What do You see ?

How would one know, what is real, and what would have to be in place to never ponder, if it is, indeed, fact, real ?

What made me ponder - I have been guided to do so.
Sharing of information has come this way, this point of you, is wonder struck, dumb founded, and have my small world blown wide open, every day.
Reality's creations, or what humanity has repeatedly performed as suggested, generations of humans in family's have be played, cause look around, tickickey tack homes on a tickickey tack street ...
How they do that ? How to put a planet in a cube.

Mathematical proof

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms.^[2]^[3]^[4] Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved statement that is believed true is known as a conjecture.

Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.

History and etymology

See also: History of logic

The word "proof" comes from the Latin probare meaning "to test". Related modern words are the English "probe", "probation", and "probability", the Spanish probar (to smell or taste, or (lesser use) touch or test),^[5] Italian provare (to try), and the German probieren (to try). The early use of "probity" was in the presentation of legal evidence. A person of authority, such as a nobleman, was said to have probity, whereby the evidence was by his relative authority, which outweighed empirical testimony.^[6]

Nature and purpose
As practiced, a proof is expressed in natural language and is a rigorous argument intended to convince the audience of the truth of a statement. The standard of rigor is not absolute and has varied throughout history. A proof can be presented differently depending on the intended audience. In order to gain acceptance, a proof has to meet communal statements of rigor; an argument considered vague or incomplete may be rejected.

In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions.
     Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
    On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third-century AD work by Heron of Alexandria.
    Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name Theon of Alexandria as a more likely author.[18]
    Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.

Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye.
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians,^[1] Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.^[2] The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.^[3]
For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only where the gravitational field is weak.^[4]
Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms to propositions without the use of coordinates. This is in contrast to analytic geometry, which uses coordinates.
The term proposition has a broad use in contemporary philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other "propositional attitudes" (i.e., what is believed, doubted, etc.), the referents of that-clauses and the meanings of declarative sentences. Propositions are the sharable objects of attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens which are not sharable, and concrete events or facts, which cannot be false.^[1]

Relation to the mind

In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes. Propositional attitudes are simply attitudes characteristic of folk psychology (belief, desire, etc.) that one can take toward a proposition (e.g. 'it is raining,' 'snow is white,' etc.). In English, propositions usually follow folk psychological attitudes by a "that clause" (e.g. "Jane believes that it is raining"). In philosophy of mind and psychology, mental states are often taken to primarily consist in propositional attitudes. The propositions are usually said to be the "mental content" of the attitude. For example, if Jane has a mental state of believing that it is raining, her mental content is the proposition 'it is raining.' Furthermore, since such mental states are about something (namely propositions), they are said to be intentional mental states. Philosophical debates surrounding propositions as they relate to propositional attitudes have also recently centered on whether they are internal or external to the agent or whether they are mind-dependent or mind-independent entities (see the entry on internalism and externalism in philosophy of mind).

It can be argued that this growth of slavery was what made Greeks particularly conscious of the value of freedom. After all, any Greek farmer might fall into debt and therefore might become a slave, at almost any time ... When the Greeks fought together, they fought in order to avoid being enslaved by warfare, to avoid being defeated by those who might take them into slavery. And they also arranged their political institutions so as to remain free men.

—Geoffrey Hosking, 2005^[10]

Slavery permitted slaveowners to have substantial free time, and enabled participation in public life.^[10] Polis citizenship was marked by exclusivity. Inequality of status was widespread; citizens had a higher status than non-citizens, such as women, slaves or barbarians.^[11]^[12] The first form of citizenship was based on the way people lived in the ancient Greek times, in small-scale organic communities of the polis. Citizenship was not seen as a separate activity from the private life of the individual person, in the sense that there was not a distinction between public and private life.

The obligations of citizenship were deeply connected into one's everyday life in the polis. These small-scale organic communities were generally seen as a new development in world history, in contrast to the established ancient civilizations of Egypt or Persia, or the hunter-gatherer bands elsewhere. From the viewpoint of the ancient Greeks, a person's public life was not separated from their private life, and Greeks did not distinguish between the two worlds according to the modern western conception.

The obligations of citizenship were deeply connected with everyday life. To be truly human, one had to be an active citizen to the community, which Aristotle famously expressed: "To take no part in the running of the community's affairs is to be either a beast or a god!" This form of citizenship was based on obligations of citizens towards the community, rather than rights given to the citizens of the community.

This was not a problem because they all had a strong affinity with the polis; their own destiny and the destiny of the community were strongly linked. Also, citizens of the polis saw obligations to the community as an opportunity to be virtuous, it was a source of honour and respect. In Athens, citizens were both ruler and ruled, important political and judicial offices were rotated and all citizens had the right to speak and vote in the political assembly.

