Maths Perspective
Bertrand Russell
English Mathematician & Philosopher
Believed in the power of mathematics to describe the world
Concerned that many mathematical axioms were not yet proven
Criticized the shaky foundations of mathematical knowledge
Axioms are statements or postulates considered to be true, forming the basis for subsequent reasoning.
Importance of proving axioms to establish valid knowledge
Russell and Whitehead’s extensive proof of 1+1=2 in Principia Mathematica
Knowledge Creation
Create valid knowledge through logical proof
Influence on subsequent mathematical theories
Co-authored with Alfred North Whitehead
Role of Pure vs. Applied Mathematics
Valid knowledge can be created through logic and deductive reasoning
Knowledge must be based on previously established truths for it to be objectively true
However, not all axioms were proven, leaving mathematical knowledge with some uncertainty.
Mathematical Platonism
Pure Mathematics: Focuses on identifying patterns without direct real-world application
Applied Mathematics: Uses mathematical patterns to make predictions and describe real-world observations
Mathematical Formalism
Mathematics Theories
Certainty vs. Truth
Example: Einstein’s Theory of General Relativity—mathematically certain but only proven true with empirical evidence.
Truth: Requires external evidence beyond axiomatic reasoning.
Certainty: Comes from mathematics’ axiomatic system.
Perspective that mathematics exists a priori, independent of human experience
Mathematical laws and axioms exist regardless of human discovery
Galileo's view that the universe is written in the language of mathematics.
Mathematical objects (like numbers) do not exist outside of the mind
Usefulness does not equate to reality
Counterclaim to Platonism, viewing mathematics as a human-invented system
Mathematics has culturally plural origins (e.g., Greek and Arabic contributions