Knowledge is always provisional, never final. Karl Popper's fallibilism rejects the search for ultimate sources of knowledge—no authority, text, or tradition provides certainty. Instead, knowledge consists of conjectures that get refined through systematic criticism and testing. This doesn't mean all beliefs are equally valid, but rather that the path to truth runs through error correction, not proclamation.

Science's essence isn't prediction—it's good explanations. Prophecies predict outcomes without explaining mechanisms. Theories explain how systems work, which enables prediction as a byproduct. This distinction matters because explanatory depth determines a theory's reach and usefulness across contexts. When we confuse correlation with causation or mistake accurate prediction for understanding, we limit our ability to solve novel problems.

How we think matters more than what we think. Tim Urban's framework distinguishes the spectrum—our positions and beliefs—from the ladder—our thinking processes. The spectrum represents what we think, which isn't very important. The ladder represents how we think, which determines everything. High-rung thinkers want to be right in the long term; low-rung thinkers want to win now.

Paradigms are universally recognized frameworks that provide model problems and solutions for communities of practitioners. Thomas Kuhn showed that science progresses not through steady accumulation but through revolutionary shifts when old paradigms can't accommodate new observations. Between revolutions, normal science optimizes within existing frameworks. During revolutions, fundamental assumptions change.

Consciousness poses philosophy's deepest mystery—how does subjective experience arise from physical processes? The "hard problem" isn't explaining cognitive functions like memory or attention, but rather why there's something it's like to be conscious at all. This question bridges philosophy, neuroscience, and fundamental questions about reality's nature.