# Is anything possible? If so, is it a paradox? **URL:** \ **Category:** Great Debates\ **Created:** [September 17, 2012, 4:09am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941 "2012-09-17T04:09:34Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [September 17, 2012, 6:58pm UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/21 "2012-09-17T18:58:55Z")
The possibility of me being dead yesterday is nada%. ---
**Author:** ![Blaster\_Master](https://avatars.discourse-cdn.com/v4/letter/b/cab0a1/32.png) [@Blaster\_Master](https://boards.straightdope.com/u/Blaster_Master)\ **Post date:** [September 17, 2012, 10:12pm UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/22 "2012-09-17T22:12:47Z")
It’s only really paradoxical if x \<=\> ~x. This is not a paradox because the equivalence doesn’t hold. We’ve already considered one direction. Suppose all things are possible (X), the proposition that not all things are possible is a thing, therefore it is possible that not all things are possible (~X). But if we try the other direction, we don’t get back the original proposition. Suppose not all things are possible (~X), the proposition that all things are possible is a thing, thus either all things are possible is true or false (~X or X), this is a tautology, thus ~X =\> True, which basically tells us nothing, since either truth case for ~X could imply true. IOW, one truth value is self-contradictory, the other isn’t, so it seems to me that the other must be the correct value. Thus, not all things are possible. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [September 17, 2012, 10:15pm UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/23 "2012-09-17T22:15:54Z")
> [@Carmady](#): > > This is a terrible example. > > 500 21’s is just as likely as any other sequence of 500 numbers. Your same argument guarantees that no sequence of length 500 is possible. > > But then what happens when you play 500 times in a row? Wrong-oh! Go ahead and specify, in advance, the sequence of results you desire for the next 500 spins. It Won’t Happen. You are attempting to “pin the tail on the donkey” by pinning the tail to the wall and then painting the donkey on the wall to fit. It isn’t a realistic way of measuring the likelihood of an event. (Gosh, I can tell you who won the last thirty Super Bowl games! How unlikely is that!) You have to specify the results first, and then observe them. ---
**Author:** ![copperwindow](https://avatars.discourse-cdn.com/v4/letter/c/4af34b/32.png) [@copperwindow](https://boards.straightdope.com/u/copperwindow)\ **Post date:** [September 17, 2012, 10:37pm UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/24 "2012-09-17T22:37:21Z")
> [@DrCube](#): > > Some things are physically possible, but so highly improbable that you can consider them impossible. Such as “sprouting wings and flying away” or your house in Scranton quantum tunneling itself onto a prime beachfront spot in Florida. You would have to wait trillions of years for the probability to approach a trillionth of a percent. > > Of course there are biological impossibilities such as jumping to the moon and surviving a nuclear explosion when you’re attached to the bomb casing. Those are really a subset of “physically possible but effectively impossible”. > > Other things are truly physically impossible, such as perpetual motion machines and faster than light communication. > > Other things are logically impossible, such as existing and not existing at the same time, or being truly omnipotent (can an omnipotent being make a rock so heavy he can’t lift it?). > > Of course, lots of people consider the Christian God (among other equally unlikely flavors of deity) to be not only possible, not only probable, but 100% certain, while actually existing in the “physically and logically impossible” categories along with perpetual motion machines and “A and not A”. So if you believe in on of those gods, yeah, anything is possible, including logical impossibilities. My friends defines it as a non-zero percent chance. ---
**Author:** ![Alan\_Smithee](https://avatars.discourse-cdn.com/v4/letter/a/2acd7d/32.png) [@Alan\_Smithee](https://boards.straightdope.com/u/Alan_Smithee)\ **Post date:** [September 17, 2012, 10:54pm UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/25 "2012-09-17T22:54:05Z")
But even something with a zero percent chance can happen. The odds of hitting any _particular_ point on an ideal dartboard are exactly zero (since there are an infinite number of points on a dartboard). That does not mean that you can never hit the dartboard. You need a more rigorous definition of possible and impossible. ---
**Author:** ![copperwindow](https://avatars.discourse-cdn.com/v4/letter/c/4af34b/32.png) [@copperwindow](https://boards.straightdope.com/u/copperwindow)\ **Post date:** [September 18, 2012, 1:25am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/26 "2012-09-18T01:25:44Z")
> [@Alan\_Smithee](#): > > But even something with a zero percent chance can happen. The odds of hitting any _particular_ point on an ideal dartboard are exactly zero (since there are an infinite number of points on a dartboard). That does not mean that you can never hit the dartboard. > > You need a more rigorous definition of possible and impossible. The odds are not zero, Zeno’s paradox explains this. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [September 18, 2012, 1:53am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/27 "2012-09-18T01:53:55Z")
