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Rule (1) In any valid categorical syllogism the middle term must be distributed at least one.
Rule 2. In any valid categorical syllogism, no term may increase its distribution i.e. no term should move from being undistributed in the premises to being distributed in the conclusion.
Rule 3. No valid categorically syllogism can have two negative premises. This is because negative premises are by nature exclusionary such that they deny class inclusion (separate minor from major term) either wholly or partially and that is all. This means that there is no link that is stated of the major and minor premises since all that is asserted is the exclusion of one class from another either in part or in whole. Concluding from the premises becomes logically impossible.
Rule 4. In any valid categorical syllogism, if a premise is negative, the conclusion must be negative. This is because a negative premise asserts and implies class exclusion such whatever conclusion is drawn must assert class exclusion also in part or in whole, as the case may be.
Rule 5
Any valid categorical syllogism with a particular conclusion cannot have two universal premises. This rule however has limitations. There are two ways of interpreting categorical propositions, hypothetical and existential. The rule only holds when the interpretation of the relevant propositions is hypothetical not existential since in the latter case the argument is valid.
francis1897 answered the question on October 4, 2022 at 09:30
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