## Notes

### 1: Introduction

Lukowski divides paradoxes into four classes:

- Paradoxes of Wrong Intuition
- Paradoxes of Ambiguity
- Paradoxes of Self-Reference
- Ontological Paradoxes

### 2: Paradoxes of Wrong Intuition

These are paradoxes that arise when logical reasoning yields surprising, counter-intuitive results.

#### 2.1: Bottle Imp Paradox (Stevenson's Bottle)

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.

#### 2.2: Newcomb's Paradox

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."

#### 2.3: Paradox of Common Birthday

On the birthday problem.

#### 2.4: Paradox of Approximation and Paradox of the Equator

Two unintuitive results from geometry.

#### 2.5: Horses' Paradox

An improper application of inductive reasoning yields an absurd result.

#### 2.6: Hempel's Paradox (Raven, Confirmation)

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.

#### 2.7: Paradoxes of Infinity

##### 2.7.1: Aristotelian Circles Paradox

On the paradox of Aristotle's Wheel.

##### 2.7.2: Holy Trinity Paradox

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.

### Reading notes

### Review by Weber

Zach Weber writes that "If Łukowski’s monograph were the only book to collect together most of the well-known paradoxes, then there would be much to recommend it." (Weber2012) This sums up my thoughts, so far.

### Bibliography

[Weber2012] Weber, Zach (2012). Piotr Łukowski, Paradoxes, Tr. Marek Gensler. Reviewed By, *Philosophy in Review*, **32(4)**, 307-309.