THE LIMITS OF PHILOSOPHICAL KNOWLEDGE
Note 1: Perhaps this hope is vain, but in saying so Russell seems to do the very thing he holds is vain. And the fact is that people are interested in philosophy because they want to have answers to general questions, and in particular to such questions as what there really is, what one should do, and how one knows whatever one supposes oneself to know. If there is only one reality, it may be safely inferred that every human being has believed and does believe many falsities about it, but this comes with being human, as does the desire to know answers to general questions about reality, knowledge and conduct. Just as pain is the price one has to pay for living, being mistaken is the price one has to pay for being intelligent. Back.
Note 2: This involves a rather misleading use of the term 'metaphysics', as if there is a - really - rather silly and obscure activity some benighted souls engage in that is 'metaphysics', that necessarily must fail in its aims and pretensions. However, metaphysics is only another name for serious attempts to find knowledge, and science likewise is a serious attempt to find knowledge.
Indeed, historically what we call 'science' is the product of a metaphysics, or perhaps a class of metaphysics, that was mostly founded in the 17th Century, that is organised around two important postulates, that there is an independent reality, and that human beings may come to know it by making guesses about them from which they can derive conclusions they can put to the test of experience, after which they know that their guess is more probable than it was (if one of its conclusions is verified) or false (if one of its conclusions is falsified). This metaphysics is known as scientific realism, and Russell and I are broadly in agreement about it. But it is a mistake it is not itself a theory about what reality is and how human beings may come to know it - which is another name for 'metaphysics'. Back.
Note 3: I agree mostly with what Russell is going about Hegel, but it is a bit unfair to deal with a philosopher whose texts will strike most people as utterly unreadable and ludicrous. Better examples of 'metaphysics' are texts of Plato, Aristotle or Aquinas. These I also mostly disagree with, but any intelligent reader will be able to appreciate that these texts - unlike Hegel's - were written by very great minds indeed, however mistaken they may have been. Back.
Note 4: This formulation clearly brings out an emotional aspect that is involved in much philosophy (for better or for worse): people who do philosophy do so in part to arrive at conclusions they like.
The reader may make up his mind whether he feels inclined to believe a philosophy that makes matter or time or space or evil disappear into illusion or deception. Speaking for myself, I am very distrustful of philosphical, religious or political theories that seem to prove what people knew they like to believe, and it is always wise to remember that from any human being's point of view and convictions, whoever he or she is, and whatever he or she believes, the great majority of other human beings must be fundamentally mistaken in their philosophical, political and religious ideas and values, since every individual is in a minority as regards most of his or her opinions when all human beings are considered. Back.
Note 5: Compare Note 2. Back.
Note 6: The metaphysicians at least used a logically correct method, which indeed is also used by science. The mistake Russell wants to attribute to 'the metaphysicians' is that they did not use the method of experimental science, and did not frame their hypotheses in such a way as to make them empirically testable. This criticism is correct as far as it goes, but if fails to note that science is a metaphysics by itself, that indeed arose in competition with the Catholic and Protestant metaphysics. Back.
Note 7: Here indeed is summarised in a few lines a very fascinating problem of the interdependence of the notions of space, time and infinity, and how these have changed over the past 200 years. Back.
Note 8: To be replaced in this century by Quantum Mechanics as supposed reason for the illusory nature of space and time or reality, which shows, whatever else it shows, that many human beings seem well pleased with arguments that conclude that very much, including space, time and reality, are not at all what they seem to be. Back.
Note 9: This at least is a reasonably accurate statement of what was shown possible in mathematics (and has since been applied in physics). Russell attributes these discoveries to logic because he believed himself to have proved that mathematics followed from logic. This belief few people at present accept. Back
Note 10: This is a good sketch of the scientific method: you may assume what you please, deduce what you can, and compare what you deduce if possible with experience. Back.
Note 11: Indeed. Back.
Note 12: This also seems correct to me, except that, as I have argued, for me universals may be simply given in our experience, and I like to replace phrases like 'wholly a priori principle' by 'assumption based on fantasy' (as contrasted by assumptions based on sensation, which we also need, indeed). Back.
Note 13: I agree, but as I have remarked before, this is a specific philosophy, called scientific realism, that I agree with. There are still plenty of philosophers who disagree. Back.
Note 14: Let's first insist again that this applies to philosophy as Russell sees it or would like to see it rather than to philosophy plain and simple (which, in point of historical accuracy, tends to produce uncritical but pompous apologists and sycophants of political and religious totalitarian systems, or else vain inhabitants of academic institutions, in whose opinions no one is interested except other academic - soi-disant - philosophers, and that only for the money).
Next, what makes the study of philosophy really distinct from that of science is that it is concerned with fundamental questions that concern all human beings and all human societies: what is knowledge, what is reality, at least in broad outlines, what are truth, beauty and probability, and what should human beings do and not do. And a large part of the study of philosophy is, of course, concerned with the answers that have been given throughout known history to these questions, and to the criticisms that have been made of these answers. Back.
Note 15: Indeed. But there is a prior and more harmful criticism of the absolute sceptic: someone who uses language to say that he does not believe anything, believes - it would seem - in language and its efficacy in expressing his doubts. Back.
Note 16: As argued in the previous note, an argument to the effect that all argumentation is inconclusive and nothing can be known seems to be necessarily inconclusive and to presuppose that the language it is stated in is known. Back.
Note 17: Let's agree, amidst these noble sentiments about the fallibility of human knowledge, that one piece of infallible knowledge human beings have is that they are fallible. Back.