Joseph: My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved. Probably this alleged theorem simply cannot be proved, since—as the article points out—no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.

Laura: Your encyclopedia is out of date. Recently someone has in fact proved Fermat’s theorem. And since the theorem is provable, your claim—that Fermat was lying or mistaken—clearly is wrong.

Summarize Argument
Joseph's main conclusion is that Fermat was lying or mistaken when he claimed to have proved his theorem. Joseph believes this because no one has been able to prove the theorem since Fermat's time, suggesting that it might be impossible to prove.

Identify Argument Part
This is a sub-conclusion that supports Joseph’s main conclusion that Fermat was either lying or mistaken in proving his theory.

A
an assumption for which no support is offered
This is factually incorrect. Joesph provides support that “no one else has been able to prove it”
B
a subsidiary conclusion on which his argument’s main conclusion is based
This is a sub-conclusion that is supported by the premise that no one else has been able to solve the theorem. Then, it supports the main conclusion that Fermat was lying or mistaken.
C
a potential objection that his argument anticipates and attempts to answer before it is raised
This is not an objection that Joseph anticipates or answers. It is a sub-conclusion on which he bases his main conclusion.
D
the principal claim that his argument is structured to refute
This is factually inaccurate. Joseph believes that no one else could solve this theorem. That is why he argues that Fermat was mistaken or lying.
E
background information that neither supports nor undermines his argument’s conclusion
This supports the argument’s main conclusion that Fermat was mistaken or lying. It is not just background information.

Comment on this

Critic: Emily Dickinson’s poetry demonstrates that meaning cannot reside entirely within a poem itself, but is always the unique result of an interaction between a reader’s system of beliefs and the poem; and, of course, any two readers from different cultures or eras have radically different systems of beliefs.

Summary

Emily Dickinson’s poetry demonstrates that meaning is not derived entirely from a poem itself, but that meaning is the unique result of the interaction between a poem and a reader’s beliefs. Any two readers from different cultures or time periods have radically different beliefs.

Notable Valid Inferences

A modern reader and an ancient reader would interpret a poem in exactly the same way.

A
A reader’s interpretation of a poem by Dickinson is affected by someone else’s interpretation of it.

Could be true. We know that any two readers have different beliefs, but it is possible that some readers’ interpretations could affect the interpretations of other readers.

B
A modern reader and a nineteenth-century reader interpret one of Shakespeare’s sonnets in the same way.

Must be false. We know that any two readers from different time periods have different beliefs. Therefore, it is impossible for a modern reader and a nineteenth-century reader to interpret a poem in exactly the same way.

C
A reader’s interpretation of a poem evolves over time.

Could be true. We know that every reader of a poem has a different interpretation, but this fact does not preclude the possibility of a reader’s interpretation changing over time. Interpretations could change over time and still be unique.

D
Two readers from the same era arrive at different interpretations of the same poem.

Could be true. We know that any two readers from different cultures have different beliefs. These different beliefs cause these readers to interpret a poem differently.

E
A reader’s enjoyment of a poem is enhanced by knowing the poet’s interpretation of it.

Could be true. We know that each reader has a unique interpretation based on each reader’s belief system. It is possible that a reader’s enjoyment is enhanced while maintaining a unique interpretation.


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