Francis Bacon, 1st Viscount St Alban, was an English philosopher and statesman who served as Attorney General and as Lord Chancellor of England. His works are credited with developing the scientific method and remained influential through the scientific revolution. Bacon has been called the father of empiricism, his works argued for the possibility of scientific knowledge based only upon inductive reasoning and careful observation of events in nature. Most he argued science could be achieved by use of a sceptical and methodical approach whereby scientists aim to avoid misleading themselves. Although his practical ideas about such a method, the Baconian method, did not have a long-lasting influence, the general idea of the importance and possibility of a sceptical methodology makes Bacon the father of the scientific method; this method was a new rhetorical and theoretical framework for science, the practical details of which are still central in debates about science and methodology. Bacon was a patron of libraries and developed a functional system for the cataloging of books by dividing them into three categories—history and philosophy—which could further be divided into more specific subjects and subheadings.
Bacon was educated at Trinity College, where he rigorously followed the medieval curriculum in Latin. Bacon was the first recipient of the Queen's counsel designation, conferred in 1597 when Queen Elizabeth reserved Bacon as her legal advisor. After the accession of King James I in 1603, Bacon was knighted, he was created Baron Verulam in 1618 and Viscount St. Alban in 1621; because he had no heirs, both titles became extinct upon his death at 65 years. Bacon died of pneumonia, with one account by John Aubrey stating that he had contracted the condition while studying the effects of freezing on the preservation of meat, he is buried at St Michael's Church, St Albans, Hertfordshire. Francis Bacon was born on 22 January 1561 at York House near the Strand in London, the son of Sir Nicholas Bacon by his second wife, Anne Bacon, the daughter of the noted humanist Anthony Cooke, his mother's sister was married to 1st Baron Burghley, making Burghley Bacon's uncle. Biographers believe that Bacon was educated at home in his early years owing to poor health, which would plague him throughout his life.
He received tuition from a graduate of Oxford with a strong leaning toward Puritanism. He went up to Trinity College at the University of Cambridge on 5 April 1573 at the age of 12, living for three years there, together with his older brother Anthony Bacon under the personal tutelage of Dr John Whitgift, future Archbishop of Canterbury. Bacon's education was conducted in Latin and followed the medieval curriculum, he was educated at the University of Poitiers. It was at Cambridge that Bacon first met Queen Elizabeth, impressed by his precocious intellect, was accustomed to calling him "The young lord keeper", his studies brought him to the belief that the methods and results of science as practised were erroneous. His reverence for Aristotle conflicted with his rejection of Aristotelian philosophy, which seemed to him barren and wrong in its objectives. On 27 June 1576, he and Anthony entered de societate magistrorum at Gray's Inn. A few months Francis went abroad with Sir Amias Paulet, the English ambassador at Paris, while Anthony continued his studies at home.
The state of government and society in France under Henry III afforded him valuable political instruction. For the next three years he visited Blois, Tours and Spain. During his travels, Bacon studied language and civil law while performing routine diplomatic tasks. On at least one occasion he delivered diplomatic letters to England for Walsingham and Leicester, as well as for the queen; the sudden death of his father in February 1579 prompted Bacon to return to England. Sir Nicholas had laid up a considerable sum of money to purchase an estate for his youngest son, but he died before doing so, Francis was left with only a fifth of that money. Having borrowed money, Bacon got into debt. To support himself, he took up his residence in law at Gray's Inn in 1579, his income being supplemented by a grant from his mother Lady Anne of the manor of Marks near Romford in Essex, which generated a rent of £46. Bacon stated that he had three goals: to uncover truth, to serve his country, to serve his church.
