Jan Lukasiewicz acknowledged that Aristotle＇s syllogistic does not admit singular terms and presents syllogism as an implication. But he failed to recognize syllogistic necessity, reducing this necessity to ＂formal ...Jan Lukasiewicz acknowledged that Aristotle＇s syllogistic does not admit singular terms and presents syllogism as an implication. But he failed to recognize syllogistic necessity, reducing this necessity to ＂formal implication＂ as introduced by Russell, when Aristotle shows it as binding relations between three terms. On the contrary, Paul Lorenzen directly recognized syllogistic necessity as the typical example of his own logical implication. His reconstruction of syllogistic differs from the original by his interpretation of particular propositions as the determination of classes which are specified by predicates. The result is the representation of valid moods as the board of all multiplications of relations which are permitted. These relations are not only the Aristotelian ,4, E,I, O, but also the new converse asymmetrical relations of A and O： （a） and （o）.展开更多
文摘Jan Lukasiewicz acknowledged that Aristotle＇s syllogistic does not admit singular terms and presents syllogism as an implication. But he failed to recognize syllogistic necessity, reducing this necessity to ＂formal implication＂ as introduced by Russell, when Aristotle shows it as binding relations between three terms. On the contrary, Paul Lorenzen directly recognized syllogistic necessity as the typical example of his own logical implication. His reconstruction of syllogistic differs from the original by his interpretation of particular propositions as the determination of classes which are specified by predicates. The result is the representation of valid moods as the board of all multiplications of relations which are permitted. These relations are not only the Aristotelian ,4, E,I, O, but also the new converse asymmetrical relations of A and O： （a） and （o）.
