Meaning, Significance, and Scope
The term “logic” originates from the Greek word “logos,” which has various meanings, including “sentence,” “discourse,” “reason,” “rule,” and “ratio.” While these translations provide some insight, they don’t fully capture the modern concept of logic.
In essence, logic is the study of the principles and criteria that determine what constitutes valid reasoning. It focuses on how we can reason correctly and make sound arguments, ensuring that our conclusions follow logically from our premises. This involves analyzing the structure of arguments, identifying logical fallacies, and understanding the rules that govern how statements and propositions relate to each other.
Understanding the Distinction: Logic vs. Psychology of Reasoning
It’s crucial to differentiate between logic and the psychology of reasoning. Logic primarily deals with the principles governing correct reasoning, focusing on prescribing how we should reason to achieve accuracy. It lays out the rules of proper reasoning, regardless of whether individuals follow these rules in practice—an empirical matter beyond logic’s domain.
In contrast, the psychology of reasoning is an empirical science that examines the actual reasoning behaviors of individuals, including their mistakes. For example, psychologists studying reasoning might explore how reasoning abilities evolve with age. However, such empirical observations are outside the realm of logic.
Principles and Examples of Logical Reasoning
Logic primarily concerns itself with principles governing the validity of arguments, determining whether specific conclusions logically follow from given assumptions.
For instance, let’s examine arguments:
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If it rains in Karachi, then the streets will be flooded.
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It rains in Karachi.
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Therefore, the streets are flooded.
In this argument:
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Premise 1 establishes a conditional relationship: If it rains in Karachi, then the streets will be flooded.
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Premise 2 states that it indeed rains in Karachi.
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Conclusion: The streets are flooded.
This argument mirrors the structure of modus ponens, demonstrating the logical validity of the conclusion based on the given premises.
Process of Logic and Aristotle’s View
Aristotle’s logical works were once highly esteemed, with Kant even suggesting that nothing had surpassed his insights for millennia. However, in the last century, modern formal logic, pioneered by Frege and Russell, revealed significant flaws in Aristotle’s logic.
While few now see it as a sufficient basis for understanding science, math, or everyday reasoning, scholars familiar with formal techniques are beginning to see Aristotle’s work in a new light. They not only acknowledge the validity of his conclusions but also note striking similarities between his approach and contemporary logic. Like modern logicians, Aristotle delved into metatheory, exploring the properties of inferential systems rather than providing a practical guide to argumentation, as Jonathan Lear summarized.
Aristotle’s Organon
Aristotle’s collection of logical treatises, collectively known as the Organon, encompasses several key works:
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Categories
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On Interpretation
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Prior Analytics
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Posterior Analytics
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Topics
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On Sophistical Refutations
The term “Organon,” meaning “Instrument,” emerged from philosophical discussions concerning the role of logic. Some, like the Stoics, regarded logic as integral to philosophy, while others, like later Peripatetics, saw it more as a tool. Referring to these treatises as “The Instrument” implies a stance on this matter.
Although Aristotle himself didn’t use this term and didn’t explicitly state that these works formed a unified group, there are frequent connections between the Topics and the Analytics. Aristotle treated the Prior and Posterior Analytics as a single entity, and he positioned On Sophistical Refutations as either a final section or an appendix to the Topics.
Additionally, we must include the Rhetoric, which openly acknowledges its reliance on the Topics.
Categories
In this work, Aristotle explores the ways in which things can be categorized and classified. He outlines ten categories or classes under which all things can be placed, such as substance, quantity, quality, relation, etc. This work serves as a basis for understanding how language and thought relate to reality.
On Interpretation
This work deals with the nature of language and its relationship to reality. Aristotle examines propositions, their truth values, and the principles of contradiction and excluded middle. He also introduces the famous square of opposition, which illustrates the relationships between different types of propositions.
Prior Analytics
This work is concerned with deductive reasoning and formal logic, particularly the syllogism. Aristotle lays out rules for valid deductive inference, including the famous syllogistic forms. This work is crucial for understanding Aristotle’s approach to logical argumentation.
Posterior Analytics
Building on the Prior Analytics, this work delves into scientific knowledge and demonstration. Aristotle discusses the nature of scientific knowledge, the structure of scientific syllogisms, and the process of scientific inquiry. It is concerned with how we acquire certain knowledge about the world.
Topics
The Topics explores dialectical argumentation and the art of persuasion. Aristotle discusses various types of arguments and methods for constructing persuasive arguments. This work is essential for understanding how arguments are formed and evaluated in rhetoric and dialectic.
On Sophistical Refutations
In this work, Aristotle examines fallacious arguments and methods of refuting them. He identifies various types of fallacies and provides strategies for identifying and responding to them. This work is valuable for critical thinking and avoiding errors in reasoning.
Ibn Sina’s Conditional Syllogism
Ibn Sina’s theory of the Conditional Syllogism from a purely logical angle. In his work “al-Shifa: al-Qiyas,” Ibn Sina presents this theory as a noteworthy addition to Aristotelian logic, claiming it as his own discovery. Ibn Sina’s methodology involves aligning hypothetical syllogisms with categorical ones, particularly focusing on the connective conditional similar to the modern material conditional.
Thomas Aquinas and Logic
Thomas Aquinas made significant contributions to logic, which he believed essential for understanding both the natural world and theological matters. Influenced by Aristotle, he blended Aristotelian logic with Christian theology to create a coherent framework for intellectual exploration.
Aquinas believed human cognition starts with sensory experiences, processed by the intellect into coherent structures for reasoning. He distinguished between real differences in the external world and conceptual differences in the mind, like the contrast between apples and oranges versus chairs and tables.
Philosophical Semantics
Philosophical semantics is a branch of philosophy that focuses on the study of meaning, especially as it relates to language and representation. It explores fundamental questions such as:
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What is meaning?
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How do linguistic representations convey meaning?
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What is the relationship between language and reality?
At its core, philosophical semantics aims to analyze and understand the nature of meaning in language, examining both theoretical foundations and practical implications.
Deductive Reasoning and Inductive Reasoning
Deductive Reasoning
Deductive reasoning, also known as deduction, is a fundamental method of reasoning that involves drawing specific conclusions from general principles or premises.
Example:
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General principle: Every mammal possesses a backbone.
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Specific observation: Humans belong to the category of mammals.
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Logical conclusion: Therefore, humans possess a backbone.
Inductive Reasoning
Inductive reasoning is a method of reasoning that involves deriving general principles or hypotheses from specific observations or instances.
Example:
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Observation: Every summer, I see fireflies in my backyard.
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Hypothesis: Therefore, I will probably see fireflies in my backyard this summer.
Logical Operations: Obversion, Conversion, and Contraposition
Obversion
Example:
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Original Proposition: All humans are mortal.
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Obverted Proposition: No humans are immortal.
Conversion
Example:
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Original Proposition: All humans are mortal.
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Converted Proposition: All mortals are human.
Contraposition
Example:
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Original Proposition: All humans are mortal.
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Contrapositive Proposition: All immortals are non-human.
