14 Destinations

14 Destinations theme by Jector

Download: 14Destinations.p3t

14 Destinations Theme Preview

P3T Unpacker v0.12
Copyright (c) 2007. Anoop Menon

This program unpacks Playstation 3 Theme files (.p3t) so that you can touch-up an existing theme to your likings or use a certain wallpaper from it (as many themes have multiple). But remember, if you use content from another theme and release it, be sure to give credit!

Download for Windows: p3textractor.zip

Instructions:

Download p3textractor.zip from above. Extract the files to a folder with a program such as WinZip or WinRAR. Now there are multiple ways to extract the theme.

The first way is to simply open the p3t file with p3textractor.exe. If you don’t know how to do this, right click the p3t file and select Open With. Alternatively, open the p3t file and it will ask you to select a program to open with. Click Browse and find p3textractor.exe from where you previously extracted it to. It will open CMD and extract the theme to extracted.[filename]. After that, all you need to do for any future p3t files is open them and it will extract.

The second way is very simple. Just drag the p3t file to p3textractor.exe. It will open CMD and extract the theme to extracted.[filename].

For the third way, first put the p3t file you want to extract into the same folder as p3textractor.exe. Open CMD and browse to the folder with p3extractor.exe. Enter the following:
p3textractor filename.p3t [destination path]Replace filename with the name of the p3t file, and replace [destination path] with the name of the folder you want the files to be extracted to. A destination path is not required. By default it will extract to extracted.filename.

World

World theme by JackKing

Download: World_2.p3t

World Theme Preview

Image of the physical world, captured by the Hubble Space Telescope

The world is the totality of entities, the whole of reality, or everything that exists.[1] The nature of the world has been conceptualized differently in different fields. Some conceptions see the world as unique while others talk of a "plurality of worlds". Some treat the world as one simple object while others analyze the world as a complex made up of parts.

In scientific cosmology, the world or universe is commonly defined as "[t]he totality of all space and time; all that is, has been, and will be". Theories of modality talk of possible worlds as complete and consistent ways how things could have been. Phenomenology, starting from the horizon of co-given objects present in the periphery of every experience, defines the world as the biggest horizon or the "horizon of all horizons". In philosophy of mind, the world is contrasted with the mind as that which is represented by the mind. Theology conceptualizes the world in relation to God, for example, as God's creation, as identical to God or as the two being interdependent. In religions, there is a tendency to downgrade the material or sensory world in favor of a spiritual world to be sought through religious practice. A comprehensive representation of the world and our place in it, as is found in religions, is known as a worldview. Cosmogony is the field that studies the origin or creation of the world while eschatology refers to the science or doctrine of the last things or of the end of the world.

In various contexts, the term "world" takes a more restricted meaning associated, for example, with the Earth and all life on it, with humanity as a whole or with an international or intercontinental scope. In this sense, world history refers to the history of humanity as a whole and world politics is the discipline of political science studying issues that transcend nations and continents. Other examples include terms such as "world religion", "world language", "world government", "world war", "world population", "world economy", or "world championship".

Etymology[edit]

The English word world comes from the Old English weorold. The Old English is a reflex of the Common Germanic *weraldiz, a compound of weraz 'man' and aldiz 'age', thus literally meaning roughly 'age of man';[2] this word led to Old Frisian warld, Old Saxon werold, Old Dutch werolt, Old High German weralt, and Old Norse verǫld.[3]

The corresponding word in Latin is mundus, literally 'clean, elegant', itself a loan translation of Greek cosmos 'orderly arrangement'. While the Germanic word thus reflects a mythological notion of a "domain of Man" (compare Midgard), presumably as opposed to the divine sphere on the one hand and the chthonic sphere of the underworld on the other, the Greco-Latin term expresses a notion of creation as an act of establishing order out of chaos.[4]

Conceptions[edit]

