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27 votes
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Why is Aristotle's objection not considered a resolution to Zeno's paradox?

Aristotle's solution was largely accepted until the end of 19th century when Cantor and Dedekind formalized the notion of continuum in terms of set theory. Under their interpretation time is in fact ...
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13 votes

Are there any philosophy books for an intelligent nine-year-old?

Sophie's World: A Novel About the History of Philosophy (Worldcat link) might be better for an 11 or 12 year-old, but is worth mentioning. It follows a 14 year-old girl who starts wondering about ...
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12 votes

Why would this not resolve the Sorites paradox?

Your proposed solution does not solve the paradox. The whole point of the paradox is that the term 'pile' is vague. That is, given an object (e.g. a collection of grains of sand) it is indeterminate ...
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12 votes
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What the Preface paradox tells us about the principle of explosion

I agree with Just Some Old Man's answer, but to expand on it a little... If we think of all the statements in the textbook as propositions A1, A2, ..., An then the situation we are trying to describe ...
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11 votes

Are there any philosophy books for an intelligent nine-year-old?

When I was young I really enjoyed the books of logician Raymond Smullyan, who wrote several books of logic puzzles held together with minimal but amusing narratives, including The Lady or the Tiger? ...
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11 votes
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Is a set containing itself already a paradox?

Russell's paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of ...
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10 votes

Could it be possible that the universe doesn't exist?

I believe it is impossible. I recommend you read (if you haven't already) Descartes' meditations where he famously concludes I think therefore I am - http://www.sacred-texts.com/phi/desc/med.txt: ...
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10 votes
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Are there rules for dealing with self-reference "paradoxes" in logic?

The same effect can be achieved with a single sentence:"This sentence is false". It is known as the Liar paradox and goes back to an ancient sophist Epimenides. Your two sentences simply split the ...
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10 votes
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What's the current status of the "paradox of analysis"? And are there any strong and widely accepted resolutions?

A good paper to read on this subject is an old classic: Gilbert Ryle's Systematically Misleading Expressions. (Proceedings of the Aristotelian Society, 32: 139-170 (1932). Also in his Collected Papers,...
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9 votes

Are all paradoxes reducible to one "fundamental" paradox?

You might find Graham Priests book The Limits of Thought helpful in refining your question. Priest argues that thought runs into true contradictions when it runs up against its own limits This ...
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9 votes
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Was Kant anticipating Gödel's incompleteness in his antinomies?

This reminds me of the older question Was Wittgenstein anticipating Gödel? There is more to it in the case of Kant than there was in the case of Wittgenstein though, at least in spirit. One could ...
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9 votes

Why would this not resolve the Sorites paradox?

This is all about the difference between natural language and formal language. In formal language, a term cannot be used unless it's well-defined according to the standards of the language. In ...
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9 votes

Is finding truth possible?

You've stumbled upon an old problem in philosophy, The Paradox of Inquiry, first formulated in Plato's Meno. The problem can be reformulated as follows: Either you know the answer to a question, ...
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9 votes

What qualifies as the solving of a paradox?

Technically speaking, a paradox isn't a problem to be solved in and of itself. A paradox points at a weakness, misconception, or internal contradiction of the philosophical/analytical structures we ...
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8 votes
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Why would this not resolve the Sorites paradox?

The previous answers betray a lack of familiarity with the literature. Your solution, using the least number principle, essentially works. It is a known argument for epistemism about vagueness, the ...
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8 votes
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Can it be rational to have beliefs one knows to be inconsistent?

It can. Ramsey put it nicely in his "last papers" written around 1929 under the influence of Peirce's pragmatism (quoted from Marion, Wittgenstein, Ramsey and British Pragmatism): "We want our ...
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7 votes

How do mathematicians reconcile that an infinite set does not have to be larger than its proper subset?

There is a long controversy as to what should count as the "size" of an infinite set, and there provably does not exist a notion that satisfies both the bijectivity principle, a.k.a. Hume's ...
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7 votes
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Is it possible that a question has only two answers?

Answer 1 - 'yes' Suppose I ask, 'Can Tom walk ?' I am asking about the truth-value of the proposition, 'Tom can walk'. I expect the answer 'Yes' or 'No'. The answer, 'Yes', is right if Tom can walk ...
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6 votes

What's the difference between a contradiction and a paradox?

Paradoxes are indeed invalid arguments, but what makes them special is that they rest on seemingly unproblematic assumptions. We know, for example, that Achilles will in fact outrun the tortoise (Zeno'...
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6 votes

Why isn't Cantor's diagonal argument just a paradox?

There is no justification for one or the other. Russell's paradox is a paradox if you believe** in unrestricted comprehension (for each P there is a set {x | P}), or at least if you believe** that ...
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6 votes

Are there any philosophy books for an intelligent nine-year-old?

I think Orwell's Animal Farm can also be a good read for 9 year old. Its not strictly philosophical but still worth a read for every smart kid ( and adult ), I think.
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6 votes

Shouldn't Last Thurdayism be able to be proved wrong by Physics?

I think you're misunderstanding the idea behind "Last Thursdayism" on two fronts. First, as can be seen from the selection of "Thursday", the main point of the posit is to point out a problem in ...
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6 votes
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Is "Intolerance of intolerance" equivalent to the Liar's Paradox?

If you take a really silly literal view of the sentence the statement is a performative contradiction but not equivalent to the liar's paradox. Let's say being intolerant of something is along the ...
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5 votes
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Is the belief "I have Impostor Syndrome" paradoxical?

This isn't a philosophy question per se, but I find it interesting because it can be addressed from a cognitive perspective that targets reasoning, which is on-topic. I don't see a paradox, strictly ...
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  • 5,262
5 votes

Are there any philosophy books for an intelligent nine-year-old?

I don't want to generalize, but when i was 9 years old (also a fan of logic) i loved reading fantasy novels. I'm 19 now and i don't claim to have any knowledge on how to bring up a child, but maybe it'...
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  • 415
5 votes

What is the "simple logical truth" that makes omniscience self-contradictory?

I am not surprised at the confusion because the theorem in question is neither simple nor entirely logical. It is Tarski's undefinability of truth theorem, which says roughly that one can not define a ...
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  • 40.6k
5 votes

Limitless Space

In physics, infinity is usually a sign that our modelling of the physical situation has broken down; generally, the only kind of infinity that is allowed is the potentially infinite; this means that ...
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