Agnosticism

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Agnosticism is the view or belief that the existence of God, of the divine or the supernatural is unknown or unknowable. Another definition provided is the view that "human reason is incapable of providing sufficient rational grounds to justify either the belief that God exists or the belief that God does not exist."

The English biologist Thomas Henry Huxley coined the word agnostic in 1869. His general definition was that "It is wrong for a man to say that he is certain of the objective truth of any proposition unless he can produce evidence which logically justifies that certainty. This is what Agnosticism asserts; and, in my opinion, it is all that is essential to Agnosticism." In response to the question "Is Agnosticism in accord with modern science?" Huxley said that "Agnosticism is of the essence of science, whether ancient or modern. It simply means that a man shall not say he knows or believes that which he has no scientific grounds for professing to know or believe."

Earlier thinkers, however, had written works that promoted agnostic points of view, such as Sanjaya Belatthaputta, a 5th-century BCE Indian philosopher who expressed agnosticism about any afterlife; and Protagoras, a 5th-century BCE Greek philosopher who expressed agnosticism about the existence of "the gods".

Defining agnosticism

[The agnostic] principle may be stated in various ways, but they all amount to this: that it is wrong for a man to say that he is certain of the objective truth of any proposition unless he can produce evidence which logically justifies that certainty. This is what Agnosticism asserts; and, in my opinion, it is all that is essential to Agnosticism.

— Thomas Henry Huxley

Agnosticism, in fact, is not a creed, but a method, the essence of which lies in the rigorous application of a single principle ... Positively the principle may be expressed: In matters of the intellect, follow your reason as far as it will take you, without regard to any other consideration. And negatively: In matters of the intellect do not pretend that conclusions are certain which are not demonstrated or demonstrable.

— Thomas Henry Huxley

That which Agnostics deny and repudiate, as immoral, is the contrary doctrine, that there are propositions which men ought to believe, without logically satisfactory evidence; and that reprobation ought to attach to the profession of disbelief in such inadequately supported propositions.

— Thomas Henry Huxley

Consequently, agnosticism puts aside not only the greater part of popular theology, but also the greater part of anti-theology. On the whole, the "bosh" of heterodoxy is more offensive to me than that of orthodoxy, because heterodoxy professes to be guided by reason and science, and orthodoxy does not.

— Thomas Henry Huxley (in response to the question "What is its relation to popular theology?")

Being a scientist, above all else, Huxley presented agnosticism as a form of demarcation. A hypothesis with no supporting, objective, testable evidence is not an objective, scientific claim. As such, there would be no way to test said hypotheses, leaving the results inconclusive. His agnosticism was not compatible with forming a belief as to the truth, or falsehood, of the claim at hand. Karl Popper would also describe himself as an agnostic. According to philosopher William L. Rowe, in this strict sense, agnosticism is the view that human reason is incapable of providing sufficient rational grounds to justify either the belief that God exists or the belief that God does not exist.

George H. Smith, while admitting that the narrow definition of atheist was the common usage definition of that word, and admitting that the broad definition of agnostic was the common usage definition of that word, promoted broadening the definition of atheist and narrowing the definition of agnostic. Smith rejects agnosticism as a third alternative to theism and atheism and promotes terms such as agnostic atheism (the view of those who do not hold a belief in the existence of any deity, but claim that the existence of a deity is unknown or inherently unknowable) and agnostic theism (the view of those who believe in the existence of a deity(s), but claim that the existence of a deity is unknown or inherently unknowable).

Etymology

Agnostic (from Ancient Greek ἀ- (a-) 'without', and γνῶσις (gnōsis) 'knowledge') was used by Thomas Henry Huxley in a speech at a meeting of the Metaphysical Society in 1869 to describe his philosophy, which rejects all claims of spiritual or mystical knowledge.

Early Christian church leaders used the Greek word gnosis (knowledge) to describe "spiritual knowledge". Agnosticism is not to be confused with religious views opposing the ancient religious movement of Gnosticism in particular; Huxley used the term in a broader, more abstract sense. Huxley identified agnosticism not as a creed but rather as a method of skeptical, evidence-based inquiry.

The term Agnostic is also cognate with the Sanskrit word Ajñasi which translates literally to "not knowable", and relates to the ancient Indian philosophical school of Ajñana, which proposes that it is impossible to obtain knowledge of metaphysical nature or ascertain the truth value of philosophical propositions; and even if knowledge was possible, it is useless and disadvantageous for final salvation.

In recent years, scientific literature dealing with neuroscience and psychology has used the word to mean "not knowable". In technical and marketing literature, "agnostic" can also mean independence from some parameters—for example, "platform agnostic" (referring to cross-platform software) or "hardware-agnostic".

Qualifying agnosticism

Scottish Enlightenment philosopher David Hume contended that meaningful statements about the universe are always qualified by some degree of doubt. He asserted that the fallibility of human beings means that they cannot obtain absolute certainty except in trivial cases where a statement is true by definition (e.g. tautologies such as "all bachelors are unmarried" or "all triangles have three corners").

Types

Strong agnosticism (also called "hard", "closed", "strict", or "permanent agnosticism")

The view that the question of the existence or nonexistence of a deity or deities, and the nature of ultimate reality is unknowable by reason of our natural inability to verify any experience with anything but another subjective experience. A strong agnostic would say, "I cannot know whether a deity exists or not, and neither can you."

Weak agnosticism (also called "soft", "open", "empirical", "hopeful" or "temporal agnosticism")

The view that the existence or nonexistence of any deities is currently unknown but is not necessarily unknowable; therefore, one will withhold judgment until evidence, if any, becomes available. A weak agnostic would say, "I don't know whether any deities exist or not, but maybe one day, if there is evidence, we can find something out."

Apathetic agnosticism

The view that no amount of debate can prove or disprove the existence of one or more deities, and if one or more deities exist, they do not appear to be concerned about the fate of humans. Therefore, their existence has little to no impact on personal human affairs and should be of little interest. An apathetic agnostic would say, "I don't know whether any deity exists or not, and I don't care if any deity exists or not."

