Epistomology

Non-Euclidean Geometry

Geometrical systems that are not based on Euclidean principles, such as hyperbolic and elliptic geometries.

Scepticism

A philosophical position that questions the possibility of knowledge, arguing that we cannot have certainty about anything.

Deceptive Senses

Our senses can deceive us; illusions, dreams, and hallucinations can lead us to form false beliefs about the world.

Infinite Regress

Every justification requires another justification, ad infinitum, leading to an endless chain of reasoning.

Empiricism

Claims that knowledge comes from sense experience, arguing that our senses provide us with reliable information about the world.

Rationalism

Claims that knowledge comes from pure reason, arguing that we can gain knowledge through intuition, deduction, and innate ideas.

Tabula Rasa (Locke)

The mind is a 'blank slate' at birth; all knowledge comes from experience.

A Posteriori Knowledge

Knowledge derived from observation (e.g., 'The sky is blue').

Triangulation

Using multiple senses to verify observations.

Normal Conditions

Assuming reliability in healthy, standard environments.

Induction

Reasoning from observed to unobserved (e.g., 'The sun has risen every morning, so it will rise tomorrow').

Hume’s Critique

Induction is invalid—past observations don’t guarantee future outcomes.

No True Scotsman

Rejecting counterexamples by redefining terms (unsatisfactory).

Principle of Uniformity of Nature (PUN)

'The future resembles the past' (but how to justify PUN?).

Probabilism

Future events are likely based on past data (still invalid).

Popper’s Deductivism

Science progresses by falsifying hypotheses, not confirming them.

Method of Doubt

Reject all beliefs that can be doubted.

Cogito Ergo Sum

'I think, therefore I am' — the one indubitable truth.

Cartesian Circle

Descartes relies on God to guarantee clear & distinct ideas, but his proof of God depends on those very ideas.

Axiomatic Method

Start with self-evident axioms (e.g., 'A straight line can be drawn between any two points').

Synthetic A Priori Knowledge

Truths known independently of experience but not tautologies (e.g., '7 + 5 = 12').

Kant’s Big Idea

The mind structures experience through innate categories (space, time, causality).

Analogy of Rose-Tinted Glasses

We can’t perceive reality 'as it is' (noumena), only as it appears (phenomena).

Fishing Net Analogy (Eddington)

We only 'catch' what our cognitive 'net' allows.

Space & Time (Kant)

Not external realities but frameworks of human perception.

Causality (Kant)

We can’t experience uncaused events because causation is a mental category.

Playfair’s Axiom

'Given a line and a point not on it, only one parallel line can be drawn.'

Hyperbolic Geometry

Angles sum to <180°.

Elliptic Geometry

Angles sum to >180°.

Einstein’s Relativity

Space is non-Euclidean; Euclidean geometry is an approximation.

Kant’s Mistake

He thought Euclidean geometry was synthetic a priori, but it’s not universally true.

Empiricist Victory

The structure of space must be discovered a posteriori (through science).