Middle Term

A Middle Term is a term that is shared by two or more premises but is not included in the conclusion of a syllogistic argument.

• AKA: Meson.
• Context
  • It can be either a predicate or a subject of a premise.
• Examples:
  • B always comes after A (major premise). C comes after B (minor premise). Therefore, C comes after A (conclusion). The middle term is B.
  • All men are mortal (major premise). Socrates is a man (minor premise). Therefore, Socrates is mortal. (conclusion). The middle term is man.
  • …
• Counter-Example(s):
  • a Major Term,
  • a Minor Term.
• See: Syllogism, Major Premise, Minor Premise, Inference, Logical Reasoning, Deductive Reasoning, Proposition, Aristotle, Socrates, Formal Argument.

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References

2018a

• (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Syllogism Retrieved:2018-11-10.
  • A syllogism (syllogismos, "conclusion, inference") is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

    In its earliest form, defined by Aristotle, from the combination of a general statement (the major premise) and a specific statement (the minor premise), a conclusion is deduced. For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form:

    All men are mortal.

    Socrates is a man.

    Therefore, Socrates is mortal.

2018b

• (Smith,2018) ⇒ Robin Smith (2018). "Aristotle's Logic", The Stanford Encyclopedia of Philosophy (Winter 2018 Edition), Edward N. Zalta (ed.).
  • QUOTE: Aristotle’s most famous achievement as logician is his theory of inference, traditionally called the syllogistic (though not by Aristotle). That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises. Aristotle calls the term shared by the premises the middle term (meson) and each of the other two terms in the premises an extreme (akron). The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises.

2018c

• (Wikiversity, 2018) ⇒ https://en.wikiversity.org/wiki/Categorical_Syllogism#Minor/Major_Premise_and_Term
  • QUOTE: As we have seen, there will always be 2 terms in a Categorical Proposition (Subject and Predicate). Therefore, the conclusion of a syllogism will have a Subject and a Predicate as well. Here are two rules to take note of:

1. The Subject of a conclusion will be the Minor Term of the syllogism.

2. The Predicate of a conclusion will be the Major Term of the syllogism.

A syllogism is made up of 2 premises and 1 conclusion. So how do we differentiate between one premise from the other? Simple, take a look at that following two rules:

3. The Premise where the Minor Term appear in, will be called the Minor Premise.

4. The Premise where the Major Term appear in, will be called the Major Premise.

But that's not all. A syllogism is actually made up of 3 terms. The third term, or the Middle Term, can be thought of as a term used to link the two premises together in forming the conclusion (...)

This brings us to a fifth and final rule.

5. The Middle Term will appear in both premises but not in the conclusion.

2016

• (Bobzien, 2016) ⇒ Susanne Bobzien (2016). "Ancient Logic", The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.)
  • QUOTE:All basic syllogisms consist of three categorical sentences, in which the two premises share exactly one term, called the middle term, and the conclusion contains the other two terms, sometimes called the extremes. Based on the position of the middle term, Aristotle classified all possible premise combinations into three figures (schêmata): the first figure has the middle term (B) as subject in the first premise and predicated in the second; the second figure has it predicated in both premises, the third has it as subject in both premises:

I	II	III
A holds of B.	B holds of A.	A holds of B.
B holds of C.	B holds of C.	C holds of B.

A is also called the major term, C the minor term. Each figure can further be classified according to whether or not both premises are universal. Aristotle went systematically through the fifty-eight possible premise combinations and showed that fourteen have a conclusion following of necessity from them, i.e. are syllogisms. His procedure was this: He assumed that the syllogisms of the first figure are complete and not in need of proof, since they are evident. By contrast, the syllogisms of the second and third figures are incomplete and in need of proof. He proves them by reducing them to syllogisms of the first figure and thereby ‘completing’ them.

2002

• (Rosdatter, 2002) ⇒ Beth Rosdatter (2002). http://www.uky.edu/~rosdatte/phi120/glossary.htm
  • middle term: The term in a standard form categorical syllogism which is in the premises but not in the conclusion. Symbolized M.

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