History

Hindu philosophy

See also: Sanjaya Belatthaputta and Ajñana

Throughout the history of Hinduism there has been a strong tradition of philosophic speculation and skepticism.

The Rig Veda takes an agnostic view on the fundamental question of how the universe and the gods were created. Nasadiya Sukta (Creation Hymn) in the tenth chapter of the Rig Veda says:

But, after all, who knows, and who can say
Whence it all came, and how creation happened?
The gods themselves are later than creation,
so who knows truly whence it has arisen?

Whence all creation had its origin,
He, whether he fashioned it or whether he did not,
He, who surveys it all from highest heaven,
He knows – or maybe even he does not know.

Hume, Kant, and Kierkegaard

Aristotle, Anselm, Aquinas, Descartes, and Gödel presented arguments attempting to rationally prove the existence of God. The skeptical empiricism of David Hume, the antinomies of Immanuel Kant, and the existential philosophy of Søren Kierkegaard convinced many later philosophers to abandon these attempts, regarding it impossible to construct any unassailable proof for the existence or non-existence of God.

In his 1844 book, Philosophical Fragments, Kierkegaard writes:

Let us call this unknown something: God. It is nothing more than a name we assign to it. The idea of demonstrating that this unknown something (God) exists, could scarcely suggest itself to Reason. For if God does not exist it would of course be impossible to prove it; and if he does exist it would be folly to attempt it. For at the very outset, in beginning my proof, I would have presupposed it, not as doubtful but as certain (a presupposition is never doubtful, for the very reason that it is a presupposition), since otherwise I would not begin, readily understanding that the whole would be impossible if he did not exist. But if when I speak of proving God's existence I mean that I propose to prove that the Unknown, which exists, is God, then I express myself unfortunately. For in that case I do not prove anything, least of all an existence, but merely develop the content of a conception.

Hume was Huxley's favourite philosopher, calling him "the Prince of Agnostics". Diderot wrote to his mistress, telling of a visit by Hume to the Baron D'Holbach, and describing how a word for the position that Huxley would later describe as agnosticism did not seem to exist, or at least was not common knowledge, at the time.

The first time that M. Hume found himself at the table of the Baron, he was seated beside him. I don't know for what purpose the English philosopher took it into his head to remark to the Baron that he did not believe in atheists, that he had never seen any. The Baron said to him: "Count how many we are here." We are eighteen. The Baron added: "It isn't too bad a showing to be able to point out to you fifteen at once: the three others haven't made up their minds."

— Denis Diderot

United Kingdom

Charles Darwin

Charles Darwin in 1854

Raised in a religious environment, Charles Darwin (1809–1882) studied to be an Anglican clergyman. While eventually doubting parts of his faith, Darwin continued to help in church affairs, even while avoiding church attendance. Darwin stated that it would be "absurd to doubt that a man might be an ardent theist and an evolutionist". Although reticent about his religious views, in 1879 he wrote that "I have never been an atheist in the sense of denying the existence of a God. – I think that generally ... an agnostic would be the most correct description of my state of mind."

Thomas Henry Huxley

Thomas Henry Huxley in the 1860s. He was the first to decisively coin the term agnosticism.

Agnostic views are as old as philosophical skepticism, but the terms agnostic and agnosticism were created by Huxley (1825–1895) to sum up his thoughts on contemporary developments of metaphysics about the "unconditioned" (William Hamilton) and the "unknowable" (Herbert Spencer). Though Huxley began to use the term agnostic in 1869, his opinions had taken shape some time before that date. In a letter of September 23, 1860, to Charles Kingsley, Huxley discussed his views extensively:

I neither affirm nor deny the immortality of man. I see no reason for believing it, but, on the other hand, I have no means of disproving it. I have no a priori objections to the doctrine. No man who has to deal daily and hourly with nature can trouble himself about a priori difficulties. Give me such evidence as would justify me in believing in anything else, and I will believe that. Why should I not? It is not half so wonderful as the conservation of force or the indestructibility of matter ...

It is no use to talk to me of analogies and probabilities. I know what I mean when I say I believe in the law of the inverse squares, and I will not rest my life and my hopes upon weaker convictions ...

That my personality is the surest thing I know may be true. But the attempt to conceive what it is leads me into mere verbal subtleties. I have champed up all that chaff about the ego and the non-ego, noumena and phenomena, and all the rest of it, too often not to know that in attempting even to think of these questions, the human intellect flounders at once out of its depth.

And again, to the same correspondent, May 6, 1863:

I have never had the least sympathy with the a priori reasons against orthodoxy, and I have by nature and disposition the greatest possible antipathy to all the atheistic and infidel school. Nevertheless I know that I am, in spite of myself, exactly what the Christian would call, and, so far as I can see, is justified in calling, atheist and infidel. I cannot see one shadow or tittle of evidence that the great unknown underlying the phenomenon of the universe stands to us in the relation of a Father [who] loves us and cares for us as Christianity asserts. So with regard to the other great Christian dogmas, immortality of soul and future state of rewards and punishments, what possible objection can I—who am compelled perforce to believe in the immortality of what we call Matter and Force, and in a very unmistakable present state of rewards and punishments for our deeds—have to these doctrines? Give me a scintilla of evidence, and I am ready to jump at them.

Of the origin of the name agnostic to describe this attitude, Huxley gave the following account:

When I reached intellectual maturity and began to ask myself whether I was an atheist, a theist, or a pantheist; a materialist or an idealist; Christian or a freethinker; I found that the more I learned and reflected, the less ready was the answer; until, at last, I came to the conclusion that I had neither art nor part with any of these denominations, except the last. The one thing in which most of these good people were agreed was the one thing in which I differed from them. They were quite sure they had attained a certain "gnosis"—had, more or less successfully, solved the problem of existence; while I was quite sure I had not, and had a pretty strong conviction that the problem was insoluble. And, with Hume and Kant on my side, I could not think myself presumptuous in holding fast by that opinion ... So I took thought, and invented what I conceived to be the appropriate title of "agnostic". It came into my head as suggestively antithetic to the "gnostic" of Church history, who professed to know so much about the very things of which I was ignorant. ... To my great satisfaction the term took.

