On Logical Forms

This page was included in order to give an overview of valid forms of classical logic (which I prefer over Symbolic Logic), so if I slip into the shorthand of describing an argument as AAA or EIO, the reader will have this page to use as reference. 

It's important to remember that just because an argument doesn't have a valid form doesn't mean the conclusion is false. It means that the conclusion is unproven from the argument ("You can't get there from here.")

For a deeper view of logic, I highly recommend Dr. Peter Kreeft's Socratic Logic.

Valid Logical Forms

A= All [A] is [B]
E= No [A] is [B]
I= Some [A] is [B]
O= Some [A] is not [B]

(and, no, I don't know why they chose AEIO instead of ABCD)

Valid Syllogisms

AAA, AEE, EIO, AII, AOO

Other forms of argument are invalid

Valid Combinations of Premises

AA, AE, AI, AO, EI
(You can reverse the order of these, for example, EA instead of AE, but EAE is the same as AEE. You can't however use EEA as a valid form of argument)

The Requirements of Premises

A valid argument must mention all the claims (A, B and C) over the major and minor premises
For example:
·         All A is B
·         All B is C
·         Therefore All A is C
If you don't do this, you have the fallacy of the Undistributed Middle

Outline of the Valid forms of Argument

So the only valid forms of argument are AAA, AEE, EIO, AII and AOO. Here are some examples of how they are structured:

AAA:
·         All A is B
·         All B is C
·         Therefore All A is C

AEE:
·         All A is B
·         No C is B
·         Therefore No C is A

EIO:
·         No A is B
·         Some A is C
·         Therefore Some C is not B

AII:
·         All A is B
·         Some C is A
·         Therefore Some B is C

AOO:
  • All A is B
  • Some C is not B
  • Therefore Some C is not A

5 comments:

  1. I have to ask about the Old McDonald form:
    EI
    EI
    O

    ReplyDelete
  2. All kidding aside, I am not familiar with the AAA etc. forms, so thank you for this handy reference.

    ReplyDelete
    Replies
    1. A good book on these forms (and logic in general) is Peter Kreeft's "Socratic Logic"
      Here's a link if you're interested:
      http://www.amazon.com/Socratic-Logic-Questions-Aristotelian-Principles/dp/1587318083

      Delete