Zeno's paradoxes Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates.[3] Some mathematicians and historians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution.[4] Some philosophers, however, say that Zeno's paradoxes and their variations (see Thomson's lamp) remain relevant metaphysical problems.[5][6][7] The origins of the paradoxes are somewhat unclear. Paradoxes of motion[edit] Achilles and the tortoise[edit] Distance vs. time, assuming the tortoise to run at Achilles' half speed Dichotomy paradox[edit] Suppose Homer wants to catch a stationary bus. The resulting sequence can be represented as: This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility. There are two versions of the dichotomy paradox.
Socrates Socrates (/ˈsɒkrətiːz/;[2] Greek: Σωκράτης [sɔːkrátɛːs], Sōkrátēs; 470/469 – 399 BC)[1] was a classical Greek (Athenian) philosopher credited as one of the founders of Western philosophy. He is an enigmatic figure known chiefly through the accounts of classical writers, especially the writings of his students Plato and Xenophon and the plays of his contemporary Aristophanes. Plato's dialogues are among the most comprehensive accounts of Socrates to survive from antiquity, though it is unclear the degree to which Socrates himself is "hidden behind his 'best disciple', Plato".[3] Through his portrayal in Plato's dialogues, Socrates has become renowned for his contribution to the field of ethics, and it is this Platonic Socrates who lends his name to the concepts of Socratic irony and the Socratic method, or elenchus. Socratic problem Nothing written by Socrates remains extant. Socrates as a figure Socrates as a philosopher Biography Early life Military service Arrest of Leon Trial and death Notes
Stoicism Philosophical system Stoicism is a school of Hellenistic philosophy founded by Zeno of Citium in Athens in the early 3rd century BCE. It is a philosophy of personal virtue ethics informed by its system of logic and its views on the natural world, asserting that the practice of virtue is both necessary and sufficient to achieve eudaimonia (happiness, lit. 'good spiritedness'): one flourishes by living an ethical life. Stoicism flourished throughout the Roman and Greek world until the 3rd century CE, and among its adherents was Emperor Marcus Aurelius. History[edit] The name Stoicism derives from the Stoa Poikile (Ancient Greek: ἡ ποικίλη στοά), or "painted porch", a colonnade decorated with mythic and historical battle scenes on the north side of the Agora in Athens where Zeno of Citium and his followers gathered to discuss their ideas, near the end of the 4th century BCE.[4] Unlike the Epicureans, Zeno chose to teach his philosophy in a public space. Scholars[who?] Logic[edit]
Zeno of Elea Zeno of Elea (/ˈziːnoʊ əv ˈɛliə/; Greek: Ζήνων ὁ Ἐλεάτης; c. 490 – c. 430 BC) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic.[1] He is best known for his paradoxes, which Bertrand Russell has described as "immeasurably subtle and profound".[2] Life[edit] Other perhaps less reliable details of Zeno's life are given by Diogenes Laërtius in his Lives and Opinions of Eminent Philosophers,[5] where it is reported that he was the son of Teleutagoras, but the adopted son of Parmenides, was "skilled to argue both sides of any question, the universal critic," and that he was arrested and perhaps killed at the hands of a tyrant of Elea. According to Plutarch, Zeno attempted to kill the tyrant Demylus, and failing to do so, "with his own teeth bit off his tongue, he spit it in the tyrant’s face Works[edit] Zeno's paradoxes[edit] See also[edit] Notes[edit] References[edit]
Immanuel Kant Immanuel Kant (/kænt/;[1] German: [ɪˈmaːnu̯eːl kant]; 22 April 1724 – 12 February 1804) was a German philosopher who is widely considered to be a central figure of modern philosophy. He argued that fundamental concepts structure human experience, and that reason is the source of morality. His thought continues to have a major influence in contemporary thought, especially the fields of metaphysics, epistemology, ethics, political philosophy, and aesthetics.[2] Kant's major work, the Critique of Pure Reason (Kritik der reinen Vernunft, 1781),[3] aimed to explain the relationship between reason and human experience. With this project, he hoped to move beyond what he took to be failures of traditional philosophy and metaphysics. Kant argued that our experiences are structured by necessary features of our minds. Kant aimed to resolve disputes between empirical and rationalist approaches. Biography[edit] Young Kant was a solid, albeit unspectacular, student. Young scholar[edit] Early work[edit]
Commentary on Wittgenstein's Philosophical Investigations Shawver Commentary: This commentary in the pages of this website is not meant to replace your reading of Wittgenstein in the original. For that, of course, you will need to acquire the book. This commentary is meant to give you a taste of Wittgentein, or, if you are really ready, to help you get started. The problem is that while Wittgenstein's writing style is quite beautiful, almost poetic, it is so unusual, that all of us, it seems, need a little help in the beginning. One of the most difficult or misleading aspects of Wittgenstein's Philosophical Investigations is the way in which he uses multiple voices to converse with himself. The Philosophical Investigations is written in aphorisms, short numbered passages that are loosely tied together in terms of theme. It is useful to think of there being two additional voices. Then, there is a third voice in which Wittgenstein makes an incisive point in the face of the tradition and aporia. So, the basic format of many of the aphorisms is:
Wittgenstein : Language Games This work is licensed under a Creative Commons Attribution-Share Alike 2.5 License In his later work Wittgenstein developed the idea that the job of philosophy was to clear up the conceptual confusions that arose through our unexamined use of language. Dissatisfied with the traditional expressionist and reflective approaches to language he sought a new model which would allow greater flexibility. Central to this was the concept of rule governed activity or 'language game'. Wittgenstein introduces the concept of 'language games' because of the analogy between using language and playing a game according to certain rules. We can easily imagine people amusing themselves in a field by playing with a ball so as to start various existing games, but playing many without finishing them and in between throwing the ball aimlessly into the air, chasing one another with the ball and bombarding one another for a joke and so on. For how is the concept of game bounded?
