We normally think that the content of judgments are dictated by the content of the concepts used inside of them. This feels especially right for artificial languages:

  • Take “If it’s a , then it’s a .”
    • Or, logically:
  • The meaning of this statement seems to depend on what concepts and we substitute in. E.g. with , it’s a good a judgment, whereas would no longer be a good judgment.

However, Kant turned this around. In this view, judgments are prior (in the order of understanding) to concepts.

The prior tradition

Traditional logic up until Kant thought of everything in terms of classification. There were three levels:

  1. Logic/semantics starts with concepts,
    • These are classified as particular or general
    • e.g. “red” (general), “colored” (general), “ball” (particular)
  2. …then built up a notion of judgments,
    • These are classified say when one judgment falls under another.
    • e.g. “the ball is red”, “red is subsumed by colored”
  3. … then built up a doctrine of conquences of syllogisms.
    • These tell you what sorts of inferences you can make.
    • e.g. “If x is red, then x is colored”.

Kant flipped the order to (think of concepts as functions of judgment). Sellars then extended this to flip to (think of judgments as functions of the inferences we make).


We normally think of logically-valid inferences (e.g. ) as something we understand prior to particular inferences (e.g. “If it’s red and triangular, then it’s triangular or heavy”). Sellars calls these particular inferences material_inferences and argues that it is only through understanding them that we could understand logically-valid inferences.

One argument for our initial intuition is that the logically-valid inferences are a priori, whereas the particular inferences are a posteriori.1 However, What the Tortoise said to Achilles articulates that, although the logically-valid inferences exist a priori as abstract mathematical/syntactical objects, without having any practical experience of actually making inferential moves we don’t have access to them qua inferences.


  1. The words priori and posteriori literally make the order clear.