Aristotle's enthymeme is also known of as the rhetorical syllogism. It is a technique of persuasion, engaging one's emotions, ethics and logic by using rhetoric. By Doug Frame on Jan 20, 2010
In explaining this device Aristotle references his Rhetoric, Prior Analytics, and Topics as well as other of his books. While Aristotle did not favor using persuasion in an unethical fashion, it became necessary to explain the enthymeme in order to refute other less ethical enthymemes that were used by some sophists of the time. To understand the enthymeme or rhetorical syllogism one must first understand a syllogism. The Syllogism - Validity and Soundness

A normal syllogism has 2 premises and a conclusion. For example one could say the following: All Men are Mortal (premise)
Socrates is a Man (premise)
Therefore Socrates is a Mortal (conclusion)
This is a valid and sound syllogism. Validity refers to when the conclusion follows from the premises, and a sound argument is a valid argument plus the premises are true. In the enthymeme one line or more in the syllogism is implied, and therefore not explicitly stated. For example in the following truncated syllogism, the premise "Socrates is a Man" is implied, and still the premises and the conclusion are clear. All Men are Mortal (premise)

Therefore Socrates is Mortal (conclusion)
But the enthymeme is not simply based on syllogistic logic, although syllogistic logic is a very important part of it. The enthymeme also tugs at the emotions. Lastly it appeals to ones sense of what is right or wrong (e.g., ethics) How is a syllogism able to accomplish this? The Persuasive Nature of the Enthymeme

The enthymeme is a popular technique of demogogues. People are persuaded to accept as true false beliefs against their will. While such a thing may not seem possible, when one examines the enthymeme one can see why this is so. Central to the enthymeme is understanding logos, pathos, and ethos (e.g., logic, emotion and ethics). First...

...1. Read the chapter syllogism.2. what are kind of syllogism?Types of syllogismAlthough there are infinitely many possible syllogisms, there are only a finite number of logically distinct types. We shall classify and enumerate them below. Note that the syllogisms above share the same abstract form:Major premise: All M are P.Minor premise: All S are M.Conclusion: All S are P.The premises and conclusion of a syllogism can be any of four types, which are labelled by letters[1] as follows. The meaning of the letters is given by the table:code quantifier subject copula predicate type exampleA 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.(See Square of opposition for a discussion of the logical relationships between these types of propositions.)In Analytics, Aristotle mostly uses the letters A, B and C as term place holders, rather than giving concrete examples, an innovation at the time. It is traditional to use is rather than are as the copula, hence All A is B rather than All As are Bs It is traditional and convenient practice to use a,e,i,o as infix operators to enable the categorical statements to be written succinctly thus:Form ShorthandAll A is B AaBNo A is B AeBSome A is B AiBSome A is not B AoB 3. What are 3...

...CATEGORICAL SYLLOGISM
Just as the verbal expression of the IDEA is the TERM, and that of the JUDGMENT is the PROPOSITION, so the verbal expression of DEDUCTIVE REASONING is called ARGUMENTATION. ARGUMENTATION is a discourse which logically deduces one proposition from other propositions. ARGUMENTATION takes the form of a SYLLOGISM. A SYLLOGISM is defined as any argumentation in which, from two propositions called the PREMISES, we conclude a third proposition called the CONCLUSION, which is so related to the premises jointly, that if the premises are true, the conclusion must also be true.
A SYLLOGISM derives its name from the kinds of propositions composing the syllogism. A SYLLOGISM is called CATEGORICAL if all the propositions composing the syllogism are CATEGORICAL PROPOSITIONS ( the predicate is affirmed or denied of the subject outright without any condition ).
Example: All fathers are male parents. No true sportsman is a cheater.
A SYLLOGISM is called HYPOTHETICAL if all the propositions composing the syllogism are HYPOTHETICAL PROPOSITIONS ( two propositions united into one, where one can only be true if the other is false or vice-versa ).
Example: If it rains, then the ground is wet. You cannot be a saint and a sinner at the same time....

...Standard Form Categorical SyllogismsSYLLOGISMS
* A syllogism is composed of two statements, from which a third one, the conclusion, is inferred.
CATEGORICAL SYLLOGISMS
* Are syllogisms made up of three categorical propositions.
* They are a type of deductive argument, that is, the conclusion (provided the argument form is valid) follows with necessity from the premises.
TWO EXAMPLES OF CATEGORICALSYLLOGISMS
1.) All Greeks are mortal.
All Athenians are Greeks.
Therefore all Athenians are mortal.
2.) All mammals are animals.
All humans are mammals.
Therefore all humans are animals
These are arguments typically known as syllogism. It has been studied and taught for more than 2 centuries.
Mood and Figure
* Every standard form categorical syllogism will have three terms, with each one used twice in the three propositions which make up the syllogism.
* The predicate term will be used in the major premise and the conclusion, the subject term in the minor premise and conclusion and the middle term in the two premises.
* The arrangement of the four propositions--A, E, I or...

