Use the five rules to determine the validity of this categorical syllogism:

All neutron stars are things that produce intense gravity.

All neutron stars are extremely dense objects.

Therefore, all extremely dense objects are things that produce intense gravity.

Question:

The five rules are;

"The middle term must be distributed in at least one premise.

If a major or minor term is distributed in the conclusion, then it must be distributed in the premises.

No syllogism can have two negative premises.

If either premise is negative, the conclusion must be negative.

No syllogism with a particular conclusion can have two universal premises."

Answer:

The categorical syllogism is invalid as it does not meet thr requirements of rule 2

Invalid because it breaks rule #2.

Explanation:

An argument whose conclusion is implied based on the logical stipulation of the premise is a deductive argument

A syllogism is a deductive argument that makes use of deductive reasoning to come to conclusion, considering a number of of two or more premises which are taken to be true.

For categorical syllogism, we have

If A is in C, then B is in C

Based on the five rules, we have

1. The middle term must be distributed at least once

Here, the middle term is all neutron stars are extremely dense hence i says something about all items in a category, therefore it is distributed

2. If a term is distributed in the conclusion, then it must be distributed in the premise.

Here, the distributed term in the conclusion are "extremely dense objects" is not distributed in the premise, therefore the categorical syllogism is invalid.