# The Principles of Mathematics

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…

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?

Sample Solution