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Sometimes I hear examples of paradoxes, like The Grandfather Paradox: if you went back in time and killed your grandfather then you wouldn't have been born, so you couldn't go back to kill your grandfather, which means you couldn't have killed your grandfather, so you would have been born so you could go back and kill him, etc.

Whenever I've heard other people interpret paradoxes, they have always seemed to interpret a paradox as a problem that needed to be solved, they seemed to put effort into looking deeper and finding a way that you could, for example, go back to kill your grandfather.

For me, paradoxes seem like a simple counterexample, or a proof against an idea.

When I hear an example like the grandfather paradox, I interpret it as a counterexample to "going back in time", or a proof that "going back in time" is not possible.

So I think that paradoxes are counterexamples, while other people seem to think that paradoxes are problems that need to be solved.

Are these other people irrational? Or am I missing something?

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    Contradiction is not just a counter-argument but a defeating argument. If a claim leads to contradiction, then the claim cannot be true. A paradox on the other hand leads to only an apparent contradiction. Usually paradoxes are resolved by specifying previously unspecified conditions of the scenario. – MichaelK Apr 13 '18 at 15:58
  • Granfather paradox does not immediately results in inability to go back in time, though. It does result in inability to change the present by moving to past. – rus9384 Apr 17 '18 at 19:06
  • Nice question. I share your view. But paradoxes vary. Some are a proof of contradiction and therefore a proof of the absurdity of the view that gives rise to them, but some are errors of language or thought that may be resolved. So perhaps there's no right answer and the decision has to be made on a case by case basis. –  Apr 19 '18 at 10:15

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I think the confusion comes from the word paradox, which unfortunately has two usages.

What you're describing sounds like a method called "reductio ad absurdum" , which I wouldn't normally call a paradox. It's a proof method in philosophy and mathematics where you draw a contradiction and use that to unwind an assumption -- because that assumption leads to a contradiction.

I can see why someone might call it a paradox...

But If you look at google's definition of paradox: a seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true. This is not going to be counterproof for anything.

If anything, it's something where on a shallow analysis, it seems false but on a deeper analysis it makes sense. E.g., if you want someone to like you, stop trying so hard. This seems wrong since it's sounds like it's saying "don't pursue your goal to succeed in your goal" but if you think about it more, it's really pointing out that desperation and/or clingy behavior doesn't make people want to be around you. (Who would want a spouse that begs them every day to like them?)

virmaior
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    +1, It might be worth noting that a paradoxical conclusion might lead us to question the premises. If we find that the premises and inferences seems more certain than the conclusion seems dubious, we should accept the conclusion. In some cases (in particular examples from Math like the Banach-Tarski paradox), what the paradox reveals is that we’re misinterpreting certain concepts, perhaps adding some additional “intuitive constraints” that do not apply in this context. (Similar to what @MichaelK mentions in a comment.) – Dennis Apr 13 '18 at 18:21
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    I've always liked to follow Quine's (I believe it's his anyway) terminology, where something that seems at first unpalatable, Skolem's paradox or as Dennis points out the Banach-Tarski paradox, should be referred to as a paradox and something like Russell's or Richard's or König's should be called an antinomy. If the premises are true and the conclusion is also true but surprising and nonintuitive, like Skolem's, then it's a paradox. If the premises are all true but the conclusion is false, then it's an antinomy and one of the premises is actually false, we just need to figure out which one. – Not_Here Apr 13 '18 at 19:19
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    @Not_Here I believe that comes from Quine's "The Ways of Paradox". Quine seems to use "antinomy" specifically for "falsidical paradoxes" that produce "a self-contradiction by accepted ways of reasoning". There's an article on the distinction by Paul Weingartner where he attributes the distinction to Quine, and Quine doesn't cite anyone in "The Ways of Paradox" (not that he was especially diligent in citation), so I think you're right. – Dennis Apr 13 '18 at 20:58
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I agree completely with your notion of a paradox. A paradox is an impossible conclusion from combining two ideas and it shows us that one or more of the two ideas can't be true.

Another way of putting it: a paradox is a syllogism in which the first two premises seem acceptable, but the third statement reveals an absurdity. Knowing a paradox means knowing that one or more of the first two premises are incorrect in some real way.

