Chapter Ten

[Sundar]

This one was pretty good, I thought, although I still need to push myself through at moments. He begins by breaking down types of universal relations: the easiest to apprehend - those that appear immediately to sense-data, e.g. 'being to the left of something' or 'taking place after something', then next-level meta-relations of e.g. greater or lesser resemblence. Then he states that all a priori knowledge has to do with relations between universals.

I really like this idea and the subsequent application of it to show that e.g. "two plus two is four" is in fact a statement about relations between universals and not about particulars:

“One way of discovering what a proposition deals with is to ask ourselves what words we must understand—in other words, what objects we must be acquainted with—in order to see what the proposition means... In the special case of 'two and two are four', even when we interpret it as meaning 'any collection formed of two twos is a collection of four', it is plain that we can understand the proposition, i.e. we can see what it is that it asserts, as soon as we know what is meant by 'collection' and 'two' and 'four'. It is quite unnecessary to know all the couples in the world: if it were necessary, obviously we could never understand the proposition, since the couples are infinitely numerous and therefore cannot all be known to us. Thus although our general statement implies statements about particular couples, as soon as we know that there are such particular couples, yet it does not itself assert or imply that there are such particular couples, and thus fails to make any statement whatever about any actual particular couple. The statement made is about 'couple', the universal, and not about this or that couple.”

The contrast between this and more inductive generalizations, e.g. as resulting from scientific discovery, was useful. I also liked the mathematical example used to demonstrate this: “.. we may sometimes know a general proposition in cases where we do not know a single instance of it. ”

The summary of what has been covered so far was useful:

“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.”

The final point that knowledge of truths raises the potential for error, unlike knowledge of things, is a valid one, which sets us up for the next chapter, which I expect will begin to explain how we evaluate knowledge of truths.