Graphs and paradoxes
A directed graph is a pair
How to be a successful special adviser: five tips
Political advice is the topic of the moment. Added to periodic quarrels about the pay and influence of special advisers, a new US President is putting the final touches to his team of advisers while the British Prime Minister faces an array of conflicting recommendations about Brexit. Advice itself seems to have become politicised.
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 a last one.
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 accuracy of the narrator’s representation of the story, and take seriously the idea that what actually happens in the story – what is fictionally true in the narrative – is different from what is being said or shown to them.
Lying, tells, and paradox
The idea that many, if not most, people exhibit physical signs – tells – when they lie is an old idea – one that has been extensively studied by psychologists, and is of obvious practical interest to fields as otherwise disparate as gambling and law enforcement. Some of the tells that indicate someone is lying include:
Where to eat in San Diego during SfN 2016
In just a few days, the Society for Neuroscience annual meeting will be kicking off in San Diego, California. I’ve had a number of homes in my 48 years; the most recent being the New York/New Jersey area for the last ten years as part of Oxford University Press. But the longest home, and the one I keep coming back to, is San Diego. The weather is perfect, the multi-cultural facets are inspiring, the local universities top-notch, and the food scene is divine.
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 something prevents her from progressing further.
Periphrastic puzzles
Let us say that a sentence is periphrastic if and only if there is a single word in that sentence such that we can remove the word and the result (i) is grammatical, and (ii) has the same truth value as the original sentence.
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, but the meaning of the term is significantly different.
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 of grey G.
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 of the Liar that I want to consider in this instalment arise by taking the implicit temporal aspect of the word “is” in the Liar paradox seriously.
The consistency of inconsistency claims
A theory is inconsistent if we can prove a contradiction using basic logic and the principles of that theory. Consistency is a much weaker condition that truth: if a theory T is true, then T consistent, since a true theory only allows us to prove true claims, and contradictions are not true. There are, however, infinitely many different consistent theories that we can construct.
Fences and paradox
Imagine that you are an extremely talented, and extremely ambitious, shepherd, and an equally talented and equally ambitious carpenter. You decide that you want to explore what enclosures, or fences, you can build, and which groups of objects, or flocks, you can shepherd around so that they are collected together inside one of these fences.
Lying, belief, and paradox
The Liar paradox is often informally described in terms of someone uttering the sentence: I am lying right now. If we equate lying with merely uttering a falsehood, then this is (roughly speaking) equivalent to a somewhat more formal, more precise version of the paradox that arises by considering a sentence like: “This sentence is false”.
The paradoxes of Christmas
While most of you probably don’t believe in Santa Claus (and some of you of course never did!), you might not be aware that Santa Claus isn’t just imaginary, he is impossible! In order to show that the very concept of Santa Claus is riddled with incoherence, we first need to consult the canonical sources to determine what properties and powers this mystical man in red is supposed to have.
Paradox and self-evident sentences
According to philosophical lore many sentences are self-evident. A self-evident sentence wears its semantic status on its sleeve: a self-evident truth is a true sentence whose truth strikes us immediately, without the need for any argument or evidence, once we understand what the sentence means.