A Survey of Symbolic Logic (1918) by C. I. Lewis – Laying the Groundwork for Modal Logic | PDF Book Free Download

A Survey of Symbolic Logic, released in 1918 by American thinker Clarence Irving Lewis, serves as a pivotal reference in the realms of mathematical logic and logical philosophy. This text holds immense significance, not merely for its historical perspective but also for presenting some of the preliminary concepts that would eventually contribute to the structured evolution of modal logic, an essential aspect of modern philosophical inquiry.
In an era where symbolic logic was just beginning to break free from the constraints of conventional syllogistic reasoning, Lewis's publication offered an essential evaluation, critique, and expansion of prior frameworks. It thoroughly investigated the ideas put forth by Boole, Peirce, Frege, Schröder, and Russell and Whitehead, identifying notable discrepancies while suggesting enhancements that would shape logical discourse throughout the 20th century.

Who Was C. I. Lewis?

Clarence Irving Lewis (1883–1964) distinguished himself as an American thinker, logician, and epistemologist. He is particularly recognized for his influential contributions to pragmatism, modal logic, and conceptual pragmatism. His teaching tenure at Harvard University left a significant mark on numerous prominent figures within American philosophy, such as Willard Van Orman Quine and Nelson Goodman.
His intellectual contributions encompass:

• The foundations of logical theory
• The evolution of modal logic (the logic concerning necessity and possibility)
• Progress in epistemology and theories surrounding meaning and verification

What Is A Survey of Symbolic Logic About?

This 1918 publication offers not only a critical overview of prevailing symbolic (mathematical) logic frameworks but also presents Lewis’s own constructive recommendations for revising and enhancing logical theory.

Key Aims of the Book:

• To elucidate and assess the symbolic logic frameworks from the 19th and early 20th centuries.
• To pinpoint shortcomings within classical logic, especially concerning the material conditional (→).
• To present a basis for a novel logic system that accommodates modalities such as necessity and possibility.
• To contend that logical implication should adhere to stricter criteria than simple material implication.

Major Themes and Contributions

1. Critique of Material Implication

Lewis notably disputed the assertion that “if p, then q” is considered true anytime p is false or q holds true—this description pertains to the material conditional recognized in classical logic. He demonstrated that this perspective fails to accurately represent the intrinsic understanding of “if. . . then. . . ” found in everyday language.

• Analogy: Material implication deems “If the moon is made of cheese, then 2+2=4” as logically true—since the moon isn’t composed of cheese. Lewis regarded this conclusion as ridiculous.

2. Need for a Stricter Implication

• Lewis proposed the concept of “strict implication,” where the conclusion must necessarily derive from the premise. This notion would lay the groundwork for modal logic.
• Example: In the case of strict implication, “If it is raining, then the ground is wet” is valid only if, in all conceivable scenarios in which it rains, the ground remains wet.

3. Historical Survey of Logic

The text presents a detailed examination of:

• George Boole’s algebraic interpretation of logic
• Charles Sanders Peirce’s relational logic
• Frege’s Begriffsschrift
• Schröder’s algebraic logic
• Russell and Whitehead’s Principia Mathematica

Lewis illustrates how these frameworks either succeed or falter in addressing implications, inferences, and meanings.

4. The Birth of Modal Logic

Although Lewis did not completely establish modal logic in this publication, he laid the groundwork for it. His subsequent partnership with C. H. Langford in the 1932 volume Symbolic Logic would refine systems S1–S5—now fundamental to the study of modal logic.

Why This Book Matters

A Survey of Symbolic Logic is vital for:

• Historians of logic and mathematics
• Philosophers focused on language, inference, and modality
• Logicians aiming to grasp the shift from classical to modal logic
• Students exploring the foundations of 20th-century analytic philosophy

It signifies a crucial point in American philosophical discourse—serving as a link between early algebraic logic and contemporary modal frameworks.