Let's put my analysis against the first four Google-search paradoxes.

"He has discovered that stepping back from his job has increased the rewards he gleans from it."

1 (unstated): Rewards result directly from effort.

2: But he did less.

3: His rewards increased. ABSURD!

"A potentially serious conflict between quantum mechanics and the general theory of relativity known as the information paradox" (Described here)

1: Information can't come out of a black hole. (Relativity)

2: Information can't be lost. (Quantum mechanics)

3: Black holes eventually disappear. (Hawking radiation)

ABSURD: Where's the information?

"The mingling of deciduous trees with elements of desert flora forms a fascinating ecological paradox"

1: Deserts have cacti, not deciduous trees.

2: This is a desert.

3: Here are deciduous trees. ABSURD!

Would "A set of all sets that do not contain themselves" contain itself? (Russel's paradox)

1: Here is a set of all the sets that don't contain themselves.

2: This set doesn't contain itself, by definition.

3: Therefore, this set must contain itself, by definition. ABSURD!

elliot svensson
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Paradoxes have driven (rather than ended a branch in) the development of science, maths, all sorts. See https://en.wikipedia.org/wiki/List_of_paradoxes

Consider Olbers paradox, a simple thought experiment that proves the universe cannot be static. The EPR paradox, revealed new fundamental physics, and showing the old rather than the new ideas were paradoxical in reality.

Schroedinger's Cat, draws attention to problems with reconciling small and large scale physics, which is still in some senses an outstanding paradox. The Fermi Paradox is another case of drawing attention to gaps between expectation and observation, which also absolutely requires 'solving' or reconciling.

The idea that a paradox is a counter-argument relies on assuming https://en.wikipedia.org/wiki/Law_of_excluded_middle But reality has shown many many times, an elegant capacity to embody things we thought were paradoxes, like wave-particle duality.

CriglCragl
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A paradox like the Grandfather paradox is not a contradiction, it is the reduction of a premise to circularity. In this case, it is the suppressed premise that there is only one sequence of causation -- the premise of physical determinism.

Only if you then assert that premise do you have a contradiction. In this case, in universes where a single deterministic timeline holds, then, there really is no paradox. Either you cannot go back in time, or if you do go back in time to kill you Grandfather, you already did so, and you cannot succeed.

But we do not really have proof this is such a universe. So to make that deduction is really begging an important question.

More direct paradoxes like the liar paradox, or the Berry Paradox or even the sorites paradox for instance do not point out a premise you did not insert.

The premises they render circular are automatic assumptions about language, that no one ever states. To assert the problematic premise and precipitate the inherent contradiction, you would have to deny the ability to refer meaningfully to arbitrary timeless, stateless true statements with discrete referents. But this is a reflex deeply embedded in our basic grammar and logic. We would find it impossible to make definitions without these premises.

(In restricted domains, like math, I assert one should do just that. But even there, I am in a tiny minority.)

It would make normal language insanely difficult to use correctly. So they remain paradoxes.

  • I disagree that the sorites paradox is just an unnecessary criticism of the workings of language, specifically. The sorites paradox (paradox of the heap) reminds us not to place undue weight on vague categories (like "a heap", "orange", or "tall"): where something is important, we need it to have a definite category. This is the basic premise of measurement as used in commerce, and also science. – elliot svensson Apr 17 '18 at 15:18
  • @elliotsvensson You may wish to dismiss the other two as 'unnecessary criticism'. But I did not do so. I think all three of these encode important assumptions about reference that we can't really get rid of. Negation is just not clear, there is not necessarily a first of anything, and all quantitative measures have an implicit, unconquerable vagueness. –  Apr 17 '18 at 21:18
  • I thought that you were saying that a person talking too much about the sorites, liar, or Berry paradox is engaging in unnecessary criticism of language... and I'm saying I think we learn an important thing at least from the sorites paradox--- I think that sorites is necessary criticism of language. It sounds like I seriously misapprehended what you were saying. I do think that we can make good use of what we learn from the sorites paradox, specifically. That's why extended descriptions are common in purchasing: I don't just want "a car", I want a specific car. – elliot svensson Apr 17 '18 at 21:53
  • @elliotsvensson Well you remain wrong about what I said, making these comments pointless. –  Apr 18 '18 at 19:03
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The Grandfather paradox comes up in science fiction.

