Book notes: The Problems of Philosophy

Hey all,

Bertrand Russell. Credit:
Wikimedia Commons.

I just finished reading (or rather, listening to) Bertrand Russell's book: The Problems of Philosophy.  The book was included in project Gutenberg and Librivox, which means it is in the public domain, and you can read it or listen to it for free. 

Whenever I quote text, the bold emphasis is mine, not the author's. Hope you enjoy it! I learned quite a number of new and interesting concepts and insights. Below are some of the notes I wrote, and some interesting bits from the book as well, which I encourage you to read/listen to because it really is very interesting. 

On the Theory of Knowledge

While the idea that we may be dreaming, and that nothing exists in the world except for ourselves, is a logical possibility, there is no good reason to believe so. It is almost like applying occam's razor to this idea. It is a logical possibility, just like the possibility that a flying teapot orbits jupiter and can never be detected by us, but there is no good reason why we should reject the more intuitive explanation: that what we see really is distinct from ourselves, as evident by the fact that unexpected things happen. i.e. indeed, the perceiving self COULD be all there is, and that's still a possibility, but there is no reason why we should accept it in favor of the other common sense explanation.

"In philosophy, again, it seems not uncommon for two rival hypotheses to be both able to account for all the facts. Thus, for example, it is possible that life is one long dream, and that the outer world has only that degree of reality that the objects of dreams have; but although such a view does not seem inconsistent with known facts, there is no reason to prefer it to the common-sense view, according to which other people and things do really exist. Thus coherence as the definition of truth fails because there is no proof that there can be only one coherent system. "

The Laws of thought: "are fundamental axiomatic rules upon which rational discourse itself is based. The rules have a long tradition in the history of philosophy and logic. They are laws that guide and underlie everyone's thinking, thoughts, expressions, discussions, etc.":

They are as follows:

(1) The law of identity: 'Whatever is, is.'

(2) The law of contradiction: 'Nothing can both be and not be.'

(3) The law of excluded middle: 'Everything must either be or not be.'

But there's no reason not to ask why these axioms are considered "self evident"? This takes a similar dimension to the induction fallacy argument.

A Priori, A Posteriori, Analytic, Synthetic

* A priori proposition - i.e. experience cannot suffice to prove it. For example, no matter how many triangles I see and I add their angles, this would never prove that ANY triangle and that ALL triangles have angles that add up to 180. I have to make abstractions and make a "hypothetical" triangle and work my way through a proof that relies on generalizations independent of any potential conceivable sensory experience. Such is also the case with proving that there are infinite numbers, and with pretty much any mathematical proof. The very idea of abstractions means it is not possible for experience to prove the rule. HOWEVER, this does NOT mean that the rule does not have a base in experience!!! A Priori refer to the POTENTIAL to be proven by experience and NOT to whether these abstractions are themselves derived from sensory experience or not.

* A posteriori proposition - i.e. a proposition which CAN be proven by sensory experience. For example, if I say "The earth is round", it is simply possible to go into outer space and see for yourself that the earth is round and this would be definitive proof of the proposition.

* Analytic truths - i.e. truths that provide nothing new to what was already contained in the premises. For example, if I say that "A red shirt is a shirt", I have added no new knowledge by saying that it is a shirt.

* Synthetic truths - i.e. truths that provide NEW INFORMATION added to the premises.

Before Immanuel Kant, it has been argued that synthetic truths can only be derived from empirical evidence. Otherwise, how can you "invent" new facts from input that did not contain them?!! Somehow, Kantt made the argument that all of pure mathematics was made of "SYNTHETIC A PRIORI TRUTHS". i.e. with a set of inputs (the basic premises, which are derived from sensory experience/empirical input) you can make abstractions and PROVE things that are true by necessity and cannot be proven empirically (a priori), even though these truths were not included in the input you put in in the first place (synthetic)!

"The question which Kant put at the beginning of his philosophy, namely 'How is pure mathematics possible? is an interesting and difficult one, to which every philosophy which is not purely skeptical must find some answer. The answer of the pure empiricists, that our mathematical knowledge is derived by induction from particular instances, we have already seen to be inadequate, for two reasons: first, that the validity of the inductive principle itself cannot be proved by induction; secondly, that the general propositions of mathematics, such as 'two and two always make four', can obviously be known with certainty by consideration of a single instance, and gain nothing by enumeration of other cases in which they have been found to be true. Thus our knowledge of the general propositions of mathematics (and the same applies to logic) must be accounted for otherwise than our (merely probable) knowledge of empirical generalizations such as 'all men are mortal'.

