MATH MODERN WORLD

Question 1

major themes in the philosophy of mathematics are mathematical

Answer 1

realism and anti-realism

Question 2

math exists objectively and independent of human thought. Mathematical concepts are disembodied in the universe and available for us to uncover and bring into practical use.

Answer 2

realism

Question 3

There are many variations on realism, but the most popular form is

Answer 3

platonism

Question 4

a metaphysical position which offers that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging.

Answer 4

platonism

Question 5

holds that mathematics is a product of the human imagination and is carefully engineered to make formal statements about nature in order to aid our understanding of the behavior of the universe

Answer 5

anti-realism

Question 6

which suggests that all of mathematics can be derived from a set of axioms or self-evident assumptions.

Answer 6

formalism

Question 7

were the first major contributors to the dialogue of mathematics

Answer 7

plato and aristotle

Question 8

Both a mathematician and a philosopher, he was the founder of the Academy in Athens (first institution of higher learning in the Western world)

Answer 8

plato

Question 9

There exists a realm of Forms, perfect ideals of which
things in this world are but imperfect copies.

Answer 9

plato’s philosophical theory

Question 10

is the heart of Platonism.

Answer 10

theory of forms

Question 11

Reality is unavailable to those who completely rely on their senses.
The material world is just a “shadow ” of the real world

Answer 11

allegory of the cave

Question 12

Knowledge can only be achieved through pure reason.

Answer 12

plato

Question 13

The ideas of Mathematics had an existence of their own, beyond the mind, in the external world.

Mathematics exists in some world out there and mathematicians are merely discovering the truths of mathematics.

Answer 13

Plato’s position of the Nature of Mathematics

Question 14

as a philosophy of mathematics is the view that at least the most basic mathematical objects (e.g., real numbers, Euclidean squares) actually exist, independently of the human mind which conceives them. Their properties are discovered, not created

Answer 14

platonism

Question 15

A student of Plato at Academy
✔ A tutor of Alexander the Great,
son of King Philip II
✔ Founder of the Lyceum in Athens (a rival institution of the Academy)

Answer 15

aristotle

Question 16

Developed the theory of “empiricism”. In order to understand the universe, one needs to observe it, measure it or try to look at it.

Answer 16

aristotle

Question 17

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality

The structures of mathematics are intrinsic to nature. Moreover, if the universe disappeared tomorrow, our eternal mathematical truth would still exist. It is up to us to discover mathematics and its workings.

Answer 17

einstein

Question 18

sets introduced by

Answer 18

george cantor

Question 19

is a collection of clearly defined objects, called elements of a set.

Answer 19

set

Sets are usually denoted by capital letters of the English alphabet while small letters denote elements of the set

Question 20

It enumerates, lists, or tabulates distinct elements of a set which are separated by a comma and enclosed by a pair of braces {}.

Answer 20

roster method

Question 21

It uses a phrase that describes the property of the elements of the set and enclosing it by a pair of braces.

Answer 21

rule method