Syllogisms



Syllogisms, which stem from deductive reasoning, are relatively simple forms of logical argument in which a conclusion is inferred by two premises. Aristotle, who established the foundation of formal logic, was the first to create a syllogism. Syllogisms are quite simple in structure. They consist of a major premise, a minor premise, and a conclusion. Each part of a syllogism contains 2 categorical terms and the the conclusion has one term in common with each premise. Each premise, in turn, is in the form "some/all A belong to B," or "some/all A is/are [not] B," where A and B are both terms. Also, the premises and conclusion can be of four types.

 

code quantifier subject copula predicate type example
A All S are P universal affirmatives All humans are mortal.
E No S are P universal negatives No humans are perfect.
I Some S are P particular affirmatives Some humans are healthy.
O Some S are not P particular negatives Some humans are not clever.

Aristotle concluded that there was 256 syllogisms, or as Aristotle called them moods. However, out of 256 only 24 are valid. Once all of the valid moods were determined Aristotle reasoned that we could obtain information about any discipline and eventually all human knowledge in the world. However, research in this area has proven that syllogisms require lots of cognitive effort. As many as 50% or more get the validity of syllogisms wrong. People have trouble with the negatives as well as with the particulars. Also, research indicates that spatial and verbal reasoners approach syllogisms very differently. Aristotle thought that this was the way humans logically processed information. Even though this might work for simple arguments it is far too difficult to apply to more diffucult reasoning, which we perform every day.

 

For more information

Wikipedia entry on Aristotelan syllogisms

A brief description and a quick history on Aristotelian syllogisms

Semantics and syllogistic reasoning

A website that shows a theory proposed by Geurt that is based on principles derived from semantics of natural language that tries to explian syllogistic reasoning.

Brief description on syllogistisms

General information and summary of syllogisms from an online cognitive psychology textbook.

Relative informativeness of quatifiers used in syllogistic reasoning

Research conducted by Mike Oaksford, Lisa Roberts, and Nick Chater on how informative the quantifiers from syllogisms are, especially the particulars.

Cognitive neuroscience/reasoning and decision making

Another wikipedia article which discusses the process and the different kinds of reasoning we use along with how we use syllogisms in everyday life.

Research on the quantifier "some" in syllogistic reasoning

A research article on why people tend to make many errors in syllogisms with particular quantifiers and whether or not pragmatic intepretations can explain the high error rates.

Effects of visual and phonological distinctiveness on syllogistic reasoning

A research article that tries to understand how important working memory sub-systems and prior knowledge are in syllogistic reasoning.

Syllogistic reasoning and cognitive aging

A quick abstract that summarizes the effects of age on how well we solve syllogisms and the importance of working memory.

Aristotle's logic

An article from the Stanford Encyclopedia of Logic that summarizes and describes Aristotelian logic.

Aristotle's work "Prior Analytics

A work of Aritotle that describes his logic and how he came up with categorical syllogisms

 

This page was created by Juan Salvatierra