Different fields often work with quite different conceptions of the essential features associated with the term "world".[5][6] Some conceptions see the world as unique: there can be no more than one world. Others talk of a "plurality of worlds".[4] Some see worlds as complex things composed of many substances as their parts while others hold that worlds are simple in the sense that there is only one substance: the world as a whole.[7] Some characterize worlds in terms of objective spacetime while others define them relative to the horizon present in each experience. These different characterizations are not always exclusive: it may be possible to combine some without leading to a contradiction. Most of them agree that worlds are unified totalities.[5][6]

Monism and pluralism[edit]

Monism is a thesis about oneness: that only one thing exists in a certain sense. The denial of monism is pluralism, the thesis that, in a certain sense, more than one thing exists.[7] There are many forms of monism and pluralism, but in relation to the world as a whole, two are of special interest: existence monism/pluralism and priority monism/pluralism. Existence monism states that the world is the only concrete object there is.[7][8][9] This means that all the concrete "objects" we encounter in our daily lives, including apples, cars and ourselves, are not truly objects in a strict sense. Instead, they are just dependent aspects of the world-object.[7] Such a world-object is simple in the sense that it does not have any genuine parts. For this reason, it has also been referred to as "blobject" since it lacks an internal structure like a blob.[10] Priority monism allows that there are other concrete objects besides the world.[7] But it holds that these objects do not have the most fundamental form of existence, that they somehow depend on the existence of the world.[9][11] The corresponding forms of pluralism state that the world is complex in the sense that it is made up of concrete, independent objects.[7]

Scientific cosmology[edit]

Scientific cosmology can be defined as the science of the universe as a whole. In it, the terms "universe" and "cosmos" are usually used as synonyms for the term "world".[12] One common definition of the world/universe found in this field is as "[t]he totality of all space and time; all that is, has been, and will be".[13][5][6] Some definitions emphasize that there are two other aspects to the universe besides spacetime: forms of energy or matter, like stars and particles, and laws of nature.[14] World-conceptions in this field differ both concerning their notion of spacetime and of the contents of spacetime. The theory of relativity plays a central role in modern cosmology and its conception of space and time. A difference from its predecessors is that it conceives space and time not as distinct dimensions but as a single four-dimensional manifold called spacetime.[15] This can be seen in special relativity in relation to the Minkowski metric, which includes both spatial and temporal components in its definition of distance.[16] General relativity goes one step further by integrating the concept of mass into the concept of spacetime as its curvature.[16] Quantum cosmology uses a classical notion of spacetime and conceives the whole world as one big wave function expressing the probability of finding particles in a given location.[17]

Theories of modality[edit]

The world-concept plays a role in many modern theories of modality, sometimes in the form of possible worlds.[18] A possible world is a complete and consistent way how things could have been.[19] The actual world is a possible world since the way things are is a way things could have been. There are many other ways things could have been besides how they actually are. For example, Hillary Clinton did not win the 2016 US election, but she could have won them. So there is a possible world in which she did. There is a vast number of possible worlds, one corresponding to each such difference, no matter how small or big, as long as no outright contradictions are introduced this way.[19]

Possible worlds are often conceived as abstract objects, for example, in terms of non-obtaining states of affairs or as maximally consistent sets of propositions.[20][21] On such a view, they can even be seen as belonging to the actual world.[22] Another way to conceive possible worlds, made famous by David Lewis, is as concrete entities.[4] On this conception, there is no important difference between the actual world and possible worlds: both are conceived as concrete, inclusive and spatiotemporally connected.[19] The only difference is that the actual world is the world we live in, while other possible worlds are not inhabited by us but by our counterparts.[23] Everything within a world is spatiotemporally connected to everything else but the different worlds do not share a common spacetime: They are spatiotemporally isolated from each other.[19] This is what makes them separate worlds.[23]

It has been suggested that, besides possible worlds, there are also impossible worlds. Possible worlds are ways things could have been, so impossible worlds are ways things could not have been.[24][25] Such worlds involve a contradiction, like a world in which Hillary Clinton both won and lost the 2016 US election. Both possible and impossible worlds have in common the idea that they are totalities of their constituents.[24][26]

Phenomenology[edit]

