Syllogism

• A Syllogism is a form of Logic used in Philosophy, to arrive at a conclusion from two given statements.
• It was widely used in Hellenistic Philosophy and is also used as a Literary device.

The Two Greek Schools of Logic

• Two great Schools of Logic existed in Antiquity, from the 3rd century BCE to the 7th century CE.
  1. Platonism:
     • based on the teachings of Socrates
     • Plato
     • Aristotle with his School of Peripatetics.
  2. Stoicism
     • based on the teachings of Zeno of Citium, Chrysippus of Soli and Epictetus.
     • Also Seneca the Younger and Marcus Aurelius.
• School of Epicureanism
  • Epicurus (341-270 BCE) developed the School of Epicureanism, which first opposed Platonism, then Stoicism.
• Eventually, there were 14 schools of Hellenistic Philosophy.

The Three Famous Socratic Philosophers

• • Socrates
  • Plato
  • Aristotle

The Aristotelian Syllogistic

• Aristotle (384-322 BCE) developed a form of Logic, known as Deductive reasoning.
• A philosophical conclusion is reached by putting together two or more facts or premises, and represented in a three line form:
  • Rex is a dog.
  • Rex has two eyes.
  • Therefore all dogs have two eyes.
• By the same reasoning, the Logic can be flawed if the two statements assume too much.
  • All men are mammals.
  • All men walk on two legs.
  • Therefore all mammals walk on two legs.

The Stoic Syllogistic

• By contrast, in the Stoic Syllogism, the conclusion is drawn by inference, stating an ‘Assertable’ or a ‘Sayable’.
• This known as Propositional Logic.
• ‘If’ such and such, ‘Then’ so and so. There were five forms of argument or ‘Indemonstrables’:
  • If it is day, then it is light: It is day, therefore it is light.
  • If the first, then the second: Not the second, so not the first.
  • Not both the first and the second: The first, so not the second.
  • Either the first or the second: The first, so not the second.
  • Either the first or the second: Not the first, so the second.

The Stoic School

• Founded by Zeno of Citium (334-262 BCE), Stoicism became the greatest rival to Aristotelian Logic.
• The third Head of the Stoic School, Chrysippus of Soli (279-206 BCE), was known as the second Founder of Stoicism. Chrysippus developed the five ‘Indemonstrables’, meaning basic forms of argument.
• None of his works have survived, of which two known Works were ‘Logical Questions’ and ‘On Providence’.
• The Stoic school of philosophy fell into disfavour by the seventh century CE.
• Our knowledge of this school comes from references made by authors such as Diogenes Laertius.

The Three most famous Stoic Philosophers

• • Marcus Aurelius
  • Epictetus
  • Seneca the Younger