Punny Logic

Update 12 Feb: This post had been expanded upon and, after submission, accepted for publication in Analysis published by Oxford University Press. View the final version here. [draft] It is hard to explain puns to kleptomaniacs because they take things literally. On the surface, this statement is a statement of logic, with a premise and conclusion. Given the premise: Kleptomaniacs take things literally. We may deduce the conclusion: It is hard to explain puns to […]

Shaking the Tree

Life often results in situations such that no strategy suggests any further moves. We just don’t know what to do next. In a game of perfect information, where each player knows all the previous moves, this can signal stalemate. Take chess: given both sides know everything that has transpired and have no reason to believe that the opponent will make a mistake, there can come a time when both sides will realize that there are […]

Яandom Logic

If we try to represent tossing a coin or a die, or picking a card out of a deck at random, in logic, how should we do it? Tossing a coin might look like: Toss(coin) → (Heads or Tails) Tossing a die might be: Toss(die) → (1 or 2 or 3 or 4 or 5 or 6) Picking a card: Pick(52 card deck) → (1♣ or 2♣ or … or k♥) This begs asking, do […]

Rock Paper Scissors

Rock Paper Scissors is a game in which 2 players each choose one of three options: either rock, paper or scissors.  Then the players simultaneously reveal their choices.  Rock beats scissors but loses to paper (rock smashes scissors); Paper beats rock and loses to scissors (paper covers rock); Scissors beats paper but loses to rock (scissors cut paper).  This cyclical payoff scheme (Rock > Scissors, Scissors > Paper, Paper > Rock) can be represented by […]

The Non-Reducibility & Scientific Explanation Problem

Q: What is a multiple star system? A: More than one star in a non-reducible mutual relationship spinning around each other. Q: How did it begin? A: Well, I guess, the stars were out in space and at some point they became close in proximity.  Then their gravitations caused each other to alter their course and become intertwined. Q: How did the gravitations cause the courses of the stars to become intertwined?  Gravity does one […]

What are Quantifiers?

What are quantifiers?  Quantifiers have been thought of things that ‘range over’ a set of objects.  For example, if I say There are people with blue eyes this statement can be represented as (with the domain restricted to people): ∃x(Bx). This statement says that there is at least one person with property B, blue eyes. So the ‘Ex’ is doing the work of looking at the people in the domain (all people) and picking out […]

Where Does Probability Come From? (and randomness to boot)

I just returned from a cruise to Alaska. It is a wonderful, beautiful place. I zip-lined in a rain forest canopy, hiked above a glacier, kayaked coastal Canada and was pulled by sled-dogs. Anywho, as on many cruises, there was a casino, which is an excellent excuse for me to discuss probability. What is probability and where does it come from? Definitions are easy enough to find. Google returns: a measure of how likely it […]

The Monty Hall Problem

[check out my more recent Monty Redux for, perhaps, a clearer exposition] The Monty Hall Problem illustrates an unusual phenomenon of changing probabilities based upon someone else’s knowledge. On the game-show Let’s Make a Deal the host, Monty Hall, asks the contestant to choose one of three possibilities – Door One, Two or Three – with one door leading to a prize and the other two leading to goats. After the contestant selects a door, […]