# Philosophy- Analytical Reasoning

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Answer all questions. The assignment is due on Friday, December 3, 11:59 pm. The assignment has to be formatted in MS Word or pdf; only Venn diagrams may be made in hand. You must submit your answers to Blackboard.

Part A

For each of the following arguments:

- Translate the argument into standard form. (3 marks)
- Symbolize the syllogism applying the bold capital letters used in the text to represent the terms in which they appear.

For example, in syllogism #1, **N**: syllogisms having two negative premises, **V**: valid syllogisms, **S**: sound arguments (1 mark)

- Name the mood and figure of its standard-form translation. (1 mark)
- Test its validity using a Venn diagram for both the Boolean and Aristotelian interpretations. On both interpretations, explain why you think the diagram shows the syllogism valid or invalid. For Aristotelian Interpretation diagrams you can use the shortcut method explained in the textbook on p. 290 and in Module 4 Section 5.2 on Blackboard. (4 marks)
- If the syllogism is invalid, name the fallacy it commits. (1 mark)

- All syllogisms having two
**N**egative premises are invalid. Some**V**alid syllogisms are**S**ound. Therefore some unsound arguments are syllogisms having two negative premises. - Where there’s
**S**moke there’s**F**ire, so there’s no fire in the**B**asement, because there is no smoke there.

Part B

For the following enthymematic argument,

- Translate the given propositions into standard form using the same terms in both propositions. (3 marks)
- Symbolize the enthymeme applying the bold capital letters used in the text to represent the terms in which they appear. The symbols should correspond to their use in
*affirmative*sentences (for example,*B*needs to refer to what you*should*believe, not*shouldn’t*). (1 mark) - If possible, formulate the missing premise or conclusion in such a way as to create a valid syllogism. (2 marks)
- Present this syllogism in standard form. (1 mark)
- Justify your solution, or the decision that no valid syllogism can be created from the enthymeme, using the method of analysis of the rules or a Venn diagram. (3 marks)

This **S**tory appeared in the *N**ational Inquirer*. Therefore, you shouldn’t **B**elieve it.

Part C

For the following sorites:

- Translate it into standard form. (3 marks)
- Next symbolize the standard-form sorites applying the bold capital letters used in the text to represent the terms in which they appear. The symbols should correspond to their use in
*affirmative*sentences (for example, R: books I*recommend*for reading). (1 mark) - Test the standard form sorites for validity. (3 marks)
- Explain your answer. (3 marks)

- The only books in the library that I do not
**R**ecommend for reading are unhealthy in tone. - The
**B**ound books are all**W**ell written. - All the
**P**oetry books are**H**ealthy in tone.

- I do not recommend that you read any of the unbound books.

Therefore, all the Poetry books in this library are well written.

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