Critical Thinking Fundamentals - Conditional Reasoning

01 May 2026 by Sufian M′Barki

In deductive reasoning, we can verify if a particular category belongs to a general category if the former meets the categorical requirements of the latter. This is how we proved Jews are indigenous to Israel in my previous seminar.

There exists another type of argumentation in the realm of critical thinking - conditional reasoning.

Defining Conditional Reasoning

Conditional reasoning is the logic of dependency. This type of logic deals with how one established truth triggers the truthfulness of another statement.

A conditional statement comprises two parts:

• The Antecedent: Representing the condition itself (the "if").
• The Consequent: Representing the result ("then").

They are formally marked with the letters P and Q respectively, and the fundamental rule in this relationship is that the reasoning direction can only go one way - from the antecedent to the consequent (P → Q). This is to say that the presence of the condition guarantees the result.

Modus Ponens

Modus Ponens is an affirmative conditional syllogism. If the antecedent P is true, then the consequent Q is also true:

1. Major Premise: If a person is a citizen of Israel (P), they have the right to vote (Q).
2. Minor Premise: Sufian is a citizen of Israel (P is true).
3. Conclusion: Therefore, Sufian has the right to vote (Q is true).

If you are really astute, you will notice that Modus Ponens can bear a resemblance to a simple categorical syllogism. If you were to use categorization, you could still build a similar argument in this context:

1. Major Premise: All citizens of Israel have the right to vote.
2. Minor Premise: Sufian is a citizen of Israel.
3. Conclusion: Sufian has the right to vote.

But Modus Ponens can be incredibly useful in scenarios where categorical syllogisms cannot be utilized. Instructions and directives, logic gates in computer science, etc. often make use of conditional syllogisms.

1. Major Premise: If the air-raid siren sounds (P), then you must go to the shelter (Q).
2. Minor Premise: The siren is sounding (P is true).
3. Conclusion: Therefore, you must go to the shelter (Q is true).

Categorical logic requires a permanent relationship between two groups (All A are B). Conditional logic is superior here because it handles event-based triggers in a specific context. We don't want to claim that all sirens lead to shelters, because this is not true. An air horn during a baseball match does not lead to shelters, for instance.

We want to establish that the air-raid sirens, in the context of Israel, lead to shelters if they are sounding, and that is where conditional logic comes into play.

Modus Tollens

Modus Tollens is a negative conditional syllogism. If affirmative conditional syllogisms work with a positive P leading to a positive Q, negative conditional syllogisms seek to confirm that if Q is negative, then P is negative.

Viewed in this way, Modus Tollens is the opposite of Modus Ponens:

1. Major Premise: If Israel were apartheid (P), it would have laws barring Arabs from the Knesset (Q).
2. Minor Premise: Israel does not have laws barring Arabs from the Knesset (Q is false).
3. Conclusion: Therefore, Israel is not apartheid (P is false).

We can use the example from before as well:

1. Major Premise: If Sufian were a citizen of Israel (P), he would have voting rights (Q).
2. Minor Premise: Sufian does not have voting rights in Israel (Q is false).
3. Conclusion: Therefore, Sufian is not a citizen of Israel (P is false).

From my experience in Hasbara circles, Modus Tollens as a logical operation seems to find its way into debates more often than Modus Ponens does. This likely has to do with the nature of our work as Zionists. It is very easy for propally death cultists to write a hundred blood libels about Israel in five minutes, but it is bitter work for us to sit down and debunk those lies.

This is to say that our work often revolves around disproving blood libels via syllogisms like Modus Tollens, instead of establishing ground truths about Israel, which reflects how disgusting the world has become.

Necessary and Sufficient Conditions

Conditions can be Sufficient and Necessary in conditional syllogisms. In informal terms, this determines the strictness of the outcome, i.e. how strict the required condition is to achieve the result in question:

• In Israel, being a Jew is a sufficient condition for citizenship under the Law of Return. This means that being Jewish is enough on its own, but it is not the only way.
• Drinking water is a necessary condition for staying alive as a human. You must drink water, but on its own, it's not enough to keep you alive - you need food, air, etc.

Let's explore a few more examples:

• In Israel, being partnered or married to a Jew is a sufficient condition for citizenship under the Law of Return.
• In Israel, being mentally stable is a necessary condition for IDF enrollment.

And a Modus Ponens, with an example individual named Julian:

1. Major Premise: If Julian is eligible to serve in the IDF (P), then he must be mentally stable (Q).
2. Minor Premise: Julian is eligible to serve in the IDF (P is true).
3. Conclusion: Therefore, Julian is mentally stable (Q is true).

Moving Forward

Both categorical and conditional reasoning are major pillars of critical thinking. Understanding them is required in all philosophical and geopolitical discourse.

In the upcoming seminar, we will explore detailed examples of conditional reasoning, applying the knowledge in this lecture to even more Israel-related scenarios.

Sufian M'Barki

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