MTE1501
Assignment 4
Unique No: 602580
DUE 20 September 2024
, Question 1: Amongst the ideas of the early mathematics philosophers, which
statement is NOT true?
To identify which statement about the early mathematics philosophers is not true, we
can examine each option in relation to the historical views of these influential figures.
1. Aristotle uses empirical study emanating from experiments and observations.
o True: Aristotle is known for his empirical approach to knowledge, which
involves systematic observation and experience. His epistemology highlighted
the importance of empirical evidence in understanding the physical world.
2. Plato reasoned that mathematics is based on experimentation and abstraction.
o NOT True: Plato viewed mathematics primarily as an abstract discipline,
emphasizing its ideal forms. He believed in the existence of abstract, eternal
truths that can be discovered through reason rather than experimentation. For
Plato, mathematics was more about deductive reasonin g and abstraction than
empirical experimentation.
3. Hilbert believed that mathematics can exist in the formal having concrete
representations in the mind.
o True: David Hilbert contributed significantly to formalism in mathematics,
asserting that mathematical statements can be symbolically represented and
manipulated without needing to refer to external interpretations.
4. Aristotle said that we can understand mathematics through experimentation,
abstraction, and observation.
o True: Aristotle indeed acknowledged mu ltiple approaches to understanding
mathematics, including empirical observations and abstractions from those
observations.
Conclusion: The statement that is NOT true is 2. Plato reasoned that mathematics is
based on experimentation and abstraction.
Assignment 4
Unique No: 602580
DUE 20 September 2024
, Question 1: Amongst the ideas of the early mathematics philosophers, which
statement is NOT true?
To identify which statement about the early mathematics philosophers is not true, we
can examine each option in relation to the historical views of these influential figures.
1. Aristotle uses empirical study emanating from experiments and observations.
o True: Aristotle is known for his empirical approach to knowledge, which
involves systematic observation and experience. His epistemology highlighted
the importance of empirical evidence in understanding the physical world.
2. Plato reasoned that mathematics is based on experimentation and abstraction.
o NOT True: Plato viewed mathematics primarily as an abstract discipline,
emphasizing its ideal forms. He believed in the existence of abstract, eternal
truths that can be discovered through reason rather than experimentation. For
Plato, mathematics was more about deductive reasonin g and abstraction than
empirical experimentation.
3. Hilbert believed that mathematics can exist in the formal having concrete
representations in the mind.
o True: David Hilbert contributed significantly to formalism in mathematics,
asserting that mathematical statements can be symbolically represented and
manipulated without needing to refer to external interpretations.
4. Aristotle said that we can understand mathematics through experimentation,
abstraction, and observation.
o True: Aristotle indeed acknowledged mu ltiple approaches to understanding
mathematics, including empirical observations and abstractions from those
observations.
Conclusion: The statement that is NOT true is 2. Plato reasoned that mathematics is
based on experimentation and abstraction.
