Eduction and Its Types

Read the right-hand column and the naming makes sense. "Partial" means one term has been replaced by its contradictory; "full" means both have. That single observation removes most of the confusion students have with these names.

How to perform a long eduction

The method is the same every time and it is worth setting out once.

Write the original and label it A, E, I or O.

Perform one operation. Write the result and label it.

Check the labels against the rules as you go. Conversion of an A gives an I; conversion of an E gives an E; conversion of an I gives an I; O has no converse. Obversion always gives the letter of the opposite quality: A becomes E, E becomes A, I becomes O, O becomes I.

Stop when the educt has the shape you were asked for, reading the shape off the table above.

And check the distribution at the end, as a separate step. If a term is distributed in the result and was not distributed in the original, an error has been made somewhere in the chain.

A worked example

Take "All agreements without consideration are void."

Label it. A proposition. S is "agreements without consideration", P is "void things".

Obverse. Change quality to negative, negate the predicate. "No agreement without consideration is a non-void thing." E proposition. This says nothing new and says it in a way that is sometimes more useful: it puts the class of non-void things on the table.

Converse. Interchange S and P, and by the distribution rule the result must be particular. "Some void things are agreements without consideration." I proposition.

Now check the distribution. In the original, S is distributed and P is not. In the converse, neither is distributed. Nothing has been distributed that was not, so the step is sound. Had the converse been written as "all void things are agreements without consideration", P would have become distributed without having been, and the step would have been invalid, and it would also have been legally absurd, since a great many things are void for reasons unconnected with consideration.

Partial contrapositive. Obvert then convert. From the obverse, "No agreement without consideration is a non-void thing", convert simply, since E converts simply. "No non-void thing is an agreement without consideration." E proposition. Read in plain words: nothing that is valid is an agreement without consideration, which is a genuinely useful restatement.

Full contrapositive. Obvert that. "All non-void things are agreements not without consideration." A proposition, and in ordinary language: everything valid is an agreement supported by consideration, within the universe of agreements.

What the exercise produced. Five ways of saying one thing, and the fourth and fifth are the ones a lawyer would actually use in argument. That is the point of eduction: it is a machine for finding the form of a proposition that answers the question in front of you.

Distinctions that carry marks

What this does not mean

Eduction does not add information. Every educt is entailed by its original, so nothing new has been learned about the world. What changes is the form, and the form is often what decides whether a proposition answers the question.

"Partial" does not mean incomplete or defective. It means one term has been negated rather than two.

Not every proposition has every educt. O has no converse, and I has no contrapositive, and only A and E can be inverted. Those gaps are results and not oversights, and each is proved in its own chapter.

Quick revision

Eduction: immediate inference by rearranging or negating the terms of a single proposition.

Two basic operations: conversion, which swaps the terms and keeps the quality; obversion, which changes the quality and negates the predicate.

Everything else is a chain of those two: obverted converse is convert then obvert; partial contrapositive is obvert then convert; full contrapositive adds an obversion; the inverses are longer chains.

"Partial" means one term negated, "full" means both.

Two governing rules: the distribution rule from sequence 310, and the rule that conversion never changes quality while obversion always does.

Method: label every step A, E, I or O, and check distribution at the end.

Test yourself

1. Define eduction and name the two operations from which all its types are built.

Eduction is a form of immediate inference in which a new proposition is drawn out of a single given proposition by rearranging its terms, replacing them by their contradictories, or altering its quality, the result being entailed by the original. The two basic operations are conversion, which interchanges subject and predicate without changing quality, and obversion, which changes the quality and replaces the predicate by its contradictory.

2. How is each of MU's six types built from those two operations?

The converse is a single conversion and the obverse a single obversion. The obverted converse is a conversion followed by an obversion. The partial contrapositive is an obversion followed by a conversion, and the full contrapositive adds a further obversion. The partial and full inverses are longer chains of the same two operations, ending with the contradictory of the original subject in the subject place.

3. What do "partial" and "full" mean in these names?

They describe how many of the two terms have been replaced by their contradictories. A partial form has one term negated: the partial contrapositive has non-P as subject and S as predicate, and the partial inverse has non-S as subject and P as predicate. A full form has both negated: the full contrapositive has non-P and non-S, and the full inverse has non-S and non-P.

4. State the two rules that govern every eduction.

First, the distribution rule: no term may be distributed in the educt unless it was distributed in the original, which is what limits the conversion of A and forbids the conversion of O. Second, the quality rule: conversion never alters quality, while obversion always does, so that in any chain the quality alternates with each obversion and remains unchanged at each conversion.

5. Educe the obverse and the converse of "All agreements without consideration are void", and check the distribution of the converse.

The obverse is "No agreement without consideration is a non-void thing", an E proposition. The converse is "Some void things are agreements without consideration", an I proposition. In the original the subject is distributed and the predicate is not; in the converse neither term is distributed, so no term has become distributed that was not, and the step is sound. Writing the converse as a universal would distribute the predicate of the original and would be invalid.

6. Why does eduction not add information?

Because every educt is entailed by the proposition it is drawn from, so anyone who accepts the original is already committed to the educt. What eduction changes is the form: it produces the version of the proposition whose subject or predicate is the class one needs to talk about. That is frequently what makes a provision answer the question in front of you, which is why the operation is useful although it is not informative.