Friday, November 15, 2019

Two Types of Logic

In the framework of its studium generale Freiburg University Freiburg offers many lectures to the general public. One prominent series is Saturday University, where the topic of this year’s winter semester is Education Today.

The talks started with a drumbeat by a theoretical physicist on Education in the Age of Science.

Forging a bridge between Greek philosophy and high-energy physics
Professor Josef Honerkamp's lecture was one of the best I have heard for long. Being a physicist myself, I knew how the thinking of the pre-socratic philosophers still influences modern physics, but in working out the difference between a logical and a dialectic deduction Honerkamp shed new light on the influence of the Greek philosophy on current thinking.

Greek philosophy and science have their origins in the Greek colonies in Asia Minor and Italy. Honerkamp stressed the fact that initially in regions where the Greek philosophers were in contact with alien cultures like Phonicien, Persian, Egyptian, their thinking advanced considerably.

Eventually, Athens became the center of cultural life in the Periclean period, and after that, and later, the specialized sciences flourished in Alexandria.

Constitutive principles of mathematics are the constituent principles of being things.

Accordingly, in modern physics, known particles could be arranged in geometrical figures allowing the prediction of missing particles, i.e., particles to be discovered.

Here, building mesons and baryons out of quarks
from the book Quarks with Color and Flavor by Nobel Price winner Sheldon Lee Glashow©
Arranging elementary particles in geometrical structures is a favorite pastime of group theory.

How can a man/woman gain insight? Can one gain sure knowledge at all? There are observations and science, there are revelations and religion.

In their quest, men* search for and find better things to add to their understanding with time. Here Professor Honerkamp distinguished between rigorous and dialectic science.
*Let's face it. The world of the ancient Greeks was dominated by males.

When do we speak about logical and when about dialectical conclusions? A conclusion is logical when it is derived from true and generally first principles. A conclusion is dialectical when it is derived from credible sentences.

Sentences are credible if they are recognized by all, or by most, or by wise men.

The seven wise men in ancient Greece

On the one hand, there are nature, discovery, and the implication of experimental results; on the other hand, there are human cohabitation, norms, and continuous discourse about those norms.

In the first case, mathematics assures logical correctness. In the second case, logic is applied instinctively and analogous (That is logical, isn't it?), leading to implications that are regarded as acceptable.

Mathematical logic had a great fascination for the German philosopher Gottfried Wilhelm Leibniz when he wrote," If one could find characters or signs capable of expressing all our thoughts just as purely and strictly as arithmetic expresses numbers or analytical geometry expresses lines, then one could obviously do what one does in arithmetic and geometry with all objects, as far as they are subject to rational thinking."

"And if someone doubted what I put forward, I would say to him, "Let us calculate, monsieur," and taking pen and ink, we would soon be out of embarrassment."

Quantum mechanics killed Leibniz's dream definitively.

Galilei experimenting at the inclined plane
Now the physicist in Professor Honerkamp broke through giving credit to Galileo Galilei for his physics experiments and Isaac Newton for providing the theoretical foundation or mathematics.

On the way to an understanding of nature. A little history of physics

Searching for the "uniform" theory or GUT, the Grand Unification Theory. First-principles are symmetries (the Greek philosophers send their regards), a constant speed of light, and the equivalence principle.

The space of phenomena. Dimensions in meters (R) vs. complexity (N). Present scientific challenges are black holes, gravitational waves, dark matter, and dark energy.

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