concluded, could only be God; He gave them to man, who had to see in them signs and symbols that carried God's word.<ref name="The Main Trends in Philosophy">[[Teodor Oizerman|Oizerman T.I.]] [https://archive.org/details/TheMainTrendsInPhilosophy The Main Trends in Philosophy]. A Theoretical Analysis of the History of Philosophy. Moscow, 1988, p. 78.</ref>}}

Here is Berkeley's proof of the existence of God:

{{blockquote|Whatever power I may have over my own thoughts, I find the ideas actually perceived by Sense have not a like dependence on my [[Will (philosophy)|will]]. When in broad daylight I open my eyes, it is not in my power to choose whether I shall see or no, or to determine what particular objects shall present themselves to my view; and so likewise as to the hearing and other senses; the ideas imprinted on them are not creatures of my will. There is therefore some other Will or Spirit that produces them. (Berkeley. ''Principles'' #29)}}

As T. I. Oizerman explained:

{{blockquote|Berkeley's [[Subjective idealism|mystic idealism]] (as [[Immanuel Kant|Kant]] aptly christened it) claimed that nothing separated man and God (except [[materialism|materialist]] misconceptions, of course), since nature or matter did not exist as a reality independent of consciousness. The revelation of God was directly accessible to man, according to this doctrine; it was the sense-perceived world, the world of man's sensations, which came to him from on high for him to decipher and so grasp the divine purpose.<ref name="The Main Trends in Philosophy"/>}}

Berkeley believed that God is not the distant engineer of [[Isaac Newton|Newtonian]] machinery that in the fullness of time led to the growth of a tree in the university quadrangle. Rather, the perception of the tree is an idea that God's mind has produced in the mind, and the tree continues to exist in the quadrangle when "nobody" is there, simply because God is an infinite [[mind]] that perceives all.

The philosophy of [[David Hume]] concerning causality and objectivity is an elaboration of another aspect of Berkeley's philosophy. [[A.A. Luce]], the most eminent Berkeley scholar of the 20th century, constantly stressed the continuity of Berkeley's philosophy. The fact that Berkeley returned to his major works throughout his life, issuing revised editions with only minor changes, also counts against any theory that attributes to him a significant volte-face.<ref>{{Cite web |title=Berkeley, George {{!}} Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/george-berkeley-british-empiricist/ |access-date=2022-06-24}}</ref>

Yet as [[Colin Murray Turbayne]] observed, late entries found amidst Berkeley's unpublished private notes in the ''Philosophical Commentaries'' point toward his inclination to withdraw from a dogmatic form of ontological idealism in order to adopt a more skeptical attitude toward the existence of an active, universal substantial mind such as God.<ref name="books.google.com">[https://books.google.com/books?id=DsKvAwAAQBAJ&dq=Colin+Murray+Turbayne&pg=PA2451 ''Dictionary of Modern American Philosophers'' Shook, John. 2005 Biography of Colin Murray Turbayne on Google Books]</ref> Here, Berkeley's "official doctrine" that "Mind is a substance." in a literal sense is accompanied by additional puzzling references to a universal "thinking substance, something unknown" (687) and "the substance of Spirit we do not know, it not being knowable" (701). In his exegesis of the term "substance", and his description of the soul as a substance in which ideas "inhere" while it "supports" ideas, Berkeley also asserts that he must "use utmost caution not to give give the least handle of offense to the Church or Church-men (715)".<ref>{{cite journal| last=Turbayne| first=C. M.| title=Berkeley's Two Concepts of Mind| journal=[[Philosophy and Phenomenological Research]]| volume=20| issue=1|  date=Sep 1959| pages=85–92| jstor=2104957| doi=10.2307/2104957}}. Repr. in {{cite book| last1=Engle| first1=Gale| last2=Taylor| first2=Gabriele| title=Berkeley's Principles of Human Knowledge: Critical Studies| location=Belmont, CA| publisher=Wadsworth| year=1968| pages=24–33}} See pp. 91-92</ref> Keeping in mind Berkeley's development of a philosophy of science and his theory of vision, this suggests that his final references to God as a universal and "substantial mind" are essentially [[metaphor|metaphorical]] in nature and indicate a willingness to diplomatically uphold a "purely substantivalist conception of the mind, confirmed by his private utterances".<ref>{{cite journal| last=Turbayne| first=C. M.| title=Berkeley's Two Concepts of Mind (Part II)| journal=[[Philosophy and Phenomenological Research]]| volume=22| issue=3|  date=March 1062| pages=383-386| jstor=2104426| doi=}}.</ref>

===Relativity arguments===
{{See also|Three Dialogues Between Hylas and Philonous}}
[[John Locke]] (Berkeley's intellectual predecessor) states that we define an object by its [[Primary/secondary quality distinction|primary and secondary qualities]]. He takes heat as an example of a secondary quality. If you put one hand in a bucket of cold water, and the other hand in a bucket of warm water, then put both hands in a bucket of lukewarm water, one of your hands is going to tell you that the water is cold and the other that the water is hot. Locke says that since two different objects (both your hands) perceive the water to be hot ''and'' cold, then the heat is not a quality of the water.