Commonwealth
The concept of "Commonwealth Citizenship" has been in place ever since the establishment of the Commonwealth of Nations. As with the EU, one holds Commonwealth citizenship only by being a citizen of a Commonwealth member state. This form of citizenship offers certain privileges within some Commonwealth countries:

Some such countries do not require tourist visas of citizens of other Commonwealth countries.
In some Commonwealth countries resident citizens of other Commonwealth countries are entitled to political rights, e.g., the right to vote in local and national elections and in some cases even the right to stand for election.
In some instances the right to work in any position (including the civil service) is granted, except for certain specific positions, such as in the defense departments, Governor-General or President or Prime Minister.

Although Ireland was excluded from the Commonwealth in 1949 because it declared itself a republic, Ireland is generally treated as if it were still a member. Legislation often specifically provides for equal treatment between Commonwealth countries and Ireland and refers to "Commonwealth countries and Ireland".^[33] Ireland's citizens are not classified as foreign nationals in the United Kingdom.
Canada departed from the principle of nationality being defined in terms of allegiance in 1921. In 1935 the Irish Free State was the first to introduce its own citizenship. However, Irish citizens were still treated as subjects of the Crown, and they are still not regarded as foreign, even though Ireland is not a member of the Commonwealth.^[34] The Canadian Citizenship Act of 1947 provided for a distinct Canadian Citizenship, automatically conferred upon most individuals born in Canada, with some exceptions, and defined the conditions under which one could become a naturalized citizen. The concept of Commonwealth citizenship was introduced in 1948 in the British Nationality Act 1948. Other dominions adopted this principle such as New Zealand, by way of the British Nationality and New Zealand Citizenship Act of 1948.

In 520, Boethius was working to revitalize the relationship between the Roman See and the Constantinopalian See; though still both a part of the same Church, serious disagreements had begun to emerge between them. This may have set in place a course of events that would lead to loss of royal favour.^[12]
Five-hundred years later, this led to the East-West Schism, in which the Roman Catholic Church separated itself from the Eastern Orthodox Church.
differentia of a maximal proposition..."^[38] Maximal propositions are "propositions [that are] known per se, and no proof can be found for these."^[39] This is the basis for the idea that demonstration (or the construction of arguments) is dependent ultimately upon ideas or proofs that are known so well and are so fundamental to human understanding of logic that no other proofs come before it. They must hold true in and of themselves. According to Stump, "the role of maximal propositions in argumentation is to ensure the truth of a conclusion by ensuring the truth of its premises either directly or indirectly."^[40] These propositions would be used in constructing arguments through the Differentia, which is the second part of Boethius' theory. This is "the genus of the intermediate in the argument."^[41] So maximal propositions allow room for an argument to be founded in some sense of logic while differentia are critical for the demonstration and construction of arguments.

De arithmetica

Boethius intended to pass on the great Greco-Roman culture to future generations by writing manuals on music and astronomy, geometry, and arithmetic.^[4]
Several of Boethius' writings, which were largely influential during the Middle Ages, drew from the thinking of Porphyry and Iamblichus.^[47] Boethius wrote a commentary on the Isagoge by Porphyry,^[48] which highlighted the existence of the problem of universals: whether these concepts are subsistent entities which would exist whether anyone thought of them, or whether they only exist as ideas. This topic concerning the ontological nature of universal ideas was one of the most vocal controversies in medieval philosophy.
In "De Musica," Boethius introduced the threefold classification of music:^[53]

Musica mundana — music of the spheres/world
Musica humana — harmony of human body and spiritual harmony
Musica instrumentalis — instrumental music

"Imagine that you have set for yourself the task of developing a totally new social contract for today's society. How could you do so fairly? Although you could never actually eliminate all of your personal biases and prejudices, you would need to take steps at least to minimize them. Rawls suggests that you imagine yourself in an original position behind a veil of ignorance. Behind this veil, you know nothing of yourself and your natural abilities, or your position in society. You know nothing of your sex, race, nationality, or individual tastes. Behind such a veil of ignorance all individuals are simply specified as rational, free, and morally equal beings. You do know that in the "real world", however, there will be a wide variety in the natural distribution of natural assets and abilities, and that there will be differences of sex, race, and culture that will distinguish groups of people from each other."^[2]

Such a concept can have grand effects if it were to be practiced both in the present and in the past. Referring again to the example of slavery, if the slave-owners were forced through the veil of ignorance to imagine that they themselves may be slaves then suddenly the practice does not seem to be justifiable. Perhaps the entire practice would have been abolished without the need for a war to settle things. A grander example would be if each individual in society were to base their practices off the fact that they could be the least advantaged member of society. In this scenario, freedom and equality could possibly coexist in a way that has been the ideal of many philosophers.^[3]
For example, in the imaginary society, one might or might not be intelligent, rich, or born into a preferred class. Since one may occupy any position in the society once the veil is lifted, the device forces the parties to consider society from the perspective of all members, including the worst-off and best-off members.

History

The concept of the veil of ignorance has been in use by other names for centuries by philosophers such as John Stuart Mill, John Rawls, and Immanuel Kant whose work discussed the concept of the social contract. John Harsanyi helped to formalize the concept in economics.^[5]^[6] The modern usage was developed by John Rawls in A Theory of Justice.^[7]^[8]
http://en.wikipedia.org/wiki/Veil_of_ignorance