# Why can't Aristotelian logic account for deductions which rely on propositional logic, or express relationships between two or more objects?

This is a summary from absurdbeing.com:

Unfortunately, as mentioned, Aristotle’s system of logic (based entirely on the deductive syllogism) was incomplete in at least three ways: first, it didn’t account for deductions which relied on propositional logic, where variables stand for whole propositions; second, it couldn’t express relationships between two or more objects; and third, it ignored inductive logic, which sacrifices certainty for the benefit of adding new knowledge.

What are the deductions which rely on propositional logic?

What does he mean 'where variables stand for whole propositions'?

Why can't it express relationships between two more objects.

• "What are the deductions which rely on propositional?" See Propositional calculus dedicated to the rules involving truth-functional connectives only: negation, conjunction, disjunction. A's Logic used some "propositional rules" but there is no systematic treatment of it. Compare with Stoic Logic. May 18, 2022 at 11:50
• "Why can't it express relationships between two more objects." Because the analysis of sentence structure provided by A was in terms of subject-predicate: La (animal is Living) and not in terms of binary (or more) relations: aLb (amy Loves bob). May 18, 2022 at 11:55
• Perhaps you do not recognize that there is a distinct subject called MATHEMATICAL LOGIC. Aristotelian logic had a different purpose. The quote you refer to does not point that out. Math people don't tend to understand what PROPOSITIONS are. The words may be the same but the meaning is different. Philosophers don't need SENTENCES. Aristotelian logic is not about how people do argue. We convert normal language into the syllogism rules which many people are not aware of. Aristotelian logic is not for persuading people. Persuasion is psychological & rhetorical not deductive per se. May 19, 2022 at 23:10
• Just to be clear: different sentences can represent the same proposition. This is what Psychology, Mathematics & Rhetoric seem to ignore. They are focused on how people actually speak and NOT the idea being expressed. Most cases can be translated into categories but it loses rhetorical impact. We can persuade people to do as we want when we want them to. So rhetorically that is more important in reality so they try to notate how people speak. Mathematical logic has a specific domain that does not always apply to reality as well. So there will always be complaints. May 19, 2022 at 23:21