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Difficulty: MediumSyllogism and Categorical Propositions

Consider the following categorical statements as the only source of absolute truth for this logical system:

1. All griffins are chimeras.
2. No chimera is a dragon.
3. All dragons are basilisks.

Based exclusively on the rules of modern formal deductive reasoning, which of the following conclusions logically follow(s)? (Select all that apply)

  1. No griffin is a dragon.Answer
  2. No dragon is a griffin.Answer
  3. C
    Some dragons are basilisks.
  4. D
    Some chimeras are griffins.

Answer

The logically valid conclusions are that no griffin is a dragon, and symmetrically, no dragon is a griffin.
The correct conclusions are standard categorical deductions. The premises establish that griffins are a subset of chimeras, and chimeras share absolutely no overlap with dragons. Therefore, griffins and dragons cannot intersect. Because universal negative statements are symmetric, both 'No griffin is a dragon' and 'No dragon is a griffin' are necessarily true.

Step-by-Step Solution

1
Analyze the relationship between griffins, chimeras, and dragons using the universal premises.
Since all griffins are chimeras, and no chimera is a dragon, the sets representing griffins and dragons are mutually exclusive.
Applying a universal negative (E) premise to a universal affirmative (A) premise yields a logically valid universal negative deduction.
2
Evaluate the symmetrical nature of the valid negative deduction.
Because no griffin is a dragon, it is equally and necessarily true that no dragon is a griffin.
Universal negative statements (E propositions) convert simply. The sets do not intersect in either direction.
3
Assess particular conclusions ('some') derived purely from universal statements.
Conclusions such as 'some dragons are basilisks' or 'some chimeras are griffins' are logically invalid.
In modern formal logic, universal statements do not prove existence. Concluding that 'some' (at least one) exists without a specific existential premise commits the existential fallacy.

Key Concept

Validating categorical deductions and identifying existential fallacies in modern formal logic.
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Topics

Syllogism and Categorical Propositions

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