Let us assume that logic cleaves the world at its corners. Then everything can be divided into the logically privileged, that which makes up the corners, and the not logically privileged, that which makes up everything else. Where then does the concept of logical privilege fall? If logical privilege is logically privileged, then it describes it as something that is at the corners, and not the content. But then it must describe not have described […]
Tag: logic
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 […]
An Introduction to the Game Theoretic Semantics view of Scientific Theory
What is a scientific theory? In an abstract sense, a scientific theory is a group of statements about the world. For instance the Special Theory of Relativity has, “The speed of light in a vacuum is invariant,” as a core statement, among others, about the world. This statement is scientific because, in part, it is meant to hold in a ‘law-like’ fashion: it holds across time, space and observer. The Popperian view is that we […]
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 […]
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 […]
Argument Structure
Basic argument structure goes like this: Premise 1 Premise 2 ———————– Conclusion Knowing how to argue is great, except when someone you disagree with is proving things you don’t like. In that case you have to know how to break your opponent’s argument or provide an argument that they cannot break. First thing that most people do to break an argument is to attack premises (assuming no fallacies are present). To avoid accepting your opponent’s […]
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 […]