The illegitimate open-mindedness of arithmetic

We are often told that we should be open-minded. In other words, we should be open to the idea that even our most cherished, most certain, most secure, most well-justified beliefs might be wrong.
We are often told that we should be open-minded. In other words, we should be open to the idea that even our most cherished, most certain, most secure, most well-justified beliefs might be wrong. [More]

Arguments about (paradoxical) arguments

As regular readers know, I understand paradoxes to be a particular type of argument. The post Arguments about (paradoxical) arguments appeared first on
As regular readers know, I understand paradoxes to be a particular type of argument. The post Arguments about (paradoxical) arguments appeared first on [More]

Graphs and paradoxes

A directed graph is a pair where N is any collection or set of objects (the nodes of the graph) and E is a relation on N (the edges). Intuitively speaking, we can think of a directed graph in terms
A directed graph is a pair where N is any collection or set of objects (the nodes of the graph) and E is a relation on N (the edges). Intuitively speaking, we can think of a directed graph in terms [More]

Really big numbers

What is the biggest whole number that you can write down or describe uniquely? Well, there isn’t one, if we allow ourselves to idealize a bit. Just write down “1”, then “2”, then… you’ll never find
What is the biggest whole number that you can write down or describe uniquely? Well, there isn’t one, if we allow ourselves to idealize a bit. Just write down “1”, then “2”, then… you’ll never find [More]

The logic of unreliable narrators

In fiction, an unreliable narrator is a narrator whose credibility is in doubt – in other words, a proper reading of a narrative with an unreliable narrator requires that the audience question the
In fiction, an unreliable narrator is a narrator whose credibility is in doubt – in other words, a proper reading of a narrative with an unreliable narrator requires that the audience question the [More]

The paradoxical intellectualism of Gershom Scholem

Gershom Scholem (1897-1982) is widely known as the founder of the academic study of Jewish mysticism or Kabbalah. In the nearly thirty-five years since his death, Scholem’s star has continue to
Gershom Scholem (1897-1982) is widely known as the founder of the academic study of Jewish mysticism or Kabbalah. In the nearly thirty-five years since his death, Scholem’s star has continue to [More]

A person-less variant of the Bernadete paradox

Before looking at the person-less variant of the Bernedete paradox, lets review the original: Imagine that Alice is walking towards a point – call it A – and will continue walking past A unless
Before looking at the person-less variant of the Bernedete paradox, lets review the original: Imagine that Alice is walking towards a point – call it A – and will continue walking past A unless [More]

Paradoxes logical and literary

For many months now this column has been examining logical/mathematical paradoxes. Strictly speaking, a paradox is a kind of argument. In literary theory, some sentences are also called paradoxes,
For many months now this column has been examining logical/mathematical paradoxes. Strictly speaking, a paradox is a kind of argument. In literary theory, some sentences are also called paradoxes, [More]

The television paradox

Imagine that we have a black and white monitor, a black and white camera, and a computer. We hook up the camera and monitor to the computer, and we write a program where, for some medium-ish shade
Imagine that we have a black and white monitor, a black and white camera, and a computer. We hook up the camera and monitor to the computer, and we write a program where, for some medium-ish shade [More]

Temporal liars

One of the most famous, and most widely discussed, paradoxes is the Liar paradox. The Liar sentence is true if and only if it is false, and thus can be neither (unless it can be both). The variants
One of the most famous, and most widely discussed, paradoxes is the Liar paradox. The Liar sentence is true if and only if it is false, and thus can be neither (unless it can be both). The variants [More]