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Dilemmas
A dilemma ( grc-gre, δίλημμα "double proposition") is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. The possibilities are termed the ''horns'' of the dilemma, a clichéd usage, but distinguishing the dilemma from other kinds of predicament as a matter of usage. Terminology The term ''dilemma'' is attributed by Gabriel Nuchelmans to Lorenzo Valla in the 15th century, in later versions of his logic text traditionally called ''Dialectica''. Valla claimed that it was the appropriate Latin equivalent of the Greek ''dilemmaton''. Nuchelmans argued that his probable source was a logic text of c.1433 of George of Trebizond. He also concluded that Valla had reintroduced to the Latin West a type of argument that had fallen into disuse. Valla's neologism did not immediately take hold, preference being given to the established Latin term ''complexio'', used by Cicero, with ''conversio'' applied to the upsetting of dilemmatic reason ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False Dichotomy
A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives, presenting the viewer with only two absolute choices when in fact, there could be many. For example, a false dilemma is committed when it is claimed that "Stacey spoke out against capitalism; therefore, she must be a communist". One of the options excluded is that Stacey may be neither communist nor capitalist. False dilemmas often have the form of treating two contraries, which may both be false, as contradictories, of which one is necessarily true. Various inferential schemes are associated with false dilemmas, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructive Dilemma
Constructive dilemmaCopi and Cohen is a valid rule of inference of propositional logic. It is the inference that, if ''P'' implies ''Q'' and ''R'' implies ''S'' and either ''P'' or ''R'' is true, then either ''Q or S'' has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too. ''Constructive dilemma'' is the disjunctive version of modus ponens, whereas, destructive dilemma is the disjunctive version of ''modus tollens''. The constructive dilemma rule can be stated: :\frac where the rule is that whenever instances of "P \to Q", "R \to S", and "P \lor R" appear on lines of a proof, "Q \lor S" can be placed on a subsequent line. Formal notation The ''constructive dilemma'' rule may be written in sequent notation: : (P \to Q), (R \to S), (P \lor R) \vdash (Q \lor S) where \vdash is a metalogical symbol meaning that Q \lor S is a syntactic consequence of P \to Q, R \to S, and P \lor R in som ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Destructive Dilemma
Destructive dilemmaMoore and Parker is the name of a valid rule of inference of propositional logic. It is the inference that, if ''P'' implies ''Q'' and ''R'' implies ''S'' and either ''Q'' is false or ''S'' is false, then either ''P'' or ''R'' must be false. In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents has to be false. ''Destructive dilemma'' is the disjunctive version of ''modus tollens''. The disjunctive version of ''modus ponens'' is the constructive dilemma. The destructive dilemma rule can be stated: :\frac where the rule is that wherever instances of "P \to Q", "R \to S", and "\neg Q \lor \neg S" appear on lines of a proof, "\neg P \lor \neg R" can be placed on a subsequent line. Formal notation The ''destructive dilemma'' rule may be written in sequent notation: : (P \to Q), (R \to S), (\neg Q \lor \neg S) \vdash (\neg P \lor \neg R) where \vdash is a metalogical symbol meaning that \neg P \lor \neg R i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greeks
The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group and nation indigenous to the Eastern Mediterranean and the Black Sea regions, namely Greece, Cyprus, Albania, Italy, Turkey, Egypt, and, to a lesser extent, other countries surrounding the Mediterranean Sea. They also form a significant diaspora (), with Greek communities established around the world.. Greek colonies and communities have been historically established on the shores of the Mediterranean Sea and Black Sea, but the Greek people themselves have always been centered on the Aegean and Ionian seas, where the Greek language has been spoken since the Bronze Age.. Until the early 20th century, Greeks were distributed between the Greek peninsula, the western coast of Asia Minor, the Black Sea coast, Cappadocia in central Anatolia, Egypt, the Balkans, Cyprus, and Constantinople. Many of these regions coincided to a large extent with the borders of the Byzantine Empire of the late 11th cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excluded Middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradiction, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law (or principle) of the excluded third, in Latin ''principium tertii exclusi''. Another Latin designation for this law is ''tertium non datur'': "no third ossibilityis given". It is a tautology. The principle should not be confused with the semantical principle of bivalence, which states that every proposition is either true or false. The principle of bivalence always implies the law of excluded middle, while the converse is not always true. A commonly cited counterexample uses statements unprovable now, but provable in the futu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Dilemma (BM 1945,0109