He sought to further these ends by seeking a prestigious post. In 1580, through his uncle, Lord Burghley, he applied for a post at court that might enable him to pursue a life of learning, but his application failed. For two years he worked at Gray's Inn, until he was admitted as an outer barrister in 1582, his parliamentary career began when he was elected MP for Bossiney, Cornwall, in a by-election in 1581. In 1584 he took his seat in parliament for Melcombe in Dorset, in 1586 for Taunton. At this time, he began to write on the condition of parties in the church, as well as on the topic of philosophical reform in the lost tract Temporis Partus Maximus, yet he failed to gain a position. He showed signs of sympathy to Puritanism, attending the sermons of the Puritan chaplain of Gray's Inn and accompanying his mother to the Temple Church to hear Walter Travers; this led to the publication of his earliest surviving tract, which criticised the English church's suppression of the Puritan clergy. In the Parliament of 1586, he urged execution for the Catholic Mary, Queen of Scots.
About this time, he again approached his powerful uncle for help. He became a bencher in 1586 and was elected a
A paradox is a statement that, despite valid reasoning from true premises, leads to an apparently-self-contradictory or logically unacceptable conclusion. A paradox involves contradictory-yet-interrelated elements that exist and persist over time; some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking. Some paradoxes have revealed errors in definitions assumed to be rigorous, have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, are not yet resolved. Examples outside logic include the ship of Theseus from philosophy. Paradoxes can take the form of images or other media. For example, M. C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, staircases that appear to climb endlessly.
In common usage, the word "paradox" refers to statements that are ironic or unexpected, such as "the paradox that standing is more tiring than walking". Common themes in paradoxes include self-reference, infinite regress, circular definitions, confusion between different levels of abstraction. Patrick Hughes outlines three laws of the paradox: Self-reference An example is "This statement is false", a form of the liar paradox; the statement is referring to itself. Another example of self-reference is the question of whether the barber shaves himself in the barber paradox. One more example would be "Is the answer to this question'No'?" Contradiction "This statement is false". Another example of contradiction is if a man talking to a genie wishes that wishes couldn't come true; this contradicts itself because if the genie grants his wish, he did not grant his wish, if he refuses to grant his wish he did indeed grant his wish, therefore making it impossible either to grant or not grant his wish because his wish contradicts itself.
Vicious circularity, or infinite regress "This statement is false". Another example of vicious circularity is the following group of statements: "The following sentence is true." "The previous sentence is false."Other paradoxes involve false statements or half-truths and the resulting biased assumptions. This form is common in howlers. For example, consider a situation in which a father and his son are driving down the road; the car crashes into a tree and the father is killed. The boy is rushed to the nearest hospital. Upon entering the surgery-suite, the surgeon says, "I can't operate on this boy. He's my son." The apparent paradox is caused by a hasty generalization, for if the surgeon is the boy's father, the statement cannot be true. The paradox is resolved. Paradoxes which are not based on a hidden error occur at the fringes of context or language, require extending the context or language in order to lose their paradoxical quality. Paradoxes that arise from intelligible uses of language are of interest to logicians and philosophers.
"This sentence is false" is an example of the well-known liar paradox: it is a sentence which cannot be interpreted as either true or false, because if it is known to be false it is known that it must be true, if it is known to be true it is known that it must be false. Russell's paradox, which shows that the notion of the set of all those sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic and set theory. Thought-experiments can yield interesting paradoxes; the grandfather paradox, for example, would arise if a time-traveler were to kill his own grandfather before his mother or father had been conceived, thereby preventing his own birth. This is a specific example of the more general observation of the butterfly effect, or that a time-traveller's interaction with the past—however slight—would entail making changes that would, in turn, change the future in which the time-travel was yet to occur, would thus change the circumstances of the time-travel itself.
