Our knowledge as to physical objects depends throughout upon this possibility of general knowledge where no instance can be given. And the same applies to our knowledge of other people's minds, or of any other class of things of which no instance is known to us by acquaintance.
In chapter ten, Russell succinctly describes our capacity for a priori knowledge. He holds that our knowledge of the physical world is available only indirectly through an inference from acquainted sense-data. Our use of inference depends on the possibility that we can know something without direct experience.
The man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions that have grown up in his mind without the co- operation of consent of his deliberate reason.
Russell theorizes that the value of philosophy appears in its very uncertainty. He criticizes any mode of thought that is closed to speculation or theory about possibility. Philosophizing allows us to see ordinary things in unfamiliar light. By exercising curiosity, we enlarge our sense of the world and our sense of wonder when we abandon the "tyranny of custom." Here, as elsewhere, Russell sounds a note that echoes the famous Socratic dictum: "The unexamined life is not worth living."
We have first to distinguish knowledge of things and knowledge of truths. In each there are two kinds, one immediate and one derivative. Our immediate knowledge of things, which we called acquaintance, consists of two sorts, according as the things known are particulars or universals. Among particulars, we have acquaintance with sense-data and (probably) with ourselves. Among universals, there seems to be no principle by which we can decide which can be known by acquaintance, but it is clear that among those that can be so known are sensible qualities, relations of space and time, similarity, and certain abstract logical universals. Our derivative knowledge of things, which we call knowledge by description, always involves both acquaintance with something and knowledge of truths. Our immediate knowledge of truths may be called intuitive knowledge, and the truths so known may be called self-evident truths. Among such truths are included those which merely state what is given in sense, and also certain abstract logical and arithmetical principles, and (though with less certainty) some ethical propositions. Our derivative knowledge of truths consists of everything that we can deduce from self-evident truths by the use of self-evident principles of deduction.
In a dense technical summary, Russell outlines all of the sources of knowledge that he discusses in The Problems of Philosophy. Reading this carefully will help to orient and interconnect all of his individually treated concepts.
The free intellect will see as God might see, without a here and now, without hopes and fears, without the trammels of customary belief and traditional prejudices, calmly, dispassionately, in the sole and exclusive desire of knowledge—knowledge the free intellect will value more the abstract and universal knowledge into which the private accidents of history do not enter, than the knowledge brought by the senses (which depend on) an exclusive and personal point of view and a body whose sense-organs distort as much as they reveal.
Here again Russell discusses the value of philosophy but he also reveals his metaphysical hierarchy. Universal knowledge is privileged above knowledge of particulars. He implies that we do not have proper knowledge without a process of reason, without an intellect freed by thought. Our senses offer our only direct access to a world of "private accidents" and they distort even that knowledge.
(a) When a thing of a certain sort A has been found to be associated with a thing of a certain other sort B, and has never been found dissociated from a thing of the sort B, the greater the number of cases in which A and B have been associated, the greater is the probability that they will be associated in a fresh case in which one of them is known to be present; (b) Under the same circumstances, a sufficient number of cases of association will make the probability of a fresh association nearly a certainty, and will make it approach certainty without limit.
This is a statement of the the principle of induction. Russell formulates it in two parts. He develops this principle from observing our expectations about the future. On this principle, the greatest degree of certainty about things that are unknown is that the more often it is the case that A signifies the occurrence of B, the more probable it is that the instance will also be the case in the future.