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 […]

# Tag: logic

## Dependence Logic vs. Independence Friendly Logic

I picked up Dependence Logic: A New Approach to Independence Friendly Logic by Jouko Väänänen. I figure I’ll write up a review when I am finished with the book, but there is one chief difference between Dependence Logic and Independence Friendly Logic that needs to be mentioned. On pages 44-47 when describing the difference between Dependence Logic and Independence Friendly Logic Väänänen says, The backslashed quantifier, ∃xn{xi0,…,xim-1}φ, introduced in ref. [20], with the intuitive meaning: […]

## 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, […]

## Paradox Analysis

Apropos my earlier rant on people who think that paradoxes are meaningless, I figured I ought to take a stab at giving some meaning to paradox. To this end I reformulated a paradox in my terms. I suppose I should called it the Mirror Paradox, though ‘Looking-Glass Paradox’ seems more lyrical and has an historical nod. My apologies to whoever actually came up with this first, though I am sure I haven’t heard it before… […]

## Are Paradoxes Meaningless?

Aaron Cotnoir has suggested that people think that paradoxes are meaningless. I think they are lucky that they hadn’t suggested that to me unless they wanted to see me freak out. It was my good fortune to have my first real exposure to the work of Frege, Russell and Wittgenstein be from Thomas Ricketts. I can’t remember verbatim what he said, but this is close: No one knows how long it took Frege to understand […]

## Positive and Negative Biological Time

In my biorelativity series I used mutations per generation as a measurement of distance. However, with my recent historical/generative musings, specifically the post on the logical foundations of biorelativity (the logic of which is at the foundation of how I arrived at biorelativity), I fear I may have ignored the distinction between a mutation and an adaptation. Consider an organism with some feature. The feature can be considered both a mutation or an adaptation depending […]

## The Logic of Biological Relativity [draft]

How can we represent biological relativity in logical notation? Organism a is adapting relative to organism b Aab Organism b is adapting relative to a Aba Organisms a and b are adapting relative to each other Aab & Aba This schema is unsatisfactory because it describes the situation from an indeterminate outside perspective: a and b are said to be adapting relative to each other without regard to the observer describing the situation. Relativity applies […]

## The Logic of Relativity [draft]

How can we represent relativity in logical notation? a is moving relative to b Mab b is moving relative to a Mba a and b are moving relative to each other Mab & Mba This schema is unsatisfactory because it describes the situation from an indeterminate outside perspective: a and b are moving relative to each other without regard to the observer describing the situation. Relativity applies to all the perspectives in question (with special […]