A paradoxical conclusion arises from an inconsistent or inherently contradictory definition of the initial premise. In the case of that apparent paradox of a time-traveler killing his own grandfather, it is the inconsistency of defining the past to which he returns as being somehow different from the one which leads up to the future from which he begins his trip, but insisting that he must have come to that past from the same future as the one that it leads up to. W. V. Quine distinguished between three classes of paradoxes: A veridical paradox produces a result that appears absurd but is demonstrated to be true nonetheless, thus the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays if he had been born on a leap day. Arrow's impossibility theorem demonstrates difficulties in mapping voting results to the will of the people; the Monty Hall paradox demonstrates that a decision which has an intuitive 50–50 chance is in fact biased towards making a decision which, given the intuitive concl
When a white horse is not a horse
When a white horse is not a horse is a famous paradox in Chinese philosophy. Around 300 BC, Gongsun Long wrote this dialectic analysis of the question "Can one legitimately assert'white horse is not horse'?", in a work now named for him, Gongsun Longzi, in a segment called the "White Horse Dialogue". The White Horse Dialogue constitutes chapter 2 of the eponymous Gongsun Longzi; the purported author known as Master Gongsun Long, was counted among the School of Names in the Hundred Schools of Thought. Most of Gongsun's writings have been lost and the received Gongsun Longzi text only contains six of the 14 original chapters. Parts of the text are dislocated and some commentators and translators rearrange them for clarity; the dialogue is between two unnamed speakers: Is "Chinese: 白馬非馬. Advocate: It is. Objector: How? Advocate: "Horse" is that by means of which one names the shape. "White" is that by means of which one names the color. What names the color is not what names the shape. Hence, one may say "white horse is not horse."
Objector: If there are white horses, one cannot say that there are no horses. If one cannot say that there are no horses, doesn't that mean that there are horses? For there to be white horses is. How could it be that the white ones are not horses? Advocate: If one wants horses, that extends to yellow or black horses, but if one wants white horses, that does not extend to a black horses. Suppose that white horses were horses. What one wants would be the same. If what one wants were the same, then'white' would not differ from'horse.' If what one wants does not differ how is it that yellow or black horses are acceptable in one case and unacceptable in the other case? It is clear that unacceptable are mutually contrary. Hence and black horses are the same, one can respond that there are horses, but one cannot respond that there are white horses. Thus, it is evident; this dialogue continues with deliberations over colored and colorless horses and whether white and horse can be separated from white horse.
Other Gongsun Longzi chapters discuss Baima-related concepts of: jian 堅'hard. The Chinese of' white horse is not horse' is bai ma fei ma 白馬非馬, whose meaning hinges upon the negative fei 非'not, is not; the Classical construction "A fei B" can ambiguously have multiple meanings: Interpreting this equivocation fallacy, A. C. Graham says this "white horse versus horse" paradox plays upon the ambiguity of whether the is in it conveys: "Is a member of the class x" "Is identical to x". In other words, the expression "white horse is not horse" is ambiguous between "white horse is not synonymous with horse", versus "a white horse is not a member of the set of horses"; the Advocate in the dialogue is asserting a lack of identity between horses and white horses, while the Objector is interpreting the Advocate's statement as a claim that the category of horses does not include white ones. An illustration of the alternative uses of fei may be found in the known "Happiness of Fish" dialogue in Zhuangzi. Huizi says "You are not a fish – how do you know what fish enjoy?", Zhuangzi replies "You are not me, so how do you know that I do not know what fish enjoy?".
Beyond the inherent semantic ambiguities of baima fei ma, the first line of the White Horse Dialogue obscurely asks ke hu 可乎,'Can it be that...?'. This dialogue could be an attempted proof that a white horse is not a horse, or a question if such a statement is possible, or both. Bryan W. Van Norden suggests that "the Advocate is only arguing that'a white horse is not a horse' could be true, given a certain interpretation, he might acknowledge that, in another interpretation,'a white horse is a horse.'"An alternative interpretation is offered in Feng Youlan's History of Chinese Philosophy: Strictly speaking, names or terms are divided into those that are abstract and those that are concrete. The abstract term denotes the concrete term the particular; the particular is the denotation, the universal the connotation, of the term. In western inflected languages there is no difficulty in distinguishing between the particular and the abstract. In Chinese, owing to the fact that the written characters are ideographic and pictorial and lack all inflection, there is no possible way, as far as the form of individual words is concerned, of distinguishing between abstract and concrete terms.
