Is the cat's conclusion valid by LAW OF DETACHMENT or LAW OF SYLLOGISM? Explain your reasoning.
"Well, then," the Cat went on, "you see a dog growls when it's angry, and wags its tall when it's pleased. Now I growl when I'm pleased, and wag my tall when I'm angry. Therefore I'm mad."
VALID or INVALID: explain
The Cat's conclusion is not valid by either the Law of Detachment or the Law of Syllogism.
The Law of Detachment states that if a conditional statement (if p, then q) is true and the antecedent (p) is true, then the consequent (q) must also be true. However, in the Cat's argument, there are no conditional statements being made.
The Law of Syllogism states that if two conditional statements are given (if p, then q and if q, then r) and the antecedent of the first statement (p) matches the consequent of the second statement (q), then the consequent of the first statement (q) implies the consequent of the second statement (r). Again, there are no conditional statements present in the Cat's argument.
The Cat's conclusion is based on faulty logic and does not follow a valid deductive reasoning pattern. Therefore, the argument is invalid.
The cat's conclusion can be evaluated using the laws of logic.
The Law of Detachment states that if the premises "If A then B" and "A" are true, then the conclusion "B" must also be true. The Law of Syllogism, on the other hand, states that if we have two premises "If A then B" and "If B then C," then we can conclude "If A then C."
In the given statement, the cat provides two premises:
1. A dog growls when it's angry and wags its tail when it's pleased.
2. The cat growls when it's pleased and wags its tail when it's angry.
The cat's conclusion is "Therefore, I'm mad."
Upon analysis, we can see that the cat's statement does not conform to either the Law of Detachment or the Law of Syllogism. The cat makes a faulty leap in reasoning, assuming that because it behaves contrary to the behavior of dogs, it must be considered "mad." However, this conclusion does not logically follow from the given premises.
Therefore, the cat's conclusion is INVALID.
To determine if the Cat's conclusion is valid by the Law of Detachment or the Law of Syllogism, we need to analyze the structure of the argument and compare it to the requirements of each law.
The Law of Detachment states that if we have a conditional statement in the form "If p, then q," and it's true that p is true, then we can validly conclude that q is true. The argument presented by the Cat does not follow this pattern, as it does not involve a conditional statement.
The Law of Syllogism, on the other hand, states that if we have two conditional statements, "If p, then q" and "If q, then r", we can combine them to conclude "If p, then r." In the Cat's argument, there are no explicit conditional statements that fit this structure.
Therefore, we can conclude that the Cat's argument does not fit either the Law of Detachment or the Law of Syllogism.
More specifically, the Cat's argument suffers from a logical flaw known as a fallacy. The Cat makes a hasty generalization by assuming that because dogs growl when angry and wag their tail when pleased, and the Cat exhibits the opposite behavior (growling when pleased and wagging its tail when angry), it must be mad. This conclusion does not logically follow from the premises provided, and thus it is invalid.
In summary, the Cat's conclusion is invalid, and it does not conform to either the Law of Detachment or the Law of Syllogism.