"A predicate expression is heterological if and only if it doesn't apply to itself, autological if and only if it does. For example, "is monosyllabic", "is a French phrase" and "is three words long" are heterological whereas "is polysyllabic", "is an English phrase" and "is four words long" are autological.
Is "is heterological" heterological?"
"Although it may be true that Marilyn committed suicide and that I don't believe she did, I cannot intelligibly say 'Marilyn committed suicide but I don't believe it.'"
"It is irrational the praise or blame people for what is not wholly within their control: 'ought implies can'. But since our actions stem from our characters, circumstances and casual factors beyond our control, and their outcome is often unpredictable, luck appears to play a large part in determining our character and conduct, for both of which we are morally accountable.
So we are morally responsible for what we can't properly be held morally responsible for."
i.e. you rush to the bathroom realizing you have left the bath water running with the baby in it. If the baby has drowned you have done something awful, and will deserve severe moral condemnation; if the baby has not drowned, you have simply been careless and got away with it.
"Although it may be true that this pill will cure me, and also true that it will cure me only because I believe it will, I cannot believe that it will cure me only because I believe it will."
-The Placebo Paradox
"A line segment can be divided, at least in thought, ad infinitum, by halving it, halving the halves, and so on without end. So it must be made up of infinitely many parts. What is the size of these parts? If it is zero the line would have no length, if it is some non-zero finite size, however small, the line segment would have to be infinitely long."
"If all events are governed by casual laws, then every event can be in principle be predicted. But if that is so, it will be possible to falsify predictions about our own actions by opting not to do something that was predicted. Then they wouldn't be correct predictions after all."
"Authors frequently write in their prefaces that there will inevitably be some errors in the body of the book. If what they write is true, there will be at least one false statement in the book; otherwise the prefatorial claim is false. Either way they are committed to a falsehood, and must be guilty of inconsistency. Yet the claim in the preface seems a perfectly reasonable one to make."
"If offered a choice between flying a glider accompanied by an experienced pilot and driving a Grand Prix car around a racing track, you would choose to fly the glider; but, if offered a choice between driving the racing car and flying a glider solo, you would choose to drive the car. If you are rational, then, given that you prefer the accompanied glider flight to the car drive and the drive to flying solo, you should choose to fly accompanied in preference to flying solo. To choose to fly solo in preference to flying accompanied would therefore be irrational.
But it is not irrational, when offered a choice between flying accompanied and flying solo, to choose to fly solo because you do not want to appear cowardly.
So it is both irrational and not irrational to choose the solo flight over the accompanied flight."
"A man creeps back home after an adulterous assignation, 'feeling a tremendous rakehell, and not liking myself much for it, and feeling rather a good chap for not liking myself much for it, and not liking myself at all for feeling rather a good chap."
"A fair coin is tossed until it lands heads up. If this happens on the nth throw the bank pays the player $(2 to the power of n). The expected or average gain is therefore infinite, and, whatever sum the player pays to play she has the advantage."
"I can be a victim of another's deception but i can also be a victim of self-deception. you cannot succeed in deceiving me if I know what you are up to. So how can I deceive myself? Won't I know what I am up to, and won't this necessarily undermine the self-deception?"
"Over a period of years, in the course of maintenance a ship has its planks replaced one by one - call this ship A. However, the old planks are retained and themselves reconstituted into a ship - call this ship B. At the end of this process there are two ships. Which one is the original ship?"
"A spaceship travels in a straight line. It doubles its speed after half a minute, doubles it again after another quarter of a minute, and continues successively to double it after half of the last interval Where is it at one minute? It is neither infinitely far away, nor at any finite distance either."
"Achilles travels at 8 mph but the tortoise manages only 1 mph. So Achilles has given it a start. At the point where Achilles catches the tortoise he draws level with a fly which proceeds to fly back and forth between them at 20 mph. After another hour Achilles is 7 miles ahead of the tortoise, but where is the fly?
It looks as if it should be possible to calculate its position and determine its direction. But the answer is that it could be anywhere, facing either direction. Working back from any possible position and direction the fly would end up level with Achilles and the tortoise regardless."
"In a town where only one person in ten is black, a man claims he was mugged by a black person. In re-enactments of the scene under comparable lighting with different people playing the assailant, he identified the assailant's race correctly 80% of the time. Members of either race are equally likely to mug.
But if calculated, the chances of him being right about the race of the assailant who mugged him is less than one in three."
random half-excerpts from "paradoxes from a to z" by michael clark.
