Connecting three terms
A categorical syllogism uses three terms. The middle term occurs in both premises and connects the two terms in the conclusion. For example, all mammals are animals and all whales are mammals; therefore all whales are animals. The inference depends on relations already stated in the premises.
Quantity and negation
Premises can affirm or deny a relation and concern all members or only some. All A are B does not mean that all B are A. Nor does a statement about some members establish a universal claim. Attention to quantity, negation and term position exposes misleading verbal transitions.
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Validity and factual truth
A valid form prevents a false conclusion when its premises are true. It does not establish that the premises actually describe the world correctly. Conversely, an accidentally true conclusion can arise from invalid reasoning. Assessing an argument therefore requires both factual examination and an account of its inferential structure.
Ancient inquiry and later logic
The Prior Analytics studies inference, while the Posterior Analytics investigates demonstration and knowledge. Later readers grouped logical treatises as the Organon and transmitted them across languages. Modern logic studies wider structures, including relations and quantified arguments. Syllogistic is an important historical system, not an exhaustive account of reasoning.
References: [1]