Thus in Chinese the word designating a particular horse and that designating the universal,'horseness,' are written and pronounced in the same way. With other terms, so that such words as'horse' and'white', being used to designate both the concrete particular and the abstract universal, thus hold two values. However, there are recent histories of Chinese philosophy do not subscribe to Feng Youlan's interpretation. Other contemporary philosophers and sinologists who have analyzed the dialogu
Epicurus was an ancient Greek philosopher who founded a influential school of philosophy now called Epicureanism. He was born on the Greek island of Samos to Athenian parents. Influenced by Democritus and the Cynics, he turned against the Platonism of his day and established his own school, known as "the Garden", in Athens, he and his followers were known for eating simple meals and discussing a wide range of philosophical subjects, he allowed women to join the school as a matter of policy. An prolific writer, he is said to have written over 300 works on various subjects, but the vast majority of these writings have been lost. Only three letters written by him—the Letters to Menoeceus and Herodotus—and two collections of quotes—the Principle Doctrines and the Vatican Sayings—have survived intact, along with a few fragments and quotations of his other writings, his teachings are better recorded in the writings of authors, including the Roman poet Lucretius, the philosopher Philodemus, the philosopher Sextus Empiricus, the biographer Diogenes Laërtius.
For Epicurus, the purpose of philosophy was to attain the happy, tranquil life, characterized by ataraxia—peace and freedom from fear— and aponia—the absence of pain— and by living a self-sufficient life surrounded by friends. He taught that the root of all human neurosis is death denial, the tendency for human beings to assume that death will be horrific and painful, which he claimed causes unnecessary anxiety, selfish self-protective behaviors, hypocrisy. According to Epicurus, death is the end of both the body and the soul and therefore should not be feared. Epicurus taught that the gods, though they do exist, have no involvement in human affairs and do not punish or reward people for their actions. Nonetheless, he maintained that people should still behave ethically because amoral behavior will burden them with guilt and prevent them from attaining ataraxia. Like Aristotle, Epicurus was an empiricist, meaning he believed that the senses are the only reliable source of knowledge about the world.
He derived much of his cosmology from the earlier philosopher Democritus. Like Democritus, Epicurus taught that the universe is infinite and eternal and that all matter is made up of tiny, invisible particles known as atoms. All occurrences in the natural world are the result of atoms moving and interacting in empty space. Epicurus deviated from Democritus in his teaching of atomic "swerve", which holds that atoms may deviate from their expected course, thus permitting humans to possess free will in an otherwise deterministic universe. Though popular, Epicurean teachings were controversial from the beginning. Epicureanism reached the height of its popularity during the late years of the Roman Republic, before declining as the rival school of Stoicism grew in popularity at its expense, it died out in late antiquity in the wake of early Christianity. Epicurus himself was popularly, though inaccurately, remembered throughout the Middle Ages as a patron of drunkards and gluttons, his teachings became more known in the fifteenth century with the rediscovery of important texts, but his ideas did not become acceptable until the seventeenth century, when the French Catholic priest Pierre Gassendi revived a modified version of them, promoted by other writers, including Walter Charleton and Robert Boyle.
His influence grew during and after the Enlightenment, profoundly impacting the ideas of major thinkers, including John Locke, Thomas Jefferson, Jeremy Bentham, Karl Marx. Epicurus was born in the Athenian settlement on the Aegean island of Samos in February 341 BC, his parents and Chaerestrate, were both Athenian-born, his father was an Athenian citizen. Epicurus grew up during the final years of the Greek Classical Period. Plato had died seven years before Epicurus was born and Epicurus was seven years old when Alexander the Great crossed the Hellespont into Persia; as a child, Epicurus would have received a typical ancient Greek education. As such, according to Norman Wentworth DeWitt, "it is inconceivable that he would have escaped the Platonic training in geometry and rhetoric." Epicurus is known to have studied under the instruction of a Samian Platonist named Pamphilus for about four years. His Letter of Menoeceus and surviving fragments of his other writings suggest that he had extensive training in rhetoric.
