On Categories and Concepts: Hofstadter Talk

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 repertoires. 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 repertoire 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 repertoires. 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.

Meaning is contextually dependent

The communication of ideas usually takes place through language: a stream of symbols flowing out of the mouth/fingers. Before symbolic exchange generates meaning, the situation must be explored and evaluated in the discourse space: a completely context dependent environment.

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

Written on March 11, 2014