Understanding Categorical Propositions: Al-Qadhiyah in Ilm al-Mantiq

The Power of Judgment: Introduction to Propositions (Al-Qadhiyah)

Up until now, we have focused on understanding single concepts—like "Human," "Animal," or "Rational." In our last post on Definitions, we learned how to clarify these concepts. But in real life, we don't just think in single words; we make claims about the world.

In Ilm al-Mantiq, when we combine concepts to make a statement that can be judged as True or False, we call this a Qadhiyah (Proposition) or Tasdiq (Assent).

What Makes a Statement a "Proposition"?

Not every sentence is a proposition. For example, "Sit down!" (a command) or "Where is the book?" (a question) cannot be true or false. A logical proposition must be a declarative statement.
Example: "The student is hardworking." This is a Qadhiyah because we can verify if it matches reality.

The Structure of a Categorical Proposition (Al-Hamliyyah)

A basic proposition, known as Al-Qadhiyah al-Hamliyyah, consists of three essential parts:

1. Al-Mawdu' (The Subject): The thing we are talking about.
   Example: In the sentence "Gold is expensive," Gold is the Mawdu'.
2. Al-Mahmul (The Predicate): The quality or hukum we are attributing to the subject.
   Example: In the same sentence, Expensive is the Mahmul.
3. Al-Rabitah (The Copula): The link between them (often implied in Arabic, or the word "is/are" in English).

Classification by Quality: Affirmative vs. Negative

Every proposition has a "quality" (Kayf). It is either:

• Mujabah (Affirmative): You are confirming a relationship.
  Example: "Knowledge is light."
• Salibah (Negative): You are denying a relationship.
  Example: "Ignorance is not beneficial."

"Why does this matter? Because all reasoning—including the famous Syllogisms we will study later—is built upon the strength of these individual propositions."

Next Up: Quantity in Logic (Universal vs. Particular)

In the next post, we will learn how to quantify our statements. Is "All humans" the same as "Some humans"? We will explore the Sur (Quantifiers) that make our arguments bulletproof.

Do you have a proposition you want to analyze? Drop it in the comments below!

Tags: #Mantiq #Logic #Propositions #IslamicPhilosophy #CriticalThinking #Education