Questions and Answers
What is the primary condition for the inference form to be valid from the Aristotelian standpoint?
The circled X represents at least one existing thing.
What is the purpose of testing the inference form from the Boolean standpoint?
To determine the validity of the inference from the Aristotelian standpoint.
What does the Venn diagram show about the inference form?
It is conditionally valid from the Aristotelian standpoint.
What is the term in the inference that corresponds to the P circle in the Venn diagram?
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What is the final step in validating the inference?
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What is the primary requirement for using modified Venn diagrams to test immediate inferences?
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What is the advantage of testing an inference from the Boolean standpoint?
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What is represented by the circled X in the Venn diagram?
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Why might it be useful to test an inference from the Aristotelian standpoint?
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What is the relationship between the validity of an inference from the Boolean and Aristotelian standpoints?
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What is the relationship between the information in the conclusion diagram and the premise diagram?
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Why do we adopt the Aristotelian standpoint in testing the inference form?
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What is the purpose of testing the inference form from multiple standpoints?
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What is the significance of the circled X in the Venn diagram?
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What is the outcome of testing the inference form from the Boolean standpoint?
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Study Notes
Venn Diagrams and Immediate Inferences
- The modified Venn diagram technique involving circled X's can be used to test immediate inferences from the Aristotelian standpoint.
- The subject and predicate terms of the conclusion must be the same as those of the premise.
- This method does not involve the operations of conversion, obversion, and contraposition.
Testing Inferences
- Venn diagrams can also be used to test inferences involving conversion, obversion, and contraposition with a further modification.
- Testing inferences from the Boolean standpoint is often simpler, and if an inference is valid from the Boolean standpoint, it is also valid from the Aristotelian standpoint.
Example Inference
- All A are B. Therefore, some A are B.
- The inference form is not valid from the Boolean standpoint, but it is conditionally valid from the Aristotelian standpoint, assuming the subject of the premise (A) denotes at least one existing thing.
Testing Complete Inferences
- To test a complete inference, begin by testing its form from the Boolean standpoint, and if it is not valid, adopt the Aristotelian standpoint.
- Example: No penguins are birds that can fly. Therefore, it is false that all penguins are birds that can fly.
- The Venn diagrams show that the inference form is conditionally valid from the Aristotelian standpoint, assuming the subject of the premise (P) denotes at least one existing thing.
Venn Diagrams and Immediate Inferences
- The modified Venn diagram technique involving circled X's can be used to test immediate inferences from the Aristotelian standpoint.
- The subject and predicate terms of the conclusion must be the same as those of the premise.
- This method does not involve the operations of conversion, obversion, and contraposition.
Testing Inferences
- Venn diagrams can also be used to test inferences involving conversion, obversion, and contraposition with a further modification.
- Testing inferences from the Boolean standpoint is often simpler, and if an inference is valid from the Boolean standpoint, it is also valid from the Aristotelian standpoint.
Example Inference
- All A are B. Therefore, some A are B.
- The inference form is not valid from the Boolean standpoint, but it is conditionally valid from the Aristotelian standpoint, assuming the subject of the premise (A) denotes at least one existing thing.
Testing Complete Inferences
- To test a complete inference, begin by testing its form from the Boolean standpoint, and if it is not valid, adopt the Aristotelian standpoint.
- Example: No penguins are birds that can fly. Therefore, it is false that all penguins are birds that can fly.
- The Venn diagrams show that the inference form is conditionally valid from the Aristotelian standpoint, assuming the subject of the premise (P) denotes at least one existing thing.
