Words As Hidden Inferences

  • Our brains automatically categorize things by similarity, regardless of the formal rules we set out
  • 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 this triggers unconscious inferences

Extensions and Intensions

  • An intensional definition is a definition given in terms of other words, like a dictionary
  • An extensional definition is a definition given in terms of a cluster of objects, all of which share some property
  • Both are ways of communicating concepts to others
  • Both have limitations
    • A complete intensional definition is extremely verbose and unwieldy, even for simple concepts
    • A complete extensional definition may require you to enumerate an infinite set
  • The strongest definitions use both extensional and intensional concepts 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
  • Most intensions are applied subconsciously - as a result, you do not, in practice, have the ability to redefine words at will since you don’t have full control over the meanings your brain assigns to words

The Cluster Structure of Thingspace

  • A configuration space is a way of translating object descriptions into positions in a multidimensional space
  • By thinking of objects as positions, we can intuitively think of similarity as distance between objects in this space
  • We can visualize categories as clouds encompassing many individual objects
  • This formalization allows us to visualize the “typical” member of a category as the object that is closest to the center of the category
  • Thinking of categories as clouds with fuzzily defined edges allows us to retain the useful properties of categories, while not getting too hung up about whether atypical members of a category “truly” belong to that category or not
  • Most intensional definitions will have exceptions, but they can still be useful if they can broad demarcate a “zone” within thingspace

Similarity Clusters

  • Intensional definitions need only serve as pointers to similarity clusters
  • Once we have a good idea of what the cluster is, we don’t need the intensional definition any more
  • We can think about the cluster directly, without worrying about whether an example near the boundary of the cluster satisfies every aspect of the intensional definition

Typicality and Asymmetrical Similarity

  • 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 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’ centrality gives it the property of “closeness” while Alaska’s position on the periphery gives it the property of “far away”
  • This is another reason to stop pretending that we can treat words as abstract Aristotleian concepts whose definitions can be manipulated at will