"The problem arises through the fact that such knowledge is general, whereas all experience is particular. It seems strange that we should apparently be able to know some truths in advance about particular things of which we have as yet no experience; but it cannot easily be doubted that logic and arithmetic will apply to such things. We do not know who will be the inhabitants of London a hundred years hence; but we know that any two of them and any other two of them will make four of them. This apparent power of anticipating facts about things of which we have no experience is certainly surprising. Kant's solution of the problem, though not valid in my opinion, is interesting. It is, however, very difficult, and is differently understood by different philosophers. We can, therefore, only give the merest outline of it, and even that will be thought misleading by many exponents of Kant's system."

"The physical object, which he calls the 'thing in itself', he regards as essentially unknowable; what can be known is the object as we have it in experience, which he calls the 'phenomenon'. The phenomenon, being a joint product of us and the thing in itself, is sure to have those characteristics which are due to us, and is therefore sure to conform to our a priori knowledge. Hence this knowledge, though true of all actual and possible experience, must not be supposed to apply outside experience. Thus in spite of the existence of a priori knowledge, we cannot know anything about the thing in itself or about what is not an actual or possible object of experience. In this way he tries to reconcile and harmonize the contentions of the rationalists with the arguments of the empiricists. "

"Apart from minor grounds on which Kant's philosophy may be criticized, there is one main objection which seems fatal to any attempt to deal with the problem of a priori knowledge by his method. The thing to be accounted for is our certainty that the facts must always conform to logic and arithmetic. To say that logic and arithmetic are contributed by us does not account for this. Our nature is as much a fact of the existing world as anything, and there can be no certainty that it will remain constant. It might happen, if Kant is right, that tomorrow our nature would so change as to make two and two become five. This possibility seems never to have occurred to him, yet it is one which utterly destroys the certainty and universality which he is anxious to vindicate for arithmetical propositions. It is true that this possibility, formally, is inconsistent with the Kantian view that time itself is a form imposed by the subject upon phenomena, so that our real Self is not in time and has no to-morrow. But he will still have to suppose that the time-order of phenomena is determined by characteristics of what is behind phenomena, and this suffices for the substance of our argument. "

"The fact seems to be that all our a priori knowledge is concerned with entities which do not, properly speaking exist, either in the mental or in the physical world. These entities are such as can be named by parts of speech which are not substantives; they are such entities as qualities and relations. Suppose, for instance, that I am in my room. I exist, and my room exists; but does 'in' exist? Yet obviously the word 'in' has a meaning; it denotes a relation which holds between me and my room. This relation is something, although we cannot say that it exists in the same sense in which I and my room exist. The relation 'in' is something which we can think about and understand, for, if we could not understand it, we could not understand the sentence 'I am in my room'. Many philosophers, following Kant, have maintained that relations are the work of the mind, that things in themselves have no relations, but that the mind brings them together in one act of thought and thus produces the relations which it judges them to have. "

How Science Works

I like to think of this as an early version of Popper's conjectures and refutations ...

"Principles such as the law of gravitation are proved, or rather are rendered highly probable, by a combination of experience with some wholly a priori principle, such as the principle of induction. Thus our intuitive knowledge, which is the source of all our other knowledge of truths, is of two sorts: pure empirical knowledge, which tells us of the existence and some of the properties of particular things with which we are acquainted, and pure a priori knowledge, which gives us connexions between universals, and enables us to draw inferences from the particular facts given in empirical knowledge. Our derivative knowledge always depends upon some pure a priori knowledge and usually also depends upon some pure empirical knowledge. Philosophical knowledge, if what has been said above is true, does not differ essentially from scientific knowledge; there is no special source of wisdom which is open to philosophy but not to science, and the results obtained by philosophy are not radically different from those obtained from science. The essential characteristic of philosophy which makes it a study distinct from science, is criticism."

"Apart from its utility in showing unsuspected possibilities, philosophy has a value -- perhaps its chief value -- through the greatness of the objects which it contemplates, and the freedom from narrow and personal aims resulting from this contemplation. "

I'll leave you with the audiobook :)