While Locke used this argument to distinguish primary from secondary qualities, Berkeley extends it to cover primary qualities in the same way. For example, he says that size is not a quality of an object because the size of the object depends on the distance between the observer and the object, or the size of the observer. Since an object is a different size to different observers, then size is not a quality of the object. Berkeley rejects shape with a similar argument and then asks: if neither primary qualities nor secondary qualities are of the object, then how can we say that there is anything more than the qualities we observe?{{clarify|reason=are size and shape the only qualities in this context?|date=October 2016|}}

Relativity is the idea that there is no objective, universal truth; it is a state of dependence in which the existence of one independent object is solely dependent on that of another. According to Locke, characteristics of primary qualities are mind-independent, such as shape, size, etc., whereas secondary qualities are mind-dependent, for example, taste and colour. George Berkeley refuted John Locke's belief on primary and secondary qualities because Berkeley believed that "we cannot abstract the primary qualities (e.g shape) from secondary ones (e.g colour)".<ref name="George Berkeley">{{cite web |last1=Downing |first1=Lisa |title=George Berkeley |url=http://plato.stanford.edu/entries/berkeley/#Bib |website=Stanford Encyclopedia of Philosophy |publisher=Stanford University |access-date=11 December 2019}}</ref> Berkeley argued that perception is dependent on the distance between the observer and the object, and "thus, we cannot conceive of mechanist material bodies which are extended but not (in themselves) colored".<ref name="George Berkeley"/> What perceived can be the same type of quality, but completely opposite from each other because of different positions and perceptions, what we perceive can be different even when the same types of things consist of contrary qualities. Secondary qualities aid in people's conception of primary qualities in an object, like how the colour of an object leads people to recognize the object itself. More specifically, the colour red can be perceived in apples, strawberries, and tomatoes, yet we would not know what these might look like without its colour. We would also be unaware of what the colour red looked like if red paint, or any object that has a perceived red colour, failed to exist. From this, we can see that colours cannot exist on their own and can solely represent a group of perceived objects. Therefore, both primary and secondary qualities are mind-dependent: they cannot exist without our minds.
 
George Berkeley was a philosopher who opposed [[rationalism]] and "classical" [[empiricism]]. He was a "[[Subjective idealism|subjective idealist]]" or "empirical idealist", who believed that reality is constructed entirely of immaterial, conscious minds and their ideas; everything that exists is somehow dependent on the subject perceiving it, except the subject themselves. He refuted the existence of abstract objects that many other philosophers believed to exist, notably Plato. According to Berkeley, "an abstract object does not exist in space or time and which is therefore entirely non-physical and non-mental";<ref name="Platonism in Metaphysics">{{cite web |last1=Balaguer |first1=Mark |title=Platonism in Metaphysics |date=12 May 2004 |url=https://plato.stanford.edu/archives/spr2016/entries/platonism/ |access-date=11 December 2019}}</ref> however, this argument contradicts his relativity argument. If "esse est percipi",<ref>{{cite book |last1=George |first1=Berkeley |title=The Works of George Berkeley, Bishop of Cloyne |publisher=London: Thomas Nelson and Sons |access-date=11 December 2019|url=https://www.gutenberg.org/files/39746/39746-pdf.pdf}}</ref> (Latin meaning that to exist is to be perceived) is true, then the objects in the relativity argument made by Berkeley can either exist or not. Berkeley believed that only the minds' perceptions and the Spirit that perceives are what exists in reality; what people perceive every day is only the idea of an object's existence, but the objects themselves are not perceived. Berkeley also discussed how, at times, materials cannot be perceived by oneself, and the mind of oneself cannot understand the objects. However, there also exists an "omnipresent, eternal mind"<ref>{{cite web |title=The Cambridge History of English and American Literature in 18 Volumes (1907–21). |date=26 June 2022 |url=https://www.bartleby.com/219/1106.html}}</ref> that Berkeley believed to consist of God and the Spirit, both omniscient and all-perceiving. According to Berkeley, God is the entity who controls everything, yet Berkeley also argued that "abstract object[s] do not exist in space or time".<ref name="Platonism in Metaphysics"/> In other words, as Warnock argues, Berkeley "had recognized that he could not square with his own talk of ''spirits'', of our minds and of God; for these are perceivers and not among objects of perception. Thus he says, rather weakly and without elucidation, that in addition to our ideas, we also have ''notions''—we know what it means to speak of ''spirits'' and their operations."<ref>G. Warnock, Introduction to G. Berkeley, ''A Treatise Concerning the Principles of Human Knowledge'', Open Court La Salle, 1986, p. 29.</ref>

