John Locke

Source - Gilbert Ryle on John Locke

Theory of Opinion: His work is less a “theory of knowledge” and more an “Ars Cogitandi … Ethics of Thinking”.
Proportionality of Belief: Locke argued that the tenacity (determined/persistent) with which we hold an opinion should always be proportional to the quantity and quality of the reasons for it.
Rejection of Innate Ideas: Locke demolished the theory that humans are born with a fund of truths (innate ideas), though he did so mostly to clear the path for observation-based learning.
Anatomy of Thought: He dissected thoughts into “constituent ideas” to help people ask what the “solidities” and “frailties” of their reasons are.
Role of Reasoning: Locke taught that even in areas where Euclidean certainty is impossible, one should remain a “judicious” rather than “bigoted” thinker.

John Stuart Mill

Source - John Stuart Mill’s On Liberty (1859)

The Harm Principle: “The only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others”.
Absolute Sovereignty: “Over himself, over his own body and mind, the individual is sovereign”.
Social Tyranny: Mill feared that society itself (collective opinion) could be a more formidable tyrant than a political ruler because it “enslaves the soul” and fetters individuality.
The “Collision with Error”: Even false opinions are valuable because they provide a “clearer perception and livelier impression of truth” through debate.
Value of Eccentricity: Precisely because the “tyranny of opinion” makes eccentricity a reproach, it is desirable for people to be eccentric to break through the tyranny of custom.
Dead Dogma vs. Living Truth: Without being “fully, frequently, and fearlessly discussed,” even a true opinion becomes a “dead dogma” rather than a “living truth”.
Self-regarding: Conduct that affects only the individual; independence is “of right, absolute”.
Other-regarding: Conduct that affects others; society has jurisdiction to discuss or interfere.