On the Possibility of Basic Concepts

TODO Excerpt from Blanché

What is “Basic”

vs. “Foundations”


Ala Kant and Aristotle

E.g., some potential candidates

  • togetherness
  • belonging
  • collection
  • symmetry
  • self
  • other
  • alterity
  • relatedness
  • space
  • time
  • order
  • conjunction
  • disjunction
  • inference
  • negation
  • affirmation
  • being
  • nothingness


Given some set of concepts, how do we determine which ones are basic?

Suspected solution

Constructivist Inferrentialism

TODO Excerpt from Paul Hertz’s Axiom Systems
TODO Excerpt from Martin-Löf’s Constructive Mathematics and Computer Programming


This is not a project of foundations: we needn’t claim that our basic concepts are the basic concepts; they needn’t transcendent force. This is an exercise in axiomatics: we are searching for a minimal set of concepts which suffices for the construction of all others (that we happen to want to make use of).


Sample concepts under concern
  • togetherness
  • relation
  • conjunction
  • symmetry
  • sameness

I suspect there is no single correct constructive genealogy, but there is at least one (the flat genealogy where all concepts are root ancestors). And we can guess at something like this:

  • relation
    • sameness
      • symmetry
    • togetherness
      • conjunction

re: Type Theory

As Martin-Löf says explicitly, ITT is explicitly following in the Kantian tradition of trying to deduce categories of the understanding from judgments.

Our aim is to extend this beyond judgment/cognition, to other forms of thought such as inquiry, instruction, speculation, and poetization.