However, the relativity argument violates the idea of immaterialism. Berkeley's immaterialism argues that "esse est percipi (aut percipere)",<ref>{{cite book |last1=George |first1=Berkeley |title=The Works of George Berkeley, Bishop of Cloyne |publisher=London: Thomas Nelson and Sons |access-date=9 December 2019|url=https://www.gutenberg.org/files/39746/39746-pdf.pdf}}</ref> which in English is: to be is to be perceived (or to perceive). That is saying only what is perceived or perceived is real, and without our perception or God's nothing can be real. Yet, if the relativity argument, also by Berkeley, argues that the perception of an object depends on the different positions, then this means that what is perceived can either be real or not because the perception does not show that whole picture and the whole picture cannot be perceived. Berkeley also believes that "when one perceives mediately, one perceives one idea by means of perceiving another".<ref>{{cite web |title=George Berkeley (1685–1753) |url=http://www.iep.utm.edu/berkeley/#H2 |website=Internet Encyclopedia of Philosophy |access-date=9 December 2019}}</ref> By this, it can be elaborated that if the standards of what perceived at first are different, what perceived after that can be different, as well. In the heat perception described above, one hand perceived the water to be hot and the other hand perceived the water to be cold due to relativity. If applying the idea "to be is to be perceived", the water should be both cold and hot because both perceptions are perceived by different hands. However, the water cannot be cold and hot at the same time for it self-contradicts, so this shows that what perceived is not always true because it sometimes can break the law of noncontradiction. In this case, "it would be arbitrary anthropocentrism to claim that humans have special access to the true qualities of objects".<ref name=sep>{{cite web |last1=Downing |first1=Lisa |title=George Berkeley |url=http://plato.stanford.edu/entries/berkeley/#Bib |website=Stanford Encyclopedia of Philosophy |publisher=Stanford University |access-date=9 December 2019}}</ref> The truth for different people can be different, and humans are limited to accessing the absolute truth due to relativity. Summing up, nothing can be absolutely true due to relativity or the two arguments, to be is to be perceived and the relativity argument, do not always work together.

===New theory of vision===
In his ''Essay Towards a New Theory of Vision'', Berkeley frequently criticised the views of the Optic Writers, a title that seems to include [[William Molyneux|Molyneux]], Wallis, [[Nicolas Malebranche|Malebranche]] and [[René Descartes|Descartes]].<ref>Schwartz, R, 1994. Vision: Variations on some Berkeleian themes. Oxford: Blackwell, p. 54.</ref> In sections 1–51, Berkeley argued against the classical scholars of optics by holding that: ''spatial depth, as the distance that separates the perceiver from the perceived object is itself invisible''. That is, we do not see space directly or deduce its form logically using the laws of optics. Space for Berkeley is no more than a contingent expectation that visual and tactile sensations will follow one another in regular sequences that we come to expect through habit.

Berkeley goes on to argue that visual cues, such as the perceived extension or 'confusion' of an object, can only be used to indirectly judge distance, because the viewer learns to associate visual cues with tactile sensations. Berkeley gives the following analogy regarding indirect distance perception: one perceives distance indirectly just as one perceives a person's embarrassment indirectly. When looking at an embarrassed person, we infer indirectly that the person is embarrassed by observing the red colour on the person's face. We know through experience that a red face tends to signal embarrassment, as we've learned to associate the two.

The question concerning the visibility of space was central to the Renaissance [[Perspective (graphical)|perspective]] tradition and its reliance on classical optics in the development of pictorial representations of spatial depth. This matter has been debated by scholars since the 11th-century Arab polymath and mathematician [[Alhazen]] (Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham) affirmed in experimental contexts the visibility of space. This issue, which was raised in Berkeley's theory of vision, was treated at length in the ''Phenomenology of Perception'' of [[Maurice Merleau-Ponty]], in the context of confirming the visual perception of spatial depth (''la profondeur''), and by way of refuting Berkeley's thesis.<ref>For recent studies on this topic refer to: [[Nader El-Bizri]], 'La perception de la profondeur: [[Alhazen]], Berkeley et Merleau-Ponty', ''Oriens-Occidens: Cahiers du centre d'histoire des sciences et des philosophies arabes et médiévales'', [[Centre National de la Recherche Scientifique]] Vol. 5 (2004), pp. 171–84.  See also: [[Nader El-Bizri]], "A Philosophical Perspective on Alhazen's Optics", ''Arabic Sciences and Philosophy'', Vol. 15 (2005), pp. 189–218 ([[Cambridge University Press]] journal), {{doi|10.1017/S0957423905000172}}.</ref>

