科技英语阅读（EST Reading）课后习题答案
(2011-12-13 18:37:16)
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Unit 1 Mathematics
Part I EST Reading
1. Who is Bertrand Russell?
Bertrand Arthur William Russell (b.1872 – d.1970) was a British philosopher, logician, essayist and social critic best known for his work in mathematical logic and analytic philosophy. His most influential contributions include his defense of logicism (the view that mathematics is in some important sense reducible to logic), his refining of the predicate calculus introduced by (which still forms the basis of most contemporary logic), his defense of (the view that the world consists of just one type of substance that is neither exclusively mental nor exclusively physical), and his theories of and . Russell is generally recognized as one of the founders of modern analytic philosophy, and is regularly credited with being one of the most important logicians of the twentieth century.
2. What is Russell’s Paradox?
Russell discovered the paradox that bears his name in 1901, while working on his Principles of Mathematics (1903). The paradox arises in connection with the set of all sets that are not members of themselves. Such a set, if it exists, will be a member of itself if and only if it is not a member of itself. The paradox is significant since, using classical logic, all sentences are entailed by a contradiction. Russell's discovery thus prompted a large amount of work in logic, set theory, and the philosophy and foundations of mathematics.
Section C Post-reading Task
Reading Comprehension
1. Directions: Work on your own and fill in the blanks with the main idea.
Part 1 (Para. 1): Brief introduction to Russell’s paradox
Part 2 (Paras. 2-5): The effect of Russell’s paradox on Gottlob Frege’s system.
Para. 2: Russell’s paradox dealt a heavy blow to Frege’s attempts to develop a foundation for all of mathematics using symbolic logic.
Para. 3: An illustration of Russell’s paradox in terms of sets
Para. 4: Contradiction found in the set.
Para. 5: Frege noticed the devastating effect of Russell’s paradox on his system and inability to solve it.
Part 3 (Paras. 6-8): Solutions offered by mathematicians to Russel’s paradox
Para. 6: Russell’s own response to the paradox with his "theory of types."
Para. 7: Zermelo's solution to Russell's paradox
Para. 8: What became of the effort to develop a logical foundation for all of mathematics?
Part 4 (Para. 9): Correspondence between Russell and Frege on the paradox
Vocabulary and Structure
2. Directions: Complete the sentences with the words given in the brackets. Change the form if necessary.
1) The key to unraveling such apparent paradoxes is to characterize the initial set of possibilities