Also, in the real world, there aren’t an infinite number of points on a dartboard. There are only so many atoms: a large, but finite number. Also the tip of the dart is a very large number of atoms wide. Instead of using atoms as a unit of measurement, you can use “width of the dart tip.” A nice sharp dart has a tip about 1/200th of an inch in diameter. Throw it at a 12-inch dartboard, and there are under six million “points” the dart can hit. Increase this a few times if you insist on measuring in less than full-dart-tip-widths. (Impossible: saying “full dart tip widths” five times fast…) ---
**Author:** ![Starving\_Artist](https://avatars.discourse-cdn.com/v4/letter/s/aeb1de/32.png) [@Starving\_Artist](https://boards.straightdope.com/u/Starving_Artist)\ **Post date:** [September 18, 2012, 2:17am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/28 "2012-09-18T02:17:54Z")
I always sort of inwardly roll my eyes whenever I hear some would be motivator (football coach, boss, whoever) declare that “Nothing is impossible”. In truth, many more things are impossible than are possible. For example, no matter how many years go by you can never turn yourself into a 1957 Buick. A street sign will never become a fish. Neither you nor the Sun will exist as you are now forever, nor, as someone alluded to upthread, can you die yesterday. Etc., etc., ad infinitum. ---
**Author:** ![Alan\_Smithee](https://avatars.discourse-cdn.com/v4/letter/a/2acd7d/32.png) [@Alan\_Smithee](https://boards.straightdope.com/u/Alan_Smithee)\ **Post date:** [September 18, 2012, 3:03am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/29 "2012-09-18T03:03:02Z")
> [@copperwindow](#): > > The odds are not zero, Zeno’s paradox explains this. Zeno’s paradox explains that an infinite series can have a finite sum, which is related but separate. From it we can deduce that if an infinite number of points each has a positive finite probability, they can still sum to one, but you cannot deduce (as far as I can tell) that each point has a positive finite probability. Since the probability of hitting one of a finite number of points is one over the cardinality of the number of points, it seems to me that the probability of hitting one of an infinite number of points is either undefined or equal to zero. I’m not a mathematician, but I’m positive I’ve seen discussions of probability on this board in which it was asserted by experts that the probability of selecting any one of an infinite number of points is equal to zero. > [@Trinopus](#): > > Also, in the real world, there aren’t an infinite number of points on a dartboard. There are only so many atoms: a large, but finite number. > > Also the tip of the dart is a very large number of atoms wide. Instead of using atoms as a unit of measurement, you can use “width of the dart tip.” A nice sharp dart has a tip about 1/200th of an inch in diameter. Throw it at a 12-inch dartboard, and there are under six million “points” the dart can hit. Increase this a few times if you insist on measuring in less than full-dart-tip-widths. > > (Impossible: saying “full dart tip widths” five times fast…) That’s why I specified an _ideal_ dartboard. And even if the tip of the dart is a large number of atoms wide, it can change it’s position by an arbitrarily small fraction of that width. Substitute a photon and a mathematically defined boundary, if you prefer. I understand there are some ideas involving Planck measurements that suggest that even for that case there may be some granularity to the universe, but I don’t believe that’s widely accepted in physics. Anyway, it was just meant as a demonstration to show that mathematical probabilities behave in non-intuitive ways, and that both they and _possibility_ need to be rigorously defined for this conversation to have any meaning. Simply defining _possible_ as “having a non-zero probability” isn’t enough. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [September 18, 2012, 3:21am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/30 "2012-09-18T03:21:59Z")
Something is being ignored here. The OP is addressing whether _anything_ is possible, not _everything_. In fact anything is not possible, because some things will contradict with things that have already happened. And as a result, everything is not possible either. ---
**Author:** ![Airman\_Doors\_USAF](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@Airman\_Doors\_USAF](https://boards.straightdope.com/u/Airman_Doors_USAF)\ **Post date:** [September 18, 2012, 3:27am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/31 "2012-09-18T03:27:17Z")
Anything is possible, but only at [zombo.com](http://zombo.com). The only limit is yourself. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [September 18, 2012, 4:58am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/32 "2012-09-18T04:58:27Z")
> [@Alan\_Smithee](#): > > . . . That’s why I specified an _ideal_ dartboard. Fair enough; I did overlook that. I will respond, however, that the ideal doesn’t exist in the real world… > [@](#): > > And even if the tip of the dart is a large number of atoms wide, it can change it’s position by an arbitrarily small fraction of that width. Substitute a photon and a mathematically defined boundary, if you prefer. I understand there are some ideas involving Planck measurements that suggest that even for that case there may be some granularity to the universe . . . Well, you don’t need Planck granularity. Just note that electron orbits are quantized, and that electron orbit interactions are what are involved in real physical encounters between physical objects. The tip of the dart cannot hit “between” two distinct electron orbits. It’s like saying that there are an infinite number of ways two Hydrogen atoms can combine to form a Hydrogen molecule. In fact, nope, there are only a very, very few. (Only one under ordinary conditions.) The number of states that the universe can exist in – and the motion of every atom produces an entirely new state – may be a really big number (by our standards) but it is finite. As a friend likes to say, take every place where there might be a particle or not, and raise two to the power of the number of such places. That is how many possible universes there are. Enough for any particular human purpose…but still finite! (And a real mathematician would note, "My goodness, that’s a very small number!) ---
