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Thursday, August 6, 2020

Douglas Hofstadter

From Wikipedia, the free encyclopedia
 
Douglas Hofstadter
Hofstadter2002.jpg
Hofstadter in Bologna, Italy, in 2002
Born
Douglas Richard Hofstadter

February 15, 1945 (age 75)
New York City, United States
NationalityAmerican
EducationStanford University (BSc)
University of Oregon (PhD, 1974)
Known forGödel, Escher, Bach
I Am a Strange Loop
Hofstadter's butterfly
Hofstadter's law
Spouse(s)Carol Ann Brush (1985–1993; her death; 2 children)
Baofen Lin (2012–present)
AwardsNational Book Award
Pulitzer Prize
Member of the American Academy of Arts and Sciences
Golden Plate Award of the American Academy of Achievement
Scientific career
FieldsCognitive science
Philosophy of mind
Translation
Physics
InstitutionsIndiana University
Stanford University
University of Oregon
University of Michigan
ThesisThe Energy Levels of Bloch Electrons in a Magnetic Field (1974)
Doctoral advisorGregory Wannier
Doctoral studentsDavid Chalmers
Robert M. French
Scott A. Jones
Melanie Mitchell
Websiteprelectur.stanford.edu/lecturers/hofstadter

Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics. His 1979 book Gödel, Escher, Bach: An Eternal Golden Braid won both the Pulitzer Prize for general nonfiction and a National Book Award (at that time called The American Book Award) for Science. His 2007 book I Am a Strange Loop won the Los Angeles Times Book Prize for Science and Technology.

Early life and education

Hofstadter was born in New York City to Jewish parents: Nobel Prize-winning physicist Robert Hofstadter and Nancy Givan Hofstadter. He grew up on the campus of Stanford University, where his father was a professor, and attended the International School of Geneva in 1958–59. He graduated with Distinction in mathematics from Stanford University in 1965, and received his Ph.D. in physics from the University of Oregon in 1975, where his study of the energy levels of Bloch electrons in a magnetic field led to his discovery of the fractal known as Hofstadter's butterfly.

Academic career

Since 1988, Hofstadter has been the College of Arts and Sciences Distinguished Professor of Cognitive Science and Comparative Literature at Indiana University in Bloomington, where he directs the Center for Research on Concepts and Cognition which consists of himself and his graduate students, forming the "Fluid Analogies Research Group" (FARG). He was initially appointed to the Indiana University's Computer Science Department faculty in 1977, and at that time he launched his research program in computer modeling of mental processes (which he called "artificial intelligence research", a label he has since dropped in favor of "cognitive science research"). In 1984, he moved to the University of Michigan in Ann Arbor, where he was hired as a professor of psychology and was also appointed to the Walgreen Chair for the Study of Human Understanding. In 1988 he returned to Bloomington as "College of Arts and Sciences Professor" in both cognitive science and computer science. He was also appointed adjunct professor of history and philosophy of science, philosophy, comparative literature, and psychology, but has said that his involvement with most of those departments is nominal. In 1988 Hofstadter received the In Praise of Reason award, the Committee for Skeptical Inquiry's highest honor. In April 2009 he was elected a Fellow of the American Academy of Arts and Sciences and a member of the American Philosophical Society. In 2010 he was elected a member of the Royal Society of Sciences in Uppsala, Sweden.

Hofstadter's many interests include music, visual art, the mind, creativity, consciousness, self-reference, translation and mathematics.

Hofstadter giving a presentation at the 2006 Singularity Summit

At the University of Michigan and Indiana University, he and Melanie Mitchell coauthored a computational model of "high-level perception"—Copycat—and several other models of analogy-making and cognition, including the Tabletop project, co-developed with Robert M. French. Hofstadter's doctoral student James Marshall subsequently extended the Copycat project under the name "Metacat".[21] The Letter Spirit project, implemented by Gary McGraw and John Rehling, aims to model artistic creativity by designing stylistically uniform "gridfonts" (typefaces limited to a grid). Other more recent models include Phaeaco (implemented by Harry Foundalis) and SeqSee (Abhijit Mahabal), which model high-level perception and analogy-making in the microdomains of Bongard problems and number sequences, respectively, as well as George (Francisco Lara-Dammer), which models the processes of perception and discovery in triangle geometry.

The pursuit of beauty has driven Hofstadter both inside and outside his professional work. He seeks beautiful mathematical patterns, beautiful explanations, beautiful typefaces, beautiful sonic patterns in poetry, etc. Hofstadter has said of himself, "I'm someone who has one foot in the world of humanities and arts, and the other foot in the world of science." He has had several exhibitions of his artwork in various university galleries. These shows have featured large collections of his gridfonts, his ambigrams (pieces of calligraphy created with two readings, either of which is usually obtained from the other by rotating or reflecting the ambigram, but sometimes simply by "oscillation", like the Necker Cube or the rabbit/duck figure of Joseph Jastrow), and his "Whirly Art" (music-inspired visual patterns realized using shapes based on various alphabets from India). Hofstadter invented the term "ambigram" in 1984; many ambigrammists have since taken up the concept.

Hofstadter collects and studies cognitive errors (largely, but not solely, speech errors), "bon mots" (spontaneous humorous quips), and analogies of all sorts, and his longtime observation of these diverse products of cognition, and his theories about the mechanisms that underlie them, have exerted a powerful influence on the architectures of the computational models he and FARG members have developed.

