Subjects logic

Invalid Argument

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Invalid Argument


1. **State the problem:** We need to determine if the argument "Some dogs are pointers. Some dogs are spaniels. Therefore, some pointers are spaniels." is valid. 2. **Understand the argument form:** The argument claims that because some dogs belong to the category of pointers and some dogs belong to the category of spaniels, it follows that some pointers are spaniels. 3. **Recall important logic rules:** Just because two groups overlap with a third group (dogs), it does not mean they overlap with each other. This is a common logical fallacy called the "undistributed middle." 4. **Analyze the premises:** - Premise 1: Some dogs are pointers. This means there exists at least one dog that is a pointer. - Premise 2: Some dogs are spaniels. This means there exists at least one dog that is a spaniel. 5. **Check the conclusion:** "Some pointers are spaniels" means there exists at least one dog that is both a pointer and a spaniel. 6. **Evaluate validity:** The premises do not guarantee that the sets of pointers and spaniels overlap. The dogs that are pointers could be completely different from the dogs that are spaniels. 7. **Conclusion:** The argument is invalid because the conclusion does not logically follow from the premises. The premises only establish that both pointers and spaniels are subsets of dogs, but do not establish any intersection between pointers and spaniels.