Lukowski divides paradoxes into four classes:
These are paradoxes that arise when logical reasoning yields surprising, counter-intuitive results.
Robert Louis Stevenson's 1891 story The Bottle Imp posits a bottle containing an imp that grants wishes. The bottle can only be sold to another at a loss, and if you die while owning it, you go to hell. The paradox is that no one should be willing to buy it for a penny, and knowing this, no one should be willing to buy it for two cents, either. By induction, no one should be willing to buy it for any price, although intuitively we feel like if the price is high enough, it should be safer to buy.
Lukowski 'solves' Newcomb's problem by declaring that the solution is to take only one box, because the flow of causation simply doesn't match the flow of time. Taking two boxes and finding cash in both is not an available option, so there is no conflict.
Many words have been spent on this problem that amount to attempts to fool the oracle. This, I think, is the sort of thing Lukowski means when he says that "Newcomb's problem really touches on human frailties: greed, underestimating other people, tendency to cheat, etc."
On the birthday problem.
Two unintuitive results from geometry.
An improper application of inductive reasoning yields an absurd result.
If seeing a black raven supports the claim that all ravens are black, then so does seeing any non-black non-raven, such as a white shoe.
On the paradox of Aristotle's Wheel.
Lukowski constructs some sequences that have relations similar to those ascribed to the holy trinity.
What is more, we have demonstrated that the concept of Trinity can be conceived of not only in theology but also in the most precise of sciences that is available for man, i.e., mathematics.