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Questions tagged [paradox]

This tag is for arguments that produce an inconsistency with common sense.

Paradoxes are interesting, because they often show places where our intuition or logic fail.

Take the Liar Paradox:

The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. As we (viz., the authors) have said it, presumably with the intention of you believing it when it is not true, it is a lie. But then it is true! ... Lying is a complicated matter, but what's puzzling about sentences like the first one of this essay isn't essentially tied to intentions, social norms, or anything like that. Rather, it seems to have something to do with truth, or at least, some semantic notion related to truth.

In this case, a single sentence leads immediately to questions about how we consider truth.

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

It seems to me, perhaps naïvely, that Aristotle resolved Zenos' famous paradoxes well, when he said that, Time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles, and that Aquinas clarified the…
martin
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Motivations for dialetheism?

At the request of the moderators, I've reformulated this question to change the emphasis of the question to something perhaps a little more broad-ranging: Question. What are the major modern motivations for Dialetheism? Context. According to the…
Niel de Beaudrap
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What formal logical systems "resolve" the Liar Paradox?

Short version of my question. What formal logical systems can represent, and seem robust against, the Liar Paradox? N.B. I would like to avoid reference to truth-values, except inasmuch as they provide semantics for the formal system. Specifically,…
Niel de Beaudrap
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Are there any philosophy books for an intelligent nine-year-old?

I would like to buy some books on philosophy for the child of a friend. He is very intelligent and mathematically able and clever for a nine-year-old. I remember near that age really enjoying the idea of logic (in particular syllogisms and some of…
Simd
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Are all paradoxes reducible to one "fundamental" paradox?

I may need to refine this question, since I am mostly grappling with a murky intuition and haven't yet done the real work. When I encounter many of the well-known paradoxes, such as Zeno's dichotomy, Russell's set containing itself, problems of…
Nelson Alexander
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What is the difference between Law of Excluded Middle and Law of Non Contradiction?

In spite of reading the SEP entry under Contradiction several times I have difficulty distinguishing between the two. We can translate the Aristotelian language, with some loss of faithfulness, into the standard modern propositional versions in…
user1207
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What's the solution to Sorites paradox?

Suppose you have a heap of sand. You remove one grain. Is there still a heap? You remove another, until you get down to a heap with three grains, a heap with two grains, a heap with one grain, and finally a heap with no grains at all. But that’s…
ActualCry
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What are the dialetheist semantics for logical negation?

This question is in a sense a follow-up, or elaboration, of the question "What are the motivations for Dialetheism?". Reflecting on the way I phrased that question, and the way I remarked on answers, it has occurred to me that my central confusion…
Niel de Beaudrap
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Could it be possible that the universe doesn't exist?

Could it be possible that the universe doesn't exist? That nothing exists, not even you or me? And by not existing, I mean totally not existing, as in not even existing as a computer simulation, or a holographic projection, or a dream by a God. Not…
just a lil kid
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What is the main message Kierkegaard is trying to deliver in his suicidal quote?

In his journal Kierkegaard wrote: I have just now come from a party where I was its life and soul; witticisms streamed from my lips, everyone laughed and admired me, but I went away — yes, the dash should be as long as the radius of the earth's…
HaneenSu
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Was Kant anticipating Gödel's incompleteness in his antinomies?

Kant's attempts to prove that there's a limit to pure reason based on the existence of antinomies, i.e. pairs of propositions where each one is rational, but the propositions contradict each other. One example is: Thesis: The world has a…
Alexander S King
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Are there rules for dealing with self-reference "paradoxes" in logic?

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false. When contradictions appear in proofs, we have rules to finish out the proof. I believe that the…
hellyale
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Does thermal time hypothesis finally resolve Zeno's paradox?

Is Time Just A Trick Of The Mind? (read article) Carlo Rovelli, one of the founder of Loop Quantum Gravity theory likes to think so. Furthermore wikipedia entry highlights: This position has lead him to face the following problem: if time is not…
user1207
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A Question Regarding Russell's Paradox

Consider the 'set' behind Russell's Paradox: R = { x | x is a set and x ∉ x } in light of Cantor's definition of set ("aggregate"/Menge) in his CONTRIBUTIONS TO THE FOUNDING OF THE THEORY OF TRANSFINITE NUMBERS (Dover edition), By an…
Thomas Benjamin
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Limitless Space

I know many talked about this, however I am not a professional philosopher, rather a mathematician. In mathematics we have the concept of infinity, so we speak about infinitely big things, we compare them, we label and order different kind of…
Euler_Salter
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