Within phenomenology, worlds are defined in terms of horizons of experiences.[5][6] When we perceive an object, like a house, we do not just experience this object at the center of our attention but also various other objects surrounding it, given in the periphery.[27] The term "horizon" refers to these co-given objects, which are usually experienced only in a vague, indeterminate manner.[28][29] The perception of a house involves various horizons, corresponding to the neighborhood, the city, the country, the Earth, etc. In this context, the world is the biggest horizon or the "horizon of all horizons".[27][5][6] It is common among phenomenologists to understand the world not just as a spatiotemporal collection of objects but as additionally incorporating various other relations between these objects. These relations include, for example, indication-relations that help us anticipate one object given the appearances of another object and means-end-relations or functional involvements relevant for practical concerns.[27]

Philosophy of mind[edit]

In philosophy of mind, the term "world" is commonly used in contrast to the term "mind" as that which is represented by the mind. This is sometimes expressed by stating that there is a gap between mind and world and that this gap needs to be overcome for representation to be successful.[30][31][32] One problem in philosophy of mind is to explain how the mind is able to bridge this gap and to enter into genuine mind-world-relations, for example, in the form of perception, knowledge or action.[33][34] This is necessary for the world to be able to rationally constrain the activity of the mind.[30][35] According to a realist position, the world is something distinct and independent from the mind.[36] Idealists conceive of the world as partially or fully determined by the mind.[36][37] Immanuel Kant's transcendental idealism, for example, posits that the spatiotemporal structure of the world is imposed by the mind on reality but lacks independent existence otherwise.[38] A more radical idealist conception of the world can be found in Berkeley's subjective idealism, which holds that the world as a whole, including all everyday objects like tables, cats, trees and ourselves, "consists of nothing but minds and ideas".[39]

Theology[edit]

Different theological positions hold different conceptions of the world based on its relation to God. Classical theism states that God is wholly distinct from the world. But the world depends for its existence on God, both because God created the world and because He maintains or conserves it.[40][41][42] This is sometimes understood in analogy to how humans create and conserve ideas in their imagination, with the difference being that the divine mind is vastly more powerful.[40] On such a view, God has absolute, ultimate reality in contrast to the lower ontological status ascribed to the world.[42] God's involvement in the world is often understood along the lines of a personal, benevolent God who looks after and guides His creation.[41] Deists agree with theists that God created the world but deny any subsequent, personal involvement in it.[43] Pantheists reject the separation between God and world. Instead, they claim that the two are identical. This means that there is nothing to the world that does not belong to God and that there is nothing to God beyond what is found in the world.[42][44] Panentheism constitutes a middle ground between theism and pantheism. Against theism, it holds that God and the world are interrelated and depend on each other. Against pantheism, it holds that there is no outright identity between the two.[42][45]

History of philosophy[edit]

In philosophy, the term world has several possible meanings. In some contexts, it refers to everything that makes up reality or the physical universe. In others, it can mean have a specific ontological sense (see world disclosure). While clarifying the concept of world has arguably always been among the basic tasks of Western philosophy, this theme appears to have been raised explicitly only at the start of the twentieth century,[46]

Plato[edit]

Plato is well known for his theory of forms, which posits the existence of two different worlds: the sensible world and the intelligible world. The sensible world is the world we live in, filled with changing physical things we can see, touch and interact with. The intelligible world is the world of invisible, eternal, changeless forms like goodness, beauty, unity and sameness.[47][48][49] Plato ascribes a lower ontological status to the sensible world, which only imitates the world of forms. This is due to the fact that physical things exist only to the extent that they participate in the forms that characterize them, while the forms themselves have an independent manner of existence.[47][48][49] In this sense, the sensible world is a mere replication of the perfect exemplars found in the world of forms: it never lives up to the original. In the allegory of the cave, Plato compares the physical things we are familiar with to mere shadows of the real things. But not knowing the difference, the prisoners in the cave mistake the shadows for the real things.[50]

Wittgenstein[edit]

