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 […]
Category: independence friendly logic
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 […]
EIFL (Domainless Logic)
I saw this post by Mark Lance over at New APPS and he brought up one of the issues that I have recently been concerned with: What is a logical domain? He said: So our ignorance of our domain has implications for which sentences are true. And if a sentence is true under one interpretation and false under another, it has different meanings under them. And if we don’t know which of these interpretations we […]
IF Logic and Cogito Ergo Sum
(∃x∃x) → ∃x Descartes Law If something has informational dependence upon itself, then that thing exists. For example, thinking that you are thinking is informationally self dependent and therefore a thinking thing (you) exists.
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] […]
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 […]
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 […]
Relativity as Informational Interdependence
Ever have the experience of sitting in traffic and believe that you are moving in reverse, only to realize a second later that you were fooled by the vehicle next to you moving forward? You were sitting still, but because you saw something moving away, you mistakenly thought you started to move in the opposite direction. Two different senses may be at work here: your sight and your balance. Lets assume that your balance did […]