Berkeley wrote about the perception of size in addition to that of distance. He is frequently misquoted as believing in size–distance invariance—a view held by the Optic Writers. This idea is that we scale the image size according to distance in a geometrical manner. The error may have become commonplace because the eminent historian and psychologist [[Edwin Boring|E. G. Boring]] perpetuated it.<ref>Boring E. G., 1942. Sensation and perception in the history of experimental psychology. New York: Appleton-Century-Crofts, pp.&nbsp;223, 298.</ref> In fact, Berkeley argued that the same cues that evoke distance also evoke size, and that we do not first see size and then calculate distance.<ref>Ross H. E., Plug, C., 1998. "The history of size constancy and size illusions." In Walsh, V. & Kulikowski, J. (Eds). ''Perceptual constancy: Why things look as they do''. Cambridge: Cambridge University Press, 499–528.</ref> It is worth quoting Berkeley's words on this issue (Section 53):
<blockquote>What inclines men to this mistake (beside the humour of making one see by geometry) is, that the same perceptions or ideas which suggest distance, do also suggest magnitude ... I say they do not first suggest distance, and then leave it to the judgement to use that as a medium, whereby to collect the magnitude; but they have as close and immediate a connexion with the magnitude as with the distance; and suggest magnitude as independently of distance, as they do distance independently of magnitude.</blockquote>

Berkeley claimed that his visual theories were "vindicated" by a 1728 report regarding the recovery of vision in a 13-year-old boy operated for congenital cataracts by surgeon William Cheselden. In 2021, the name of Cheselden's patient was published for the first time: Daniel Dolins.<ref name=":10">{{cite journal|last1=Leffler|first1=CT|last2=Schwartz|first2=SG|date=February 2021|title=The First Cataract Surgeons in the British Isles|url=https://www.researchgate.net/publication/350148285|journal=American Journal of Ophthalmology|volume=230|pages=75–122|doi=10.1016/j.ajo.2021.03.009|pmid=33744237|pmc=8446104}}</ref> Berkeley knew the Dolins family, had numerous social links to Cheselden, including the poet Alexander Pope, and Princess Caroline, to whom Cheselden's patient was presented.<ref name=":10" /> The report misspelt Cheselden's name, used language typical of Berkeley, and may even have been ghost-written by Berkeley.<ref name=":10" /> Unfortunately, Dolins was never able to see well enough to read, and there is no evidence that the surgery improved Dolins' vision at any point prior to his death at age 30.<ref name=":10" />

===Philosophy of physics===
{{See also|De Motu (Berkeley's essay)}}
"Berkeley's works display his keen interest in natural philosophy [...] from his earliest writings (''Arithmetica'', 1707) to his latest (''Siris'', 1744). Moreover, much of his philosophy is shaped fundamentally by his engagement with the science of his time."<ref>{{Cite book |author=Lisa Downing |editor=[[Kenneth P. Winkler]] |title=The Cambridge Companion to Berkeley |chapter=Berkeley's natural philosophy and philosophy of science |publisher=Cambridge University Press |location=Cambridge |page=230 |year=2005 |isbn=978-0-521-45033-1 |chapter-url=https://books.google.com/books?id=ER3vQcE1v9AC&pg=PA230}}</ref> The profundity of this interest can be judged from numerous entries in Berkeley's ''Philosophical Commentaries'' (1707–1708), e.g. "Mem. to Examine & accurately discuss the scholium of the 8th Definition of Mr Newton's Principia." (#316)

Berkeley argued that forces and gravity, as defined by Newton, constituted "occult qualities" that "expressed nothing distinctly". He held that those who posited "something unknown in a body of which they have no idea and which they call the principle of motion, are in fact simply stating that the principle of motion is unknown". Therefore, those who "affirm that active force, action, and the principle of motion are really in bodies are adopting an opinion not based on experience".<ref>De Motu, in Berkeley, George, and Jessop, T.&nbsp;E. The Works of George Berkeley, Bishop of Cloyne. London: Thomas Nelson and Son Ltd., 1948–1957, 4:36–37.</ref> Forces and gravity existed nowhere in the phenomenal world. On the other hand, if they resided in the category of "soul" or "incorporeal thing", they "do not properly belong to physics" as a matter. Berkeley thus concluded that forces lay beyond any kind of empirical observation and could not be a part of proper science.<ref>Downing, Lisa. Berkeley's Case Against Realism About Dynamics. In Robert G. Muehlmann (ed.), Berkeley's Metaphysics: Structural, Interpretive, and Critical Essays. The Pennsylvania State University Press, 1995.</ref> He proposed his theory of signs as a means to explain motion and matter without reference to the "occult qualities" of force and gravity.

