Intuitionism

Intuitionism is a philosophical approach to ethics and mathematics that posits that moral or mathematical truths are not discovered through reasoning or empirical observation but are instead directly apprehended through intuition or immediate insight. Intuitionists argue that certain moral principles or mathematical propositions are self-evident and do not require proof or deduction.

There are two main branches of intuitionism:

1. Moral Intuitionism: In ethics, moral intuitionism holds that moral truths are not based on reason or derived from empirical data but are intuitively known or perceived by individuals. Moral intuitions are considered self-evident and do not require complex moral theories or reasoning. This approach suggests that humans have an innate capacity to recognize moral principles or ethical truths.
2. Mathematical Intuitionism: In mathematics, intuitionism is associated with the work of mathematician L.E.J. Brouwer and others. Mathematical intuitionists reject the idea of abstract mathematical objects that exist independently of human thought. They argue that mathematical truth is constructed through mental processes, and mathematical statements are meaningful only if they can be verified through constructive methods.

Key points of intuitionism include:

• Rejecting a priori proofs: Intuitionists do not accept a priori proof methods, which rely on logical deduction to establish the truth of a statement. They view such proofs as insufficient for validating moral or mathematical truths.
• Emphasis on direct experience: Intuitionism places importance on direct experience or insight rather than relying on external evidence or reasoning to grasp truths.
• Non-objectivity in mathematics: In mathematical intuitionism, mathematical truth is seen as a mental construct that varies from one individual to another. It challenges the traditional view of mathematics as an objective and universal discipline.
• Ethical foundationalism: In moral intuitionism, certain moral principles are considered foundational, requiring no further justification or reduction to other principles.

Intuitionism has been influential in the history of ethical philosophy, particularly in moral intuitionism, which found proponents in figures like G.E. Moore. However, it also faces criticisms, such as the difficulty of reconciling conflicting moral intuitions and the challenge of determining whose intuitions are valid in ethical disagreements.

In mathematical intuitionism, while it provides an alternative perspective on the nature of mathematical truth, it has not gained widespread acceptance in the mathematical community, where conventional mathematical practices and methods are still widely used.