Two definitions that were both put forward in the 1920s, however, suggest the range of available opinion. "The world is everything that is the case", wrote Ludwig Wittgenstein in his influential Tractatus Logico-Philosophicus, first published in 1921.[51]

Heidegger[edit]

Martin Heidegger, meanwhile, argued that "the surrounding world is different for each of us, and notwithstanding that we move about in a common world".[52]

Eugen Fink[edit]

"World" is one of the key terms in Eugen Fink's philosophy.[53] He thinks that there is a misguided tendency in western philosophy to understand the world as one enormously big thing containing all the small everyday things we are familiar with.[54] He sees this view as a form of forgetfulness of the world and tries to oppose it by what he calls the "cosmological difference": the difference between the world and the inner-worldly things it contains.[54] On his view, the world is the totality of the inner-worldly things that transcends them.[55] It is itself groundless but it provides a ground for things. It therefore cannot be identified with a mere container. Instead, the world gives appearance to inner-worldly things, it provides them with a place, a beginning and an end.[54] One difficulty in investigating the world is that we never encounter it since it is not just one more thing that appears to us. This is why Fink uses the notion of play or playing to elucidate the nature of the world.[54][55] He sees play as a symbol of the world that is both part of it and that represents it.[56] Play usually comes with a form of imaginary play-world involving various things relevant to the play. But just like the play is more than the imaginary realities appearing in it so the world is more than the actual things appearing in it.[54][56]

Goodman[edit]

The concept of worlds plays a central role in Nelson Goodman's late philosophy.[57] He argues that we need to posit different worlds in order to account for the fact that there are different incompatible truths found in reality.[58] Two truths are incompatible if they ascribe incompatible properties to the same thing.[57] This happens, for example, when we assert both that the earth moves and that the earth is at rest. These incompatible truths correspond to two different ways of describing the world: heliocentrism and geocentrism.[58] Goodman terms such descriptions "world versions". He holds a correspondence theory of truth: a world version is true if it corresponds to a world. Incompatible true world versions correspond to different worlds.[58] It is common for theories of modality to posit the existence of a plurality of possible worlds. But Goodman's theory is different since it posits a plurality not of possible but of actual worlds.[57][5] Such a position is in danger of involving a contradiction: there cannot be a plurality of actual worlds if worlds are defined as maximally inclusive wholes.[57][5] This danger may be avoided by interpreting Goodman's world-concept not as maximally inclusive wholes in the absolute sense but in relation to its corresponding world-version: a world contains all and only the entities that its world-version describes.[57][5]

Religion[edit]

Yggdrasil, an attempt to reconstruct the Norse world tree which connects the heavens, the world, and the underworld.

Mythological cosmologies depict the world as centered on an axis mundi and delimited by a boundary such as a world ocean, a world serpent or similar.[59][60]

Hinduism[edit]

Hinduism constitutes a family of religious-philosophical views.[61] These views present perspectives on the nature and role of the world. Samkhya philosophy, for example, is a metaphysical dualism that understands reality as comprising 2 parts: purusha and prakriti.[62] The term "purusha" stands for the individual conscious self that each of "us" possesses. Prakriti, on the other hand, is the 1 world inhabited by all these selves.[63] Samkhya understands this world as a world of matter governed by the law of cause and effect.[62] The term "matter" is understood in a sense in this tradition including physical and mental aspects.[64] This is reflected in the doctrine of tattvas, according to which prakriti is made up of 23 principles or elements of reality.[64] These principles include physical elements, like water or earth, and mental aspects, like intelligence or sense-impressions.[63] The relation between purusha and prakriti is conceived as 1 of observation: purusha is the conscious self aware of the world of prakriti and does not causally interact with it.[62]

A conception of the world is present in Advaita Vedanta, the monist school among the Vedanta schools.[61] Unlike the realist position defended in Samkhya philosophy, Advaita Vedanta sees the world of multiplicity as an illusion, referred to as Maya.[61] This illusion includes impression of existing as separate experiencing selfs called Jivas.[65] Instead, Advaita Vedanta teaches that on the most fundamental level of reality, referred to as Brahman, there exists no plurality or difference.[65] All there is is 1 all-encompassing self: Atman.[61] Ignorance is seen as the source of this illusion, which results in bondage to the world of mere appearances. Liberation is possible in the course of overcoming this illusion by acquiring the knowledge of Brahman, according to Advaita Vedanta.[65]

