PARAGRAPH: Aristotle, an ancient philosopher, was one of the first to discuss syllogisms. In Prior Analytics, published around 350 BCE, Aristotle outlined the basic form of syllogism which represented the earliest branch of formal logic. For Aristotle, logic revolved around deduction : “speech in which certain things having been supposed something different from those supposed results of necessity because of their being so.”
If that sounds confusing – that’s ancient philosophy for you! Let’s break it down. “The things that have been supposed” are what we now call “premises”. “What results necessarily” from those premises being true is a conclusion.
To Aristotle, if an argument was valid, it would be impossible for premises X and Y to be true and for conclusion Z to be false. Aristotle named this method of proving validity “reductio ad impossibile” : a syllogism is valid when the denial of the conclusion but acceptance of the premises would lead to a contradiction.
Aristotle divided syllogistic propositions into four different categories : universal
affirmative, particular affirmative, universal negative and particular negative. A universal affirmative syllogistic sentence : All humans need food.
A particular affirmative syllogistic sentence : Some birds can fly.
A universal negative syllogistic sentence : No dogs are cats.
A particular negative syllogistic sentence : Not all cars have four doors.
During the rise of modern formal logic, German philosopher Gottlob Frege refined Aristotle’s syllogistic theory through the addition of non-categorical syllogisms. These are syllogisms that rely on premises and can be hypothetical, or which include disjunctions like ‘or’. The hypothetical form of syllogisms can be traced back to Stoic philosophy, but modern philosophers tend to attribute the theory to Frege. In the
19th century, British philosopher and economist John Neville Keynes also helped
make non-categorical syllogisms popular.
Here’s an example of a hypothetical syllogism :
1. If it is sunny tomorrow, I can go running.
2. It is sunny.
3. Therefore, I can go running.
Here’s an example of a disjunctive syllogism :
1. Patrick studies English or Linguistics.
2. Patrick is not studying Linguistics.
3. Therefore, he is studying English.
In the Begriffsschrift (German for “Concept-Script”), he refined Aristotle’s system by developing a logical system that explained how quantifiers (words like “all” and “some”) work. His system also became the basis for modern computer science.