In 1889, Huxley wrote:

Therefore, although it be, as I believe, demonstrable that we have no real knowledge of the authorship, or of the date of composition of the Gospels, as they have come down to us, and that nothing better than more or less probable guesses can be arrived at on that subject.

William Stewart Ross

William Stewart Ross (1844–1906) wrote under the name of Saladin. He was associated with Victorian Freethinkers and the organization the British Secular Union. He edited the Secular Review from 1882; it was renamed Agnostic Journal and Eclectic Review and closed in 1907. Ross championed agnosticism in opposition to the atheism of Charles Bradlaugh as an open-ended spiritual exploration.

In Why I am an Agnostic (c. 1889) he claims that agnosticism is "the very reverse of atheism".

Bertrand Russell

Bertrand Russell

Bertrand Russell (1872–1970) declared Why I Am Not a Christian in 1927, a classic statement of agnosticism. He calls upon his readers to "stand on their own two feet and look fair and square at the world with a fearless attitude and a free intelligence".

In 1939, Russell gave a lecture on The existence and nature of God, in which he characterized himself as an atheist. He said:

The existence and nature of God is a subject of which I can discuss only half. If one arrives at a negative conclusion concerning the first part of the question, the second part of the question does not arise; and my position, as you may have gathered, is a negative one on this matter.

However, later in the same lecture, discussing modern non-anthropomorphic concepts of God, Russell states:

That sort of God is, I think, not one that can actually be disproved, as I think the omnipotent and benevolent creator can.

In Russell's 1947 pamphlet, Am I An Atheist or an Agnostic? (subtitled A Plea For Tolerance in the Face of New Dogmas), he ruminates on the problem of what to call himself:

As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one can prove that there is not a God. On the other hand, if I am to convey the right impression to the ordinary man in the street I think I ought to say that I am an Atheist, because when I say that I cannot prove that there is not a God, I ought to add equally that I cannot prove that there are not the Homeric gods.

In his 1953 essay, What Is An Agnostic? Russell states:

An agnostic thinks it impossible to know the truth in matters such as God and the future life with which Christianity and other religions are concerned. Or, if not impossible, at least impossible at the present time.

Are Agnostics Atheists?

No. An atheist, like a Christian, holds that we can know whether or not there is a God. The Christian holds that we can know there is a God; the atheist, that we can know there is not. The Agnostic suspends judgment, saying that there are not sufficient grounds either for affirmation or for denial.

Later in the essay, Russell adds:

I think that if I heard a voice from the sky predicting all that was going to happen to me during the next twenty-four hours, including events that would have seemed highly improbable, and if all these events then produced to happen, I might perhaps be convinced at least of the existence of some superhuman intelligence.

Leslie Weatherhead

See also: Christian agnosticism

In 1965, Christian theologian Leslie Weatherhead (1893–1976) published The Christian Agnostic, in which he argues:

... many professing agnostics are nearer belief in the true God than are many conventional church-goers who believe in a body that does not exist whom they miscall God.

Although radical and unpalatable to conventional theologians, Weatherhead's agnosticism falls far short of Huxley's, and short even of weak agnosticism:

Of course, the human soul will always have the power to reject God, for choice is essential to its nature, but I cannot believe that anyone will finally do this.

United States

Robert G. Ingersoll

Robert G. Ingersoll

Robert G. Ingersoll (1833–1899), an Illinois lawyer and politician who evolved into a well-known and sought-after orator in 19th-century America, has been referred to as the "Great Agnostic".

In an 1896 lecture titled Why I Am An Agnostic, Ingersoll related why he was an agnostic:

Is there a supernatural power—an arbitrary mind—an enthroned God—a supreme will that sways the tides and currents of the world—to which all causes bow? I do not deny. I do not know—but I do not believe. I believe that the natural is supreme—that from the infinite chain no link can be lost or broken—that there is no supernatural power that can answer prayer—no power that worship can persuade or change—no power that cares for man.

I believe that with infinite arms Nature embraces the all—that there is no interference—no chance—that behind every event are the necessary and countless causes, and that beyond every event will be and must be the necessary and countless effects.

Is there a God? I do not know. Is man immortal? I do not know. One thing I do know, and that is, that neither hope, nor fear, belief, nor denial, can change the fact. It is as it is, and it will be as it must be.

In the conclusion of the speech he simply sums up the agnostic position as:

We can be as honest as we are ignorant. If we are, when asked what is beyond the horizon of the known, we must say that we do not know.

In 1885, Ingersoll explained his comparative view of agnosticism and atheism as follows:

The Agnostic is an Atheist. The Atheist is an Agnostic. The Agnostic says, 'I do not know, but I do not believe there is any God.' The Atheist says the same.

See also: Physical determinism

Bernard Iddings Bell

Canon Bernard Iddings Bell (1886–1958), a popular cultural commentator, Episcopal priest, and author, lauded the necessity of agnosticism in Beyond Agnosticism: A Book for Tired Mechanists, calling it the foundation of "all intelligent Christianity". Agnosticism was a temporary mindset in which one rigorously questioned the truths of the age, including the way in which one believed God. His view of Robert Ingersoll and Thomas Paine was that they were not denouncing true Christianity but rather "a gross perversion of it". Part of the misunderstanding stemmed from ignorance of the concepts of God and religion. Historically, a god was any real, perceivable force that ruled the lives of humans and inspired admiration, love, fear, and homage; religion was the practice of it. Ancient peoples worshiped gods with real counterparts, such as Mammon (money and material things), Nabu (rationality), or Ba'al (violent weather); Bell argued that modern peoples were still paying homage—with their lives and their children's lives—to these old gods of wealth, physical appetites, and self-deification. Thus, if one attempted to be agnostic passively, he or she would incidentally join the worship of the world's gods.

