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 long as change is gradual and function continuous; perdurantists model objects as four-dimensional entities whose temporal parts differ while belonging to a single “spacetime worm.” Contemporary solutions appeal to constitutional relations (the vessel is constituted by but not identical with its timbers) or to contextual criteria (legal ownership vs museum display). The paradox remains foundational for debates on persistence, personal identity, and artifact ontology.
27 Buridan’s Bridge
Socrates wishes to cross a bridge controlled by Plato, who vows: “If you speak truth, I’ll let you pass; if you lie, I’ll throw you in the river.” Socrates declares, “You are about to throw me in the river.” Plato faces a contradiction: if he throws Socrates in, the statement was true and Socrates should have been allowed across; if he lets him pass, the statement was false and Socrates should have been thrown in. The scenario exposes how self-referential predictions collide with rule-based obligations. Modern logicians classify the utterance as ungrounded—lacking stable truth value—so Plato’s conditional cannot apply. The bridge puzzle illuminates deontic logic’s need to handle sentences that reference their own future status.
28 Omnipotence Paradox (Heavy Stone)
“Can an omnipotent being create a stone so heavy that it cannot lift it?” If yes, it lacks power to lift the stone; if no, it lacks power to create it—either way omnipotence seems compromised. The standard resolution restricts omnipotence to logically possible acts; self-contradictory tasks (making a four-sided triangle, creating an unliftable stone for an all-powerful agent) are dismissed as pseudo-tasks. By clarifying that “all-powerful” does not include the illogical, theologians preserve divine omnipotence while defusing the puzzle.
29 Omniscience & Free Will
If a deity eternally knows you will order tea tomorrow, are you free to order coffee instead? Any deviation would falsify the prior knowledge, contradicting omniscience. Compatibilists answer that divine knowledge is timeless observation: God sees what you freely choose; knowledge does not cause choice. Another reply invokes middle knowledge—God foreknows future contingents without predetermining them. The paradox clarifies different conceptions of freedom (could-have-done-otherwise vs acting from one’s own reasons) and their fit with exhaustive foreknowledge.
30 Brain-in-a-Vat
Imagine technology that removes your brain, immerses it in nutrient fluid, and feeds it electrical signals perfectly duplicating real experiences. You could not tell vat life from embodied life. Therefore, how can you know you are not a vat brain? Skepticism threatens all empirical knowledge. Externalist responses argue that words like “tree” refer via causal history; in the vat you lack that history, so the skeptical hypothesis undermines its own meaningfulness. Alternatively, one may retreat to modest foundational beliefs (e.g., “seems-to-me” statements) or rely on transcendental arguments that the coherence of experience presupposes a stable world.
31 Cartesian Evil Demon
Descartes entertains a malicious spirit deceiving his senses and even arithmetic. Stripped of trust in perception and reason, he finds one certainty: the act of doubting proves he exists as a thinking thing. From “I think, therefore I am,” Descartes rebuilds knowledge—first of mind, then of God (as a guarantor against systematic deception), and finally of the external world. The demon experiment inaugurates modern epistemology, framing the challenge of global skepticism.
32 Meno’s Paradox
“How will you search for what you do not know? If you recognise it, you already know it; if you don’t, you won’t recognise it when found.” Plato answers via innate recollection: souls possess prenatal knowledge, and learning is recollecting latent truths. Contemporary epistemology counters with observation, experimentation, and concept acquisition—showing inquiry proceeds by hypothesis and feedback, not by prior possession of all truths.
33 Euthyphro Dilemma
Is an action good because the gods will it, or do the gods will it because it is good? If goodness is mere divine fiat, morality is arbitrary; if morality is independent, the gods are redundant as moral authorities. Modern theists often propose that God’s nature (necessarily good) grounds moral facts, fusing voluntarism and moral realism. Non-theists cite the dilemma to defend morality’s autonomy from religion.
34 Problem of Induction
All observed swans have been white; therefore all swans are white. Induction generalises from past cases, yet its reliability cannot be proved without circularity: justification would itself use inductive assumptions about future resemblance to the past. Hume’s challenge endures. Pragmatists defend induction as a policy that has worked; Bayesians recast it as probabilistic updating; philosophers of science invoke uniformity principles anchored in the success of science, though ultimate rational grounding remains contested.
35 Goodman’s “Grue”
Define grue = “green before 1 Jan 2100 and blue thereafter.” Every emerald observed so far is both green and grue. Purely from past observation, which predicate—green or grue—should we project forward? Good-man shows that evidence alone cannot choose; we require a notion of law-like or entrenched predicates. Debates now explore simplicity, natural kinds, and Bayesian priors as ways to privilege some descriptions over gerrymandered ones.
36 Lottery Paradox
It is rational to believe of ticket #1 that it will lose (probability 0.999 999); likewise for every other ticket. Yet believing all such propositions together implies believing “no ticket wins,” contradicting certainty that one ticket must win. The puzzle reveals that high-probability rational acceptance is not closed under conjunction. Proposed fixes raise the threshold for acceptance, adopt paraconsistent belief sets, or replace outright belief with graded credence.
37 Gettier Problem
Smith has strong evidence that “Jones owns a Ford.” Smith therefore believes “Either Jones owns a Ford or Brown is in Barcelona.” Unknown to Smith, Jones recently sold his car, but by coincidence Brown is in Barcelona, making the disjunction true and justified—yet intuitively Smith lacks knowledge. Gettier cases reveal that justified true belief is insufficient; additional conditions (truth-tracking, safety, anti-luck) are needed. No consensus has ended the post-Gettier quest for a flawless analysis of knowledge.
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