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Some logical paradoxes are known to be invalid arguments, so I want to know what are some of the paradoxes based on valid logic in philosophy. So could you identify some of them?

  • Possible duplicate of Can a "real" paradox exist? – Math Bob Feb 26 at 0:48
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    Everybody wants to go to heaven but nobody wants to die. – user4894 Feb 26 at 1:11
  • Why does a god defined as infallible, omnipotent and omnibenevolent, allow childhood leukemia. – Richard Feb 26 at 11:33
  • This may interest you en.wikipedia.org/wiki/L%C3%B6b%27s_theorem . Lobs sentence is the first order analogue of the so called truth-teller sentence, "This sentence is true." The latter can be proved to be true (loosely speaking) with a hand-wavy folksy argument. But Lobs sentence can be proved rigorously. – Tim kinsella Feb 26 at 12:57
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    Read Quine's paper "Ways of Paradox", the term you're looking for is "veridical paradox". Banach-Tarski, Skolem, Hilbert's Hotel, Birthday, Hat puzzle are some standard examples. Veridical paradoxes have true premises and a true conclusion, but seem counter intuitive which is why they're called paradoxes. – Not_Here Feb 28 at 0:58
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Here is a non-comprehensive list of classical paradoxa that are not only surprising (Banach-Tarski-Paradox) or based on misunderstanding (Twin-Paradox, Achilles-Tortoise, Zeno's Arrow), but seem to constitute real problems with the notions involved. There is one paradox, the Skolem-Paradox, which is worth knowing. I purposefully omitted it from the list, since it is debatable whether it belongs there.

For all of these you can find formal analyses.

Semantic Paradoxa

Liar Paradox: Is "This sentence is false." a true or false sentence? (Or look up Revenge Liar if you have more than two truth values). Related: Grelling's Paradox (truth of sentence is replaced by the meaning of a word) and Yablo's Paradox (Replace the circle by an infinite chain).

Curry's Paradox: This one you best look up by yourself. It makes similar trouble as the Liar-Paradox, but contains no negation, and an implication instead.

Epistemic Paradoxa

Fitch's Paradox: If you accept the seemingly innocuous principle that truths are in principle knowable, you somehow can conclude that all truths are already known.

Surprise Paradox: If you announce a surprise test next week, you can use backward induction to show that the test won't happen at all, otherwise it wouldn't been surprising.

Preface Paradox: Rational belief that every sentence in a text/theory is true seems to be different from rational belief in each sentence. (Note the quantifier change).

Vagueness

Sorites Paradox: Removing one straw from a heap leaves you still with a heap. So by backwards induction a single straw is heap.

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    I have to congratulate you, "This one you best look up by yourself," is an extremely novel way of saying "I have no idea what it is but I think it fits here." This is an incorrect answer and shouldn't be accepted; many of the paradoxes you've listed are falsidical, not veridical which is what the OP asked for. – Not_Here Feb 28 at 1:02
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    @Not_here I don't see any falsidical paradoxes here. – Jishin Noben Feb 28 at 8:22
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    There is also no reason to assume that Quine's distinction is authorative. Then, the OP's question is about valid reasoning, so the question is (speaking in Quine's terms) not only about veridical paradoxes, but also antimonies. Lastly, please mind your manners. Wild assumptions are not helpful. – Jishin Noben Feb 28 at 8:38
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I would call Zeno’s motion paradoxes true paradoxes. Rather sensible assumptions lead to rather absurd conclusions.

An arrow can never move because at any given instant it is motionless, and all the motionless instants add up to zero progress through the air.

Achilles can never outrace a tortoise if the tortoise is given a head start. When Achilles reaches the point where the tortoise started, the tortoise has already moved some distance forward. When Achilles reaches that second point, the plodding tortoise has moved forward yet again. And so forth.

For further reading, you can spend many happy hours reviewing attempts to resolve the motion paradoxes by viewing YouTube or reading the entries in the Stanford Encyclopedia of Philosophy.

  • Problem: No such thing as an instant. The instant, just like a pen's point on paper has a defined amount (or duration / space). Adding those up leads to no paradox. – Overmind Feb 26 at 8:14
  • @Overmind - An instant cannot have a duration. This is what 'instant' means. . – PeterJ Feb 26 at 13:28
  • Yes, but it's an artificial concept, it does not exist in practice, just like many other things defined this way. – Overmind Feb 26 at 13:46
  • The issue with the "instant" logic is that by the nature of instants, adding up any number of instant moments of time will not get you any further in the temporal direction. If an instant has no duration, then a series of instants also has no duration, and therefore nothing happens regardless of the amount of instantaneous moments you compare. It's a useless metric. To try to extrapolate off those instants gives you meaningless results. Of course a series of instants results in no motion; because without having any duration, they also add up to no time, no distance in no time doesn't mean – JMac Feb 26 at 20:04
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    zeno conflates philosophy with mathematics and claims a paradox. he's been proven wrong. no paradox. – niels nielsen Feb 27 at 4:14
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What are some true paradoxes in philosophy?

Here’s one I came across recently in the context of a legal argument:

Neccesitas non habet legem

Necessity knows no law.

This of course is a law, in the sense that it lays down a law in the world of laws; but also, notably, in the natural world, amongst natural laws, one might say, necessity, is the only law, and the closer our understanding approaches that ideal, the closer we are to a true law of nature. This might be one reason as to why logic and mathematics is so often seen as true laws of nature, as they can’t be seen otherwise.

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    You're conflating two different definitions of "law". This isn't a veridical paradox, it's a fallacious equivocation. – Not_Here Feb 28 at 1:03
  • @Not_Here: Have a look at Georgio Agambens State of Exception, where he presents a book length exposition of this notion in terms of soverignty. – Mozibur Ullah Feb 28 at 1:06
  • @Not_here: It may not be a pure logical paradox, but nevertheless, it is ‘a true paradox in philosophy’. – Mozibur Ullah Feb 28 at 1:08

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