Descartes' demon scenario demonstrates that even deductively valid chains from seemingly certain premises can fail to produce certainty if foundational beliefs are themselves vulnerable to doubt.

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Certainty(Rosmini, NE, vol. 3, 1044): A firm and reasonable persuasion that conforms to the truth; a characteristic of the person who knows
Deductively valid(as used in logic): An argument where the conclusion *must* be true if all the starting claims (premises) are true. There's no wiggle room—it's airtight logic.
Demon scenario(as a method of testing what we can truly know): A thought experiment where Descartes imagines an all-powerful evil demon that deceives him about everything he perceives, raising the question: how can we be certain about anything if we might be completely fooled?
Descartes: # Descartes René Descartes was a French philosopher and mathematician from the 1600s who fundamentally changed how people think about knowledge and the mind. He's famous for the idea "I think, therefore I am" (cogito ergo sum), which means that the very fact that you can think proves you exist—a foundation for modern philosophy. He also invented the coordinate system used in mathematics (the x and y axes on a graph), which connects geometry and algebra in practical ways we still use today.

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