All FARG computational models share certain key principles, including:
  • that human thinking is carried out by thousands of independent small actions in parallel, biased by the concepts that are currently activated
  • that activation spreads from activated concepts to less activated "neighbor concepts"
  • that there is a "mental temperature" that regulates the degree of randomness in the parallel activity
  • that promising avenues tend to be explored more rapidly than unpromising ones
FARG models also have an overarching philosophy that all cognition is built from the making of analogies. The computational architectures that share these precepts are called "active symbols" architectures. 

Hofstadter's thesis about consciousness, first expressed in Gödel, Escher, Bach (GEB) but also present in several of his later books, is that it is an emergent consequence of seething lower-level activity in the brain. In GEB he draws an analogy between the social organization of a colony of ants and the mind seen as a coherent "colony" of neurons. In particular, Hofstadter claims that our sense of having (or being) an "I" comes from the abstract pattern he terms a "strange loop", an abstract cousin of such concrete phenomena as audio and video feedback that Hofstadter has defined as "a level-crossing feedback loop". The prototypical example of a strange loop is the self-referential structure at the core of Gödel's incompleteness theorems. Hofstadter's 2007 book I Am a Strange Loop carries his vision of consciousness considerably further, including the idea that each human "I" is distributed over numerous brains, rather than being limited to one.

Hofstadter's writing is characterized by an intense interaction between form and content, as exemplified by the 20 dialogues in GEB, many of which simultaneously discuss and imitate strict musical forms used by Bach, such as canons and fugues. Most of Hofstadter's books feature some kind of structural alternation: in GEB between dialogues and chapters, in The Mind's I between selections and reflections, in Metamagical Themas between Chapters and Postscripts, and so forth. In both his writing and his teaching, Hofstadter stresses the concrete, constantly using examples and analogies, and avoids the abstract. Typical of the courses he teaches is his seminar "Group Theory and Galois Theory Visualized", in which abstract mathematical ideas are rendered as concretely as possible. He puts great effort into making ideas clear and visual, and asserts that when he teaches, if his students do not understand something, it is never their fault but always his own.

Hofstadter is passionate about languages. In addition to English, his mother tongue, he speaks French and Italian fluently (the language spoken at home with his children is Italian). At various times in his life, he has studied (in descending order of level of fluency reached) German, Russian, Spanish, Swedish, Mandarin, Dutch, Polish, and Hindi. His love of sounds pushes him to strive to minimize, and ideally get rid of, any foreign accent. 

Le Ton beau de Marot: In Praise of the Music of Language is a long book devoted to language and translation, especially poetry translation, and one of its leitmotifs is a set of 88 translations of "Ma Mignonne", a highly constrained poem by 16th-century French poet Clément Marot. In this book, Hofstadter jokingly describes himself as "pilingual" (meaning that the sum total of the varying degrees of mastery of all the languages that he's studied comes to 3.14159 ...), as well as an "oligoglot" (someone who speaks "a few" languages).

In 1999, the bicentennial year of Russian poet and writer Alexander Pushkin, Hofstadter published a verse translation of Pushkin's classic novel-in-verse Eugene Onegin. He has translated many other poems too (always respecting their formal constraints), and two novels (in prose): La Chamade (That Mad Ache) by French writer Françoise Sagan, and La Scoperta dell'Alba (The Discovery of Dawn) by Walter Veltroni, the then head of the Partito Democratico in Italy. The Discovery of Dawn was published in 2007, and That Mad Ache was published in 2009, bound together with Hofstadter's essay Translator, Trader: An Essay on the Pleasantly Pervasive Paradoxes of Translation.

God

From Wikipedia, the free encyclopedia

Representation (for art or for worship) of God in (from upper left, clockwise) Christianity, Atenism, Zoroastrianism, and Balinese Hinduism.
 
In monotheistic thought, God is conceived of as the supreme being, creator deity, and principal object of faith. God is usually conceived as being omniscient (all-knowing), omnipotent (all-powerful), omnipresent (all-present) and as having an eternal and necessary existence. These attributes are used either in way of analogy or are taken literally. God is most often held to be incorporeal (immaterial). Incorporeality and corporeality of God are related to conceptions of transcendence (being outside nature) and immanence (being in nature) of God, with positions of synthesis such as the "immanent transcendence".

Some religions describe God without reference to gender, while others or their translations use terminology that is gender-specific and gender-biased.

God has been conceived as either personal or impersonal. In theism, God is the creator and sustainer of the universe, while in deism, God is the creator, but not the sustainer, of the universe. In pantheism, God is the universe itself. In atheism, there is an absence of belief in God. In agnosticism, the existence of God is deemed unknown or unknowable. God has also been conceived as the source of all moral obligation, and the "greatest conceivable existent". Many notable philosophers have developed arguments for and against the existence of God.

Monotheists refer to their gods using names prescribed by their respective religions, with some of these names referring to certain cultural ideas about their god's identity and attributes. In the ancient Egyptian era of Atenism, possibly the earliest recorded monotheistic religion, this deity was called Aten, premised on being the one "true" Supreme Being and creator of the universe. In the Hebrew Bible and Judaism, Elohim, Adonai, YHWH (Hebrew: יהוה‎) and other names are used as the names of God. Yahweh and Jehovah, possible vocalizations of YHWH, are used in Christianity. In the Christian doctrine of the Trinity, God, coexisting in three "persons", is called the Father, the Son, and the Holy Spirit. In Islam, the name Allah is used, while Muslims also have a multitude of titular names for God. In Hinduism, Brahman is often considered a monistic concept of God. In Chinese religion, Shangdi is conceived as the progenitor (first ancestor) of the universe, intrinsic to it and constantly bringing order to it. Other religions have names for the concept of God, including Baha in the Bahá'í Faith, Waheguru in Sikhism, Sang Hyang Widhi Wasa in Balinese Hinduism, and Ahura Mazda in Zoroastrianism.

