1.2 The Importance of Logic
What we refer to as “Critical Thinking” is the application of Logic to the formulation of thoughts, ideas and observations. Logical thinking has evolved over thousands of years, shaping the way we reason and the manner in which we analyze arguments. The origins of logic can be traced back to ancient civilizations, including the works of Babylonian and Egyptian mathematicians. However, it was in ancient Greece that logic truly flourished. Aristotle played a pivotal role in formalizing logical principles by introducing syllogisms.
A syllogism is a form of deductive reasoning that consists of three parts: a major premise, a minor premise, and a conclusion. If the premises are true and logically structured, the conclusion must also be true. Here are a few examples:
Major premise: All mammals are animals
Minor Premise: All rabbits are mammals
Conclusion: All rabbits are animals
And, in fact, we can also say:
Major premise: All mammals are animals
Minor Premise: All humans are mammals
Conclusion: All humans are animals
Do we have to be careful? Of course we do. There are different categories of syllogisms. They are an invitation to deeper contemplation and thought.
Common Syllogisms
These are the most frequent syllogisms:
Categorical Syllogism: It is based on categories that follow the structure: “If A is part of C, then B is part of C”. Here is an example used in programming logic:
- Major premise: All valid algorithms follow logical rules.
- Minor premise: This computer model program we are working on follows logical rules.
- Conclusion: Therefore, this model is a valid algorithm[1].
Conditional (Hypothetical) Syllogism: “If A is true, then B is true” pattern. Here is an example used in scientific reasoning:
- Major premise: If a substance reacts with acid, then it is a base.
- Minor premise: This substance reacts with acid.
- Conclusion: Therefore, this substance is a base.
And another example when it is used for political debate:
- Major premise: If a policy benefits the majority, then it should be implemented.
- Minor premise: This policy benefits the majority.
- Conclusion: Therefore, this policy should be implemented.
Disjunctive Syllogism: “Either A or B is true; if A is false, then B must be true” pattern. Here is an example used in ethical reasoning:
- Major premise: Either an action is morally right or morally wrong.
- Minor premise: This action is not morally wrong.
- Conclusion: Therefore, this action is morally right.
Universal Syllogism: Uses absolute terms like “all” or “none”. Used for metaphysical debates:
- Major premise: All humans seek meaning in life.
- Minor premise: Socrates was a human.
- Conclusion: Therefore, Socrates sought meaning in life.
Particular Syllogism: Uses terms like “some” or “most” instead of absolutes. Used in legal reasoning:
- Major premise: Some contracts require written consent.
- Minor premise: This contract does not have written consent.
- Conclusion: Therefore, this contract may not be legally binding.
Syllogisms do play a crucial role in legal reasoning, helping judges, lawyers, and scholars structure arguments logically. In legal frameworks, a legal syllogism follows a deductive structure:
- Major premise – A general legal rule or principle.
- Minor premise – The specific facts of a case.
- Conclusion – The legal judgment or decision.
In Judicial Decisions, courts use syllogisms to apply laws to cases. For example:
- Major premise: Theft is punishable by law.
- Minor premise: The defendant stole property.
- Conclusion: The defendant is guilty of theft.
Legislators and legal scholars use syllogisms to analyze laws and determine their applicability, and lawyers construct syllogistic arguments to persuade judges and juries by demonstrating logical consistency in their arguments.
However, while syllogisms are used to provide clarity, some legal scholars argue that the idea that legal decisions can always be justified through strict deductive reasoning oversimplifies complex cases. Legal interpretation often requires a deeper context, greater analysis of precedent, and more detailed moral reasoning, which syllogisms alone may not fully capture.
Logic: A Brief Overview
Let’s go back to our introduction to Logic. Socrates played a crucial role in shaping logical thinking through his Socratic method, a form of inquiry that uses systematic questioning to expose contradictions and refine ideas. His approach emphasized critical thinking, dialogue, and self-examination, laying the groundwork for Plato’s dialectical reasoning and influencing Aristotle’s formal logic.
Socrates believed that true wisdom comes from recognizing one’s ignorance, which encouraged deeper intellectual inquiry. His unrelenting examination of assumptions helped develop rigorous argumentation, which is the essential foundation of logical reasoning. The influence of Socrates extended beyond philosophy, shaping education, law, and ethics, where structured debate and logical analysis remain essential to this day.
Later, during the Middle Ages, scholars refined Aristotelian logic, developing new methods of categorization and inference. The Renaissance and Enlightenment periods challenged traditional logic, leading to advancements in reasoning techniques. By the 19th and 20th centuries, logic underwent a revolution with the introduction of symbolic notation and mathematical methods, and today, logic extends beyond philosophy into fields like computer science, artificial intelligence, and decision-making, influencing how we structure arguments and analyze information.
The Socratic Method, which relies on systematic questioning, has influenced modern logic by encouraging structured argumentation and identifying contradictions or flaws in the premises of critical thinking. These flaws are called Fallacies. These flaws, or “defective”, “uninformed”, or otherwise illogical ideas, usually appear in the form of statements uttered or written by an author, who pretends to influence the reader’s perception, feelings or ideas about a specific problem, impose a possible solution, or “sell” a course of action to their audience. Sometimes the fallacies are born of ignorance on the part of the writer who presents a piece of reasoning about something, but on many occasions, they are expressed with the intent of wrongful manipulation and purposeful deception on the part of the author.
- “An algorithm is a set of steps for accomplishing a task or solving a problem. Typically, algorithms are executed by computers, but we also rely on algorithms in our daily lives. Each time we follow a particular step-by-step process, like making coffee in the morning or tying our shoelaces, we are in fact following an algorithm.In the context of computer science, an algorithm is a mathematical process for solving a problem using a finite number of steps. Algorithms are a key component of any computer program and are the driving force behind various systems and applications, such as navigation systems, search engines, and music streaming services.” (Nikolopoulou, 2023) ↵
