Frege and Functions

What was the primary contribution of Fraga to the field of logic?

• He created a new mathematical theorem.

• He introduced the concept of non-computable functions.

• He applied the notion of functions from mathematics to logic.

• He developed the first computer.

How do quantifiers contribute to the power of functions in logic?

• They simplify complex formulas.

• They assign truth values to arguments.

• They eliminate the need for proof procedures.

• They make claims about the properties of functions.

What is the significance of having an effective positive test for logical truth?

• It simplifies the process of computation.

• It distinguishes between computable and non-computable functions.

• It ensures that if premises are true, the conclusion is also true.

• It allows for the creation of new mathematical functions.

What is the key difference between computable and non-computable functions?

• Computable functions can be expressed in terms of quantifiers.

• Non-computable functions are always false.

• Non-computable functions are more powerful.

• Computable functions can be calculated using a decision procedure.

How did the concept of computability transform the modern world?

• It eliminated the need for logical proofs.

• It led to the development of new mathematical theorems.

• It revolutionized the field of philosophy.

• It paved the way for the creation of computers and computational technology.