The problem of multiple generality names a failure in Aristotelian logic to describe certain intuitively valid inferences. For example, it is intuitively clear that if: Aristotelian logic, also known as syllogistic logic, is the particular type of logic created by Aristotle, primarily in his works Prior Analytics and De Interpretatione. ...
 Some cat is feared by every mouse
then it follows logically that:  All mice are afraid of at least one cat
However, it is possible to express this inference in Aristotle's system, with such expressions as the following:  There exists cat such that for all mouse, cat is feared by mouse.
 For all mouse, there exists cat such that mouse fears cat.
When medieval logicians recognised this problem, they saw that it was possible to add further, more complex syllogisms to the theory to allow such inferences. They developed the "for all" and "there exists" statements to account for this. The first logical calculus capable of dealing with such inferences was the above "regular" logic. Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Modern research on term logic have shown how the problem may be solved in a syllogistic theory, as well. Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ...
