Edify MinistriesŽ

Building up the Body of Christ (Eph. 4:11-13)

***

Immediate Deductions
from
Simple Statements

Given any true simple statement, at least two other true simple statements can be immediately made based solely on that one true statement. [N.B. The information below applies only to simple statements. It does NOT apply to immediate deductions from the conditional statement (if p then q). The terms are similar and so is the process, but don't get them confused. The operations here do not change the truth value of the statement. Similar operations done on the conditional sometimes changes its truth value.]

There are several reasons one may wish to do this. First, it can help validate the truth of the original statement. Given a statement that appears true then each of the immediate deductions must also be true. If one of the immediate deductions is not true then the original statement is not true. Often the problem is that we have omitted a limiting condition or have not considered all the attributes of a person or thing.

Another reason to do this is to change a statement to a form that will yield a valid syllogism or a stronger syllogism. See the the page on moods of the categorical syllogism.

Obversion of Statements

Changes the quantity of a proposition without affecting the meaning. Done by negating the predicate and either in the copula or quantifier. [Be careful here. One does not falsify the statement. One simply negates both the subject and predicate terms.]

Obverts to		Example
A	E	All cows eat are grass eaters.	No cows are non-grass eaters. All cows are not non-grass eaters
E	A	No cows are two legged animals. All cows are not two legged animals	All cows are non-two legged animals.
I	O	Some cows are black animals.	Some cows are not non-black animals.
O	I	Some cows are not pretty beasts.	Some cows are non-pretty beasts.*

Conversion of Statements

Switch the subject with the predicate without affecting the meaning. The quantifier may have to be changed.

Converts to		Example
A	I	All cow eat are grass eaters.	Some grass eaters are cows
E	E	No cows are two legged animals. Cow are not two legged animals.	No two legged animals are cows. Two legged animals are not cows.
I	I	Some cows are black animals.	Some black animals are cows
O		Does not convert.

Contraposition of Statements

An original statement is obverted, the result is converted and that result is obverted again.

Contraposits to		Example (showing the steps)
A	A	All cows are grass eaters.	All cows are not non-grass eaters. All non-grass eaters are not cows All non-grass eaters are non-cows.*
E	O	No cows are two legged animals. Cows are not two legged animals	All cows are non-two legged animals.* Some non-two legged animals are cows. Some non-two legged animals are not non-cows.
I		Does not contraposit.
O	O	Some cows are not pretty beasts.	Some cows are non-pretty beasts.* Some non-pretty beasts are cows. Some non-pretty beasts are not non-cows.

* Result after removing a double negative.

Click here to send us questions or comments about this web site.
Updated: September 09, 2008 00:46 -0400
This ministry is funded by voluntary gifts.

This work is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. To view a copy of this license, click on the graphic. If a copyright notice appears in the material above that copyright takes precedence.