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 […]

# Category: game theory

## Wittgenstein and Sun Tzu (on throwing the ladder away)

Wittgenstein, Tractatus Logico-Philosophicus #6.54 My Propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them — as steps — to climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must overcome these propositions, and then he will see the world aright. Sun Tzu, The Art of War, Chapter XI #38 At the critical […]

## New Quantifier Angle-I, and Agent Logic

I was thinking that upside down A and backwards E were feeling lonely. Yes, ∀ and ∃ love each other very much, but they could really use a new friend. Introducing Angle I: Now, Angle I, , is just like her friends ∀ and ∃. She can be used in a formula such as ∀x∃yz(Pxyz). But how should we understand what is going on with the failure of the quantified tertium non datur? With that […]

## 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 […]

## Revision and Hypothesis Introduction

Say we have some theory that we represent with a formula of logic. In part it looks like this: [1] …(∃z) … Pz … This says that at some point in the theory there is some object z that has property P. After much hard work, we discover that the object z with property P can be described as the combination of two more fundamental objects w and v with properties R and S: [2] […]

## Monty Redux

In the Monty Hall Problem a contestant is given a choice between one of three doors, with a fabulous prize behind only one door. After the initial door is selected the host, Monty Hall, opens one of the other doors that does not reveal a prize. Then the contestant is given the option to switch his or her choice to the remaining door, or stick with the original selection. The question is whether it is […]

## Sexual Reproduction

Say you are a single celled organism. To reproduce you have to double your size and then you need to split yourself in half. Repeat indefinitely. Now say you are a single celled organism that has the option to reproduce sexually. To reproduce you need to increase yourself to 3/2 your original size and find a similar mate. Then you both contribute 1/2 to the new organism and repeat indefinitely. Asexual reproduction requires you to […]

## The Deal with ‘Deal or No Deal’

I just saw the hit game show ‘Deal or No Deal‘. It wasn’t the first time, but this episode had a contestant with folksiness to rival Palin, so I was entertained and kept watching. But is there any gamesmanship to the ‘Deal or No Deal’ gameshow? The short answer is: No. The show begins with the contestant choosing a briefcase that contains a number that represents a real monetary amount. The case is chosen from […]

## 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 […]

## Monty Hall Update

I wrote out an example playing of the Monty Hall Problem in Independence Friendly Logic as a game of incomplete information and appended it to my post here. I also left an extended comment on Dependence Logic vs. Independence Friendly Logic about some of the tribulations encountered as a non-academic trying to get my grubby little hands on obscure logic papers.