In Unfashionable Convictions (1931), he criticized the Enlightenment's complete faith in human sensory perception, augmented by scientific instruments, as a means of accurately grasping Reality. Firstly, it was fairly new, an innovation of the Western World, which Aristotle invented and Thomas Aquinas revived among the scientific community. Secondly, the divorce of "pure" science from human experience, as manifested in American Industrialization, had completely altered the environment, often disfiguring it, so as to suggest its insufficiency to human needs. Thirdly, because scientists were constantly producing more data—to the point where no single human could grasp it all at once—it followed that human intelligence was incapable of attaining a complete understanding of universe; therefore, to admit the mysteries of the unobserved universe was to be actually scientific.

Bell believed that there were two other ways that humans could perceive and interact with the world. Artistic experience was how one expressed meaning through speaking, writing, painting, gesturing—any sort of communication which shared insight into a human's inner reality. Mystical experience was how one could "read" people and harmonize with them, being what we commonly call love. In summary, man was a scientist, artist, and lover. Without exercising all three, a person became "lopsided".

Bell considered a humanist to be a person who cannot rightly ignore the other ways of knowing. However, humanism, like agnosticism, was also temporal, and would eventually lead to either scientific materialism or theism. He lays out the following thesis:

1. Truth cannot be discovered by reasoning on the evidence of scientific data alone. Modern peoples' dissatisfaction with life is the result of depending on such incomplete data. Our ability to reason is not a way to discover Truth but rather a way to organize our knowledge and experiences somewhat sensibly. Without a full, human perception of the world, one's reason tends to lead them in the wrong direction.
2. Beyond what can be measured with scientific tools, there are other types of perception, such as one's ability know another human through loving. One's loves cannot be dissected and logged in a scientific journal, but we know them far better than we know the surface of the sun. They show us an undefinable reality that is nevertheless intimate and personal, and they reveal qualities lovelier and truer than detached facts can provide.
3. To be religious, in the Christian sense, is to live for the Whole of Reality (God) rather than for a small part (gods). Only by treating this Whole of Reality as a person—good and true and perfect—rather than an impersonal force, can we come closer to the Truth. An ultimate Person can be loved, but a cosmic force cannot. A scientist can only discover peripheral truths, but a lover is able to get at the Truth.
4. There are many reasons to believe in God but they are not sufficient for an agnostic to become a theist. It is not enough to believe in an ancient holy book, even though when it is accurately analyzed without bias, it proves to be more trustworthy and admirable than what we are taught in school. Neither is it enough to realize how probable it is that a personal God would have to show human beings how to live, considering they have so much trouble on their own. Nor is it enough to believe for the reason that, throughout history, millions of people have arrived at this Wholeness of Reality only through religious experience. The aforementioned reasons may warm one toward religion, but they fall short of convincing. However, if one presupposes that God is in fact a knowable, loving person, as an experiment, and then lives according that religion, he or she will suddenly come face to face with experiences previously unknown. One's life becomes full, meaningful, and fearless in the face of death. It does not defy reason but exceeds it.
5. Because God has been experienced through love, the orders of prayer, fellowship, and devotion now matter. They create order within one's life, continually renewing the "missing piece" that had previously felt lost. They empower one to be compassionate and humble, not small-minded or arrogant.
6. No truth should be denied outright, but all should be questioned. Science reveals an ever-growing vision of our universe that should not be discounted due to bias toward older understandings. Reason is to be trusted and cultivated. To believe in God is not to forego reason or to deny scientific facts, but to step into the unknown and discover the fullness of life.

Demographics

Nonreligious population by country, 2010

Percentage of people in various European countries who said: "I don't believe there is any sort of spirit, God or life force." (2005)

Demographic research services normally do not differentiate between various types of non-religious respondents, so agnostics are often classified in the same category as atheists or other non-religious people.

A 2010 survey published in Encyclopædia Britannica found that the non-religious people or the agnostics made up about 9.6% of the world's population. A November–December 2006 poll published in the Financial Times gives rates for the United States and five European countries. The rates of agnosticism in the United States were at 14%, while the rates of agnosticism in the European countries surveyed were considerably higher: Italy (20%), Spain (30%), Great Britain (35%), Germany (25%), and France (32%).

A study conducted by the Pew Research Center found that about 16% of the world's people, the third largest group after Christianity and Islam, have no religious affiliation. According to a 2012 report by the Pew Research Center, agnostics made up 3.3% of the US adult population. In the U.S. Religious Landscape Survey, conducted by the Pew Research Center, 55% of agnostic respondents expressed "a belief in God or a universal spirit", whereas 41% stated that they thought that they felt a tension "being non-religious in a society where most people are religious".

According to the 2021 Australian Bureau of Statistics, 38.9% of Australians have "no religion", a category that includes agnostics. Between 64% and 65% of Japanese and up to 81% of Vietnamese are atheists, agnostics, or do not believe in a god. An official European Union survey reported that 3% of the EU population is unsure about their belief in a god or spirit.

Criticism

Agnosticism is criticized from a variety of standpoints. Some atheists criticize the use of the term agnosticism as functionally indistinguishable from atheism; this results in frequent criticisms of those who adopt the term as avoiding the atheist label.

Theistic

Theistic critics claim that agnosticism is impossible in practice, since a person can live only either as if God did not exist (etsi deus non-daretur), or as if God did exist (etsi deus daretur).

Christian

According to Pope Benedict XVI, strong agnosticism in particular contradicts itself in affirming the power of reason to know scientific truth. He blames the exclusion of reasoning from religion and ethics for dangerous pathologies such as crimes against humanity and ecological disasters. "Agnosticism", said Benedict, "is always the fruit of a refusal of that knowledge which is in fact offered to man ... The knowledge of God has always existed". He asserted that agnosticism is a choice of comfort, pride, dominion, and utility over truth, and is opposed by the following attitudes: the keenest self-criticism, humble listening to the whole of existence, the persistent patience and self-correction of the scientific method, a readiness to be purified by the truth.

The Catholic Church sees merit in examining what it calls "partial agnosticism", specifically those systems that "do not aim at constructing a complete philosophy of the unknowable, but at excluding special kinds of truth, notably religious, from the domain of knowledge". However, the Church is historically opposed to a full denial of the capacity of human reason to know God. The Council of the Vatican declares, "God, the beginning and end of all, can, by the natural light of human reason, be known with certainty from the works of creation".

