The Philosophy of Mathematics

OVERVIEW

Mathematics developed in parallel and in relation to the world of philosophy. Turning to the past, the researcher comes in contact with ideas developed by important philosophical schools of thought, especially the mathematical ones. The aim of this module is to search for the first principles of Mathematics and understand their relationship with the distinctive ideas of the various contemporary philosophical schools. Through our highly curated and thought-provoking trip, this search will enrich our modern knowledge and experience, giving a fresh impetus to our thinking that will enable us to make new developments. After all, the past can always constitute a source of inspiration for the present towards a better future.

OVERVIEW

Mathematics developed in parallel and in relation to the world of philosophy. Turning to the past, the researcher comes in contact with ideas developed by important philosophical schools of thought, especially the mathematical ones. The aim of this module is to search for the first principles of Mathematics and understand their relationship with the distinctive ideas of the various contemporary philosophical schools. Through our highly curated and thought-provoking trip, this search will enrich our modern knowledge and experience, giving a fresh impetus to our thinking that will enable us to make new developments. After all, the past can always constitute a source of inspiration for the present towards a better future.

THE SYLLABUS

Pythagoras and Mathematics

Pythagoras, the son of a humble seal engraver from the island of Samos, became an esteemed philosopher and founder of a movement that transformed ancient Greek philosophical thinking. Most students across the western world were first introduced to his thinking thanks to the famous Pythagorean theorem but his work and ideas encompassed many disparate fields such as geometry, cosmology, harmony, and vegetarianism. This module will offer a biographical sketch of Pythagoras and will explore the most significant features of his religio-philosophical school of thought. Finally, a brief presentation of the influence of Platonic thought in later mathematicians will be given.

Plato and Platonism in Mathematical Philosophy

Plato is probably the most famous ancient Greek philosopher and a pivotal figure in the development of western philosophical thought. This module will commence by placing Plato in his contemporary context of place and time, and with describe basic features of his philosophical system, which constitute an apogee of Greek thought.

The Platonic solids

This module will refer to and define the five platonic solids, and will describe their geometrical features and properties. Plato attempted to articulate a theory of a geometrical understanding of the world, based precisely on his regular polyhedrons. Finally, these solids will be connected with the four basic elements of fire, air, water, and earth, since Plato believed that everything that can be conceived by the human senses consists of different quantities of these basic elements.

Aristotle’s ideas

Following an introduction to the biography of Aristotle, we will present the basic features of Aristotelian philosophy and its interrelation with the Platonic one. Then we will investigate the importance of abstract process in mathematical objects, which, according to abstract thinking, can be defined as equivalence classes of other objects. The module will conclude with a reference to the need for a mathematical proving process as the appropriate way of thinking, by using the four basic structural elements that should characterize all mathematical theories.

Continuity and Infinity

Can Achilles run faster that a tortoise? The Greek philosopher Zeno of Elea did not think so but then again he was a man who loved a good paradox and provided us with a whole array of them. This module will study the so-called Eleatic paradoxes to demonstrate the importance of studying the notions of continuity and infinity. Two concepts that also attracted the attention of Aristotle, who argued that “the infinite first manifests itself in the continuous”.

This part will concern itself with the Eleatic paradoxes in order to manifest the importance of studying the notions of continuity and infinity. The relevant Aristotelian ideas will follow.

PROGRAM HIGHLIGHTS

• Indulge in the philosophy of mathematics in ancient Greece through truly original workshops and on-site seminars that will enable you to discover the extraordinary ideas of Pythagoras, Plato and Aristotle

• Explore Ancient Corinth; Greece’s richest port, as well as a vital, robust city-state in Classical, Hellenistic and Roman times

• Marvel at the foremost masterpieces of Classical Greece, the eternal Parthenon and the exquisite Acropolis of Athens

• Discover the finest and best-preserved of all classical Greek theaters, the spectacular theater of Epidaurus

• Visit fascinating archaeological museums, such as the Acropolis Museum and the stunning Archaeological Museum of Nafplio, guided by highly-qualified, licensed archaeologists

PERKS

What is included in our programs?

  • 3 US credits provided by the Hellenic American University
  • Accommodation in hand-picked and well-located superior class hotels
  • Breakfast and lunch
  • Professionals e.g. licensed guides, lecturers, and tour managers
  • Entrance fees to museums and archaeological sites
  • All land and sea transportation included in the itinerary of the specific program
  • Information material
  • Local taxes
  • Travel insurance
  • Transport to and from the airport in Greece

Optional

  • Airfares to and from Greece
  • Any custom request

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