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Philosophy 103: Introduction to Logic
Test on Categorical Propositions Part III: Successive Immediate Inferences.

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Given the truth of "No splitscreens are practicums" what can be validly inferred about the truth or falsity of each of the following propositions?

(Cite the proper logical relation and appropriate truth value for each successive inference. You may abbreviate by using "S" and "P" for the appropriate classes in this section of the test only.)

1. Some practicums are not splitscreens. (Note: This statement is the last line in the proof..)



Truth Value

1. No splitscreens are practicums.



2. No practicums are splitscreens. conversion true
3. Some practicums are not splitscreens. subalternation true
... . .
... . .
... . .
... . .

2. All nonpracticums are nonsplitscreens. (Note: This statement is the last line in the proof..)



1. No splitscreens are practicums.



2. All splitscreens are practicums contrary false
3. All nonpracticums are nonsplitscreens. contrapositive false
... . .
... . .
... . .
... . .
... . .

Part IV. Venn Diagrams: Symbolize the following statements by drawing the appropriate Venn Diagram.

1. Some sculptors are painters.

2. No peddlers are millionaires.

3. All merchants are speculators.

4. Some musicians are not pianists.

5. All ribosomes are structures in the cytoplasm.

Optional Problems:

1. Translate the following statement into standard form:

"Any strain imposed on the mind will be reflected in the eyes, and similarly anything which rests the mind will benefit them." (C.S. Price, The Improvement of Sight.)

Several ways are possible for translation. One way is ...
"All strains on the mind are strains on the eyes." and
" All nonstrains on the mind are nonstrains on the eyes."

Next, state the logical relation obtaining between the first independent clause and the second independent clause.

First, contrapose; second, convert.

Finally, if the first independent clause is false, what is the truth value of the second?
Since you cannot validly convert an A proposition, the resultant truth value is "'undetermined."

2. Watson writes, "Monday morning found us on our way to the famous university town--an easy effort on the part of Holmes, who had no roots to pull up, but one which involved frantic planning and hurrying on my part, as my practice was by this time not inconsiderable." (A. Conan Doyle, "The Adventure of the Creeping Man") Supposing that what Watson writes is true, does it follow that Watson's practice is large? What is the logical relation involved in this inference?

One translation of Watson's statement is "'No things which are my practice are non-considerable things."  By obverting one obtains "All things which are my practice are considerable things."  Hence, Watson\'s practice is large.

End of Test on Categorical Propositions

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