# In chapter V of The Principles of Mathematics, Russell addresses a problem that becomes apparent when you contrast simple subject/predicate sentences in English (like “Alys is altruistic” or “Bertrand is bookish”) with sentences that have grammatically complex subjects (like “Every cabin is cozy”).

Write a 9 page paper (double spaced, 12 pt font, 1 inch margins) on one of the topics below. Answer each part of the question directly.

1. In chapter V of The Principles of Mathematics, Russell addresses a problem that becomes apparent when you contrast simple subject/predicate sentences in English (like “Alys is altruistic” or “Bertrand is bookish”) with sentences that have grammatically complex subjects (like “Every cabin is cozy”). This question asks you to explain various aspects of this problem.

(a) How would Russell analyze the proposition expressed by the sentence “Bertrand is bookish”? What is its structure? What are its constituents? What is the proposition about? How can we use this information to determine when it is true or false?

(b) How would Russell analyze the proposition expressed by the sentence “All athletes are altruistic”? What is its structure? What are its constituents? What is the proposition about? How can we use this information to determine when it is true or false?

(c) Russell claims that the proposition expressed by “I met a man” is not about the denoting concept a man. Explain briefly why he thinks this.

(d) Do you find the theory that Russell presents in this chapter satisfactory? Give at least one reason in favor of the view, and at least one reason against it. Which considerations do you find the most compelling, and why?

1. In the opening paragraphs of “On Denoting”, Russell overturns almost every aspect of the theory he earlier proposed in The Principles of Mathematics. This question asks you to explain the new theory, and to compare it with its predecessor.

(a) Russell claims in 1905 that an expression counts as a denoting phrase in virtue of its “form.” What does he mean by this? How does it distinguish his new theory from the one he proposed in Principles of Mathematics?

(b) Russell distinguishes between knowledge by acquaintance and knowledge by description. Explain this distinction and give an example of something you know in each of these ways, respectively. Which of these two sorts of knowledge is dependent on knowledge of propositions?

(c) Explain the notion of a propositional function. What does it mean to say that a propositional function is always true? Using these resources, how would the Russell of “On Denoting” analyze the proposition expressed by the sentence “Some philosopher admires Flaubert”?

(d) In “On Denoting” Russell famously claims that the “principle” of his new theory of denoting is that denoting phrases never have any meaning in isolation, although they contribute to the meaning of every sentence in which they occur. Describe how his new theory illustrates this principle. In what ways is this new principle incompatible with the view he developed in Principles of Mathematics?

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