Etymology and usage

The Mesha Stele bears the earliest known reference (840 BCE) to the Israelite God Yahweh

The earliest written form of the Germanic word God comes from the 6th-century Christian Codex Argenteus. The English word itself is derived from the Proto-Germanic * ǥuđan. The reconstructed Proto-Indo-European form * ǵhu-tó-m was likely based on the root * ǵhau(ə)-, which meant either "to call" or "to invoke". The Germanic words for God were originally neuter—applying to both genders—but during the process of the Christianization of the Germanic peoples from their indigenous Germanic paganism, the words became a masculine syntactic form.

The word 'Allah' in Arabic calligraphy
 
In the English language, capitalization is used for names by which a god is known, including 'God'. Consequently, the capitalized form of god is not used for multiple gods (polytheism) or when used to refer to the generic idea of a deity. The English word God and its counterparts in other languages are normally used for any and all conceptions and, in spite of significant differences between religions, the term remains an English translation common to all. The same holds for Hebrew El, but in Judaism, God is also given a proper name, the tetragrammaton YHWH, in origin possibly the name of an Edomite or Midianite deity, Yahweh. In many translations of the Bible, when the word LORD is in all capitals, it signifies that the word represents the tetragrammaton.

Allāh (Arabic: الله‎) is the Arabic term with no plural used by Muslims and Arabic speaking Christians and Jews meaning "The God" (with the first letter capitalized), while "ʾilāh" (Arabic: إِلَٰه‎, plural “`āliha” آلِهَة) is the term used for a deity or a god in general.

God may also be given a proper name in monotheistic currents of Hinduism which emphasize the personal nature of God, with early references to his name as Krishna-Vasudeva in Bhagavata or later Vishnu and Hari.

Ahura Mazda is the name for God used in Zoroastrianism. "Mazda", or rather the Avestan stem-form Mazdā-, nominative Mazdå, reflects Proto-Iranian *Mazdāh (female). It is generally taken to be the proper name of the spirit, and like its Sanskrit cognate medhā, means "intelligence" or "wisdom". Both the Avestan and Sanskrit words reflect Proto-Indo-Iranian *mazdhā-, from Proto-Indo-European mn̩sdʰeh1, literally meaning "placing (dʰeh1) one's mind (*mn̩-s)", hence "wise".

Waheguru (Punjabi: vāhigurū) is a term most often used in Sikhism to refer to God. It means "Wonderful Teacher" in the Punjabi language. Vāhi (a Middle Persian borrowing) means "wonderful" and guru (Sanskrit: guru) is a term denoting "teacher". Waheguru is also described by some as an experience of ecstasy which is beyond all descriptions. The most common usage of the word "Waheguru" is in the greeting Sikhs use with each other:
Waheguru Ji Ka Khalsa, Waheguru Ji Ki Fateh
Wonderful Lord's Khalsa, Victory is to the Wonderful Lord.
Baha, the "greatest" name for God in the Baha'i faith, is Arabic for "All-Glorious".

General conceptions

There is no clear consensus on the nature or the existence of God. The Abrahamic conceptions of God include the monotheistic definition of God in Judaism, the trinitarian view of Christians, and the Islamic concept of God.

There were also various conceptions of God in the ancient Greco-Roman world, such as Aristotle's view of an unmoved mover, the Neoplatonic concept of the One and the pantheistic God of Stoic Physics.

The dharmic religions differ in their view of the divine: views of God in Hinduism vary by region, sect, and caste, ranging from monotheistic to polytheistic. Many polytheistic religions share the idea of a creator deity, although having a name other than "God" and without all of the other roles attributed to a singular God by monotheistic religions. Sikhism is sometimes seen as being pantheistic about God, see: God in Sikhism

Śramaṇa religions are generally non-creationist, while also holding that there divine beings (called Devas in Buddhism and Jainism) of limited power and lifespan. Jainism has generally rejected creationism, holding that soul substances (Jīva) are uncreated and that time is beginningless. Depending on one's interpretation and tradition, Buddhism can be conceived as being either non-theistic, trans-theistic, pantheistic, or polytheistic. However, Buddhism has generally rejected the specific monotheistic view of a Creator God. The Buddha criticizes the theory of creationism in the early buddhist texts. Also, the major Indian Buddhist philosophers, such as such as Nagarjuna, Vasubandhu, Dharmakirti and Buddhaghosa, consistently critiqued Creator God views put forth by Hindu thinkers.

Oneness

The Trinity is the belief that God is composed of The Father, The Son (embodied metaphysically in the physical realm by Jesus), and The Holy Spirit.
 
Monotheists believe that there is only one god, and may also believe this god is worshipped in different religions under different names. The view that all theists actually worship the same god, whether they know it or not, is especially emphasized in the Bahá'í Faith, Hinduism and Sikhism.

In Christianity, the doctrine of the Trinity describes God as one God in three divine Persons (each of the three Persons is God himself). The Most Holy Trinity comprises God the Father, God the Son (Jesus), and God the Holy Spirit. In the past centuries, this fundamental mystery of the Christian faith was also summarized by the Latin formula Sancta Trinitas, Unus Deus (Holy Trinity, Unique God), reported in the Litanias Lauretanas.