Blaise Pascal argued that even if there were truly no evidence for God, agnostics should consider what is now known as Pascal's Wager: the infinite expected value of acknowledging God is always greater than the finite expected value of not acknowledging his existence, and thus it is a safer "bet" to choose God.

Atheistic

According to Richard Dawkins, a distinction between agnosticism and atheism is unwieldy and depends on how close to zero a person is willing to rate the probability of existence for any given god-like entity. About himself, Dawkins continues, "I am agnostic only to the extent that I am agnostic about fairies at the bottom of the garden." Dawkins also identifies two categories of agnostics; "Temporary Agnostics in Practice" (TAPs), and "Permanent Agnostics in Principle" (PAPs). He states that "agnosticism about the existence of God belongs firmly in the temporary or TAP category. Either he exists or he doesn't. It is a scientific question; one day we may know the answer, and meanwhile we can say something pretty strong about the probability" and considers PAP a "deeply inescapable kind of fence-sitting".

Ignosticism

A related concept is ignosticism, the view that a coherent definition of a deity must be put forward before the question of the existence of a deity can be meaningfully discussed. If the chosen definition is not coherent, the ignostic holds the noncognitivist view that the existence of a deity is meaningless or empirically untestable. A. J. Ayer, Theodore Drange, and other philosophers see both atheism and agnosticism as incompatible with ignosticism on the grounds that atheism and agnosticism accept the statement "a deity exists" as a meaningful proposition that can be argued for or against.

Reductionism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Reductionism

René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck

Reductionism is any of several related philosophical ideas regarding the associations between phenomena which can be described in terms of other simpler or more fundamental phenomena. It is also described as an intellectual and philosophical position that interprets a complex system as the sum of its parts.

Definitions

The Oxford Companion to Philosophy suggests that reductionism is "one of the most used and abused terms in the philosophical lexicon" and suggests a three-part division:

1. Ontological reductionism: a belief that the whole of reality consists of a minimal number of parts.
2. Methodological reductionism: the scientific attempt to provide an explanation in terms of ever-smaller entities.
3. Theory reductionism: the suggestion that a newer theory does not replace or absorb an older one, but reduces it to more basic terms. Theory reduction itself is divisible into three parts: translation, derivation, and explanation.

Reductionism can be applied to any phenomenon, including objects, problems, explanations, theories, and meanings.

For the sciences, application of methodological reductionism attempts explanation of entire systems in terms of their individual, constituent parts and their interactions. For example, the temperature of a gas is reduced to nothing beyond the average kinetic energy of its molecules in motion. Thomas Nagel and others speak of 'psychophysical reductionism' (the attempted reduction of psychological phenomena to physics and chemistry), and 'physico-chemical reductionism' (the attempted reduction of biology to physics and chemistry). In a very simplified and sometimes contested form, reductionism is said to imply that a system is nothing but the sum of its parts.

However, a more nuanced opinion is that a system is composed entirely of its parts, but the system will have features that none of the parts have (which, in essence is the basis of emergentism). "The point of mechanistic explanations is usually showing how the higher level features arise from the parts."

Other definitions are used by other authors. For example, what John Polkinghorne terms 'conceptual' or 'epistemological' reductionism is the definition provided by Simon Blackburn and by Jaegwon Kim: that form of reductionism which concerns a program of replacing the facts or entities involved in one type of discourse with other facts or entities from another type, thereby providing a relationship between them. Richard Jones distinguishes ontological and epistemological reductionism, arguing that many ontological and epistemological reductionists affirm the need for different concepts for different degrees of complexity while affirming a reduction of theories.

The idea of reductionism can be expressed by "levels" of explanation, with higher levels reducible if need be to lower levels. This use of levels of understanding in part expresses our human limitations in remembering detail. However, "most philosophers would insist that our role in conceptualizing reality [our need for a hierarchy of "levels" of understanding] does not change the fact that different levels of organization in reality do have different 'properties'."

Reductionism does not preclude the existence of what might be termed emergent phenomena, but it does imply the ability to understand those phenomena completely in terms of the processes from which they are composed. This reductionist understanding is very different from ontological or strong emergentism, which intends that what emerges in "emergence" is more than the sum of the processes from which it emerges, respectively either in the ontological sense or in the epistemological sense.

Ontological reductionism

Richard Jones divides ontological reductionism into two: the reductionism of substances (e.g., the reduction of mind to matter) and the reduction of the number of structures operating in nature (e.g., the reduction of one physical force to another). This permits scientists and philosophers to affirm the former while being anti-reductionists regarding the latter.

Nancey Murphy has claimed that there are two species of ontological reductionism: one that claims that wholes are nothing more than their parts; and atomist reductionism, claiming that wholes are not "really real". She admits that the phrase "really real" is apparently senseless but she has tried to explicate the supposed difference between the two.

Ontological reductionism denies the idea of ontological emergence, and claims that emergence is an epistemological phenomenon that only exists through analysis or description of a system, and does not exist fundamentally.

In some scientific disciplines, ontological reductionism takes two forms: token-identity theory and type-identity theory. In this case, "token" refers to a biological process.

Token ontological reductionism is the idea that every item that exists is a sum item. For perceivable items, it affirms that every perceivable item is a sum of items with a lesser degree of complexity. Token ontological reduction of biological things to chemical things is generally accepted.

Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.

Michael Ruse has criticized ontological reductionism as an improper argument against vitalism.

Methodological reductionism

In a biological context, methodological reductionism means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.

In religion

Anthropologists Edward Burnett Tylor and James George Frazer employed some religious reductionist arguments.

Theory reductionism

Theory reduction is the process by which a more general theory absorbs a special theory. It can be further divided into translation, derivation, and explanation. For example, both Kepler's laws of the motion of the planets and Galileo's theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because Newtonian mechanics is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.

In mathematics

In mathematics, reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually axiomatic set theory. Ernst Zermelo was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical axioms by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.

Jouko Väänänen has argued for second-order logic as a foundation for mathematics instead of set theory, whereas others have argued for category theory as a foundation for certain aspects of mathematics.

