In 1912, Bertrand Russell made several claims in his 'Problems of Philosophy'.
Is there any knowledge in the world which is so certain that no reasonable man could doubt it?
Knowledge does not have to be certain so as to be knowledge. This is not to say that one can't say that you are more certain of some of the things that you know than of others. Similarly, a cat does not have to be a dog to be a cat though, no doubt, thanks to co-evolution with our species, cats and dogs have some traits in common- e.g. being able to play with children- while specific cats may show behavior which we normally associate with dogs.
When we apply a predicate to a thing, the thing does not change. What changes is how it is viewed with respect to other things. If a particular cat has more dog like traits than is usual or if a particular proposition is known with greater certainty, then it may be preferred for some particular purpose. But it is not the case that a cat has become a dog or that Knowledge has turned into Certainty.
Russell firmly believed that anything implied by a true elementary proposition is true. If a given set of axioms generate a contradiction at least one of the axioms must be false. The problem here is that the 'intension' of even an elementary proposition (or what we believe is such) can have a different 'extension' as the knowledge base or context changes. I suppose propositions about cats and dogs aren't 'elementary'. Still there may be some more elementary propositions underlying 'my cat is dog-like' and, unless great care is taken or you have a highly ramified type theory, at some point you could get a contradictory statement like 'my cat is a cat because it is a dog.'
This question, which at first sight might not seem difficult, is really one of the most difficult that can be asked.
It is like the question 'why must cats be dogs in order to be cats?' It isn't difficult. It is nonsense.
Berkeley [shows] that the existence of matter is capable of being denied without absurdity,
just as it isn't absurd to say that one's cat is as loyal and devoted as a dog. Also, it bites the postman. On the other hand, though the claim is not absurd, it is absurd to think that other people want to hear about your cat or your thoughts regarding the existence of matter. True, there may be a small number of cat-fanciers or philosophers who do get very excited over such claims. But they don't greatly matter.
and that if there are any things that exist independently of us they cannot be the immediate objects of our sensations.
Why not? A rock exists independently of us. We may trip over that rock. The sensation won't be pleasant.
‘I think, therefore I am’ says rather more than is strictly certain.
It says nothing. It is said.
It might seem as though we were quite sure of being the same person today as we were yesterday, and this is no doubt true in some sense.
'being the same' is a predicate just like 'dog-like'. For some purposes it may be true.
But the real Self is as hard to arrive at as the real table,
only in the sense that the cat that is a dog is difficult to find. 'Real' is a predicate applied to an object. It does not change the object nor does any entity correspond to a name formed by joining the predicate with the object. This may not be obvious. After all, we may speak of 'the real Mona Lisa'. Surely it exists? The answer is no. There is the Mona Lisa. There are copies of the Mona Lisa. Suppose there is an art expert who has been called in to authenticate the painting. He says 'this is it'. He may amplify his statement by saying 'this is the real, hundred percent authentic, item'. But there is no 'authentic Mona Lisa' which is different from the Mona Lisa. True, a poet may say 'the true Mona Lisa is not the painting hanging in the Louvre. It is the memory of mother's smile we will carry with us to our death'. But the poet isn't speaking of the Mona Lisa. He is praising Mummy due to she is so nice.
and does not seem to have that absolute, convincing certainty that belongs to particular experiences.
Because the Real Self may be memory of mother's smile which is the true Mona Lisa of the Human Spirit.
All knowledge must be built up upon our instinctive beliefs,
Where do instincts come from? Presumably, the answer has to do with evolution by natural selection. But no body of knowledge that we have heard of has been 'built upon instinctive beliefs'. The reverse is the case. Careful observation and ratiocination have given rise to knowledge systems.
and if these are rejected, nothing is left.
If you reject your instinct not to take up residence at the bottom of the sea, you will die.
We cannot have reason to reject a belief except on the ground of some other belief.
Nonsense! I reject the beliefs of lunatics even though I don't know what those beliefs are.
Do any number of cases of a law being fulfilled in the past afford evidence that it will be fulfilled in the future?
No. That's why Sherlock Holmes could not solve the mystery of my missing TV remote. Evidence regarding it did not exist back when he was alive.
If not, it becomes plain that we have no ground whatever for expecting the sun to rise tomorrow,
Expectations are based on induction and observation. We expect the planet to continue to go around the Sun. Hopefully, our astronomers will notify us if the Sun shows signs of packing its bags and moving to a nicer part of the Galaxy.
or for expecting the bread we shall eat at our next meal not to poison us, or for any of the other scarcely conscious expectations that control our daily lives.
Our grounds for having expectations is that they are useful to us. It isn't useful to expect not to be poisoned unless there is evidence that somebody is out to get you or that some sort of serial killer is on the loose.
The inductive principle is incapable of being proved by an appeal to experience.
