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A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true. [3] It is shown below in logical form. Either A or B Not A Therefore B. When A and B are replaced with real life examples it looks like below.
In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to the works of Theophrastus and Eudemus for the first investigation of this kind of syllogisms.
Syllogistic fallacies – logical fallacies that occur in syllogisms. Affirmative conclusion from a negative premise (illicit negative) – a categorical syllogism has a positive conclusion, but at least one negative premise. [11] Fallacy of exclusive premises – a categorical syllogism that is invalid because both of its premises are negative ...
Stoic logic is the system of propositional logic developed by the Stoic philosophers in ancient Greece. It was one of the two great systems of logic in the classical world. It was largely built and shaped by Chrysippus , the third head of the Stoic school in the 3rd-century BCE.
B is the common term between the two premises (the middle term) but is never distributed, so this syllogism is invalid. B would be distributed by introducing a premise which states either All B is Z, or No B is Z. Also, a related rule of logic is that anything distributed in the conclusion must be distributed in at least one premise. All Z is B
The central aspect of Aristotelian logic involves classifying all possible syllogisms into valid and invalid arguments according to how the propositions are formed. [ 112 ] [ 115 ] For example, the syllogism "all men are mortal; Socrates is a man; therefore Socrates is mortal" is valid.
But it can be rewritten as a standard form AAA-1 syllogism by first substituting the synonymous term "humans" for "people" and then by reducing the complementary term "immortal" in the first premise using the immediate inference known as obversion (that is, the statement "No humans are immortal." is equivalent to the statement "All humans are ...