Bertrand Russell’s account of knowledge is one of the forms of Cartesian skepticism. Russell claims that we can never truly know the physical object itself without knowing all its relations and all its qualities. Knowing something would mean knowing all the facts of which a thing is a constituent. From which we would deduce that the world is an interdependent whole and we cannot know a thing without knowing everything in the universe.

Let’s take a piece of chalk. To know that this is a piece of chalk we should not think about the symbol “chalk”, but of predicates that are used to designate a quality such as white, small, crumbly. We have to understand what one would call “being chalk”. What is the meaning of saying that a thing is a chalk?

The Russell’s argument runs as follows.
I do not know for certain that this a piece of chalk.
Assumptions:
1) I do not know these things immediately. My knowledge about these things is based on data, inference from the data.
2) These things do not follow logically from any thing or things that I do know immediately like color or shape.
That if (1) and (2) are true, my belief in knowledge of them must be based on a analogical or inductive argument.
That what is based cannot be certain knowledge.

No inductive generalization can give certainty since the conclusion of the inductive argument does not follow logically from the statements. For example, cold water will freeze faster than hot. Certainty requires probability in all possible worlds, in all possible cases.
Similarly, no analogical argument can give a certainty. For instance, these two things are similar in this way then they can be similar in other ways.
So, we have to be skeptical about knowledge.

For Russell, knowledge requires absolute certainty. To be fully justified in believing a proposition (P) to be true one (S) must be acquainted with all the true propositions in which a thing is mentioned. Justified true belief in “This is a piece of chalk” can only occur if one know what “This is a piece of chalk” stands for.

If knowledge requires absolute certainty, then one can never know with certainty about the world of external objects since:

  1. one can never know with certainty about myself,
  2. one can never know with certainty using any memory,
  3. one can never know with certainty by appeal of five senses.

Bibliography:

  • Bertrand Russell, The Philosophy of Logical Atomism, Lecture 3, “Atomic and Molecular Propositions,” The Monist 29 (Jan 1919), 32-47
  • Bertrand Russell, The Problems of Philosophy (1912). Project Gutenberg, Chp. 5, p. 18–19.