After the death of Alexander the Great, Perdiccas expelled the Athenian settlers on Samos to Colophon, on the coast of what is now Turkey. After the completion of his military service, Epicurus joined his family there, he studied under Nausiphanes. Epicurus's teachings were influenced by those of earlier philosophers Democritus. Nonetheless, Epicurus differed from his predecessors on several key points of determinism and vehemently denied having been influenced by any previous philosophers, whom he denounced as "confused". Instead, he insisted that he had been "self-taught". According to DeWitt, Epicurus's teachings show influences from the contemporary philosophical school of Cynicism; the Cynic philosopher Diogenes of Sinope was still alive when Epicurus would have been in Athens for his required military training and it is possible they may have met. Diogenes's pupil Crates of Thebes was a close contemporary of Epicurus. Epicurus agreed with the Cynics' quest for honesty, but rejected their "insolence and vulgarity", instead teaching that honesty must be coupled with courtesy and kindness.
Epicurus shared this view with the comic playwright Menander. Epicurus's Lett
The Epimenides paradox reveals a problem with self-reference in logic. It is named after the Cretan philosopher Epimenides of Knossos, credited with the original statement. A typical description of the problem is given in the book Gödel, Bach, by Douglas Hofstadter: Epimenides was a Cretan who made one immortal statement: "All Cretans are liars."A paradox of self-reference arises when one considers whether it is possible for Epimenides to have spoken the truth. Thomas Fowler states the paradox as follows: "Epimenides the Cretan says,'that all the Cretans are liars,' but Epimenides is himself a Cretan, but if he is a liar, what he says is untrue, the Cretans are veracious. Thus we may go on alternately proving that Epimenides and the Cretans are truthful and untruthful."The Epimenides paradox in this form, can be solved. There are two options: it is either true or false. First, assume that it is true, but Epimenides, being a Cretan, would be a liar, making the assumption that liars only make false statements, the statement is false.
So, assuming the statement is true leads us to conclude that the statement is false. This is a contradiction, so the option of the statement being true is not possible; this leaves the second option:. If we assume the statement is false and that Epimenides is lying about all Cretans being liars there must exist at least one Cretan, honest; this does not lead to a contradiction. This means that Epimenides can say the false statement that all Cretans are liars while knowing at least one honest Cretan and lying about this particular Cretan. Hence, from the assumption that the statement is false, it does not follow that the statement is true. So we can avoid a paradox as seeing the statement "all Cretans are liars" as a false statement, made by a lying Cretan, Epimenides; the mistake made by Thomas Fowler above is to think that the negation of "all Cretans are liars" is "all Cretans are honest" when in fact the negation is "there exists a Cretan, honest", or "not all Cretans are liars". The Epimenides paradox can be modified as to not allow the kind of solution described above, as it was in the first paradox of Eubulides but instead leading to a non-avoidable self-contradiction.
Paradoxical versions of the Epimenides problem are related to a class of more difficult logical problems, including the liar paradox, Socratic paradox, the Burali-Forti paradox, all of which have self-reference in common with Epimenides. Indeed, the Epimenides paradox is classified as a variation on the liar paradox, sometimes the two are not distinguished; the study of self-reference led to important developments in logic and mathematics in the twentieth century. In other words, it is not a paradox once one realizes "All Cretans are liars" being untrue only means "Not all Cretans are liars" instead of the assumption that "All Cretans are honest". Better put, for "All Cretans are liars" to be a true statement, it does not mean that all Cretans must lie all the time. In fact, Cretans could tell the truth quite but still, all be liars in the sense that liars are people prone to deception for dishonest gain. Considering that “All Cretans are liars” has been seen as a paradox only since the 19th century, this seems to resolve the alleged paradox.