Islam's most fundamental concept is tawhid meaning "oneness" or "uniqueness". God is described in the Quran as: "He is Allah, the One and Only; Allah, the Eternal, Absolute; He begetteth not, nor is He begotten; And there is none like unto Him." Muslims repudiate the Christian doctrine of the Trinity and the divinity of Jesus, comparing it to polytheism. In Islam, God is transcendent and does not resemble any of his creations in any way. Thus, Muslims are not iconodules, and are not expected to visualize God.

Henotheism is the belief and worship of a single god while accepting the existence or possible existence of other deities.

Theism, deism, and pantheism

Theism generally holds that God exists realistically, objectively, and independently of human thought; that God created and sustains everything; that God is omnipotent and eternal; and that God is personal and interacting with the universe through, for example, religious experience and the prayers of humans. Theism holds that God is both transcendent and immanent; thus, God is simultaneously infinite and, in some way, present in the affairs of the world. Not all theists subscribe to all of these propositions, but each usually subscribes to some of them (see, by way of comparison, family resemblance). Catholic theology holds that God is infinitely simple and is not involuntarily subject to time. Most theists hold that God is omnipotent, omniscient, and benevolent, although this belief raises questions about God's responsibility for evil and suffering in the world. Some theists ascribe to God a self-conscious or purposeful limiting of omnipotence, omniscience, or benevolence. Open Theism, by contrast, contends that, due to the nature of time, God's omniscience does not mean the deity can predict the future. Theism is sometimes used to refer in general to any belief in a god or gods, i.e., monotheism or polytheism.

God Blessing the Seventh Day, 1805 watercolor painting by William Blake

Deism holds that God is wholly transcendent: God exists, but does not intervene in the world beyond what was necessary to create it. In this view, God is not anthropomorphic, and neither answers prayers nor produces miracles. Common in Deism is a belief that God has no interest in humanity and may not even be aware of humanity. Pandeism combines Deism with Pantheistic beliefs. Pandeism is proposed to explain as to Deism why God would create a universe and then abandon it, and as to Pantheism, the origin and purpose of the universe.

Pantheism holds that God is the universe and the universe is God, whereas Panentheism holds that God contains, but is not identical to, the Universe. It is also the view of the Liberal Catholic Church; Theosophy; some views of Hinduism except Vaishnavism, which believes in panentheism; Sikhism; some divisions of Neopaganism and Taoism, along with many varying denominations and individuals within denominations. Kabbalah, Jewish mysticism, paints a pantheistic/panentheistic view of God—which has wide acceptance in Hasidic Judaism, particularly from their founder The Baal Shem Tov—but only as an addition to the Jewish view of a personal god, not in the original pantheistic sense that denies or limits persona to God.

Other concepts

Dystheism, which is related to theodicy, is a form of theism which holds that God is either not wholly good or is fully malevolent as a consequence of the problem of evil. One such example comes from Dostoevsky's The Brothers Karamazov, in which Ivan Karamazov rejects God on the grounds that he allows children to suffer.

In modern times, some more abstract concepts have been developed, such as process theology and open theism. The contemporaneous French philosopher Michel Henry has however proposed a phenomenological approach and definition of God as phenomenological essence of Life.

God has also been conceived as being incorporeal (immaterial), a personal being, the source of all moral obligation, and the "greatest conceivable existent". These attributes were all supported to varying degrees by the early Jewish, Christian and Muslim theologian philosophers, including Maimonides, Augustine of Hippo, and Al-Ghazali, respectively.

Non-theistic views

Non-theist views about God also vary. Some non-theists avoid the concept of God, whilst accepting that it is significant to many; other non-theists understand God as a symbol of human values and aspirations. The nineteenth-century English atheist Charles Bradlaugh declared that he refused to say "There is no God", because "the word 'God' is to me a sound conveying no clear or distinct affirmation"; he said more specifically that he disbelieved in the Christian god. Stephen Jay Gould proposed an approach dividing the world of philosophy into what he called "non-overlapping magisteria" (NOMA). In this view, questions of the supernatural, such as those relating to the existence and nature of God, are non-empirical and are the proper domain of theology. The methods of science should then be used to answer any empirical question about the natural world, and theology should be used to answer questions about ultimate meaning and moral value. In this view, the perceived lack of any empirical footprint from the magisterium of the supernatural onto natural events makes science the sole player in the natural world.

Another view, advanced by Richard Dawkins, is that the existence of God is an empirical question, on the grounds that "a universe with a god would be a completely different kind of universe from one without, and it would be a scientific difference." Carl Sagan argued that the doctrine of a Creator of the Universe was difficult to prove or disprove and that the only conceivable scientific discovery that could disprove the existence of a Creator (not necessarily a God) would be the discovery that the universe is infinitely old.

Stephen Hawking and co-author Leonard Mlodinow state in their book, The Grand Design, that it is reasonable to ask who or what created the universe, but if the answer is God, then the question has merely been deflected to that of who created God. Both authors claim however, that it is possible to answer these questions purely within the realm of science, and without invoking any divine beings.

Agnosticism and atheism

Agnosticism is the view that the truth values of certain claims—especially metaphysical and religious claims such as whether God, the divine or the supernatural exist—are unknown and perhaps unknowable.

Atheism is, in a broad sense, the rejection of belief in the existence of deities. In a narrower sense, atheism is specifically the position that there are no deities, although it can be defined as a lack of belief in the existence of any deities, rather than a positive belief in the nonexistence of any deities.

