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Epistemological Puzzles
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The Surprise Examination Paradox involves a teacher announcing there will be a surprise test next week, leading to a logical contradiction.
The paradox suggests a surprise test is impossible since students could predict the last day for the test and it wouldn't be a surprise. Solutions involve understanding the nature of surprise, temporal logic, or the context of the announcement as affecting the capability to anticipate the test.
The Paradox of the Raven purports to show that observing a green apple can confirm the hypothesis that all ravens are black.
The paradox arises from the use of logic in confirmation theory where 'All ravens are black' is equivalent to 'All non-black things are not ravens'. Observing a non-black non-raven (like a green apple) does logically confirm the hypothesis. Resolutions include questioning the principles of confirmation theory or suggesting that some evidence is more useful than others.
The Münchhausen Trilemma challenges the possibility of proving any truth, stating that all justifications can lead to one of three problems.
This trilemma suggests that any knowledge claim can be based on either circular reasoning, infinite regress, or unprovable axioms. Potential resolutions include foundationalism, which accepts basic beliefs as self-evident, coherentism, which seeks to build a web of mutually reinforcing beliefs, or embracing the uncertainty as a fundamental aspect of human knowledge.
The Gettier Problem demonstrates that having a justified true belief may still fail to be knowledge.
The Gettier Problem indicates that classical definitions of knowledge as 'justified true belief' are not sufficient. Proposals to resolve this include adding a fourth condition to preclude luck (e.g., a 'no false lemmas' condition), or redefining justification.
The Paradox of Analysis concerns the possibility of an informative analysis of a concept without ending up in a circular explanation.
This paradox poses the problem that a satisfactory analysis seems to state nothing new, as it should be equivalent to the concept. One route to resolution may involve distinguishing between linguistic and informative equivalences, thereby allowing for informative, non-circular analyses.
The Paradox of Fitch’s Knowability poses that for any truth, we must be able to know it exists, which leads to a conflict with the existence of unknown truths.
Fitch's paradox asserts that if all truths are knowable in principle, then all truths are known. Some resolutions entertain the idea of rejecting the principle of knowability or distinguishing between potential and actual knowledge to reconcile with the existence of unknown truths.
The Lottery Paradox arises when considering that, while each lottery ticket is unlikely to win, one must win, conflicting with the rational belief that no individual ticket will win.
This paradox illuminates the conflict between high probability and certain belief. One way to approach the paradox is by distinguishing between 'reasonable to believe' and 'rational certainty', such that it's reasonable to believe each ticket will lose, but not rationally certain.
The Problem of the Criterion questions how we can know without criteria and how we can establish criteria without already knowing.
The Problem of the Criterion highlights a circular relationship between knowing criteria and applying them. Responses include skepticism about our knowledge, methodism (starting with criteria), particularism (starting with known instances), or accepting a kind of epistemic circularity.
Zeno's paradoxes, such as Achilles and the tortoise, challenge the concepts of infinity and continuity in space, time, and motion.
Zeno’s paradoxes ostensibly show logical inconsistencies in our understanding of movement and time. Nowadays, resolutions are typically provided by calculus, specifically through the concept of limits and infinite series, which allows for an infinite number of events to occur in a finite period.
The brain in a vat thought experiment suggests that we might be deceived into thinking our experiences are reality when they could be simulations.
This thought experiment raises questions about how we can know the external world. Responses vary from skepticism (we can't really know), to pragmatic arguments (acting as if the external world is real is the most practical option), or using arguments like Descartes' evil demon, 'Cogito, ergo sum,' to prove existence.
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