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Enthymeme and Syllogisms

syllogism is a set of chained ‘IF THEN‘ statements in which the conclusion of one statement becomes premise of another statement. It is a basic building block of all rhetorical arguments. In its simple form a syllogism resembles with logical statements in mathematics:
If A equals B and B equals C then A equals C

“An enthymeme is what has the function of a proof or demonstration in the domain of public speech, since a demonstration is a kind of sullogismos and the enthymeme is said to be a sullogismos too.” (Aristotle)

“Enthymeme is an informally stated syllogism with an unstated assumption that must be true for the premises to lead to the conclusion. In an enthymeme, part of the argument is missing because it is assumed.” (Wikipedia)

The formal definitions of ‘what is enthymeme?’ might look a little complicated but Prof. Drout makes it clear by saying: can we at least agree that statement ABC is true and stop repeating ABC in every rhetorical argument? If we agree then ABC is an enthymeme here. For instance, can we at least agree that ‘all human beings are equal‘? if true then ‘all human beings are equal is an enthymeme for every rhetorical argument made in favor of human rights. For Drout, 
‘An enthymeme is the point of the argument where you lean forward, look the other person in the eye and say: “Can’t we at least agree that . . .” and then go on from there.’

Enthymeme is very important for any real argument but it is very hard to find one. For instance, ‘Democracy is the best form of government‘ is an enthymeme in civilized world but apparently this is not the case in various Arab and third world countries. That means advocates of democracy still have to work hard to find a shared assumption as an enthymeme to prove ‘democracy is the best form of government true, before making it an enthymeme for further arguments.

For Drout, a very complex syllogism (logical argument) can be developed based on just a few rules.
  • Identity: A = A, H = H, a human equals an other human
  • If -> Then: is a reasoning or inference based on some ‘if then‘ statement. IF ‘all human beings are equals‘ THEN ‘each and everyone has the right to live a healthy life and have basic education‘ … and this may lead to each state should evolve as a welfare state rather than a security state’. This is an example of a complex political reasoning; lets not go there and stick with Drout’s simple example: 

IF its raining THEN sky is cloudy (TRUE)

  • Inversion: is adding a NOT on both sides of a logical statement; and the inverse of a true statement may not always true. 

IF ‘its NOT raining’ THEN ‘sky is NOT cloudy’ (FALSE)

  • Converse: is changing the order (directionality) of an IF-THEN statement. Similar to inversion, converse of a true statement may not true all the time. For instance, it could be false most of the time by saying: 

IF sky is cloudy THEN its raining. (FALSE)

So directionality of a logical statement is very important and a converse statement may not be true all the time

  • Contrapositive: is applying both inversion and conversion to a true statement, and a contrapositive statement is always true. e.g. 

IF the sky is NOT cloudy THEN its NOT raining (TRUE)

This kind of rules underlies all of the logical arguments; start at one step and try to chain things together with emerging conclusions of each syllogism. 

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