The Syllogism

One of the oldest tools in philosophical argumentation is the syllogism, which continues to underpin contemporary discussions. A syllogism involves drawing conclusions from premises using a logical structure, similar to mathematical reasoning. For instance:

• Abortion is equivalent to murder.
• Susie had an abortion.
• Therefore, Susie is a murderer.

Aristotle's view on syllogisms is that if the premises are true, the conclusion must also hold true. This logical framework is commonly used in philosophical debates, particularly on contentious topics like abortion. Thus, recognizing, analyzing, and utilizing syllogisms is crucial for effective discourse.

Validity

Assessing the validity of an argument involves scrutinizing its structure rather than its content. Take this syllogism as an example:

• All abortion providers have Watergate Salad for brains.
• Jim is an abortion provider.
• Therefore, Jim has Watergate Salad for brains.

While the premises lead to a logical conclusion, the absurdity of the premises does not undermine the argument's validity. Conversely, if the conclusion does not logically follow from the premises, the argument is deemed invalid, even if the conclusion itself is true:

• All abortion providers have Watergate Salad for brains.
• Jim has Watergate Salad for brains.
• Therefore, Jim is an abortion provider.

In this case, the conclusion does not logically follow, rendering the argument invalid.

Soundness

Once we determine an argument's validity, we must evaluate the truth of its premises. Consider this syllogism:

• Abortion is equivalent to murder.
• Susie had an abortion.
• Therefore, Susie is a murderer.

While the conclusion might logically follow, the premise that equates abortion with murder is highly disputed. Thus, although the argument is valid, it is unsound due to the contentious nature of its premise. A sound argument requires both validity and truth across all assertions.

Formal Fallacy

A frequent source of invalid reasoning is the formal fallacy known as "affirming the consequent." This occurs when conditional premises lead to ambiguous conclusions. For example:

• If Jim the abortion provider encounters protesters, he will enter through the back.
• Jim entered through the back.
• Therefore, he encountered protesters.

This argument is invalid because the premises do not guarantee the conclusion's truth. If we alter the premise to "If and only if Jim meets protesters, he will take the back entrance," the argument becomes valid. This distinction highlights the importance of precision in our reasoning.

Axioms

Axioms are statements considered true by definition. A classic example is, "All unmarried men are bachelors." While this seems solid, it merely restates the definition without providing substantive content. In our ongoing discussion, an axiom might be, "All murderers kill people," which is true but also prompts deeper questions about personhood and the nature of abortion.

Debates surrounding these axioms can be complex, particularly in contentious topics like abortion, where definitions and assumptions are often challenged. Recognizing and questioning these foundational assumptions can provide a significant advantage in philosophical discussions.

Conclusion

The five tools discussed here are invaluable for challenging common beliefs regarding ethics, politics, culture, and justice. They not only enhance your ability to critique others but also refine your own thinking. Embrace these tools and strive not just to read philosophical works but to embody the philosopher's role in everyday conversations.

For more insights from Dustin T. Cox at Plato’s Gymnasium, explore the following resources:

• How to Write Philosophy Like the Pros: Argumentative writing demands adherence to specific conventions.
• How to Write for Plato’s Gymnasium: Engage actively with philosophical thought and practice.