The incompleteness theorems of Kurt Gödel, published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any consistent recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) true propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally undecidable propositions. For example, the continuum hypothesis is undecidable in the Zermelo–Fraenkel set theory as shown by Cohen.

In science

Reductionist thinking and methods form the basis for many of the well-developed topics of modern science, including much of physics, chemistry and molecular biology. Classical mechanics in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions. Statistical mechanics can be considered as a reconciliation of macroscopic thermodynamic laws with the reductionist method of explaining macroscopic properties in terms of microscopic components, although it has been argued that reduction in physics 'never goes all the way in practice'.

In computer science

The role of reduction in computer science can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "theory reductionism". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "hard" to solve as the former.

Reduction in theoretical computer science is pervasive in both: the mathematical abstract foundations of computation; and in real-world performance or capability analysis of algorithms. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in computability (or recursive) theory, where it assumes the form of e.g. Turing reduction, but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. polynomial-time reduction.

Criticism

Free will

Main article: Free will

Philosophers of the Enlightenment worked to insulate human free will from reductionism. Descartes separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "noumenal" realm that is not governed by the deterministic laws of "phenomenal" nature, where every event is completely determined by chains of causality. The most influential formulation was by Immanuel Kant, who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially Friedrich Schleiermacher and Albrecht Ritschl, used the Romantic method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.

Causation

Most common philosophical understandings of causation involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.

Alfred North Whitehead's metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.

In science

An alternative term for ontological reductionism is fragmentalism, often used in a pejorative sense. In cognitive psychology, George Kelly developed "constructive alternativism" as a form of personal construct psychology and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful mental models of the exterior world, rather than the accumulation of independent "nuggets of truth". Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist Robert Ulanowicz says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) information theory as a framework to study propensities in natural systems. The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater complexity, including living cells, neural networks, ecosystems, society, and other systems formed from assemblies of large numbers of diverse components linked by multiple feedback loops.

History of general relativity

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/History_of_general_relativity 

 

General relativity
${\displaystyle G_{\mu \nu }+\mathrm{\Lambda }{g}_{\mu \nu }=\kappa T_{\mu \nu }}$
Introduction History Timeline Tests Mathematical formulation

General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.

Before the advent of general relativity, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses, even though Newton himself did not regard the theory as the final word on the nature of gravity. Within a century of Newton's formulation, careful astronomical observation revealed unexplainable differences between the theory and the observations. Under Newton's model, gravity was the result of an attractive force between massive objects. Although even Newton was bothered by the unknown nature of that force, the basic framework was extremely successful at describing motion.

However, experiments and observations show that Einstein's description accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the orbits of Mercury and other planets. General relativity also predicts novel effects of gravity, such as gravitational waves, gravitational lensing and an effect of gravity on time known as gravitational time dilation. Many of these predictions have been confirmed by experiment or observation, while others are the subject of ongoing research.

General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is so strong that not even light can escape. Their strong gravity is thought to be responsible for the intense radiation emitted by certain types of astronomical objects (such as active galactic nuclei or microquasars). General relativity is also part of the framework of the standard Big Bang model of cosmology.

Creation of general relativity

Early investigations

The first relativistic theory of gravity was proposed by Henri Poincaré in 1905. He published a Lorentz invariant theory on four-dimensional spacetime, where gravity is transmitted by gravitational waves that travel at the speed of light.

As Einstein later said, the reason for the development of general relativity was the preference of inertial motion within special relativity, while a theory which from the outset prefers no particular state of motion appeared more satisfactory to him. So, while still working at the patent office in 1907, Einstein had what he would call his "happiest thought". He realized that the principle of relativity could be extended to gravitational fields.

Consequently, in 1907 he wrote an article, published in 1908, on acceleration under special relativity. In that article, he argued that free fall is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the equivalence principle. In the same article, Einstein also predicted the phenomenon of gravitational time dilation.

In 1911, Einstein published another article expanding on the 1907 article. There, he considered the case of a uniformly accelerated box not in a gravitational field, and noted that it would be indistinguishable from a box sitting still in an unchanging gravitational field. He used special relativity to show that clocks at the top of a box accelerating upward would run faster than clocks at the bottom. He concluded that the rate at which time passes depends on the position in a gravitational field, and that the difference in rate is proportional to the gravitational potential to a first approximation.

The article also predicted the deflection of light by massive bodies, e.g., Jupiter, the Sun. Although the approximation was crude, it allowed him to calculate that the deflection is nonzero. Einstein urged astronomers to attempt direct observation of light deflection of fixed stars near the Sun during solar eclipses when they would be visible. German astronomer Erwin Finlay-Freundlich publicized Einstein's challenge to scientists around the world.

In October 1911, Freundlich contacted astronomer Charles D. Perrine in Berlin to inquire as to the suitability of examining existing solar eclipse photographs to prove Einstein's prediction of light deflection. Perrine, the director of the Argentine National Observatory at Cordoba, had participated in four solar eclipse expeditions while at the Lick Observatory, in 1900, 1901, 1905, and 1908. "...he had become, in the opinion of the director of the Lick Observatory, W. W. Campbell, an observer without peer in the field of solar eclipses." He did not believe existing eclipse photos would be useful in proving Einstein's claim. In 1912 Freundlich asked if Perrine would include observation of light deflection as part of his program for the solar eclipse of October 10, 1912, in Brazil. W. W. Campbell, director of the Lick Observatory, loaned Perrine its intramercurial camera lenses. Perrine and the Cordoba team were the only eclipse expedition to construct specialized equipment dedicated to observing light deflection. Unfortunately all the expeditions experienced heavy rain which prevented any observations. Nevertheless Perrine was the first astronomer to make a dedicated attempt to observe light deflection to test Einstein's prediction.

Two years later, the three observatory directors, Perrine, Freundlich, and Campbell included light deflection in their expeditions to the Russian Empire for the solar eclipse of August 21, 1914. Unfortunately due to clouds and the outbreak of World War I, no results were possible. However, Perrine was able to take the first photographs in an attempt to verify Einstein's prediction of light deflection. A light cloud cover prevented determining accurate star positions.

