Concepts and judgment

Overview §

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 $P$, then it’s a $Q$.”
  • Or, logically: $\forall x,P(x)⟹Q(x)$
• The meaning of this statement seems to depend on what concepts $P$ and $Q$ we substitute in. E.g. with $P\mapsto \mathrm{red}\mathrm{thing},Q\mapsto \mathrm{colored}\mathrm{thing}$, it’s a good a judgment, whereas $Q\mapsto \mathrm{rectangular}\mathrm{thing}$ 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 $1\to 2$ to $2\to 1$ (think of concepts as functions of judgment). Sellars then extended this to flip $2\to 3$ to $3\to 2$ (think of judgments as functions of the inferences we make).

Sellars §

We normally think of logically-valid inferences (e.g. $A\wedge B⟹B\vee C$) 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.

Footnotes §

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