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Essay / Research Paper Abstract
A 4 page research paper that discusses an aspect of Russell's career and philosophy. Between the publication of Principles of Mathematics in 1903 and his article "On Denoting" in 1905, the views of Bertrand Russell on the semantics of propositions in sentence that contain denoting phrases changed considerably. This examination of this factor in Russell's work looks at the impetus behind change and how the change expressed Russell's views on the relationship between the grammatical form of a denoting phrase and the logical form of the proposition that it expresses. In so doing, Russell logically connects the realms of logic in the study of mathematics and semantics. Bibliography lists 2 sources.
Page Count:
4 pages (~225 words per page)
File: D0_khbrus.rtf
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Unformatted sample text from the term paper:
that contain denoting phrases changed considerably. The following examination of this factor in Russells work looks at the impetus behind change and how the change expressed Russells views on the
relationship between the grammatical form of a denoting phrase and the logical form of the proposition that it expresses. In so doing, Russell logically connects the realms of logic in
the study of mathematics and semantics. In Russells 1903 text The Principles of Mathematics, the purpose of his writing was to demonstrate not only that mathematics has a
logically foundation, but also that math is entirely logical ("Bertrand Russell"). He maintained that math can be derived from a few simple axioms that are not specifically mathematical in themselves,
such as number and square root ("Bertrand Russell"). However, in writing his 1903 text, Russell became aware of a profound contradiction that lay at the heart of his system of
logic and which has subsequently become known as Russells Paradox. This contradiction evolves form the face that some classes of things are members of themselves and some are not.
Consequently, to ask if a class is a member of itself is to engage in a contradiction. This paradox has been compared to defining a barber as someone who
"shaves all those who do not shave themselves" and then inquiring if the barber shaves himself or not ("Bertrand Russell"). Another example might be to ask if God, who is
all-powerful and the creator of all could create a rock too large for Him to lift. Considering this problem demonstrates the inherent contradictions in the axiom. The longer that Russell
contemplated this problem, the more it seemed to him that the views he had expressed pertaining to class in Principles of Mathematics were fundamentally wrong ("Bertrand Russell"). The changes
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