Of course, if ‘all Cretans are continuous liars’ is true asking a Cretan if they are honest would always elicit the dishonest answer ‘yes’. So arguably the original proposition is not so much paradoxical as invalid. A contextual reading of the contradiction may provide an answer to the paradox; the original phrase, "The Cretans, always liars, evil beasts, idle bellies!" Asserts not an intrinsic paradox, but rather an opinion of the Cretans from Epimenides. A stereotyping of his people not intended to be an absolute statement about the people as a whole. Rather it is a claim made about their position regarding their religious beliefs and socio-cultural attitudes. Within the context of his poem the phrase is specific to a certain belief, a context that Callimachus repeats in his poem regarding Zeus. Further, a more poignant answer to the paradox is that to be a liar is to state falsehoods, nothing in the statement asserts everything said is false, but rather they're "always" lying; this is not an absolute statement of fact and thus we cannot conclude there's a true contradiction made by Epimenides with this statement.
Epimenides was a 6th-century BC philosopher and religious prophet who, against the general sentiment of Crete, proposed that Zeus was immortal, as in the following poem: They fashioned a tomb for thee, O holy and high oneThe Cretans, always liars, evil beasts, idle bellies! But thou art not dead: thou livest and abidest forever,For in thee we live and move and have our being. Denying the immortality of Zeus was the lie of the Cretans; the phrase "Cretans, always liars" was quoted by the poet Callimachus in his Hymn to Zeus, with the same theological intent as Epimenides: O Zeus, some say that thou wert born on the hills of Ida. -- “Cretans are liars.” Yea, a tomb, O Lord, for thee the Cretans builded. The logical inconsistency of a Cretan asserting all Cretans are always liars may not have occurred to Epimenides, nor to Callimachus, who both used the phrase to emphasize their point, without irony meaning that all Cretans lie but not
Henry VII of England
Henry VII was the King of England and Lord of Ireland from his seizure of the crown on 22 August 1485 to his death on 21 April 1509. He was the first monarch of the House of Tudor. Henry attained the throne when his forces defeated King Richard III at the Battle of Bosworth Field, the culmination of the Wars of the Roses, he was the last king of England to win his throne on the field of battle. He cemented his claim by marrying Elizabeth of York, daughter of Edward IV and niece of Richard III. Henry was successful in restoring the power and stability of the English monarchy after the civil war, his supportive stance of the British Isles' wool industry and his standoff with the Low Countries had long-lasting benefits to all of the British economy. However, the capriciousness and lack of due process that indebted many would tarnish his legacy and were soon ended upon Henry VII's death, after a commission revealed widespread abuses. According to the contemporary historian Polydore Vergil, simple "greed" underscored the means by which royal control was over-asserted in Henry's final years.
Henry can be credited with a number of administrative and diplomatic initiatives. He paid close attention to detail, instead of spending lavishly he concentrated on raising new revenues and after a reign of nearly 24 years, he was peacefully succeeded by his son, Henry VIII; the new taxes were unpopular and two days after his coronation, Henry VIII arrested his father's two most unpopular ministers, Sir Richard Empson and Edmund Dudley. They were charged with high treason and were executed in 1510. Henry VII was born at Pembroke Castle on 28 January 1457 to Countess of Richmond, his father, Edmund Tudor, 1st Earl of Richmond, died three months before his birth. Henry's paternal grandfather, Owen Tudor from the Tudors of Penmynydd, Isle of Anglesey in Wales, had been a page in the court of Henry V, he rose to become one of the "Squires to the Body to the King" after military service at the Battle of Agincourt. Owen is said to have secretly married the widow of Catherine of Valois. One of their sons was Edmund Tudor, father of Henry VII.