In hindsight, the occluding weather and lack of results in 1912 and 1914 favored Einstein. If clear photographs and measurable results had been possible, Einstein's 1911 prediction might have been proven wrong. The amount of deflection that he calculated in 1911 was too small (0.83 seconds of arc) by a factor of two because the approximation he used does not work well for things moving at near the speed of light. When Einstein completed the full theory of general relativity in 1915, he rectified this error and predicted the correct amount of light deflection caused by the Sun (1.75 seconds of arc). Eddington and Dyson in 1919 and W. W. Campbell in 1922 were able to compare their results to Einstein's corrected prediction.

Another of Einstein's notable thought experiments about the nature of the gravitational field is that of a rotating disk (a variant of the Ehrenfest paradox). He imagined an observer performing experiments on a rotating turntable. He noted that such an observer would find a different value for the mathematical constant π than the one predicted by Euclidean geometry. The reason is that the radius of a circle would be measured with an uncontracted ruler, but, according to special relativity, the circumference would seem to be longer because the ruler would be contracted. Since Einstein believed that the laws of physics were local, described by local fields, he concluded from this that spacetime could be locally curved. This led him to study Riemannian geometry, and to formulate general relativity in this language.

Developing general relativity

Eddington's photograph of a solar eclipse, which confirmed Einstein's theory that light "bends".

 

The New York Times reported confirmation of "the Einstein theory" (specifically, the bending of light by gravitation) based on 29 May 1919 eclipse observations in Principe (Africa) and Sobral (Brazil), after the findings were presented on 6 November 1919 to a joint meeting in London of the Royal Society and the Royal Astronomical Society.

In 1912, Einstein returned to Switzerland to accept a professorship at his alma mater, ETH Zurich. Once back in Zurich, he immediately visited his old ETH classmate Marcel Grossmann, now a professor of mathematics, who introduced him to Riemannian geometry and, more generally, to differential geometry. On the recommendation of Italian mathematician Tullio Levi-Civita, Einstein began exploring the usefulness of general covariance (essentially the use of tensors) for his gravitational theory. For a while, Einstein thought that there were problems with the approach, but he later returned to it and, by late 1915, had published his general theory of relativity in the form in which it is used today. This theory explains gravitation as the distortion of the structure of spacetime by matter, affecting the inertial motion of other matter.

During World War I, the work of Central Powers scientists was available only to Central Powers academics, for national security reasons. Some of Einstein's work did reach the United Kingdom and the United States through the efforts of the Austrian Paul Ehrenfest and physicists in the Netherlands, especially 1902 Nobel Prize-winner Hendrik Lorentz and Willem de Sitter of Leiden University. After the war, Einstein maintained his relationship with Leiden University, accepting a contract as an Extraordinary Professor; for ten years, from 1920 to 1930, he travelled to the Netherlands regularly to lecture.

In 1917, several astronomers accepted Einstein's 1911 challenge from Prague. The Mount Wilson Observatory in California, United States, published a solar spectroscopic analysis that showed no gravitational redshift. In 1918, the Lick Observatory, also in California, announced that it too had disproved Einstein's prediction, although its findings were not published.

However, in May 1919, a team led by the British astronomer Arthur Stanley Eddington claimed to have confirmed Einstein's prediction of gravitational deflection of starlight by the sun while photographing a solar eclipse with dual expeditions in Sobral, northern Brazil, and Príncipe, a west African island. Nobel laureate Max Born praised general relativity as the "greatest feat of human thinking about nature"; fellow laureate Paul Dirac was quoted saying it was "probably the greatest scientific discovery ever made".

There have been claims that scrutiny of the specific photographs taken on the Eddington expedition showed the experimental uncertainty to be comparable to the magnitude of the effect Eddington claimed to have demonstrated, and that a 1962 British expedition concluded that the method was inherently unreliable. The deflection of light during a solar eclipse was confirmed by later, more accurate observations. Some resented the newcomer's fame, notably some nationalistic German physicists, who later started the Deutsche Physik (German Physics) movement.

General covariance and the hole argument

By 1912, Einstein was actively seeking a theory in which gravitation was explained as a geometric phenomenon. At the urging of Tullio Levi-Civita, Einstein began by exploring the use of general covariance (which is essentially the use of curvature tensors) to create a gravitational theory. However, in 1913 Einstein abandoned that approach, arguing that it is inconsistent based on the "hole argument". In 1914 and much of 1915, Einstein was trying to create field equations based on another approach. When that approach was proven to be inconsistent, Einstein revisited the concept of general covariance and discovered that the hole argument was flawed.

The development of the Einstein field equations

Main article: Einstein field equations

When Einstein realized that general covariance was tenable, he quickly completed the development of the field equations that are named after him. However, he made a now-famous mistake. The field equations he published in October 1915 were

${\displaystyle R_{\mu \nu }=T_{\mu \nu }}$,

where ${\displaystyle R_{\mu \nu }}$ is the Ricci tensor, and ${\displaystyle T_{\mu \nu }}$ the energy–momentum tensor. This predicted the non-Newtonian perihelion precession of Mercury, and so had Einstein very excited. However, it was soon realized that they were inconsistent with the local conservation of energy–momentum unless the universe had a constant density of mass–energy–momentum. In other words, air, rock and even a vacuum should all have the same density. This inconsistency with observation sent Einstein back to the drawing board and, on 25 November 1915, Einstein presented the updated Einstein field equations to the Prussian Academy of Sciences:

${\displaystyle R_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu }=T_{\mu \nu }}$,

where ${\displaystyle R}$ is the Ricci scalar and ${\displaystyle g_{\mu \nu }}$ the metric tensor. With the publication of the field equations, the issue became one of solving them for various cases and interpreting the solutions. This and experimental verification have dominated general relativity research ever since.

