2018-04-16 RRG Notes

Our brains automatically categorize things by similarity, regardless of the formal logical rules we set out
This is a good thing
The brain does not treat words as purely logical construsts
Given that, it is a mistake to rely on any system of thinking that relies on you being able to treat words as purely logical constructs
The mere act of creating a word causes your mind to create a category and thus trigger unconscious inferences

An intensional definition is a definition given in terms of other words, as a dictionary does
An extensional definition is a definition given by showing a cluster of objects that share the given property
Both are ways of communicating concepts to others
Both have their limitations
- A complete intensional definition that fully captures a concept is extremely verbose and unwieldy, even for simple concepts
- A complete extensional definition for a concept might require enumerating an infinite set
The strongest definitions use a combination of intensional and extensional communication to draw a boundary that captures a concept
However, even a perfect definition is only instructions for building a concept, not a concept in and of itself
You can't control a concept's intension, because most intensions are applied subconsciously
As a result, you can't make a word mean anything you want - you don't have full control over the meanings your brain assigns to words

The notion of a configuration space is a way of translating object descriptions to positions in a multidimensional space
We can think of individual objects as being positions in a vast multi-dimensional thingspace
We can visualize categories as clouds within this thingspace, encompassing many individual objects
This gives us a way of thinking about what constitutes a "typical" element of a category - it is the object that is closest to the center of the cloud
Visualizing categories in this manner allows us to retain flexibility regarding atypical members of a category
- Instead of arguing whether ostriches and penguins are or are not birds, we can say they're atypical birds, whereas a robin is a more typical bird
Most intensional definitions will have a few exceptions, but they can still be useful if they can broadly demarcate a "cloud of things"

Intensional definitions need only to serve as pointers to similarity clusters
Once we have the similarity cluster in our head, we can think about the cluster directly, without necessarily worrying about whether a particular element of the cluster satisfies every aspect of the intensional definition, or whether the intensional definition captures things outside of the cluster

Our notions of typicality bias our thinking
People say that it is more likely that a disease will spread from robins to ducks than from ducks to robins, presumably because robins are the more "typical" bird
People say that 98 is closer to 100 than 100 is to 98
People take typicality as an inherent property of an object, rather than a property derived from the set that the object belongs to
Kansas is "close" and Alaska is "far away" regardless of where you are, because Kansas is a central state whereas Alaska is a peripheral state
This is another reason to stop pretending that words can be treated as purely abstract classes