Philosophy of mathematics

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/philosophy-of-mathematics

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the ontological debate?Central question: Do mathematical objects exist independently or are they human constructs?
2. What is the epistemological challenge?How do we acquire and justify knowledge of abstract mathematical truths?
3. What big questions do philosophers ask about numbers and math?They wonder if numbers exist on their own or only in our heads, and whether math is discovered or invented.
4. Who thinks math objects live outside our minds?Realists, like Platonists, say math objects are real and timeless, living in a special realm.

Ontology: The philosophical study of the nature of being, existence, and reality.
A Priori Knowledge: Knowledge that is independent of experience or empirical evidence.
Axiomatic System: A set of fundamental assumptions (axioms) from which theorems are logically derived.