ࡱ> qsp7 AbjbjUU \?7|7|Al        )2.DDDD a)c)c)c)c)c)c)$+ 4-|)  " )3  DD)3 3 3 ^ D Da)3 a)3 3 q'  a)D" 0L%G j(a))0)+(6- -a)3     Criticisms of Logic  Bertrand Russell is considered one of the founders of Analytic Philosphy, along with Wittgenstein (his pupil), and Frege. He is considered likely the most notable logician of the 20th C. Russell, along with Alfred North Whitehead, published Principia Mathematica (in 3 volumes, 1910-1913) a seminal work focused on providing a logical foundation for mathematics. In it, they take 362 pages to prove that: 1 + 1 = 2.  INCLUDEPICTURE "http://www.cut-the-knot.org/selfreference/principia.gif" \* MERGEFORMAT  Analytic Philosophy Russell, amongst others, is famous for his work in Analytic Philosophy, most common in Britain, the US, and other English-speaking countries. It essentially seeks to replace language with a system of symbols and reduce any kind of meaning (and, indeed, possibly even experiences and material objects) to equations that can be solved by the application of rules of formal logic. It attempts to apply mathematical rigour to language itself. In Russells (and others work), however, it was discovered that there are several problems with traditional logic: 1. The word is has a variety of meanings associated with it: Bertrand Russell called is a disgrace to the human race in Introduction to Mathematical Philosophy (1919). For example: The raven is black. This means the colour is black, an attribute. The spoon is silver. This also means the spoon is composed of silver. A bachelor is an unmarried man. This is a definition. Pierre Trudeau was a Prime Minister. He belongs to a class or grouping. St. Anne is the mother of Mary. This shows family relationship. All politicians are liars. This shows a quality learned from experience. All full professors are Ph.D.s. This shows a requirement for the job. To strive is to succeed. This form works like an if---then statement (see following). All citizens of authoritarian dictatorships who openly oppose the regime are brave. Hypothetical statement that if indeed there are any such citizens, they would be brave; but there may be none. Therefore Aristotles logic incorrectly assumes the forms of All x is y, some x are y, or no x are y are all the same. (This was made famous by Bill Clintons grand jury testimony,it depends on what the meaning of is, is) 2. Some other connective words (conjunctions) also display ambiguity. For example the word And: I love peaches and cream. vs. I love apples and oranges. They got married and had children. vs. They had children and got married. 3. Russell is also famous for discovering forms of paradox that resist being logically solved. Paradoxes are a category of statement which are generally understood by people yet are impossible to properly logically diagram without creating a new class of objects. The problem, as Russell wrote in his three volume Autobiography (19671969) is that it led [him] to consider those classes which are not members of themselves, and to ask whether the class of such classes is or is not a member of itself. [He] found that either answer implies its contradictory. He gives the ancient example of Epimenides the Cretan, who said that all Cretans are liars. He continues, A contradiction essentially similar to that of Epimenides can be created by giving a person a piece of paper on which is written: The statement on the other side of this paper is false. The person turns the paper over, and finds on the other side: The statement on the other side of this paper is true. While initially he thought this contradiction would be easy to solve and accounted for, it wasnt: It is known as Russells Paradox. Here are some other examples: All men of Seville are shaved by the barber of Seville if and only if the men do not shave themselves. Does the barber shave himself? This sentence has six words. All rules have exceptions. This is not a sentence. I am lying. (No region can include itself as well) (A. N. Whitehead). Continental Philosophy A term originated by English speaking philosophers, specifically to distinguish it from Analytical Philosophy (referencing the continent i.e. Europe), not only in practices but also in origins. Unlike Analytic Philosophy, which treats philosophical problems independently through logic (like an equation), Continental Philosophy argues that philosophical questions cannot be divorced from their context: era (time), locus (place), language, culture, the history of ideas, etc. This branch of philosophy has been deeply influential in the human sciences like anthropology, psychology, psychoanalysis, etc. but also in literary theory (including linguistics). It spawned such critical movements as Structuralism (the idea that everything in the human sciences is a scaffolding of ideas (a structure) and complex interactions within them), which in turn led to movements in the 1960s and 1970s such as Post-Structuralism, Deconstruction, etc. (more on this in the Language Unit). Generally Continental Philosophy rejects mathematical theories or those of the natural sciences applied to philosophy, arguing that there are pre-theoretical states of existence that cannot be discovered or explained by theory in these disciplines (much like Kants theory of noumena: that the best we can ever hope to do is grasp the surface level of things (phenomena) and that the deeper/true nature of things will always be out of our grasp). L^ _r_a 0 ] s ! B a } 5 N T X d k u ?A 6\]\5>*mH sH 5\ jU65jUmHnHu 5CJ$aJ$;,Z[\]^_   ^ " b  & F hh^h`$a$A G > ? 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