===Berkeley's razor===
'''Berkeley's razor''' is a rule of reasoning proposed by the philosopher [[Karl Popper]] in his study of Berkeley's key scientific work ''De Motu''.<ref name="Berkeley's Philosophical Writings 1974"/> Berkeley's razor is considered by Popper to be similar to [[Ockham's razor]] but "more powerful". It represents an extreme, [[Empiricism|empiricist]] view of scientific observation that states that the scientific method provides us with no true insight into the nature of the world. Rather, the scientific method gives us a variety of partial explanations about regularities that hold in the world and that are gained through experiments. The nature of the world, according to Berkeley, is only approached through proper [[Metaphysics|metaphysical]] speculation and reasoning.<ref>"To be of service to reckoning and mathematical demonstrations is one thing, to set forth the nature of things is another" (''De Motu''), cited by G. Warnock in the introduction to ''A Treatise Concerning the Principles of Human Knowledge'', Open Court La Salle, 1986, p. 24.</ref> Popper summarises Berkeley's razor as such:
<blockquote>A general practical result—which I propose to call "Berkeley's razor"—of [Berkeley's] analysis of physics allows us ''a priori'' to eliminate from physical science all [[Essentialism|essentialist]] explanations. If they have a mathematical and predictive content they may be admitted ''qua'' mathematical hypotheses (while their essentialist interpretation is eliminated). If not they may be ruled out altogether. This razor is sharper than Ockham's: ''all'' entities are ruled out except those which are perceived.<ref>Karl Popper, ''Conjectures and Refutations: The Growth of Scientific Knowledge'', New York: Routledge, 2002, p. 231.</ref></blockquote>

In another essay of the same book<ref>K. Popper ''Conjectures and Refutations'', Part I, 3.</ref> titled "Three Views Concerning Human Knowledge", Popper argues that Berkeley is to be considered as an [[Instrumentalism|instrumentalist]] philosopher, along with [[Robert Bellarmine]], [[Pierre Duhem]] and [[Ernst Mach]]. According to this approach, scientific theories have the status of serviceable fictions, useful inventions aimed at explaining facts, and without any pretension to being true. Popper contrasts instrumentalism with the above-mentioned essentialism and his own "[[critical rationalism]]".

===Philosophy of mathematics===
In addition to his contributions to philosophy, Berkeley was also very influential in the development of [[mathematics]], although in a rather indirect sense. "Berkeley was concerned with mathematics and its philosophical interpretation from the earliest stages of his intellectual life."<ref name=Jesseph>{{Cite book|author= Douglas M. Jesseph| editor= Kenneth P. Winkler |title= The Cambridge Companion to Berkeley |publisher= Cambridge University Press |location= Cambridge |chapter= Berkeley's philosophy of mathematics|page= 266 |year= 2005 |isbn= 978-0-521-45033-1 |url= https://books.google.com/books?id=ER3vQcE1v9AC}}</ref> Berkeley's "Philosophical Commentaries" (1707–1708) witness to his interest in mathematics:
<blockquote>
Axiom. No reasoning about things whereof we have no idea. Therefore no reasoning about Infinitesimals. (#354)

Take away the signs from Arithmetic & Algebra, & pray what remains? (#767)
These are sciences purely Verbal, & entirely useless but for Practise in Societys of Men. No speculative knowledge, no comparison of Ideas in them. (#768)</blockquote>
In 1707, Berkeley published two treatises on mathematics. In 1734, he published ''[[The Analyst]]'', subtitled ''A DISCOURSE Addressed to an Infidel Mathematician'', a critique of [[calculus]]. [[Florian Cajori]] called this treatise "the most spectacular event of the century in the history of British mathematics."<ref>{{Cite book|author= Florian Cajori |title= A History of the Conceptions of Limits and Fluxions in Great Britain, from Newton to Woodhouse  |url= https://books.google.com/books?id=3YAVRAAACAAJ&q=cajori+%22history+of+the+conceptions+of+limits%22 |publisher= BiblioBazaar |year= 2010 |isbn= 978-1-143-05698-7|author-link= Florian Cajori }}</ref> However, a recent study suggests that Berkeley misunderstood Leibnizian calculus.<ref>{{citation
 | last1 = Katz | first1 = Mikhail
 | author1-link = Mikhail Katz
 | last2 = Sherry | first2 = David
 | s2cid = 119329569
 | author2-link = David Sherry (philosopher)
 | arxiv = 1205.0174
 | doi = 10.1007/s10670-012-9370-y
 | issue =3
 | journal = [[Erkenntnis]]
 | pages =571–625
 | title = Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond
 | volume =78
 | year = 2012}}</ref> The mathematician in question is believed to have been either [[Edmond Halley]], or [[Isaac Newton]] himself—though if to the latter, then the discourse was posthumously addressed, as Newton died in 1727. ''The Analyst'' represented a direct attack on the foundations and principles of [[calculus]] and, in particular, the notion of [[Method of Fluxions|fluxion]] or [[infinitesimal]] change, which Newton and [[Gottfried Leibniz|Leibniz]] used to develop the calculus. In his critique, Berkeley coined the phrase "[[ghosts of departed quantities]]", familiar to students of calculus. [[Ian Stewart (mathematician)|Ian Stewart]]'s book [[From Here to Infinity (book)|''From Here to Infinity'']] captures the gist of his criticism.

