What is the relationship between mathematics and philosophy?

Mathematics is quantitative in nature, whereas Philosophy is qualitative. Mathematics is about numbers; Philosophy is about ideas. The key link then between the two subjects is logical problem solving. The mathematical proof and philosophical argument bear a strong resemblance.

What does Russell argue is the real value of philosophy?

The primary value of philosophy according to Russell is that it loosens the grip of uncritically held opinion and opens the mind to a liberating range of new possibilities to explore.

What was Russell’s view on philosophy?

Russell, in particular, saw formal logic and science as the principal tools of the philosopher. Russell did not think we should have separate methods for philosophy. Russell thought philosophers should strive to answer the most general of propositions about the world and this would help eliminate confusions.

How is philosophy connected to the sciences according to Russell?

As far as the main value of philosophy, Russell says philosophy seeks knowledge like science, but is different from science. Recognizing that there is no absolute certainty, philosophy shows unsuspected possibilities about matters of fact.

Why is philosophy of mathematics important?

It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people’s lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.