Edmund was created Earl of Richmond in 1452, "formally declared legitimate by Parliament". Henry's main claim to the English throne derived from his mother through the House of Beaufort. Henry's mother, Lady Margaret Beaufort, was a great-granddaughter of John of Gaunt, Duke of Lancaster, fourth son of Edward III, his third wife Katherine Swynford. Katherine was Gaunt's mistress for about 25 years, thus Henry's claim was somewhat tenuous: it was from a woman, by illegitimate descent. In theory, the Portuguese and Castilian royal families had a better claim as descendants of Catherine of Lancaster, the daughter of John of Gaunt and his second wife Constance of Castile. Gaunt's nephew Richard II legitimised Gaunt's children by Katherine Swynford by Letters Patent in 1397. In 1407, Henry IV, Gaunt's son by his first wife, issued new Letters Patent confirming the legitimacy of his half-siblings, but declaring them ineligible for the throne. Henry IV's action was of doubtful legality, as the Beauforts were legitimised by an Act of Parliament, but it further weakened Henry's claim.
Nonetheless, by 1483 Henry was the senior male Lancastrian claimant remaining, after the deaths in battle or by murder or execution of Henry VI, his son Edward of Westminster, Prince of Wales, the other Beaufort line of descent through Lady Margaret's uncle, the 2nd Duke of Somerset. Henry made some political capital out of his Welsh ancestry, for example in attracting military support and safeguarding his army's passage through Wales on its way to the Battle of Bosworth, he came from an old, established Anglesey family that claimed descent from Cadwaladr, on occasion Henry displayed the red dragon of Cadwaladr. He took it, as well as the standard of St George, on his procession through London after the victory at Bosworth. A contemporary writer and Henry's biographer, Bernard André made much of Henry's Welsh descent. In reality, his hereditary connections to Welsh aristocracy were not strong, he was descended by the paternal line, through several generations, from Ednyfed Fychan, the seneschal of Gwynedd and through this seneschal's wife from Rhys ap Tewdwr, the King of Deheubarth in South Wales.
His more immediate ancestor, Tudur ap Goronwy, had aristocratic land rights, but his sons, who were first cousins to Owain Glyndŵr, sided with Owain in his revolt. One son was executed and the family land was forfeited. Another son, Henry's great-grandfather, became a butler to the Bishop of Bangor. Owen Tudor, the son of the butler, like the children of other rebels, was provided for by Henry V, a circumstance that precipitated his access to Queen Catherine of Valois. Notwithstanding this lineage, to the bards of Wales, Henry was a candidate for Y Mab Darogan – "The Son of Prophecy" who would free the Welsh from oppression. In 1456, Henry's father Edmund Tudor was captured while fighting for Henry VI in South Wales against the Yorkists, he died in three months before Henry was born. Henry's uncle Jasper Tudor, the Earl of Pembroke and Edmund's younger brother, undertook to protect the young widow, 13 years old when she gave birth to Henry; when Edward IV became King in 1461, Jasper Tudor went into exile abroad.
Pembroke Castle, the Earldom of Pembroke, were granted to the Yorkist William Herbert, who assumed the guardianship of Margaret Beaufort and the young Henry. Henry lived in the Herbert household
The Pinocchio paradox arises when Pinocchio says "My nose grows now" and is a version of the liar paradox. The liar paradox is defined in philosophy and logic as the statement "This sentence is false." Any attempts to assign a classical binary truth value to this statement lead to a contradiction, or paradox. This occurs because if the statement "This sentence is false" is true it is false. Although the Pinocchio paradox belongs to the liar paradox tradition, it is a special case because it has no semantic predicates, as for example "My sentence is false" does; the Pinocchio paradox has nothing to do with Pinocchio being a known liar. If Pinocchio were to say "I am getting sick," this could be either true or false, but Pinocchio's sentence "My nose grows now" can be neither true nor false. Pinocchio is a hero of the children's novel The Adventures of Pinocchio by Italian author Carlo Collodi. Pinocchio, an animated puppet, is punished for each lie that he tells by undergoing further growth of his nose.