Christianity[edit]

Contemptus mundi is the name given to the belief that the world, in all its vanity, is nothing more than a futile attempt to hide from God by stifling our desire for the good and the holy.[66] This view has been criticised as a "pastoral of fear" by historian Jean Delumeau.[67]

Orbis Catholicus is a Latin phrase meaning 'Catholic world', per the expression Urbi et Orbi, and refers to that area of Christendom under papal supremacy.[68]

Islam[edit]

In Islam, the term "dunya" is used for the world. Its meaning is derived from the root word "dana", a term for "near".[69] It is associated with the temporal, sensory world and earthly concerns, i.e. with this world in contrast to the spiritual world.[70] Religious teachings warn of a tendency to seek happiness in this world and advise a more ascetic lifestyle concerned with the afterlife.[71] Other strands in Islam recommend a balanced approach.[70]

Mandaeism[edit]

In Mandaean cosmology, the world or earthly realm is known as Tibil. It is separated from the World of Light (alma d-nhūra) above and the World of Darkness (alma d-hšuka) below by aether (ayar).[72][73]

Related terms and problems[edit]

Worldviews[edit]

Scientific worldview.

A worldview is a comprehensive representation of the world and our place in it.[74] As a representation, it is a subjective perspective of the world and thereby different from the world it represents.[75] All higher animals need to represent their environment in some way in order to navigate it. But it has been argued that only humans possess a representation encompassing enough to merit the term "worldview".[75] Philosophers of worldviews commonly hold that the understanding of any object depends on a worldview constituting the background on which this understanding can take place. This may affect not just our intellectual understanding of the object in question but the experience of it in general.[74] It is therefore impossible to assess one's worldview from a neutral perspective since this assessment already presupposes the worldview as its background. Some hold that each worldview is based on a single hypothesis that promises to solve all the problems of our existence we may encounter.[76] On this interpretation, the term is closely associated to the worldviews given by different religions.[76] Worldviews offer orientation not just in theoretical matters but also in practical matters. For this reason, they usually include answers to the question of the meaning of life and other evaluative components about what matters and how we should act.[77][78] A worldview can be unique to one individual but worldviews are usually shared by many people within a certain culture or religion.

Paradox of many worlds[edit]

The idea that there exist many different worlds is found in various fields. For example, theories of modality talk about a plurality of possible worlds and the many-worlds interpretation of quantum mechanics carries this reference even in its name. Talk of different worlds is also common in everyday language, for example, with reference to the world of music, the world of business, the world of football, the world of experience or the Asian world. But at the same time, worlds are usually defined as all-inclusive totalities.[5][6][15][14] This seems to contradict the very idea of a plurality of worlds since if a world is total and all-inclusive then it cannot have anything outside itself. Understood this way, a world can neither have other worlds besides itself or be part of something bigger.[5][57] One way to resolve this paradox while holding onto the notion of a plurality of worlds is to restrict the sense in which worlds are totalities. On this view, worlds are not totalities in an absolute sense.[5] This might be even understood in the sense that, strictly speaking, there are no worlds at all.[57] Another approach understands worlds in a schematic sense: as context-dependent expressions that stand for the current domain of discourse. So in the expression "Around the World in Eighty Days", the term "world" refers to the earth while in the colonial[79] expression "the New World" it refers to the landmass of North and South America.[15]

Cosmogony[edit]

Cosmogony is the field that studies the origin or creation of the world. This includes both scientific cosmogony and creation myths found in various religions.[80][81] The dominant theory in scientific cosmogony is the Big Bang theory, according to which both space, time and matter have their origin in one initial singularity occurring about 13.8 billion years ago. This singularity was followed by an expansion that allowed the universe to sufficiently cool down for the formation of subatomic particles and later atoms. These initial elements formed giant clouds, which would then coalesce into stars and galaxies.[16] Non-scientific creation myths are found in many cultures and are often enacted in rituals expressing their symbolic meaning.[80] They can be categorized concerning their contents. Types often found include creation from nothing, from chaos or from a cosmic egg.[80]

