Logical Conversion: How to Flip Statements in Ilm al-Mantiq

Flipping the Script: The Rules of Logical Conversion (Al-'Aks)

In our last lesson on Contradiction, we learned how to find the opposite of a statement. Today, we explore another transformation: Al-'Aks al-Mustawi (Logical Conversion). This is the art of swapping the Subject (Mawdu') and Predicate (Mahmul) of a sentence while keeping its truth intact.

What is Al-'Aks al-Mustawi?

Conversion occurs when you take a proposition and make its Subject the Predicate, and its Predicate the Subject, without changing its truth or its quality (Affirmative remains Affirmative, Negative remains Negative).

However, you cannot always keep the Quantity the same. If you flip a "Universal" statement, it might only remain true as a "Particular."

The Three Main Rules of Conversion

Not every statement flips perfectly. Here are the rules according to the four standard propositions:

1. Universal Affirmative (All A are B) flips to Particular Affirmative (Some B are A).
   Example: "All Humans are Animals" flips to "Some Animals are Humans." (You cannot say all animals are humans!)


2. Universal Negative (No A are B) flips to Universal Negative (No B are A).
   Example: "No Human is a Stone" flips to "No Stone is a Human." (This is a perfect flip).


3. Particular Affirmative (Some A are B) flips to Particular Affirmative (Some B are A).
   Example: "Some Students are Writers" flips to "Some Writers are Students."

The Exception: Particular Negative (Juz'iyyah Salibah)

One of the most important things to remember in Ilm al-Mantiq is that the Particular Negative (Some A are not B) has NO valid conversion.
Example: "Some Animals are not Humans" is true. But if you flip it to "Some Humans are not Animals," it becomes false! Therefore, logic tells us this form cannot be converted reliably.

Why is Conversion Useful?

Conversion is a "truth test." If you have a complex argument, converting the sentences helps you see if the logic still holds up. It is also a bridge to the final stage of logic: The Syllogism (Al-Qiyas), where we combine multiple sentences to reach a brand-new conclusion.

The Grand Finale Awaits: Al-Qiyas (The Syllogism)

You have mastered definitions and single propositions. Now, we are ready for the most famous part of Logic: The Syllogism. This is where we learn how to say: "A is B, and B is C, therefore A is C."

Try flipping this: "All Gold is Metal." What is its valid conversion? Let me know in the comments!

Tags: #Mantiq #Logic #Philosophy #Conversion #AksMustawi #IslamicScience #CriticalThinking