Berkeley regarded his criticism of calculus as part of his broader campaign against the religious implications of Newtonian mechanics{{spaced ndash}}as a defence of traditional Christianity against [[deism]], which tends to distance God from His worshipers. Specifically, he observed that both Newtonian and Leibnizian calculus employed infinitesimals sometimes as positive, nonzero quantities and other times as a number explicitly equal to zero. Berkeley's key point in "The Analyst" was that Newton's calculus (and the laws of motion based on calculus) lacked rigorous theoretical foundations. He claimed that:
<blockquote>
In every other Science Men prove their Conclusions by their Principles, and not their Principles by the Conclusions. But if in yours you should allow your selves this unnatural way of proceeding, the Consequence would be that you must take up with Induction, and bid adieu to Demonstration. And if you submit to this, your Authority will no longer lead the way in Points of Reason and Science.<ref>The Analyst, in Berkeley, George, and Jessop, T.E. The Works of George Berkeley, Bishop of Cloyne. London: Thomas Nelson and Son Ltd., 1948–1957, 4:76</ref>
</blockquote>

Berkeley did not doubt that calculus produced real-world truth; simple physics experiments could verify that Newton's method did what it claimed to do. "The cause of Fluxions cannot be defended by reason",<ref>Defence of Free-Thinking in Mathematics, in Berkeley, George, and Jessop, T.E. The Works of George Berkeley, Bishop of Cloyne. London: Thomas Nelson and Son Ltd., 1948–1957, 4:113</ref> but the results could be defended by empirical observation, Berkeley's preferred method of acquiring knowledge at any rate. Berkeley, however, found it paradoxical that "Mathematicians should deduce true Propositions from false Principles, be right in Conclusion, and yet err in the Premises." In ''The Analyst'' he endeavoured to show "how Error may bring forth Truth, though it cannot bring forth Science".<ref>The Analyst, in Berkeley, George, and Jessop, T.E. The Works of George Berkeley, Bishop of Cloyne. London: Thomas Nelson and Son Ltd., 1948–1957, 4:77</ref> Newton's science, therefore, could not on purely scientific grounds justify its conclusions, and the mechanical, deistic model of the universe could not be rationally justified.<ref>Cantor, Geoffrey. "Berkeley's The Analyst Revisited". ''Isis'', Vol. 75, No. 4 (Dec. 1984), pp. 668–83. {{JSTOR|232412}}. {{doi|10.1086/353648}}.</ref>

The difficulties raised by Berkeley were still present in the work of [[Cauchy]] whose approach to calculus was a combination of infinitesimals and a notion of limit, and were eventually sidestepped by [[Weierstrass]] by means of his [[(ε, δ)-definition of limit|(ε, δ)]] approach, which eliminated infinitesimals altogether. More recently, [[Abraham Robinson]] restored infinitesimal methods in his 1966 book ''[[Non-standard analysis]]'' by showing that they can be used rigorously.

===Moral philosophy===
{{See also|Passive obedience}}
The tract ''A Discourse on Passive Obedience'' (1712) is considered Berkeley's major contribution to moral and political philosophy.

In ''A Discourse on Passive Obedience'', Berkeley defends the thesis that people have "a moral duty to observe the negative precepts (prohibitions) of the law, including the duty not to resist the execution of punishment."<ref name=":0">Häyry, Matti. "[http://berkeleystudies.philosophy.fsu.edu/content/download/95864/978821/file/BS_023 ''Passive Obedience'' and Berkeley's Moral Philosophy]." Berkeley Studies 23 (2012): 3–13.</ref> However, Berkeley does make exceptions to this sweeping moral statement, stating that we need not observe precepts of "usurpers or even madmen"<ref>Berkeley, George. Passive Obedience: Or, the Christian Doctrine of Not Resisting the Supreme Power, Proved and Vindicated ... In a Discourse Deliver'd at the College-chapel. By George Berkeley, M.A. Fellow of Trinity College, Dublin. London: Printed for H. Clements, 1712. Print.</ref> and that people can obey different supreme authorities if there are more than one claims to the highest authority.