**Author:** ![That\_Don\_Guy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/that_don_guy/32/538_2.png) [@That\_Don\_Guy](https://boards.straightdope.com/u/That_Don_Guy)\ **Post date:** [September 18, 2012, 9:05pm UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/33 "2012-09-18T21:05:26Z")
If “anything” is possible, then it would be possible for something not to be possible, which would contradict the condition that “anything” is possible. Therefore, there is at least one thing that is not possible. ---
**Author:** ![Kozmik](https://avatars.discourse-cdn.com/v4/letter/k/8dc957/32.png) [@Kozmik](https://boards.straightdope.com/u/Kozmik)\ **Post date:** [September 19, 2012, 1:39am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/34 "2012-09-19T01:39:15Z")
> [@DrCube](#): > > Other things are logically impossible, such as existing and not existing at the same time At one time, though, _everything_ did not exist. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [September 23, 2012, 2:44am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/35 "2012-09-23T02:44:05Z")
> [@Kozmik](#): > > At one time, though, _everything_ did not exist. We can’t know that. Anyhow, as stated, things that violate the laws of physics are, inherently, intrinsically not possible (e.g. There is _zero_ chance that matter and antimatter colliding would spit out a pack of Skittles, instead of annihilating each other). Also, it goes without saying that anything that’s possible is possible. But this isn’t useful or insightful. Now, we can sit here and argue over philosophical and epistemological points and counter-points all day, but just because you can define anything you can imagine having a non-zero chance of occurring, due to some far-out, astronomical, quantum occurrence, isn’t meaningful at all (e.g. A random occurrence of atoms forming a living, breathing Chewbacca in Rhode Island). Indeed, entropy will continue to make things more and more unlikely/impossible. ---
**Author:** ![Siam\_Sam](https://avatars.discourse-cdn.com/v4/letter/s/d78d45/32.png) [@Siam\_Sam](https://boards.straightdope.com/u/Siam_Sam)\ **Post date:** [September 23, 2012, 3:12am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/36 "2012-09-23T03:12:43Z")
It is not true that anything is possible. If that were true, then it would be possible for at least one thing not to be possible, so that alone would obviate the saying. Forgive me if this has been covered upthread already. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [September 24, 2012, 2:50am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/37 "2012-09-24T02:50:27Z")
> [@Siam\_Sam](#): > > It is not true that anything is possible. If that were true, then it would be possible for at least one thing not to be possible, so that alone would obviate the saying. . . . Not sure if meta-possibility is in the same category as ordinary possibility. What does it mean, exactly, to say “It is possible that it is possible that X?” ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [September 24, 2012, 4:48am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/38 "2012-09-24T04:48:41Z")
I just wanted to note that I think I may have used the Chewbacca Defense when it comes to existential philosophy. Chewbacca is not possible, Therefore, anything is not possible. The defense rests. ---
**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\ **Post date:** [September 24, 2012, 5:54am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/39 "2012-09-24T05:54:34Z")
Is it possible that one really is equal to two (sans division by zero)? ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [September 24, 2012, 6:10am UTC](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941/40 "2012-09-24T06:10:09Z")
> [@cmyk](#): > > I just wanted to note that I think I may have used the Chewbacca Defense when it comes to existential philosophy. > > Chewbacca is not possible, Therefore, anything is not possible. The defense rests. Why isn’t Chewbacca possible? All in all, he seems more plausible than a lot of things that are theoretically possible. Big, furry, growly guy with surprising technical skills? My old high school shop teacher! > [@For You](#): > > Is it possible that one really is equal to two (sans division by zero)? Another meta-question: is it fair to exclude contradictions by definition? It seems to be trivial to argue: “One is defined as being not equal to two; since one cannot equal two, therefore not everything is possible.” And yet, if we do exclude contradictions by definition, then some might argue, “You’re just arguing that ‘anything possible is possible,’” and thus accuse us of winning the debate by exactly the same kind of sophistry. Shall we indulge in defining levels of impossible? The impossible, level one, consists of things which are defined to be impossible. Red can’t be blue; one can’t be two; morble-whoosh cannot equal not-morble-whoosh. Setting that aside, is there an “impossible, level two?” [Previous page](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941.md?page=1) [Next page](https://boards.straightdope.com/t/is-anything-possible-if-so-is-it-a-paradox/634941.md?page=3)