In philosophy, axioms are fundamental principles or starting points that are assumed to be true without proof, forming the basis for further reasoning. Different branches of philosophy and different thinkers propose their own sets of axioms. Here’s a structured list across major domains:

1. Metaphysics

Identity: A is A (Law of Identity).
Non-Contradiction: A cannot both be and not be in the same respect at the same time.
Excluded Middle: Every proposition is either true or false.
Causality: Everything that begins to exist has a cause.

2. Epistemology (Theory of Knowledge)

Principle of Sufficient Reason (Leibniz): Nothing happens without a reason.
Reliability of Reason: Human reason is generally a trustworthy guide to truth.
Perception as a Source: Our senses provide (at least some) knowledge of the external world.
Coherence/Consistency: Contradictory beliefs cannot both be true.

3. Logic

Formal Axioms: Foundational rules (identity, non-contradiction, excluded middle, transitivity).
Inference Rules: If A → B and A, then B (modus ponens).
Consistency Requirement: No valid system tolerates contradictions without collapsing (principle of explosion).

4. Ethics

Ought Implies Can (Kant): If someone morally ought to do something, they must be able to do it.
Universality Principle: Moral principles must apply universally to all relevantly similar cases.
Value of Persons: Many ethical systems assume persons have intrinsic worth.

5. Political Philosophy

Natural Equality (Locke, Rousseau): Humans are equal in fundamental rights by nature.
Consent Principle: Legitimate political power must rest on consent of the governed.
No Harm Principle (Mill): Liberty can only be limited to prevent harm to others.

6. Philosophy of Science

Uniformity of Nature: Laws of nature are consistent across time and space.
Empirical Testability: Hypotheses must be open to observation or experiment.
Simplicity (Occam’s Razor): Prefer simpler explanations unless complexity is required.

7. Phenomenology/Existentialism

Intentionality of Consciousness (Husserl): Consciousness is always about something.
Existence Precedes Essence (Sartre): Humans define themselves through choices, not fixed essences.
Authenticity as a Value: Living in accordance with one’s true self is foundational.

8. Other General Axioms Often Invoked

Trust in Memory: Memory is generally reliable.
Continuity of the Self: The “I” persists over time.
Language Meaningfulness: Words and concepts can correspond to reality.

Would you like me to expand each category with examples of philosophers who explicitly formulated these axioms(e.g., Aristotle’s logical laws, Kant’s ethical axioms, Descartes’ epistemic axioms), or keep it as a general overview list?
Perfect. Here’s the expanded version of axioms in philosophy, now tied to the philosophers who formulated or emphasized them.

Axioms in Philosophy (with Philosophers)

1. Metaphysics

Law of Identity (A = A) – Aristotle (Metaphysics): A thing is what it is. This is the most basic axiom of thought and being.
Law of Non-Contradiction – Aristotle: The same thing cannot both be and not be in the same respect, at the same time.
Law of Excluded Middle – Aristotle: Every proposition must be either true or false, no middle state.
Causality Principle – Aristotle (Four Causes), Aquinas (First Cause argument), Leibniz (Principle of Sufficient Reason): Nothing comes from nothing.

2. Epistemology (Theory of Knowledge)

Cogito, ergo sum (“I think, therefore I am”) – Descartes: Self-awareness is the first indubitable axiom of knowledge.
Principle of Sufficient Reason – Leibniz: For every fact, there is a reason why it is so and not otherwise.
Reliability of Reason – Plato and Descartes: Rational inquiry is the surest path to truth.
Empiricism Axiom – Locke: Knowledge begins in sense experience; “Nothing in the intellect that was not first in the senses.”

3. Logic

First Principles of Thought – Aristotle: Identity, Non-Contradiction, and Excluded Middle form the foundation of logic.
Rules of Inference – Stoics (Chrysippus) and later medieval logicians: If A → B, and A, then B (modus ponens).
Principle of Explosion – Medieval logicians: From a contradiction, anything follows (hence the need to avoid contradictions).

4. Ethics

Ought Implies Can – Kant: If you morally ought to do something, you must have the ability to do it.
Categorical Imperative (Universality Principle) – Kant: Act only on maxims you could will to be universal law.
Greatest Happiness Principle – Bentham and Mill: The morally right act maximizes happiness/utility.
Virtue as the Mean – Aristotle: Virtue lies between excess and deficiency, an axiom of his Nicomachean Ethics.

5. Political Philosophy

Natural Equality of Humans – Locke: All humans are naturally free and equal in rights.
Consent of the Governed – Locke, Rousseau: Legitimate authority rests on social contract and consent.
No Harm Principle – Mill: Liberty is only justifiably limited to prevent harm to others.
General Will – Rousseau: The foundation of political legitimacy is the collective will of the people.

6. Philosophy of Science

Uniformity of Nature – Hume: Science assumes laws of nature hold consistently, though Hume noted this cannot itself be proven.
Falsifiability/Testability – Popper: A scientific hypothesis must be testable and refutable.
Parsimony (Occam’s Razor) – William of Ockham: Do not multiply entities beyond necessity.

7. Phenomenology & Existentialism

Intentionality of Consciousness – Husserl: Consciousness is always directed at or about something.
Existence Precedes Essence – Sartre: Humans exist first, and only later define their essence through choices.
Being-in-the-World – Heidegger: Human existence is fundamentally embedded in a world of relations, not isolated.
Authenticity as Axiom – Kierkegaard and Sartre: The highest value lies in living authentically and taking responsibility for one’s choices.

8. Other Commonly Assumed Axioms

Continuity of the Self – Locke: Personal identity persists through memory and consciousness.
Trust in Memory – Hume, Reid: Basic reliance on memory as a source of knowledge.
Language Correspondence – Wittgenstein (early): Language maps onto facts about the world (Tractatus).

Would you like me to arrange these into a table format (Philosopher | Axiom | Branch of Philosophy | Source) so you can use it as a reference guide in Obsidian or your notes system? That way it’s easily searchable and structured.