What is a formal system?

An alphabet + rules of inference.

What is the formalist's position in the philosophy of mathematics?

All of Math can be reduced to symbols.

What is the Platonist's position in the philosophy of mathematics?

Mathematical entites exist in the world.

The study of God and its nature.

What is an axiomatic system?

A set of truths used to derive other ones.

The study of numbers and certain operations.

A proposition derived from other inferences.

What is the constructivist's position in the philosophy of mathematics?

Math is a creative product of the human mind.

What does 'positivism' mean in philosophy?

All knowledge is scientific knowledge.

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Philosophy of Mathematics 101

15 termsStudBud Administration53 plays

Before the reading, I'll be testing your knowledge on some basic concepts and discussions in (the philosophy of) mathematics and logic: from Platonism and constructivism, to Gödel's theorems and first-order logic. Answer each question, even if you don't know the correct answer.

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Questions 15

Answers

1
What is a formal system?
An alphabet + rules of inference.
A set of axioms.
A well-behaved one.
A set of symbols.
2
What is the formalist's position in the philosophy of mathematics?
Kurt Gödel sucks.
Mathematics can be rigorously formalized.
Mathematicians should dress adequately.
All of Math can be reduced to symbols.
3
Did you learn something from this? (No wrong answers!)
Yes
No
4
What is the Platonist's position in the philosophy of mathematics?
Plato and Kurt Gödel are the best!
The World of Ideas exists outside the Cave.
Mathematical entites exist in the world.
Having a crush on someone but doing nothing.
5
What is theology?
The discipline that studies the Bible.
The study of God and its nature.
The field whose goal is to prove God exists.
The philosophy that concerns itself with God.
6
What is an axiomatic system?
A set of truths used to derive other ones.
The Cartesian plane.
Any sort of formal system.
The set of natural numbers.
7
What is epistemology?
The study of science and mathematics.
The study of knowledge itself.
The field of biology which studies insects.
The field of medicine which studies the skin.
8
What is arithmetic?
The study of numbers and certain operations.
The study of rhythm.
The field of sets and their properties.
Adding 2 and 2 together.
9
Who was this physicist?
Albert Einstein
Isaac Newton
Ernest Rutherford
Max Planck
10
A theorem is...
An obvious truth.
A self-evident proposition.
A rule one can use to infer other stuff.
A proposition derived from other inferences.
11
Who was this philosopher?
Aristotle
Ludwig Wittgenstein
Bertrand Russell
Gottlob Frege
12
What is the constructivist's position in the philosophy of mathematics?
Kurt Gödel sucks as well.
Math results are relative to each individual.
People shouldn't criticize so hard sometimes.
Math is a creative product of the human mind.
13
What does 'positivism' mean in philosophy?
An optimistic, happy outlook on life.
All we ought to do is scientific research.
Philosophy shouldn't exist.
All knowledge is scientific knowledge.
14
Who was this logician?
Kurt Gödel
Euclid
Rudolf Carnap
David Hilbert
15
Logic is the study of...
Thought.
What there is.
Valid inferences.
The obvious.

Philosophy of Mathematics 101 Flashcards | StudBud

Philosophy of Mathematics 101

15 termsStudBud Administration53 plays

Flashcards15 cardsFPractice quizPHost liveL

Questions 15

Answers

1
What is a formal system?
An alphabet + rules of inference.
A set of axioms.
A well-behaved one.
A set of symbols.
2
What is the formalist's position in the philosophy of mathematics?
Kurt Gödel sucks.
Mathematics can be rigorously formalized.
Mathematicians should dress adequately.
All of Math can be reduced to symbols.
3
Did you learn something from this? (No wrong answers!)
Yes
No
4
What is the Platonist's position in the philosophy of mathematics?
Plato and Kurt Gödel are the best!
The World of Ideas exists outside the Cave.
Mathematical entites exist in the world.
Having a crush on someone but doing nothing.
5
What is theology?
The discipline that studies the Bible.
The study of God and its nature.
The field whose goal is to prove God exists.
The philosophy that concerns itself with God.
6
What is an axiomatic system?
A set of truths used to derive other ones.
The Cartesian plane.
Any sort of formal system.
The set of natural numbers.
7
What is epistemology?
The study of science and mathematics.
The study of knowledge itself.
The field of biology which studies insects.
The field of medicine which studies the skin.
8
What is arithmetic?
The study of numbers and certain operations.
The study of rhythm.
The field of sets and their properties.
Adding 2 and 2 together.
9
Who was this physicist?
Albert Einstein
Isaac Newton
Ernest Rutherford
Max Planck
10
A theorem is...
An obvious truth.
A self-evident proposition.
A rule one can use to infer other stuff.
A proposition derived from other inferences.
11
Who was this philosopher?
Aristotle
Ludwig Wittgenstein
Bertrand Russell
Gottlob Frege
12
What is the constructivist's position in the philosophy of mathematics?
Kurt Gödel sucks as well.
Math results are relative to each individual.
People shouldn't criticize so hard sometimes.
Math is a creative product of the human mind.
13
What does 'positivism' mean in philosophy?
An optimistic, happy outlook on life.
All we ought to do is scientific research.
Philosophy shouldn't exist.
All knowledge is scientific knowledge.
14
Who was this logician?
Kurt Gödel
Euclid
Rudolf Carnap
David Hilbert
15
Logic is the study of...
Thought.
What there is.
Valid inferences.
The obvious.