Anthropomorphism

Pascal Boyer argues that while there is a wide array of supernatural concepts found around the world, in general, supernatural beings tend to behave much like people. The construction of gods and spirits like persons is one of the best known traits of religion. He cites examples from Greek mythology, which is, in his opinion, more like a modern soap opera than other religious systems. Bertrand du Castel and Timothy Jurgensen demonstrate through formalization that Boyer's explanatory model matches physics' epistemology in positing not directly observable entities as intermediaries. Anthropologist Stewart Guthrie contends that people project human features onto non-human aspects of the world because it makes those aspects more familiar. Sigmund Freud also suggested that god concepts are projections of one's father.

Likewise, Émile Durkheim was one of the earliest to suggest that gods represent an extension of human social life to include supernatural beings. In line with this reasoning, psychologist Matt Rossano contends that when humans began living in larger groups, they may have created gods as a means of enforcing morality. In small groups, morality can be enforced by social forces such as gossip or reputation. However, it is much harder to enforce morality using social forces in much larger groups. Rossano indicates that by including ever-watchful gods and spirits, humans discovered an effective strategy for restraining selfishness and building more cooperative groups.

Existence

St. Thomas Aquinas summed up five main arguments as proofs for God's existence. Painting by Carlo Crivelli, 1476)
 
Isaac Newton saw the existence of a Creator necessary in the movement of astronomical objects. Painting by Godfrey Kneller, 1689

Arguments about the existence of God typically include empirical, deductive, and inductive types. Different views include that: "God does not exist" (strong atheism); "God almost certainly does not exist" (de facto atheism); "no one knows whether God exists" (agnosticism); "God exists, but this cannot be proven or disproven" (de facto theism); and that "God exists and this can be proven" (strong theism).

Countless arguments have been proposed to prove the existence of God. Some of the most notable arguments are the Five Ways of Aquinas, the Argument from desire proposed by C.S. Lewis, and the Ontological Argument formulated both by St. Anselm and René Descartes.

St. Anselm's approach was to define God as, "that than which nothing greater can be conceived". Famed pantheist philosopher Baruch Spinoza would later carry this idea to its extreme: "By God I understand a being absolutely infinite, i.e., a substance consisting of infinite attributes, of which each one expresses an eternal and infinite essence." For Spinoza, the whole of the natural universe is made of one substance, God, or its equivalent, Nature. His proof for the existence of God was a variation of the Ontological argument.

Scientist Isaac Newton saw the nontrinitarian God as the masterful creator whose existence could not be denied in the face of the grandeur of all creation. Nevertheless, he rejected polymath Leibniz' thesis that God would necessarily make a perfect world which requires no intervention from the creator. In Query 31 of the Opticks, Newton simultaneously made an argument from design and for the necessity of intervention:
For while comets move in very eccentric orbs in all manner of positions, blind fate could never make all the planets move one and the same way in orbs concentric, some inconsiderable irregularities excepted which may have arisen from the mutual actions of comets and planets on one another, and which will be apt to increase, till this system wants a reformation.
St. Thomas believed that the existence of God is self-evident in itself, but not to us. "Therefore I say that this proposition, "God exists", of itself is self-evident, for the predicate is the same as the subject.... Now because we do not know the essence of God, the proposition is not self-evident to us; but needs to be demonstrated by things that are more known to us, though less known in their nature—namely, by effects." St. Thomas believed that the existence of God can be demonstrated. Briefly in the Summa theologiae and more extensively in the Summa contra Gentiles, he considered in great detail five arguments for the existence of God, widely known as the quinque viae (Five Ways).

  1. Motion: Some things undoubtedly move, though cannot cause their own motion. Since there can be no infinite chain of causes of motion, there must be a First Mover not moved by anything else, and this is what everyone understands by God.
  2. Causation: As in the case of motion, nothing can cause itself, and an infinite chain of causation is impossible, so there must be a First Cause, called God.
  3. Existence of necessary and the unnecessary: Our experience includes things certainly existing but apparently unnecessary. Not everything can be unnecessary, for then once there was nothing and there would still be nothing. Therefore, we are compelled to suppose something that exists necessarily, having this necessity only from itself; in fact itself the cause for other things to exist.
  4. Gradation: If we can notice a gradation in things in the sense that some things are more hot, good, etc., there must be a superlative that is the truest and noblest thing, and so most fully existing. This then, we call God (Note: Thomas does not ascribe actual qualities to God Himself).
  5. Ordered tendencies of nature: A direction of actions to an end is noticed in all bodies following natural laws. Anything without awareness tends to a goal under the guidance of one who is aware. This we call God (Note that even when we guide objects, in Thomas's view, the source of all our knowledge comes from God as well).
Some theologians, such as the scientist and theologian A.E. McGrath, argue that the existence of God is not a question that can be answered using the scientific method. Agnostic Stephen Jay Gould argues that science and religion are not in conflict and do not overlap.

Some findings in the fields of cosmology, evolutionary biology and neuroscience are interpreted by some atheists (including Lawrence M. Krauss and Sam Harris) as evidence that God is an imaginary entity only, with no basis in reality. These atheists claim that a single, omniscient God who is imagined to have created the universe and is particularly attentive to the lives of humans has been imagined, embellished and promulgated in a trans-generational manner. Richard Dawkins interprets such findings not only as a lack of evidence for the material existence of such a God, but as extensive evidence to the contrary. However, his views are opposed by some theologians and scientists including Alister McGrath, who argues that existence of God is compatible with science.