Eschatology[edit]

Eschatology refers to the science or doctrine of the last things or of the end of the world. It is traditionally associated with religion, specifically with the Abrahamic religions.[82][83] In this form, it may include teachings both of the end of each individual human life and of the end of the world as a whole. But it has been applied to other fields as well, for example, in the form of physical eschatology, which includes scientifically based speculations about the far future of the universe.[84] According to some models, there will be a Big Crunch in which the whole universe collapses back into a singularity, possibly resulting in a second Big Bang afterward. But current astronomical evidence seems to suggest that our universe will continue to expand indefinitely.[84]

World history[edit]

World history studies the world from a historical perspective. Unlike other approaches to history, it employs a global viewpoint. It deals less with individual nations and civilizations, which it usually approaches at a high level of abstraction.[85] Instead, it concentrates on wider regions and zones of interaction, often interested in how people, goods and ideas move from one region to another.[86] It includes comparisons of different societies and civilizations as well as considering wide-ranging developments with a long-term global impact like the process of industrialization.[85] Contemporary world history is dominated by three mai

Space

Space theme by DiSanti

Download: Space_4.p3t

Space Theme Preview 4

A right-handed three-dimensional Cartesian coordinate system used to indicate positions in space

Space is a three-dimensional continuum containing positions and directions.[1] In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime.[2] The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat, as in the Euclidean space. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.[3] Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.

Philosophy of space[edit]

Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates in his reflections on what the Greeks called khôra (i.e. "space"), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or in the later "geometrical conception of place" as "space qua extension" in the Discourse on Place (Qawl fi al-Makan) of the 11th-century Arab polymath Alhazen.[4] Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics.

Isaac Newton viewed space as absolute, existing permanently and independently of whether there was any matter in the.[5] In contrast, other natural philosophers, notably Gottfried Leibniz, thought that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision. Later, the metaphysician Immanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of the outside world—they are elements of an already given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition".

Galileo[edit]

Galilean and Cartesian theories about space, matter, and motion are at the foundation of the Scientific Revolution, which is understood to have culminated with the publication of Newton's Principia Mathematica in 1687.[6] Newton's theories about space and time helped him explain the movement of objects. While his theory of space is considered the most influential in physics, it emerged from his predecessors' ideas about the same.[7]

As one of the pioneers of modern science, Galileo revised the established Aristotelian and Ptolemaic ideas about a geocentric cosmos. He backed the Copernican theory that the universe was heliocentric, with a stationary Sun at the center and the planets—including the Earth—revolving around the Sun. If the Earth moved, the Aristotelian belief that its natural tendency was to remain at rest was in question. Galileo wanted to prove instead that the Sun moved around its axis, that motion was as natural to an object as the state of rest. In other words, for Galileo, celestial bodies, including the Earth, were naturally inclined to move in circles. This view displaced another Aristotelian idea—that all objects gravitated towards their designated natural place-of-belonging.[8]

René Descartes[edit]

Descartes set out to replace the Aristotelian worldview with a theory about space and motion as determined by natural laws. In other words, he sought a metaphysical foundation or a mechanical explanation for his theories about matter and motion. Cartesian space was Euclidean in structure—infinite, uniform and flat.[9] It was defined as that which contained matter; conversely, matter by definition had a spatial extension so that there was no such thing as empty space.[6]

The Cartesian notion of space is closely linked to his theories about the nature of the body, mind and matter. He is famously known for his "cogito ergo sum" (I think therefore I am), or the idea that we can only be certain of the fact that we can doubt, and therefore think and therefore exist. His theories belong to the rationalist tradition, which attributes knowledge about the world to our ability to think rather than to our experiences, as the empiricists believe.[10] He posited a clear distinction between the body and mind, which is referred to as the Cartesian dualism.

