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:
Existence
There are Mathematical Objects.
Abstractness
Mathematical Objects are Abstract.
Independence
Mathematical Objects are
Independent of Intelligent Agents.

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

11. 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.

12. REFERENCES
• www.wikipedia.org
• www.slideserve.com
• www.slideshare.net
• www.youtube.com

13. THANK YOU