Specific attributes

Different religious traditions assign differing (though often similar) attributes and characteristics to God, including expansive powers and abilities, psychological characteristics, gender characteristics, and preferred nomenclature. The assignment of these attributes often differs according to the conceptions of God in the culture from which they arise. For example, attributes of God in Christianity, attributes of God in Islam, and the Thirteen Attributes of Mercy in Judaism share certain similarities arising from their common roots.

Names

99 names of Allah, in Chinese Sini (script)

The word God is "one of the most complex and difficult in the English language." In the Judeo-Christian tradition, "the Bible has been the principal source of the conceptions of God". That the Bible "includes many different images, concepts, and ways of thinking about" God has resulted in perpetual "disagreements about how God is to be conceived and understood".

Many traditions see God as incorporeal and eternal, and regard him as a point of living light like human souls, but without a physical body, as he does not enter the cycle of birth, death and rebirth. God is seen as the perfect and constant embodiment of all virtues, powers and values and that he is the unconditionally loving Father of all souls, irrespective of their religion, gender, or culture.

Throughout the Hebrew and Christian Bibles there are many names for God. One of them is Elohim. Another one is El Shaddai, translated "God Almighty". A third notable name is El Elyon, which means "The High God". Also noted in the Hebrew and Christian Bibles is the name "I Am that I Am".

God is described and referred in the Quran and hadith by certain names or attributes, the most common being Al-Rahman, meaning "Most Compassionate" and Al-Rahim, meaning "Most Merciful". Many of these names are also used in the scriptures of the Bahá'í Faith.

Vaishnavism, a tradition in Hinduism, has a list of titles and names of Krishna.

Gender

The gender of God may be viewed as either a literal or an allegorical aspect of a deity who, in classical western philosophy, transcends bodily form. Polytheistic religions commonly attribute to each of the gods a gender, allowing each to interact with any of the others, and perhaps with humans, sexually. In most monotheistic religions, God has no counterpart with which to relate sexually. Thus, in classical western philosophy the gender of this one-and-only deity is most likely to be an analogical statement of how humans and God address, and relate to, each other. Namely, God is seen as begetter of the world and revelation which corresponds to the active (as opposed to the receptive) role in sexual intercourse.

Biblical sources usually refer to God using male words, except Genesis 1:26–27, Psalm 123:2–3, and Luke 15:8–10 (female); Hosea 11:3–4, Deuteronomy 32:18, Isaiah 66:13, Isaiah 49:15, Isaiah 42:14, Psalm 131:2 (a mother); Deuteronomy 32:11–12 (a mother eagle); and Matthew 23:37 and Luke 13:34 (a mother hen).

Relationship with creation

And Elohim Created Adam by William Blake, c. 1795

Prayer plays a significant role among many believers. Muslims believe that the purpose of existence is to worship God. He is viewed as a personal God and there are no intermediaries, such as clergy, to contact God. Prayer often also includes supplication and asking forgiveness. God is often believed to be forgiving. For example, a hadith states God would replace a sinless people with one who sinned but still asked repentance. Christian theologian Alister McGrath writes that there are good reasons to suggest that a "personal god" is integral to the Christian outlook, but that one has to understand it is an analogy. "To say that God is like a person is to affirm the divine ability and willingness to relate to others. This does not imply that God is human, or located at a specific point in the universe."

Adherents of different religions generally disagree as to how to best worship God and what is God's plan for mankind, if there is one. There are different approaches to reconciling the contradictory claims of monotheistic religions. One view is taken by exclusivists, who believe they are the chosen people or have exclusive access to absolute truth, generally through revelation or encounter with the Divine, which adherents of other religions do not. Another view is religious pluralism. A pluralist typically believes that his religion is the right one, but does not deny the partial truth of other religions. An example of a pluralist view in Christianity is supersessionism, i.e., the belief that one's religion is the fulfillment of previous religions. A third approach is relativistic inclusivism, where everybody is seen as equally right; an example being universalism: the doctrine that salvation is eventually available for everyone. A fourth approach is syncretism, mixing different elements from different religions. An example of syncretism is the New Age movement.

Jews and Christians believe that humans are created in the image of God, and are the center, crown and key to God's creation, stewards for God, supreme over everything else God had made (Gen 1:26); for this reason, humans are in Christianity called the "Children of God".

Depiction

Zoroastrianism

Ahura Mazda (depiction is on the right, with high crown) presents Ardashir I (left) with the ring of kingship. (Relief at Naqsh-e Rustam, 3rd century CE)

During the early Parthian Empire, Ahura Mazda was visually represented for worship. This practice ended during the beginning of the Sassanid empire. Zoroastrian iconoclasm, which can be traced to the end of the Parthian period and the beginning of the Sassanid, eventually put an end to the use of all images of Ahura Mazda in worship. However, Ahura Mazda continued to be symbolized by a dignified male figure, standing or on horseback which is found in Sassanian investiture.

Judaism

At least some Jews do not use any image for God, since God is the unimaginable Being who cannot be represented in material forms.

The burning bush that was not consumed by the flames is described in Book of Exodus as a symbolic representation of God when he appeared to Moses.

Christianity

Early Christians believed that the words of the Gospel of John 1:18: "No man has seen God at any time" and numerous other statements were meant to apply not only to God, but to all attempts at the depiction of God.