On Certainty On Certainty (German: Über Gewißheit) is a philosophical book composed from the notes written by Ludwig Wittgenstein just prior to his death. Some of the notes were left at the home of G. E. M. Anscombe, who later compiled the notes into a book. The book's concerns are largely epistemological, its main theme being that there are some things which must be exempt from doubt in order for human practices to be possible (i.e. Another important point is his claim that all doubt is embedded into underlying beliefs and therefore that the most radical forms of doubt must be rejected since they form a contradiction within the system that expressed them. See also[edit] External links[edit] On Certainty - translation by Denis Paul and G.
Truth table Practically, a truth table is composed of one column for each input variable (for example, A and B), and one final column for all of the possible results of the logical operation that the table is meant to represent (for example, A XOR B). Each row of the truth table therefore contains one possible configuration of the input variables (for instance, A=true B=false), and the result of the operation for those values. See the examples below for further clarification. Ludwig Wittgenstein is often credited with their invention in the Tractatus Logico-Philosophicus.[1] Unary operations[edit] Logical identity[edit] Logical identity is an operation on one logical value, typically the value of a proposition, that produces a value of true if its operand is true and a value of false if its operand is false. The truth table for the logical identity operator is as follows: Logical negation[edit] The truth table for NOT p (also written as ¬p, Np, Fpq, or ~p) is as follows: Binary operations[edit] Key:
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.[4] From 1939–1947, Wittgenstein taught at the University of Cambridge.[5] During his lifetime he published just one slim book, the 75-page Tractatus Logico-Philosophicus (1921), one article, one book review and a children's dictionary.[6] His voluminous manuscripts were edited and published posthumously. Philosophical Investigations appeared as a book in 1953 and by the end of the century it was considered an important modern classic.[7] Philosopher Bertrand Russell described Wittgenstein as "the most perfect example I have ever known of genius as traditionally conceived; passionate, profound, intense, and dominating".[8] Born in Vienna into one of Europe's richest families, he inherited a large fortune from his father in 1913. Background[edit] The Wittgensteins[edit]
Rabindranath Tagore Rabindranath Tagoreβ[›] (Bengali pronunciation: [rəˈbindrəˈnɑt ˈtɑɡɔr] ( )), also written Rabīndranātha Thākura (Bengali: রবীন্দ্রনাথ ঠাকুর; pronounced: [rəˈbindrəˈnɑtə ˈtɑkʊrə]),[2] (7 May 1861 – 7 August 1941),γ[›] sobriquet Gurudev,δ[›] was a Bengali polymath who reshaped his region's literature and music. Author of Gitanjali and its "profoundly sensitive, fresh and beautiful verse", he became the first non-European to win the Nobel Prize in Literature in 1913. A Pirali Brahmin from Calcutta, Tagore wrote poetry as an eight-year-old. Early life: 1861–1878 The youngest of thirteen surviving children, Tagore was born in the Jorasanko mansion in Calcutta, India to parents Debendranath Tagore (1817–1905) and Sarada Devi (1830–1875).ε[›] The Tagore family came into prominence during the Bengal Renaissance that started during the age of Hussein Shah (1493–1519). "Rabi" was raised mostly by servants; his mother had died in his early childhood and his father travelled widely. Germany, 1931.