This is a summary of a talk I attended at Stanford by Douglas Hofstadter (well known for his authorship of *Gödel, Escher, Bach: An Eternal Golden Braid*). He prefers lecturing without notes. I found it interesting/challenging to sort and summarize the main points of an improvised talk. Enjoy!

The label of a category can be anything from a conjunction to the essence of a situation

A paradigm for the situational label is *Danny at the Grand Canyon*.

Hofstadter’s family traveled to see the Grand Canyon. As Hofstadter turned his entranced gaze away from the great abyss, he rested his eyes on his son. His 1 year old son, Danny, sat facing away from the Grand Canyon and staring at ants. He was a child so young that he had no idea of distance. **This situation can be generalized** to the idea of focusing on what you’re interested in (and are capable of focusing on), harboring little interest in what others consider as gems.

Similarly, **idioms are categories**:

Left hand doesn’t know what the right hand is doing $\equiv$ One part of an organization is contradicting the other

Tail wagging a dog $\equiv$ small things have inordinately large control over a situation.

**Conjunctions (logical connectives) are categories**:

The conjunction “/” ($\equiv$ “slash”) is two things that aren’t quite exclusive combined together. Formally, let $A$ and $B$ be categories, a slash denotes ${A \cup B : A \cap B \neq \varnothing}$. For example: they’re a bimbo/self-marketing genius.

We may consider ourselves as each having a unique, private repertoire of categories (memories and thoughts)

We are a composition of public and private repertiores. The action of categorization is at the core of cognition. The difference between humans and other animals is the snowballing of categories; we continue to accrete categories to our repertiore through analogy.

These categories begin as a singleton: a set with one member. They evolve and blur into analogies as we add experiences to our private repitiores. This blurring may be coined as “pluralization”.

Reminders are analogies: unconscious thought pushed into consciousness by a situational queue.

**The evolution of a category:**

$$\text{Singleton}\rightarrow\text{Superimposed idea}\rightarrow\text{Pluralization}\rightarrow\text{Label}$$

He defines **intelligence **as** the ability to put one’s finger on the essence of a situation rapidly. **In other words, finding propelling analogies quickly.

Circumstances that evoke the choice of a category are extremely subtle

Without getting bogged down in examples, subtlety in is demonstrable in the difference between appropriate use-cases of “go to school” and “go to the school”.

- “I have to stop by the school today to pick up my spectrometer.”
- “Ender, you must go to school today.”

Many of cognitive science’s esoterics are bastardized versions of terms inherited from formal logic

**
**In mathematics,

*predicate logic*is an umbrella term for symbolic formal systems, informally, a predicate is a statement that is true or false depending on the values of its elements.

However, *predicate calculus* is “a general system of logic that accurately expresses a large variety of assertions and modes of reasoning”, capturing the essential logical structure of a complex idea independent of its elements.

The proposition *Matvei loves Ubuntu *can be represented by a predicate calculus in the form:

[Relationship between elements]([Subject element], [Object element])

However, a predicate calculus does not emit a yes or no. Likewise, **category membership is not a boolean**. Membership is fuzzy: the strength of membership is on a spectrum including central and peripheral membership of a given category.

*Sidenote: Hofstadter realized that meaning had a contextual dependence after he decided that his mathematically based notion that “all that matters in language is truth and falsehood” was incorrect.*

Often, meaningful sounding questions are in fact meaningless due to ill-defined terms

When queried: *How many languages do you know? *He answers, “I’m $\pi$lingual”.

$\pi$lingual not in the sense that his knowledge of language is transcendental. Instead, $\pi$ is the result of summing of pieces of languages he knows into blurred fractions.

Before the question is meaningful, the questions *What does it mean to know?* let alone *What does it mean to know a language? *must be addressed.

Is it an efficient way to equate the meaning of 2 sentences to represent a network of word-relationships as a weighted graph? Or is this a seemingly logical but meaningless question due to fuzzy definitions?

My question, left unanswered/as an exercise for the reader.

Sources:

*Cognitive Science: An Introduction to the Study of Mind* Jay Friedenberg, Gordon Silverman