Berkeley defends this thesis with deductive proof stemming from the laws of nature. First, he establishes that because God is perfectly good, the end to which he commands humans must also be good, and that end must not benefit just one person, but the entire human race. Because these commands—or laws—if practised, would lead to the general fitness of humankind, it follows that they can be discovered by the right reason—for example, the law to never resist supreme power can be derived from reason because this law is "the only thing that stands between us and total disorder".<ref name=":0" /> Thus, these laws can be called the [[Natural law|laws of nature]], because they are derived from God—the creator of nature himself. "These laws of nature include duties never to resist the supreme power, lie under oath ... or do evil so that good may come of it."<ref name=":0" />

One may view Berkeley's doctrine on Passive Obedience as a kind of 'Theological Utilitarianism', insofar as it states that we have a duty to uphold a moral code which presumably is working towards the ends of promoting the good of humankind. However, the concept of 'ordinary' [[utilitarianism]] is fundamentally different in that it "makes utility the one and only ''ground'' of obligation"<ref>{{Cite web|url=http://www.ditext.com/broad/berkeley.html|title=Berkeley's Theory of Morals|website=ditext.com|access-date=27 May 2016}}</ref>—that is, Utilitarianism is concerned with whether particular actions are morally permissible in specific situations, while Berkeley's doctrine is concerned with whether or not we should follow moral rules in any and all circumstances. Whereas [[Act Utilitarianism|act utilitarianism]] might, for example, justify a morally impermissible act in light of the specific situation, Berkeley's doctrine of Passive Obedience holds that it is never morally permissible to not follow a moral rule, even when it seems like breaking that moral rule might achieve the happiest ends. Berkeley holds that even though sometimes, the consequences of an action in a specific situation might be bad, the general tendencies of that action benefit humanity.

Other important sources for Berkeley's views on morality are ''[[Alciphron (book)|Alciphron]]'' (1732), especially dialogues I–III, and the ''Discourse to Magistrates'' (1738)."<ref>Jakapi, Roomet. "Was Berkeley a [[Utilitarianism|Utilitarian]]?" // Lemetti, Juhana and Piirimäe, Eva, eds. Human Nature as the Basis of Morality and Society in Early Modern Philosophy. [[Acta Philosophica Fennica]] 83. Helsinki: ''Philosophical Society of Finland, 2007''. p. 53. (The article contains an extensive cover of literature on the topic from [[Alexander Campbell Fraser]] to up-to-date investigations including [[Matti Häyry]]'s article on Berkeley's ethics.)</ref> ''Passive Obedience'' is notable partly for containing one of the earliest statements of [[rule utilitarianism]].<ref>[[Brad Hooker|Hooker, Brad]] (2008). [http://plato.stanford.edu/entries/consequentialism-rule/ "Rule Consequentialism."] In ''[[Stanford Encyclopedia of Philosophy]]''.</ref>

===Immaterialism===
George Berkeley’s theory that matter does not exist comes from the belief that "sensible things are those only which are immediately perceived by sense."<ref>Berkeley, George, and Howard Robinson. Principles of Human Knowledge and Three Dialogues. Oxford, Oxford University Press, 2009.</ref> Berkeley says in his book called ''Principles of Human Knowledge'' that "the ideas of sense are stronger, livelier, and clearer than those of the imagination; and they are also steady, orderly and coherent."<ref name=":4">Berkeley, George. "Principles of Human Knowledge." The Empiricists: Locke, Berkeley, and Hume. Anchor Books, 1974, pp. 151–62.</ref> From this we can tell that the things that we are perceiving are truly real rather than it just being a dream.