Leibniz and Newton[edit]

Gottfried Leibniz

Following Galileo and Descartes, during the seventeenth century the philosophy of space and time revolved around the ideas of Gottfried Leibniz, a German philosopher–mathematician, and Isaac Newton, who set out two opposing theories of what space is. Rather than being an entity that independently exists over and above other matter, Leibniz held that space is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together".[11] Unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete.[12] Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people.[13] Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes must therefore be wrong.[14]

Isaac Newton

Newton took space to be more than relations between material objects and based his position on observation and experimentation. For a relationist there can be no real difference between inertial motion, in which the object travels with constant velocity, and non-inertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates forces, it must be absolute.[15] He used the example of water in a spinning bucket to demonstrate his argument. Water in a bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water.[16] Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was considered decisive in showing that space must exist independently of matter.

Kant[edit]

Immanuel Kant

In the eighteenth century the German philosopher Immanuel Kant published his theory of space as "a property of our mind" by which "we represent to ourselves objects as outside us, and all as in space" in the Critique of Pure Reason[17] On his view the nature of spatial predicates are "relations that only attach to the form of intuition alone, and thus to the subjective constitution of our mind, without which these predicates could not be attached to anything at all."[18] This develops his theory of knowledge in which knowledge about space itself can be both a priori and synthetic.[19] According to Kant, knowledge about space is synthetic because any proposition about space cannot be true merely in virtue of the meaning of the terms contained in the proposition. In the counter-example, the proposition "all unmarried men are bachelors" is true by virtue of each term's meaning. Further, space is a priori because it is the form of our receptive abilities to receive information about the external world. For example, someone without sight can still perceive spatial attributes via touch, hearing, and smell. Knowledge of space itself is a priori because it belongs to the subjective constitution of our mind as the form or manner of our intuition of external objects.

Non-Euclidean geometry[edit]

Spherical geometry is similar to elliptical geometry. On a sphere (the surface of a ball) there are no parallel lines.

Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate, has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line L1 and a point P not on L1, there is exactly one straight line L2 on the plane that passes through the point P and is parallel to the straight line L1. Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory that could be derived from the other axioms.[20] Around 1830 though, the Hungarian János Bolyai and the Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called hyperbolic geometry. In this geometry, an infinite number of parallel lines pass through the point P. Consequently, the sum of angles in a triangle is less than 180° and the ratio of a circle's circumference to its diameter is greater than pi. In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180° and circles have a ratio of circumference-to-diameter that is less than pi.

Type of geometry Number of parallels Sum of angles in a triangle Ratio of circumference to diameter of circle Measure of curvature
Hyperbolic Infinite < 180° > π < 0
Euclidean 1 180° π 0
Elliptical 0 > 180° < π > 0

Gauss and Poincaré[edit]

Carl Friedrich Gauss
Henri Poincaré

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved. Carl Friedrich Gauss, a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle, and there are reports that he actually carried out a test, on a small scale, by triangulating mountain tops in Germany.[21]

Henri Poincaré, a French mathematician and physicist of the late 19th century, introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment.[22] He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a sphere-world. In this world, the temperature is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface.[23] In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space was a matter of convention.[24] Since Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.[25]

Einstein[edit]

Albert Einstein

In 1905, Albert Einstein published his special theory of relativity, which led to the concept that space and time can be viewed as a single construct known as spacetime. In this theory, the speed of light in vacuum is the same for all observers—which has the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to tick more slowly than one that is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer.

Subsequently, Einstein worked on a general theory of relativity, which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself.[26] According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars, confirming the predictions of Einstein's theories, and non-Euclidean geometry is usually used to describe spacetime.

Mathematics[edit]

In modern mathematics spaces are defined as sets with some added structure. They are typically topological spaces, in which a concept of neighbourhood is defined, frequently by means of a distance (metric spaces). The elements of a space are often called points, but they can have other names such as vectors in vector spaces and functions in function spaces.

Physics[edit]