...VARIETIES OF CATEGORICAL SYLLOGISM
The previous chapter focused on the simple categorical syllogism. The present chapter deals with other varieties of categorical syllogism which in some arguments will prove useful in arriving at a conclusion. These varieties include the enthymeme, the epichereme, the polysyllogism, the sorites and the dilemma.
The Enthymeme
The enthymeme is an abbreviated or shortened type of categoricalsyllogism in that one of its premises or its conclusion is left unexpressed. Enthymemes are of three categories, distinguished on the basis of the missing [art of an argument.
1. Missing Major – enthymemes are of the missing major category when the major premise of an argument is not expressed. For example,
Africans are men,
Therefore, they are mortal beings.
2. Missing Minor – enthymemes belong to the missing minor category when the minor premise of an argument is omitted. For example,
Men are mortal beings,
Therefore, Africans are mortal beings.
3. Missing Conclusion – enthymemes whose conclusion is not expresses belong to the missing conclusion category. For example,
Men are mortal beings,
Therefore, Africans are men.
Enthymemes are categorical syllogism because of the presence of three syllogism terms. In the example for each category, above the syllogistic are men,” “Africans,” and “mortal beings.”
To check to which category an...

...along with some interesting syllogisms that provide validity and soundness
Interestingly enough, the author supplies the reader with the intrinsic motives of many of the characters, demonstrating their true nature as one read’s along. The first syllogism we encounter states,“ What strikes us about the second Mrs. de Winter is her timidity, her pre-pubescence, her asexuality. The way she dresses in sexless sweaters and plain shoes suggest a vicar’s daughter rather than a worldly man’s wife” (134). The first premise that indicates that the second Mrs. de Winter is timid and lacks the sexual attraction to anyone, which ties to the conclusion that she portrays the role of a vicar’s daughter rather than a worldly man’s wife. The name for the second Mrs. de Winter is never given reinforcing her invisibility throughout the story. The second premise goes in more in depth by giving the vivid picture on the second Mrs. de winter dresses in sweats and plain shoes and not giving her the role of loyalty. It can be argued that by the way she dresses, she has no control over her and over the house, comparing her more to low-rank label known as vicar’s daughter. The way she dresses lacks the reinforcement of her role in society because she simply does not dress to impress, but rather just to stay comfortable making the connection between her asexuality and the label the author gives her as a vicar’s daughter as valid syllogism. Nevertheless the...

...Kinds of Syllogisms
We focus our discussion to the most important kind of syllogism where we can apply different rules in order to distinguish good or valid syllogisms from invalid ones. These syllogisms are under the category, by comparison to the Inferential Laws.
1. Correct: when it observes the Rules and the legitimate patterns (Figure and Mood) for valid inference.
2. Incorrect: Syllogism that violates one or several of the Rules for valid inference, or the legitimate patterns (Figure and Mood) for valid inference.
In order for us to determine the validity or acceptability of a syllogism (following the Rules), let us focus our discussion on the particular rules governing the terms and syllogistic propositions.
Particular Rules Governing the Terms
1. The Syllogism must contain Three Terms, not less nor more. This is a requirement of the reasoning process of the categorical inference. If there are only two terms, only a proposition can be made; and there will be no Middle or Common term with which to compare the two terms, in order to verify their agreement, or disagreement, in case this is not known: in other words, no conclusion can be inferred. On the other hand, if there are four terms, there will be more than one Middle term, which is tantamount to having no middle term at all. In other words, no effective comparison of each of the two terms with a common term is...

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CHAPTER V
The Categorical Syllogism
Definition:
Categorical Syllogism
* A verbal expression of an inference.
* It is “an oral or written discourse showing the agreement or disagreement between two terms on the basis of their respective relation to a third term.
* It is also an “an any argumentation in which, from two propositions called the conclusion, which is so related to the premises taken jointly that if the premises are true, the conclusion must also be true.
* It must always have that SEQUENTIAL RELATION as a differentiating mark of a true and valid syllogism from what is not.
Examples:
All creatures are mortal.
But a person is a creature.
Therefore, a person is a mortal.
*A syllogism is called “categorical”, if the premises and the conclusion composing it are categorical propositions expressed in a declarative form.
Sequential Relation
* The interdependence of the premises upon one another.
* Indicated by the presence of a middle term in the premises.
Components of a Categorical Syllogism
1. Premises (two propositions)
* Vehicles for truths assumed to be contained by them
* These truths give rise to a new knowledge or truth in the conclusion.
Classifications of premises:
a) Major premise
* First proposition in the syllogism
* It contains the major term
*...

...University of Phoenix Material
Syllogisms & Logic
PART I: SYLLOGISMS
To be a valid syllogism, the conclusion must be proven by the reasons. Carefully study the following syllogisms and decide if they are valid or invalid:
1. All zebras are striped animals.
No zebras are polar bears.
Therefore, no polar bears are striped animals.
2. All clowns are funny individuals.
Some sad people are clowns.
Therefore, some sad people are funny individuals.
3. Some sticky substances are yucky things.
All taffy is a sticky substance.
Therefore, some taffy is a yucky thing.
4. All items made of gold are expensive items.
Some rings are items made of gold.
Therefore, some rings are expensive items.
5. All flies are winged creatures.
All butterflies are winged creatures.
Therefore, all butterflies are flies.
The following are examples of syllogistic arguments that are missing the conclusions. Study the two reasons very carefully and complete the syllogism with the conclusion that logically follows.
6. All fragile things are breakable things.
Some glasses are fragile things.
Therefore
7. All mammals are warm-blooded animals.
All whales are mammals.
Therefore
8. All books are things with pages.
Some books are mysteries.
Therefore
9. All flowers are pretty objects.
All pansies are flowers....