There are four solutions that I found in science fiction:

  1. The time loop. You go back in the past, make changes, and somehow the changes affect the future in exactly the right way to make you go back in the past, make the same changes etc etc etc.

  2. The impossibility. Not the impossibility of time travel, but the impossibility of making the change. You can go back in the past, but something, somehow will prevent you from killing your grandfather.

  3. Multiple universes. You don't travel back in time, but you travel into a different universe that looks exactly like ours 50 years ago. Since it is a different universe, there is no paradox. In half the universes a visitor killed your grandfather so you don't even exist. In the other half you visit another universe and kill someone there looking like your grandfather.

  4. The laws of physics don't like it. You try to build a time machine, something will destroy it. If necessary, your sun turns into a nova and wipes out your planet including the time machine. If you put the plans on a spaceship and sent it off to a neighbouring star, more novae and more planets wiped out. The time machine won't be built.

gnasher729
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The Grandfather paradox is not actually a paradox because that situation is not possible.

Time travel is a movie concept and that's it.

"Going back in time" is not possible not due to a possible paradox resulting from that but because time is was a concept created to be able to measure the speed differences in state changes, it is a logical construct using various measurements in order to sequence events.

Also, there is no such thing as time dilation. Time was conceived as constant exactly so we have a good scale for measuring differences. In Einstein's formulas, it is not the time that varies it is the space that compresses or decompresses in situations of different gravimetric interactions. Time cannot be altered because it is not a physical construct but a conceptual one.

A ruler that has centimeters on it, although it was designed also as a measurement system can be altered because it is a physical object. For example it will contract or compress because of temperature variations.

Therefore, I can say that time travel in an absurd concept (and more and more scientists agree to this), it's like saying we can do a 'current travel' in a wire.

I also do not consider Schroedinger's Cat a paradox. In that case it's all about how you display the problem. Not knowing a result does not mean it is in both states, it means you just don't know it's state. Think of a school test. You do the test, but you do not know the result. The professors checks the test and gives you the score accordingly. That's the end of it. You obtained a score (let's say 90) based on what you completed on a paper. That cannot change. The paper sits in the professor's desk with the score on it. The fact that you are not yet informed of your score and that you can assume you either got a 90 or an 80 does not change anything, does not influence the result and does not mean you have both 90 and 80. Therefore, your knowledge about the state of the Cat is irrelevant for the Cat.

So as you can see, to use a paradox as a counter-argument it must first not be a pseudo-paradox.

Overmind
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  • Can you give an example of a paradox? –  Apr 17 '18 at 06:13
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    Time dilation absolutely does happen, and quantum variables are fundamentally different e.g. https://physics.stackexchange.com/questions/284724/how-do-we-know-a-quantum-state-isnt-just-an-unknown-classical-state You are practically a Flat Earther – CriglCragl Apr 17 '18 at 11:05
  • Also https://en.m.wikipedia.org/wiki/Closed_timelike_curve – CriglCragl Apr 17 '18 at 11:06
  • Time dilation is an absurdity as large as saying in math sometimes 1 can equal more or less than 1. It will in time be proven deadly wrong, just like many things along the evolution of physics. – Overmind Apr 18 '18 at 13:01
  • @Jimmy Smith - People gave up almost all their liberties in the name of freedom. – Overmind Apr 20 '18 at 08:39
  • So by definition a paradox requires the reader to be unable to interpret language accurately, or means that the reader has some fundamental inability to understand reasonable statements? –  Apr 20 '18 at 08:53
  • The effect of time dilation is strong enough that it can be measured. The clocks on GPS satellites are about 30 nanoseconds off every day; exactly the effect predicted by the formulas for a clock moving at high speed, and the opposing effect predicted by a clock being further away from earth's gravity. – gnasher729 Sep 11 '22 at 12:53
  • And on the microscopic level, things are in two (or an infinite number) of states. An electron circling around the atom's kernel isn't just in an unknown position, it is in an infinite number of positions with certain probabilities. There are experiments that can distinguish this. – gnasher729 Sep 11 '22 at 12:56