Unit 4 TOK Quiz 3

What do you call a body of knowledge that is built upon a small number of self-evident statements using deductive reasoning?

• Complete system
• Axiomatic system
• Deductive system
• Consistent system

Why can there exist multiple different mathematics?

• Because they were developed by different mathematicians at different times
• Because these mathematics reflect different aspects of reality
• Because axioms are, in a certain sense, arbitrary
• Because mathematics is, according to one view, discovered

Mathematical proof is an example of the following kind of reasoning:

• Inductive
• Deductive
• Hypothetico-deductive
• Both inductive and deductive (depending on the type of proof)

Which of the following uses the super-mathematical criterion of truth? (tick all that apply)

• Mathematical anti-realism
• Mathematical realism
• “Mathematics is discovered” position
• “Mathematics is invented” position

“Mathematics is unnaturally natural: the fit to reality is too miraculous for an invention”. What concept does this argument support?

• Inconsistency of axiomatic systems
• Mathematical realism
• Certainty of mathematical proof
• Gödel’s second incompleteness theorem

Can mathematics prove its own consistency?

• Yes
• No
• Yes, but only if mathematics is consistent
• Yes, but only if the axioms upon which mathematics is based are true

Which of the following describes the criterion or truth used in the “mathematics is invented” position? (tick all that apply)

• Intra-mathematical
• Super-mathematical
• Coherence test for truth
• Correspondence test for truth

According to the “mathematics is invented” position (intra-mathematical criterion of truth), to be “true” in mathematics means to be:

• Falsifiable
• Supported by evidence
• Successful
• Provable

In mathematics, a deductive argument showing that a statement is true because it logically follows with certainty from other true statements (one word)