Category: Paradoxes
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The Sorites Paradox, Ship of Theseus, and the smoke that broke the Planet’s back.
Introduction The Sorites Paradox, often called the paradox of the heap, is a classic philosophical riddle that arises from the vagueness of our language. It asks: at what point do small changes make a big difference? If removing a single grain of sand from a heap leaves it still a heap, and repeating this seems…
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Significant Paradoxes: Science, Technology, and Ecology
97 Paradox of Enrichment In laboratory predator-prey systems (e.g., algae and zooplankton), adding extra nutrients seems beneficial but can trigger large-amplitude oscillations leading to extinction. Abundant food lets prey over-populate, predators then explode, prey crash, and predators starve. Real ecosystems show similar instability when fertiliser run-off spurs algal blooms. The paradox warns that interventions geared…
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Significant Paradoxes: Psychology and Behaviour
87 Abilene Paradox Four relatives sit on a Texas porch in blistering heat. Someone suggests driving 53 miles to Abilene for dinner. Nobody really wants to go, but each, fearing disapproval, says “sounds good.” They endure the hot, dusty trip and a mediocre meal, only to discover afterward that none of them actually desired the…
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Significant Paradoxes: Social Choice and Politics
79 Condorcet (Voting-Cycle) Paradox Three citizens rank policies A, B, C such that majority prefers A > B, B > C, and C > A, creating a cycle with no clear winner. Individual rankings are rational; the collective ranking is not. The paradox proves that simple majority voting can violate transitivity, foreshadowing complexities in committee…
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Significant Paradoxes: Economics and Political Economy
61 Jevons Paradox (Rebound Effect) When James W. Jevons studied Britain’s coal industry (1865) he noticed a counter-intuitive cycle: improvements in steam-engine efficiency lowered the cost of using coal-powered machinery, which in turn raised total coal demand nationwide. Efficiency that should have conserved the resource instead accelerated its depletion. Modern energy economics calls this the…
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Significant Paradoxes: Decision Theory and Game Theory
52 Prisoner’s Dilemma Two accomplices are interrogated separately. Each may Co-operate (stay silent) or Defect (betray). Mutual co-operation yields 2 years each; mutual defection 5 years each; unilateral betrayal frees the defector and jails the co-operator for 10 years. Because defection strictly dominates, rational agents defect, landing at 5 + 5 instead of 2 +…
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Significant Paradoxes: Epistemology and Probability
38 Hempel’s Raven Scientific hypotheses are usually universal claims—for example, “All ravens are black.” By standard logic that statement is equivalent to its contrapositive “All non-black things are non-ravens.” Hempel pointed out a tension between that equivalence and ordinary confirmation. A sighting of a black raven clearly supports the hypothesis, yet the contrapositive implies that…
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Significant Paradoxes: Identity and Metaphysics
26 Ship of Theseus The Athenian hero’s ship has planks replaced over decades until none of the original timbers remain. Is it the same ship? If the original planks are reassembled elsewhere, which is authentic? The puzzle distinguishes numerical identity (being one and the same object) from qualitative similarity. Endurantists say the ship persists so…
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Significant Paradoxes: Space, Time, and Infinity
12 Zeno’s Dichotomy Zeno asks you to walk from point A to point B. First you must cover half the distance, then half of what remains, then half of that remainder, and so on. Because the sequence of steps is infinite, Zeno insists the journey cannot be completed. The puzzle trades on an intuitive link…
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Significant Paradoxes: Formal Logic
1 The Liar A single sentence—“This statement is false”—defies binary truth assignment. If it is true, then what it asserts must obtain: the statement is false. Yet if it is false, its content is not the case, which makes it true. The oscillation exposes a basic flaw in applying ordinary two-valued semantics to self-referential assertions.…