There are no restrictions on the length of Pinocchio's nose. It grows as he tells lies and at one point grows so long that he can not get his nose "through the door of the room"; the Pinocchio paradox was proposed in February 2001 by 11-year-old Veronique Eldridge-Smith. Veronique is the daughter of Peter Eldridge-Smith, who specializes in logic and the philosophy of logic. Peter Eldridge-Smith explained the liar paradox to Veronique and Veronique's older brother, asked the children to come up with their own versions of the famous paradox. In a few minutes Veronique suggested: "Pinocchio says,'My nose will be growing'." Eldridge-Smith liked the formulation of the paradox suggested by his daughter and wrote an article on the subject. The article was published in the journal Analysis, the Pinocchio paradox became popularized on the Internet; the paradox suggested by Veronique, "My nose grows now", or in future tense: "will be growing", leaves room for different interpretations. In the novel Pinocchio's nose continues to grow as he lies: "As he spoke, his nose, long though it was, became at least two inches longer."
So logicians question if the sentence "My nose will be growing" was the only sentence that Pinocchio spoke, did he tell a lie before he said "My nose will be growing", or was he going to tell a lie—and how long would it take for his nose to start growing? The present tense of the same sentence "My nose is growing now" or "My nose grows", appears to provide a better opportunity to generate the liar paradox; the sentence "My nose grows" could be either false. Assume the sentence: "My nose grows now" is true: Which means that Pinocchio's nose grows now because he truthfully says it is, but Pinocchio's nose does not grow now because according to the novel it grows only as Pinocchio lies, but Pinocchio's nose grows now because Pinocchio's nose does not grow now, Pinocchio trustfully says it grows now, it is false, that makes Pinocchio's sentence to be false, but Pinocchio's nose does not grow now because Pinocchio's nose grows now, Pinocchio trustfully says it grows now, it is true that makes Pinocchio's sentence to be true, but And so on without end.
Assume the sentence: "My nose grows now" is false: Which means that Pinocchio's nose does not grow now because he falsely says it is, but Pinocchio's nose grows now because according to the novel it grows only as Pinocchio lies, but Pinocchio's nose does not grow now because Pinocchio's nose grows now, Pinocchio falsely says it grows now, it is false that makes Pinocchio's sentence to be true, but Pinocchio's nose grows now because Pinocchio's nose does not grow now, Pinocchio falsely says it grows now, it is true, that makes Pinocchio's sentence to be false, but And so on without end. And just to make it easier, as Eldridge-Smith states, "Pinocchio's nose is growing if and only if it is not growing," which makes Pinocchio's sentence to be "a version of the Liar". Eldridge-Smith argues that because the phrases "is not true" and "is growing" are not synonyms, the Pinocchio paradox is not a semantic paradox: The Pinocchio paradox is, in a way, a counter–example to solutions to the Liar that would exclude semantic predicates from an object–language, because "is growing" is not a semantic predicate.
Eldridge-Smith believes Alfred Tarski's theory, in which he states that liar paradoxes should be diagnosed as arising only in languages that are "semantically closed". By this he means a language in which it is possible for one sentence to predicate the truth of a sentence in the same language should not be applied to the Pinocchio paradox: The Pinocchio paradox raises a purely logical issue for any metalanguage–hierarchy solution, strict or liberal; the Pinocchio scenario is not going to arise in our world, so it is not a pragmatic issue. It seems though that there could be a logically possible world in which Pinocchio's nose grows if and only if he is saying something not true. However, there cannot be such a logically possible world wherein he makes the statement "My nose is growing." A metalanguage hierarchy approach cannot explain this based on Tarski's analysis, therefore cannot solve the Pinocchio paradox, a version of the Liar. In his next article, "Pinocchio against the dialetheists", Eldridge-Smith states: "If it is a true contradiction that Pinocchio's nose grows and does not grow such a world is metaphysically impossible, not semantically impossible."
He reminds the readers that, when Socrates asked if he may cross a bridge, Plato responded that he may cross the bridge only "if in the first proposition that you wo