---
title: "Empiricism"
chunk: 5/7
source: "https://en.wikipedia.org/wiki/Empiricism"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:39:07.136928+00:00"
instance: "kb-cron"
---

[Mill] claimed that mathematical truths were merely very highly confirmed generalizations from experience; mathematical inference, generally conceived as deductive [and a priori] in nature, Mill set down as founded on induction.  Thus, in Mill's philosophy there was no real place for knowledge based on relations of ideas.  In his view logical and mathematical necessity is psychological; we are merely unable to conceive any other possibilities than those that logical and mathematical propositions assert. This is perhaps the most extreme version of empiricism known, but it has not found many defenders.
Mill's empiricism thus held that knowledge of any kind is not from direct experience but an inductive inference from direct experience.  The problems other philosophers have had with Mill's position center around the following issues: Firstly, Mill's formulation encounters difficulty when it describes what direct experience is by differentiating only between actual and possible sensations.  This misses some key discussion concerning conditions under which such "groups of permanent possibilities of sensation" might exist in the first place.  Berkeley put God in that gap; the phenomenalists, including Mill, essentially left the question unanswered. 
In the end, lacking an acknowledgement of an aspect of "reality" that goes beyond mere "possibilities of sensation", such a position leads to a version of subjective idealism. Questions of how floor beams continue to support a floor while unobserved, how trees continue to grow while unobserved and untouched by human hands, etc., remain unanswered, and perhaps unanswerable in these terms. Secondly, Mill's formulation leaves open the unsettling possibility that the "gap-filling entities are purely possibilities and not actualities at all".  Thirdly, Mill's position, by calling mathematics merely another species of inductive inference, misapprehends mathematics.  It fails to fully consider the structure and method of mathematical science, the products of which are arrived at through an internally consistent deductive set of procedures which do not, either today or at the time Mill wrote, fall under the agreed meaning of induction.
The phenomenalist phase of post-Humean empiricism ended by the 1940s, for by that time it had become obvious that statements about physical things could not be translated into statements about actual and possible sense data.  If a physical object statement is to be translatable into a sense-data statement, the former must be at least deducible from the latter. But it came to be realized that there is no finite set of statements about actual and possible sense-data from which we can deduce even a single physical-object statement.  The translating or paraphrasing statement must be couched in terms of normal observers in normal conditions of observation. 
There is, however, no finite set of statements that are couched in purely sensory terms and can express the satisfaction of the condition of the presence of a normal observer. According to phenomenalism, to say that a normal observer is present is to make the hypothetical statement that were a doctor to inspect the observer, the observer would appear to the doctor to be normal.  But, of course, the doctor himself must be a normal observer. If we are to specify this doctor's normality in sensory terms, we must make reference to a second doctor who, when inspecting the sense organs of the first doctor, would himself have to have the sense data a normal observer has when inspecting the sense organs of a subject who is a normal observer. And if we are to specify in sensory terms that the second doctor is a normal observer, we must refer to a third doctor, and so on (also see the third man).

=== Logical empiricism ===