The Role of Logic in Modern Physics: Classical vs. Modern Logic

Astronomy, as a science, has advanced remarkably even before the advent of formal logic in the 19th century. Key figures like Newton have used their intuition and pen and paper to predict the orbits of planets using Newton’s law of gravitation in the 18th century. This innovative use of intuition paved the way for further scientific developments in space travel and exploration without the necessity of advanced mathematical logic.

Classical vs. Modern Logic

The separation of classical and modern logic is crucial to understanding the different approaches in science and mathematics. Classical logic, primarily based on the works of Aristotle, governs logical reasoning and has influenced the development of scientific theories for centuries. However, with the advent of mathematical logic in the 19th century and its finalization in the 1930s, a new branch emerged, distinct from classical logic. Despite these advancements, the fundamental principles of physics, such as the law of gravitation, still rely heavily on intuition rather than formal logical systems.

The Controversies in Mathematical Logic

One of the most significant issues in mathematical logic is the Principle of Explosion, a concept that accepts the idea that from a contradiction, anything can follow. This principle, although widely accepted in mathematical logic, is rejected by most traditional logicians. The Principle of Explosion can be illustrated with a simple example:

Statement 1: God exists

Statement 2: God does not exist

Conclusion: Therefore, you owe me one billion dollars.

This conclusion is clearly fallacious, and it raises doubts about the logical consistency of mathematical logic. In contrast, classical logic, as defined by Aristotle, explicitly states that nothing can logically follow from a contradiction. Aristotle himself wrote, “It is impossible that the same thing should be necessitated by the being and by the not-being of the same thing” (Prior Analytic II 4 57b3). This statement directly contradicts the Principle of Explosion, making it evident that mathematical logic is not consistent with Aristotelian logic.

The Practical Implications

Even today, in the context of modern physics and space exploration, traditional logical principles guide our understanding and application of physical laws. The fact that the mathematical logic used to send space probes to other planets relies heavily on the same principles as those established by Newton’s law of gravitation highlights the enduring relevance of classical logic in scientific practice. For example, astronauts still use Newton’s formula for interplanetary missions, underscoring that mathematical logic is not a prerequisite for such endeavors.

The Views of Modern Logicians

It is worth noting that not all modern logicians call mathematical logic “classical logic” as misleadingly done. For instance, Professor Irving M. Copi, a prominent logician, clearly distinguishes between two types of logic:

The theory of deduction aims to explain the relations of premises and conclusion in valid arguments. It also aims to provide techniques for the appraisal of deductive arguments—that is for discriminating between valid and invalid deductions. To accomplish this two large bodies of theory have been developed. The first is called classical logic or Aristotelian logic after the Greek philosopher who initiated this study. The second is called modern logic or modern symbolic logic developed mainly during the nineteenth and twentieth centuries.

— Copi, Irving M., Carl Cohen, and Kenneth McMahon. "Introduction to Logic," 14th edition, 2014

Copi’s work, widely recognized and taught in American universities, further reinforces the distinction between classical and modern logic. His clear and comprehensive explanation highlights the differences and ensures that the terms are used appropriately in the academic and scientific communities.

Conclusion

The role of logic in the development and application of modern physics is complex and multifaceted. While mathematical logic has contributed significantly to the expansion of scientific knowledge, classical logic continues to play a vital role in practical applications such as sending space probes and predicting planetary orbits. The ongoing debates and controversies in mathematical logic, particularly the Principle of Explosion, highlight the importance of maintaining a clear distinction between these two types of logic. As we continue to explore the cosmos, the principles of classical logic will likely remain an indispensable tool in our scientific endeavors.