A, or a, is the first Letter (alphabet), letter and the first vowel of the Latin alphabet, Latin alphabet, used in the English alphabet, modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is English alphabet#Letter names, ''a'' (pronounced ), plural English alphabet#Letter names, ''aes''. It is similar in shape to the Greek alphabet#History, Ancient Greek letter alpha, from which it derives. The Letter case, uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, "English articles, a", and its variant "English articles#Indefinite article, an", are Article (grammar)#Indefinite article, indefinite arti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Presocratic
Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of these early philosophers spanned the workings of the natural world as well as human society, ethics, and religion. They sought explanations based on natural law rather than the actions of gods. Their work and writing has been almost entirely lost. Knowledge of their views comes from ''testimonia'', i.e. later authors' discussions of the work of pre-Socratics. Philosophy found fertile ground in the ancient Greek world because of the close ties with neighboring civilizations and the rise of autonomous civil entities, ''poleis''. Pre-Socratic philosophy began in the 6th century BCE with the three Milesians: Thales, Anaximander, and Anaximenes. They all attributed the ''arche'' (a word that could take the meaning of "origin," "substance" or "pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rules Of Inference
In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called ''modus ponens'' takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion. Typically, a rule of inference preserves truth, a semantic property. In many-valued logic, it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rules suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melissus Of Samos
Melissus of Samos (; grc, Μέλισσος ὁ Σάμιος; ) was the third and last member of the ancient school of Eleatic philosophy, whose other members included Zeno and Parmenides. Little is known about his life, except that he was the commander of the Samian fleet in the Samian War. Melissus’ contribution to philosophy was a treatise of systematic arguments supporting Eleatic philosophy. Like Parmenides, he argued that reality is ungenerated, indestructible, indivisible, changeless, and motionless. In addition, he sought to show that reality is wholly unlimited, and infinitely extended in all directions; and since existence is unlimited, it must also be one. Life Not much information remains regarding the life of Melissus. He may have been born around 500 BC; the date of his death is unknown. The little which is known about him is mostly gleaned from a small passage in Plutarch’s ''Life of Pericles''. He was the commander of the Samian fleet in the Samian War, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeno Of Elea
Zeno of Elea (; grc, Ζήνων ὁ Ἐλεᾱ́της; ) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, which Bertrand Russell described as "immeasurably subtle and profound". Life Little is known for certain about Zeno's life. Although written nearly a century after Zeno's death, the primary source of biographical information about Zeno is Plato's ''Parmenides'' and he is also mentioned in Aristotle's ''Physics''. In the dialogue of ''Parmenides'', Plato describes a visit to Athens by Zeno and Parmenides, at a time when Parmenides is "about 65", Zeno is "nearly 40", and Socrates is "a very young man".Plato, ''Parmenides'127b–e (at footnote n. 2) Assuming an age for Socrates of around 20 and taking the date of Socrates' birth as 469 BC gives an approximate date of birth for Zeno of 490 BC. Plato says that Zeno was "tall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diodorus Cronus
Diodorus Cronus ( el, Διόδωρος Κρόνος; died c. 284 BC) was a Greek philosopher and dialectician connected to the Megarian school. He was most notable for logic innovations, including his master argument formulated in response to Aristotle's discussion of future contingents. Life Diodorus was the son of Ameinias of Iasus in Caria. He lived in the court of Alexandria in the reign of Ptolemy I Soter, who is said to have given him the surname of Cronus ("old fogey") on account of his inability to solve at once some dialectic problem proposed by Stilpo, when the two philosophers were dining with the king. Diodorus is said to have taken that disgrace so much to heart that after his return from the meal, and writing a treatise on the problem, he died in despair. However, according to Strabo, Diodorus himself adopted the surname of Cronus from his teacher, Apollonius Cronus. Diodorus is thought to have died around 284 BC; his date of birth is unknown. It was once thought tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum and the wider Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was born in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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