In the Problems of Philosophy, chapter 10: ON OUR KNOWLEDGE OF UNIVERSALS (p.57 in my book), Russel writes the following:

The thing that seemed mysterious, when we formerly considered such knowledge, was that it seemed to anticipate and control experience. This, however, we can now see to have been an error. No fact concerning anything capable of being experienced can be known independently of experience. We know a priori that two things and two other things together make four things, but we do not know a priori that if Brown and Jones are two, and Robinson and Smith are two, then Brown and Jones and Robinson and Smith are four. The reason is that this proposition cannot be understood at all unless we know that there are such people as Brown and Jones and Robinson and Smith, and this we can only know by experience.

Initially I could not see why Russel argues it to be impossible to know a priori the second proposition involving Brown, Jones, etc. I certainly could understand the proposition even though I did not know the individuals Russell refers to, and I could clearly see its truth despite my ignorance. I thought that given our a priori knowledge of the first proposition involving the universal of two things, or alternatively a couple, shouldn't we by extension, since Brown and Jones, and Robinson and Smith both partake as particular couples of this universal, know a priori the truth of this proposition as well? I mean the principle that the truth of a proposition involving a given particular does not change under the substitution of a particular of said universal felt to me also to be a priori knowable. At this point I realised I was confused and that it probably was because I, in part, grappled with the notion of a priori, so I retraced to Russel's introduction to a priori knowledge in chapter 7: ON OUR KNOWLEDGE OF GENERAL PRINCIPLES (p.41), where he clarifies this notion in the following manner:

[...] all knowledge is elicited and caused by experience, [and] some knowledge is a priori, in the sense that the experience which makes us think of it does not suffice to prove it, but merely so directs our attention that we see its truth without requiring any proof from experience.

I was still befundled so eventually I started thinking about how I interpreted Russell's propositions, especially the second one, and realized finally what I think Russell means with the first paragraph. Due to my estrangement with Brown, Jones and their pals, I had when reading their proposition replaced their names with arbitrary people, i.e. the universal of arbitrary person. As such the proposition I formerly thought dealt with particular individuals was in fact still dealing with universals, i.e. its truth was independent of experience all along. When I instead deliberately thought of the proposition as referring to particulars, which in my case only amounted to names on a paper, I realized that I could not have known this proposition without referring to experience: namely by me having read the proposition on the page. What helped me was forcing myself to interpret the names as proper and as such as referring to some particulars. By doing so I could not have understood the proposition a priori, exactly as Russell clarifies, since my understanding of it could only have come about by acquisition of some experience with regards to the particulars the names refer to, even such superficial experience as scribbles on a paper.

After this insight I shifted my focus to the problem at Russell's hand, namely that of a priori knowledge seemingly anticipating and controlling experience, and it thence became evident what Russell means by this being an "error". For any inferences made from a priori knowledge which do not refer to experience, i.e. to no particulars, can only refer to universals. And this seems like exactly the sort of reasoning I carried out initially: namely inferring from Russell's universal proposition that "if Brown and Jones [the arbitrary individuals] are two, and Robinson and Smith [also arbitrary] are two, then Brown, Jones, Robinson and Smith are four". And as to the principle of substitution I thought countered Russell's reasoning I now see that all it allows me to infer (without referring to experience) from the universal proposition is a proposition of the like: "if particular A and particular B are two, and particular C and particular D are two, then A, B, C, and D are four". i.e. it still deals with universals: namely those of arbitrary particulars.

Now then: have I deluded myself entirely and missed Russell's point by a long shot, or am I onto his meaning? I would be very happy to receive some input on my thoughts and/or alternative perspectives with regards to the text itself.


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