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In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to logic that began with Aristotle and was developed further in ancient times mostly by his followers, the peripatetics, but largely fell into decline by the third century CE. Term logic revived in medieval times, first in Islamic logic by Alpharabius in the tenth century, and later in Christian Europe in the twelfth century with the advent of new logic, and remained dominant until the advent of modern predicate logic in the late nineteenth century. This entry is an introduction to the term logic needed to understand philosophy texts written before it was replaced as a formal logic system by predicate logic. Readers lacking a grasp of the basic terminology and ideas of term logic can have difficulty understanding such texts, because their authors typically assumed an acquaintance with term logic.

Aristotle's system

Aristotle's logical work is collected in the six texts that are collectively known as the Organon. Two of these texts in particular, namely the Prior Analytics and De Interpretatione, contain the heart of Aristotle's treatment of judgements and formal inference, and it is principally this part of Aristotle's works that is about term logic. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Jan Lukasiewicz of a revolutionary paradigm.[1] The Jan Lukasiewicz approach was reinvigorated in the early 1970s by John Corcoran and Timothy Smiley – which informs modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009.[2]

Basics

The fundamental assumption behind the theory is that propositions are composed of two terms – hence the name "two-term theory" or "term logic" – and that the reasoning process is in turn built from propositions:

  • The term is a part of speech representing something, but which is not true or false in its own right, such as "man" or "mortal".
  • The proposition consists of two terms, in which one term (the "predicate") is "affirmed" or "denied" of the other (the "subject"), and which is capable of truth or falsity.
  • The syllogism is an inference in which one proposition (the "conclusion") follows of necessity from two other propositions (the "premises").

A proposition may be universal or particular, and it may be affirmative or negative. Traditionally, the four kinds of propositions are:

  • A-type: Universal and affirmative ("All philosophers are mortal")
  • I-type: Particular and affirmative ("Some philosophers are mortal")
  • E-type: Universal and negative ("All philosophers are not mortal")
  • O-type: Particular and negative ("Some philosophers are not mortal")

This was called the fourfold scheme of propositions (see types of syllogism for an explanation of the letters A, I, E, and O in the traditional square). Aristotle's original square of opposition, however, does not lack existential import.

In the Aristotle's logical work is collected in the six texts that are collectively known as the Organon. Two of these texts in particular, namely the Prior Analytics and De Interpretatione, contain the heart of Aristotle's treatment of judgements and formal inference, and it is principally this part of Aristotle's works that is about term logic. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Jan Lukasiewicz of a revolutionary paradigm.[1] The Jan Lukasiewicz approach was reinvigorated in the early 1970s by John Corcoran and Timothy Smiley – which informs modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009.[2]

Basics

The fundamental assumption behind the theory is that propositions are composed of two terms – hence the name "two-term theory" or "term logic" – and that the reasoning process is in turn built from propositions:

  • The term is a part of speech representing something, but which is not true or false in its own right, such as "man" or "mortal".
  • The proposition consists of two terms, in which one term (the "predicate") is "affirmed" or "denied" of the other (the "subject"), and which is capable of truth or falsity.
  • The syllogism is an inference in which one proposition (the "conclusion") follows of necessity from two other propositions (the "premises").

A proposition may be universal or particular, and it may be affirmative or negative. Traditionally, the four kinds of propositions are:

  • A-type: Universal and affirmative ("All philosophers are mortal")
  • I-type: Particular and affirmative ("Some philosophers are mortal")
  • E-type: Universal and negative ("All philosophers are not mortal")
  • O-type: Particular and negative ("Some philosophers are not mortal")

This was called the fourfold scheme of propositions (see types of syllogism for an explanation of the letters A, I, E, and O in the traditional square). Aristotle's original square of opposition, however, does not lack propositions are composed of two terms – hence the name "two-term theory" or "term logic" – and that the reasoning process is in turn built from propositions:

  • The term is a part of speech representing something, but which is not true or false in its own right, such as "man" or "mortal".
  • The proposition consists of two terms, in which one term (the "predica

    A proposition may be universal or particular, and it may be affirmative or negative. Traditionally, the four kinds of propositions are:

    • A-type: Universal and affirmative ("All philosophers are mortal")
    • I-type: Particular and affirmative ("Some philosophers are mortal")
    • E-type: Universal and negative ("All philosophers are not mortal")
    • O-type: Particular and negative ("Some philosophers are not mortal")

    This was called the fourfold scheme of propositions (see types of syllogism for an explanation of the letters A, I, E, and O in the traditional square). Aristotle's original square of opposition, however, does not lack existential import.

    In the Stanford Encyclopedia of Philosophy article, "The Traditional Square of Opposition",

    This was called the fourfold scheme of propositions (see types of syllogism for an explanation of the letters A, I, E, and O in the traditional square). Aristotle's original square of opposition, however, does not lack existential import.

    In the Stanford Encyclopedia of Philosophy article, "The Traditional Square of Opposition", Terence Parsons explains:

    • Propositional calculus
    • Notes
      1. ^ Degnan, M. 1994. Recent Work in Aristotle's Logic. Philosophical Books 35.2 (April, 1994): 81-89.
      2. ^ *Review of "Aristotle, Prior Analytics: Book I, Gisela Striker (translation and commentary), Oxford UP, 2009, 268pp., $39.95 (pbk),