Use of the symbolic Hand of God in the Ascension from the Drogo Sacramentary, c. 850

However, later depictions of God are found. Some, like the Hand of God, are depiction borrowed from Jewish art.

The beginning of the 8th century witnessed the suppression and destruction of religious icons as the period of Byzantine iconoclasm (literally image-breaking) started. The Second Council of Nicaea in 787 effectively ended the first period of Byzantine iconoclasm and restored the honouring of icons and holy images in general. However, this did not immediately translate into large scale depictions of God the Father. Even supporters of the use of icons in the 8th century, such as Saint John of Damascus, drew a distinction between images of God the Father and those of Christ.

Prior to the 10th century no attempt was made to use a human to symbolize God the Father in Western art. Yet, Western art eventually required some way to illustrate the presence of the Father, so through successive representations a set of artistic styles for symbolizing the Father using a man gradually emerged around the 10th century AD. A rationale for the use of a human is the belief that God created the soul of Man in the image of his own (thus allowing Human to transcend the other animals).

It appears that when early artists designed to represent God the Father, fear and awe restrained them from a usage of the whole human figure. Typically only a small part would be used as the image, usually the hand, or sometimes the face, but rarely a whole human. In many images, the figure of the Son supplants the Father, so a smaller portion of the person of the Father is depicted.

By the 12th century depictions of God the Father had started to appear in French illuminated manuscripts, which as a less public form could often be more adventurous in their iconography, and in stained glass church windows in England. Initially the head or bust was usually shown in some form of frame of clouds in the top of the picture space, where the Hand of God had formerly appeared; the Baptism of Christ on the famous baptismal font in Liège of Rainer of Huy is an example from 1118 (a Hand of God is used in another scene). Gradually the amount of the human symbol shown can increase to a half-length figure, then a full-length, usually enthroned, as in Giotto's fresco of c. 1305 in Padua. In the 14th century the Naples Bible carried a depiction of God the Father in the Burning bush. By the early 15th century, the Très Riches Heures du Duc de Berry has a considerable number of symbols, including an elderly but tall and elegant full-length figure walking in the Garden of Eden, which show a considerable diversity of apparent ages and dress. The "Gates of Paradise" of the Florence Baptistry by Lorenzo Ghiberti, begun in 1425 use a similar tall full-length symbol for the Father. The Rohan Book of Hours of about 1430 also included depictions of God the Father in half-length human form, which were now becoming standard, and the Hand of God becoming rarer. At the same period other works, like the large Genesis altarpiece by the Hamburg painter Meister Bertram, continued to use the old depiction of Christ as Logos in Genesis scenes. In the 15th century there was a brief fashion for depicting all three persons of the Trinity as similar or identical figures with the usual appearance of Christ.




In an early Venetian school Coronation of the Virgin by Giovanni d'Alemagna and Antonio Vivarini (c. 1443), The Father is depicted using the symbol consistently used by other artists later, namely a patriarch, with benign, yet powerful countenance and with long white hair and a beard, a depiction largely derived from, and justified by, the near-physical, but still figurative, description of the Ancient of Days.


. ...the Ancient of Days did sit, whose garment was white as snow, and the hair of his head like the pure wool: his throne was like the fiery flame, and his wheels as burning fire. (Daniel 7:9)

Usage of two Hands of God (relatively unusual) and the Holy Spirit as a dove in Baptism of Christ by Verrocchio, 1472.
 
In the Annunciation by Benvenuto di Giovanni in 1470, God the Father is portrayed in the red robe and a hat that resembles that of a Cardinal. However, even in the later part of the 15th century, the symbolic representation of the Father and the Holy Spirit as "hands and dove" continued, e.g. in Verrocchio's Baptism of Christ in 1472.

God the Father with His Right Hand Raised in Blessing, with a triangular halo representing the Trinity, Girolamo dai Libri, c. 1555
 
In Renaissance paintings of the adoration of the Trinity, God may be depicted in two ways, either with emphasis on The Father, or the three elements of the Trinity. The most usual depiction of the Trinity in Renaissance art depicts God the Father using an old man, usually with a long beard and patriarchal in appearance, sometimes with a triangular halo (as a reference to the Trinity), or with a papal crown, specially in Northern Renaissance painting. In these depictions The Father may hold a globe or book (to symbolize God's knowledge and as a reference to how knowledge is deemed divine). He is behind and above Christ on the Cross in the Throne of Mercy iconography. A dove, the symbol of the Holy Spirit may hover above. Various people from different classes of society, e.g. kings, popes or martyrs may be present in the picture. In a Trinitarian Pietà, God the Father is often symbolized using a man wearing a papal dress and a papal crown, supporting the dead Christ in his arms. They are depicted as floating in heaven with angels who carry the instruments of the Passion.

Representations of God the Father and the Trinity were attacked both by Protestants and within Catholicism, by the Jansenist and Baianist movements as well as more orthodox theologians. As with other attacks on Catholic imagery, this had the effect both of reducing Church support for the less central depictions, and strengthening it for the core ones. In the Western Church, the pressure to restrain religious imagery resulted in the highly influential decrees of the final session of the Council of Trent in 1563. The Council of Trent decrees confirmed the traditional Catholic doctrine that images only represented the person depicted, and that veneration to them was paid to the person, not the image.

Artistic depictions of God the Father were uncontroversial in Catholic art thereafter, but less common depictions of the Trinity were condemned. In 1745 Pope Benedict XIV explicitly supported the Throne of Mercy depiction, referring to the "Ancient of Days", but in 1786 it was still necessary for Pope Pius VI to issue a papal bull condemning the decision of an Italian church council to remove all images of the Trinity from churches.


