Consistency

High school (ages 12+)
Thinking & Learning

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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/consistency

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 gödel's incompleteness theorems?Showed that sufficiently strong formal systems cannot prove their own consistency
2. What does it mean for a theory to be consistent?A theory is consistent if you can never prove both a statement and its opposite from its rules. If you could prove both, the theory would be useless.
3. Why is consistency important in math and science?Consistency lets us trust proofs and experiments. If a theory has contradictions, we could prove anything and it would break our understanding.

Formal System: A system of axioms and rules of inference used to derive theorems.
Model Theory: A branch of mathematical logic that studies the relationship between formal theories and their interpretations.
Proof Theory: A branch of mathematical logic concerned with formal proofs as mathematical objects.