Einstein and Hilbert

See also: General relativity priority dispute

Although Einstein is credited with finding the field equations, the German mathematician David Hilbert published them in an article before Einstein's article. This has resulted in accusations of plagiarism against Einstein, although not from Hilbert, and assertions that the field equations should be called the "Einstein–Hilbert field equations". However, Hilbert did not press his claim for priority and some have asserted that Einstein submitted the correct equations before Hilbert amended his own work to include them. This suggests that Einstein developed the correct field equations first, though Hilbert may have reached them later independently (or even learned of them afterwards through his correspondence with Einstein). However, others have criticized those assertions. Kip Thorne stated, "Remarkably, Einstein was not the first to discover the correct form of the law of warpage [. . . .] Recognition for the first discovery must go to Hilbert."

Sir Arthur Eddington

In the early years after Einstein's theory was published, Sir Arthur Eddington lent his considerable prestige in the British scientific establishment in an effort to champion the work of this German scientist. Because the theory was so complex and abstruse (even today it is popularly considered the pinnacle of scientific thinking; in the early years it was even more so), it was rumored that only three people in the world understood it. There was an illuminating, though probably apocryphal, anecdote about this. As related by Ludwik Silberstein, during one of Eddington's lectures he asked "Professor Eddington, you must be one of three persons in the world who understands general relativity." Eddington paused, unable to answer. Silberstein continued "Don't be modest, Eddington!" Finally, Eddington replied "On the contrary, I'm trying to think who the third person is."

Solutions

The Schwarzschild solution

Since the field equations are non-linear, Einstein assumed that they were unsolvable. However, Karl Schwarzschild discovered in 1915 and published in 1916 an exact solution for the case of a spherically symmetric spacetime surrounding a massive object in spherical coordinates. This is now known as the Schwarzschild solution. Since then, many other exact solutions have been found.

The expanding universe and the cosmological constant

Main article: Cosmological constant

In 1922, Alexander Friedmann found a solution in which the universe may expand or contract, and later Georges Lemaître derived a solution for an expanding universe. However, Einstein believed that the universe was static, and since a static cosmology was not supported by the general relativistic field equations, he added a cosmological constant Λ to the field equations, which became

${\displaystyle R_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu }+\mathrm{\Lambda }{g}_{\mu \nu }=T_{\mu \nu }}$.

This permitted the creation of steady-state solutions, but they were unstable: the slightest perturbation of a static state would result in the universe expanding or contracting. In 1929, Edwin Hubble found evidence for the universe expanding. This resulted in Einstein dropping the cosmological constant, referring to it as "the biggest blunder in my career". At the time, it was an ad hoc hypothesis to add in the cosmological constant, as it was only intended to justify one result (a static universe).

More exact solutions

Progress in solving the field equations and understanding the solutions has been ongoing. The solution for a spherically symmetric charged object was discovered by Reissner and later rediscovered by Nordström, and is called the Reissner–Nordström solution. The black hole aspect of the Schwarzschild solution was very controversial, and Einstein did not believe that singularities could be real. However, in 1957 (two years after Einstein's death), Martin Kruskal published a proof that black holes are called for by the Schwarzschild solution. Additionally, the solution for a rotating massive object was obtained by Roy Kerr in the 1960s and is called the Kerr solution. The Kerr–Newman solution for a rotating, charged massive object was published a few years later.

Testing the theory

Main articles: Tests of general relativity and Gravitational wave observation

The first piece of evidence in support of general relativity came from its correct prediction of the anomalous rate of precession of Mercury's orbit. Subsequently, Arthur Stanley Eddington's 1919 expedition confirmed Einstein's prediction of the deflection of light by the Sun during the total solar eclipse of 29 May 1919, which helped to cement the status of general relativity as a viable theory. Since then, many observations have shown agreement with the predictions of general relativity. These include studies of binary pulsars, observations of radio signals passing the limb of the Sun, and even the global positioning system.

First image of the event horizon of a black hole (M87*) captured by the Event Horizon Telescope

The theory predicts gravitational waves, which are ripples in the curvature of spacetime that propagate as waves, travelling outward from the source. The first observation of gravitational waves, which came from the merger of two black holes, was made on 14 September 2015 by the Advanced LIGO team, corroborating another prediction of the theory 100 years after it was published.

The first image of a black hole, the supermassive one at the center of galaxy Messier 87, was published by the Event Horizon Telescope Collaboration on 10 April 2019.

Alternative theories

Main article: Alternatives to general relativity

There have been various attempts to find modifications to general relativity. The most famous of these are the Brans–Dicke theory (also known as scalar–tensor theory), and Rosen's bimetric theory. Both of these theories proposed changes to the field equations of general relativity, and both suffer from these changes permitting the presence of bipolar gravitational radiation. As a result, Rosen's original theory has been refuted by observations of binary pulsars. As for Brans–Dicke (which has a tunable parameter ω such that ω = ∞ is the same as general relativity), the amount by which it can differ from general relativity has been severely constrained by these observations. Many other alternatives to general relativity have also been ruled out by analyses of the neutron-star merger GW170817.

In addition, general relativity is inconsistent with quantum mechanics, the physical theory that describes the wave–particle duality of matter, and quantum mechanics does not currently describe gravitational attraction at relevant (microscopic) scales. There is a great deal of speculation in the physics community as to the modifications that might be needed to both general relativity and quantum mechanics in order to unite them consistently. The speculative theory that unites general relativity and quantum mechanics is usually called quantum gravity, prominent examples of which include string theory and loop quantum gravity.

Golden age

Kip Thorne identifies the "golden age of general relativity" as the period roughly from 1960 to 1975, during which the study of general relativity, which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics. During this period, many of the concepts and terms which continue to inspire the imaginations of gravitation researchers and the general public were introduced, including black holes and gravitational singularities. At the same time, in a closely related development, the study of physical cosmology entered the mainstream and the Big Bang became well established.

Fulvio Melia refers frequently to the "golden age of relativity" in his book Cracking the Einstein Code. Andrzej Trautman hosted a relativity conference in Warsaw in 1962 to which Melia refers:

General relativity moved very successfully from that meeting in Warsaw, hot on the heels of the Pound–Rebka experiment, and entered its golden age of discovery that lasted into the mid-1970s.

Roy Kerr, protagonist of the book, contributed an Afterword, saying of the book: "It is a remarkable piece of writing capturing beautifully the period we now refer to as the golden age of relativity."