All knowledge comes from perception; what we perceive are ideas, not things in themselves; a thing in itself must be outside experience; so the world only consists of ideas and minds that perceive those ideas; a thing only exists so far as it perceives or is perceived.<ref name=":1">Buckingham, Will. "To Be Is To Be Perceived". ''The Philosophy Book: Big Ideas Simply Explained'', DK Publishing, New York, 2011, pp. 138–41.</ref> Through this we can see that consciousness is considered something that exists to Berkeley due to its ability to perceive. "'To be,' said of the object, means to be perceived, 'esse est percipi'; 'to be', said of the subject, means to perceive or 'percipere'."<ref>The Editors of Encyclopædia Britannica. [https://www.britannica.com/biography/George-Berkeley "George Berkeley"]. Encyclopædia Britannica, Encyclopædia Britannica, Inc., 2012. Accessed 15 March 2017.</ref> Having established this, Berkeley then attacks the "opinion strangely prevailing amongst men, that houses, mountains, rivers, and in a word all sensible objects have an existence natural or real, distinct from being perceived".<ref name=":4" /> He believes this idea to be inconsistent because such an object with an existence independent of perception must have both sensible qualities, and thus be known (making it an idea), and also an insensible reality, which Berkeley believes is inconsistent.<ref>Flage, Daniel E. "George Berkeley". Internet Encyclopedia of Philosophy, www.iep.utm.edu/berkeley. Accessed 20 May 2019.</ref> Berkeley believes that the error arises because people think that perceptions can imply or infer something about the material object. Berkeley calls this concept ''abstract ideas''. He rebuts this concept by arguing that people cannot conceive of an object without also imagining the sensual input of the object. He argues in ''Principles of Human Knowledge'' that, similar to how people can only sense matter with their senses through the actual sensation, they can only conceive of matter (or, rather, ideas of matter) through the idea of sensation of matter.<ref name=":4" /> This implies that everything that people can conceive in regards to matter is only ideas about matter. Thus, matter, should it exist, must exist as collections of ideas, which can be perceived by the senses and interpreted by the mind. But if matter is just a collection of ideas, then Berkeley concludes that matter, in the sense of a material substance, does not exist as most philosophers of Berkeley's time believed. Indeed, if a person visualizes something, then it must have some colour, however dark or light; it cannot just be a shape of no colour at all if a person is to visualize it.<ref name=":2">Urmson, J. O., et al. "The Attack on Matter". ''British Empiricists'', Oxford University Press, Oxford, 1992, pp. 106–24.</ref>

Berkeley's ideas raised controversy because his argument refuted [[René Descartes|Descartes]]' philosophy, which was expanded upon by Locke, and resulted in the rejection of Berkeley's form of empiricism by several philosophers of the eighteenth century. In Locke's philosophy, "the world causes the perceptual ideas we have of it by the way it interacts with our senses."<ref name=":1" /> This contradicts with Berkeley's philosophy because not only does it suggest the existence of physical causes in the world, but in fact, there is no physical world beyond our ideas. The only causes that exist in Berkeley's philosophy are those that are a result of the use of the will.

Berkeley's theory relies heavily on his form of [[empiricism]], which in turn relies heavily on the senses. His empiricism can be defined by five propositions: all significant words stand for ideas; all knowledge of things is about ideas; all ideas come from without or from within; if from without it must be by the senses, and they are called sensations (the real things), if from within they are the operations of the mind, and are called thoughts.<ref name=":2" /> Berkeley clarifies his distinction between ideas by saying they "are imprinted on the senses," "perceived by attending to the passions and operations of the mind," or "are formed by help of memory and imagination."<ref name=":2" /> One refutation of his idea was: if someone leaves a room and stops perceiving that room does that room no longer exist? Berkeley answers this by claiming that it is still being perceived and the consciousness that is doing the perceiving is [[God]]. (This makes Berkeley's argument hinge upon an [[Omniscience|omniscient]], [[Omnipresence|omnipresent]] deity.) This claim is the only thing holding up his argument which is "depending for our knowledge of the world, and of the existence of other minds, upon a God that would never deceive us."<ref name=":1" /> Berkeley anticipates a second objection, which he refutes in ''Principles of Human Knowledge''. He anticipates that the materialist may take a representational materialist standpoint: although the senses can only perceive ideas, these ideas resemble (and thus can be compared to) the actual, existing object. Thus, through the sensing of these ideas, the mind can make inferences as to matter itself, even though pure matter is non-perceivable. Berkeley's objection to that notion is that "an idea can be like nothing but an idea; a colour or figure can be like nothing but another colour or figure".<ref name=":4" /> Berkeley distinguishes between an idea, which is mind-dependent, and a material substance, which is not an idea and is mind-independent. As they are not alike, they cannot be compared, just as one cannot compare the colour red to something that is invisible, or the sound of music to silence, other than that one exists and the other does not. This is called the likeness principle: the notion that an idea can only be like (and thus compared to) another idea.

Berkeley attempted to show how ideas manifest themselves into different objects of knowledge:

{{blockquote|It is evident to anyone who takes a survey of the objects of human knowledge, that they are either ''ideas'' actually imprinted on the senses; or else such as are perceived by attending to the passions and operations of the mind; or lastly ''ideas'' formed by help of memory and imagination—either compounding, dividing, or barely representing those originally perceived in the aforesaid ways". (Berkeley's emphasis.)<ref>George Berkeley, ''A Treatise Concerning the Principles of Human Knowledge'', Open Court La Salle, 1986, p. 65.</ref>}}

Berkeley also attempted to prove the existence of God throughout his beliefs in immaterialism.<ref name=sep/>