Plato's Philosophy of Mathematics

This PPT Contains All about Plato's Philosophy of Mathematics. His early life and how he get interest in Mathematics and his great contribution to Mathematics.

1. Central university of rajasthan Submitted to: DR. gobind singh Submitted by: Jagrati mehra (2020imsbmt015) Int. m.sc. B.ed. II Semester Mathematics department Plato’s philosophy of mathematics

2. content Early life of Plato Plato : The Academy Plato’s contribution in Mathematics Plato’s philosophy of Mathematics The Theory of Two Worlds Plato’s Metaphor of line Classical Views on Nature of Mathematics Conclusion References

3. Early Life of Plato Plato was born in aristocratic family in 427 BC in Athens. Plato is considered to be one of the great philosopher who contributed much in shaping western philosophy. His early interest were in poetry and politics. He learnt philosophy from famous Greek philosopher Socrates. Along with Socrates and his student Aristotle, Plato helped to lay the foundations of western Philosophy and science. In his travels, he got acquainted with Pythagoras. From Pythagoreans, He gained the interest in the study of mathematics.

4. Plato: The Academy He returned to Athens about 385 BC and founded his academy. The academy was considered one of the main centers of intellectual life at that time. First 10-15 years course at the Academy involved the study of science and mathematics, including plane and solid geometry and harmonics. In particular, he was convinced that geometry was the key to unlocking the secrets of the universe. The sign above the academy entrance read –”Let no-one ignorant of geometry enter here.” In the academy, he proposed many mathematical problems and encouraged the student of the academy to investigate. His academy taught mathematics as a branch of philosophy as Pythagoras has done. Plato became known as the “Maker of Mathematics” His academy boosted most prominent mathematician of the ancient world, including Eudoxus , Theaetetus and Archytas.

5. Plato’s contribution in Mathematics Plato’s contribution to mathematics were focused on the foundations of mathematics. He discussed the importance of examining the hypothesis of mathematics. He also drew attention toward the importance of making mathematical definition clear and precise as these definitions are fundamental entities in mathematics. He played important role in encouraging and inspiring people to study mathematics He wrote dozens of books but why did Plato stress on the study of mathematics ? One can find answer in the seventh book of his masterpiece. The republic, where he stated some of his views on the importance of mathematics.

6. Plato’s philosophy of Mathematics The philosophy of Plato is known as Platonism. He told that “Mathematics is language in which the god talk to people.” According to Plato “Knowledge is a subset of that which is both truth & beliefs.” To the Plato, the idea of good is the ultimate objective of philosophy. He thinks that “In the world of knowledge, the idea of good appears last of all, and is seen only with an effort; and when seen, is also inferred to be the universal author of all thing beautiful and right.” To help in understanding and attaining the idea of good, one has to study arithmetic and geometry. This two subjects have two important characteristic that make them valuable in comprehending the idea of good: They invite thought and lead the mind to reflect and hence enabling the mind to reach truth. They have power to draw the soul from becoming to beings. To Plato, this is true use of Mathematics.

7. Plato’s philosophy of Mathematics Plato Quoted that, ”Mathematics is like draughts in being suitable for young, not to difficult, amusing and without peril to the state.” Plato drew much attention to irrationals. Plato strongly encouraged the students of the academy to pursue the study of irrationals. His opinion was that science is incomplete without them. He thought that People who are good in Mathematics will do well in other field of Knowledge. Mathematical Platonism can be defined as a combination of three views:

8. The Theory of Two Worlds Sensible World World of the Forms Appearance (seems real) Reality (is real) Immanent (within space & time) Transcendent(beyond space &time) Becoming (ever changing) Being (eternal & unchanging) Particular & imperfect Absolute & perfect Many instances (copy; imitation) One essence (archetype) Perceived by senses Known by reason Subjective (dependent upon my perception) Objective (exist independently of my mind) Also known as immaterial Also known as material Examples: a computer, a person Examples: Justice, Goodness

9. Plato’s Metaphor of line External Invisible Immaterial Temporal Sensory Materials Reason Imagination Belief Intellect World of Being World of Images World of Objects World of Numbers Being Goodness Painting Sculpture Shadow Reflection Fiction Unicorn Tables Dogs Humans Birds Numbers Shapes Universals Souls

10. Conclusion According to Seneca, Plato died in 347 BC at the age of 81 on the same day he was born. The Suda indicates that he lived to 82 years, while Neanthes claims an age of 84. He was lecturing in his Academy for the rest of his life. Plato did not deny the important applications of mathematics in People’s daily life. To Plato, The philosophical importance of Mathematics is more important and more rewarding.

11. References www.wikipedia.org www.slideserve.com www.slideshare.net www.youtube.com

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