God the Father is symbolized in several Genesis scenes in Michelangelo's Sistine Chapel ceiling, most famously The Creation of Adam (whose image of near touching hands of God and Adam is iconic of humanity, being a reminder that Man is created in the Image and Likeness of God (Gen 1:26)).God the Father is depicted as a powerful figure, floating in the clouds in Titian's Assumption of the Virgin in the Frari of Venice, long admired as a masterpiece of High Renaissance art. The Church of the Gesù in Rome includes a number of 16th-century depictions of God the Father. In some of these paintings the Trinity is still alluded to in terms of three angels, but Giovanni Battista Fiammeri also depicted God the Father as a man riding on a cloud, above the scenes.

In both the Last Judgment and the Coronation of the Virgin paintings by Rubens he depicted God the Father using the image that by then had become widely accepted, a bearded patriarchal figure above the fray. In the 17th century, the two Spanish artists Diego Velázquez (whose father-in-law Francisco Pacheco was in charge of the approval of new images for the Inquisition) and Bartolomé Esteban Murillo both depicted God the Father using a patriarchal figure with a white beard in a purple robe.

While representations of God the Father were growing in Italy, Spain, Germany and the Low Countries, there was resistance elsewhere in Europe, even during the 17th century. In 1632 most members of the Star Chamber court in England (except the Archbishop of York) condemned the use of the images of the Trinity in church windows, and some considered them illegal. Later in the 17th century Sir Thomas Browne wrote that he considered the representation of God the Father using an old man "a dangerous act" that might lead to Egyptian symbolism. In 1847, Charles Winston was still critical of such images as a "Romish trend" (a term used to refer to Roman Catholics) that he considered best avoided in England.

In 1667 the 43rd chapter of the Great Moscow Council specifically included a ban on a number of symbolic depictions of God the Father and the Holy Spirit, which then also resulted in a whole range of other icons being placed on the forbidden list, mostly affecting Western-style depictions which had been gaining ground in Orthodox icons. The Council also declared that the person of the Trinity who was the "Ancient of Days" was Christ, as Logos, not God the Father. However some icons continued to be produced in Russia, as well as Greece, Romania, and other Orthodox countries.

Islam

The Arabic script of "Allah" in the Hagia Sophia, Istanbul

Muslims believe that God (Allah) is beyond all comprehension and equal, and does not resemble any of his creations in any way. Thus, Muslims are not iconodules, are not expected to visualize God, and instead of having pictures of Allah in their mosques, typically have religious calligraphy written on the wall.

Bahá'í Faith

In the Kitáb-i-Íqán, the primary theological work of the Bahá’í Faith, God is described as “Him Who is the central Orb of the universe, its Essence and ultimate Purpose.” Bahá'u'lláh taught that God is directly unknowable to common mortals, but that his attributes and qualities can be indirectly known by learning from and imitating his divine Manifestations, which in Bahá'í theology are somewhat comparable to Hindu avatars or Abrahamic prophets. These Manifestations are the great prophets and teachers of many of the major religious traditions. These include Krishna, Buddha, Jesus, Zoroaster, Muhammad, Bahá'ú'lláh, and others. Although the faith is strictly monotheistic, it also preaches the unity of all religions and focuses on these multiple epiphanies as necessary for meeting the needs of humanity at different points in history and for different cultures, and as part of a scheme of progressive revelation and education of humanity.

Theological approaches

Classical theists (such as ancient Greco-Medieval philosophers, Roman Catholics, Eastern Orthodox Christians, many Jews and Muslims, and some Protestants) speak of God as a divinely simple 'nothing' that is completely transcendent (totally independent of all else), and having attributes such as immutability, impassibility, and timelessness. Theologians of theistic personalism (the view held by Rene Descartes, Isaac Newton, Alvin Plantinga, Richard Swinburne, William Lane Craig, and most modern evangelicals) argue that God is most generally the ground of all being, immanent in and transcendent over the whole world of reality, with immanence and transcendence being the contrapletes of personality. Carl Jung equated religious ideas of God with transcendental metaphors of higher consciousness, in which God can be just as easily be imagined "as an eternally flowing current of vital energy that endlessly changes shape ... as an eternally unmoved, unchangeable essence."

Many philosophers developed arguments for the existence of God, while attempting to comprehend the precise implications of God's attributes. Reconciling some of those attributes—particularly the attributes of the God of theistic personalism—generated important philosophical problems and debates. For example, God's omniscience may seem to imply that God knows how free agents will choose to act. If God does know this, their ostensible free will might be illusory, or foreknowledge does not imply predestination, and if God does not know it, God may not be omniscient.

The last centuries of philosophy have seen vigorous questions regarding the arguments for God's existence raised by such philosophers as Immanuel Kant, David Hume and Antony Flew, although Kant held that the argument from morality was valid. The theist response has been either to contend, as does Alvin Plantinga, that faith is "properly basic", or to take, as does Richard Swinburne, the evidentialist position. Some theists agree that only some of the arguments for God's existence are compelling, but argue that faith is not a product of reason, but requires risk. There would be no risk, they say, if the arguments for God's existence were as solid as the laws of logic, a position summed up by Pascal as "the heart has reasons of which reason does not know."

Many religious believers allow for the existence of other, less powerful spiritual beings such as angels, saints, jinn, demons, and devas.

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