But we can see if it held in the past. Another approach- that of the intuitionist Brouwer- would be to use 'bar induction'. Essentially this aims to prove the existence of properties of infinite sequence by inductively reducing them to finite lists. This could be called 'upward hereditary'. Put simply, there can be a consistent axiom system in which propositions about the future can be proved. It is a different matter that there may be no 'absolute' or even 'natural' proof of anything at all.
Experience might conceivably confirm the inductive principle as regards the cases that have been already examined; but as regards unexamined cases, it is the inductive principle alone that can justify any inference from what has been examined to what has not been examined.
But this could be an argument for Brouwer's 'creating subject'! In any case, no justification is non-arbitrary.
When we see what looks like our best friend approaching us, we have no reason to suppose that his body is not inhabited by the mind of our worst enemy or of some total stranger.
We have no reason to believe we have a best friend. Not in my case. Beyonce really is my bffl. Someday soon she will drop by and braid my hair and ask me to dish about my complicated, on-off, relationship with the photocopier.
Knowledge as to what is intrinsically of value is a priori in the same sense in which logic is a priori, namely in the sense that the truth of such knowledge can be neither proved nor disproved by experience.
Nor can it be gained save at the expense of much burning of the midnight oil and years of study at Collidge.
There is no reasoning which, starting from some simpler self-evident principle, leads us to the principle of induction as its conclusion.
There is no 'self-evident' principle. We trust others with expert knowledge and years of lived experience to formulate such principles and impart them to us in a lucid manner.
All a priori knowledge deals exclusively with the relations of universals.
But the knower is an individual. Knowledge is relation between an individual and a proposition. If a priori knowledge exists it must still involve a relationship between an individual and a proposition. Some propositions may be said to relate to universals- i.e. qualities shared in common by particular things. But these may be deceptive.
Logical principles are known to us, and cannot be themselves proved by experience, since all proof presupposes them.
What we know is that our 'logical principles' are faulty. Moreover, unless there is such a thing as what Godel called an 'absolute proof', then all proofs are more or less arbitrary.
Our immediate knowledge of truths may be called intuitive knowledge, and the truths so known may be called self-evident truths.
Why not just say we have intuitions? Some turn out to be very very wrong. Truth is a predicate we apply to objects. I suppose you may say the things we have faith in are things we consider true. But faith is founded on a mystery, not on anything self-evident. The plain fact is, like doubting Thomas, even if I had sat at the feet of the Lord and witnessed the Resurrection, I would not consider the truths of Religion to be 'self-evident'. I know in my heart that I am a lazy sod. I would look for some excuse to continue a swinish existence. But, God may give me the gift of Faith. Why He would want to must remain a mystery.
All our knowledge of truths depends upon our intuitive knowledge.
Knowledge may be distinguished on the basis of greater or lesser truth, or sweetness, or bitterness, or utility. But this does not mean any piece of knowledge is itself truth or niceness or sweetness or utility. The cat which I consider dog-like is still a cat.
It is felt by many that a belief for which no reason can be given is an unreasonable belief.
No. An unreasonable belief is one it is harmful to have. If the thing is useful, you have reason enough to stick to it.
In the main, this view is just... But let us imagine some insistent Socrates, who, whatever reason we give him, continues to demand a reason for the reason.
We retaliate by demanding a reason we should provide that reason.
We must sooner or later, and probably before very long, be driven to a point where we cannot find any further reason, and where it becomes almost certain that no further reason is even theoretically discoverable.
No. Suppose this 'Socrates' is Peter Drucker (the management guru). He asks- 'what is the reason you are doing such and such?' We give the reply 'to make a profit'. He asks 'why do you want to make a profit'. Eventually, we say 'look, if we don't make a profit, the owners of the company will sack us. No one will hire us. We will starve.' At this point it occurs to us that the owners of the company are the shareholders. We must put aside our internal squabbles and work as a team to increase shareholder value. But this gives us a reason to look at markets from a broader perspective. We begin to see opportunities where previously we saw threats or impediments. Drucker has more than earned the fee we paid him for acting as our Socrates.
Starting with the common beliefs of daily life, we can be driven back from point to point, until we come to some general principle, which seems luminously evident, and is not itself capable of being deduced from anything more evident.
Is this what Russell or other mathematicians actually did? No. The looked at beliefs common in a highly specialized field. Often, as in Russell's case, their hard work caused them- and everybody else- to realize that the belief that motivated them was false. But this was useful.
I am absolutely certain that half a minute ago I was sitting in the same chair in which I am sitting now.
This may be a confabulation. I suppose what Russell meant was 'I'm certain I'm not drunk, mentally impaired or under the control of a hypnotist. My memory is very reliable. Of that I am certain.' However this certainty would not be irrefragable. If video evidence were produced showing that Russell, in an unconscious state, was placed in the chair just ten seconds ago, his certainty would disappear.
Russell's mistake is to think that being certain of something is the same as certainty regarding that something. I am certain my cat is just as devoted and loyal as any dog. Indeed, I may feel it possesses more of any canine attribute than your Fido. But my cat is certainly not a dog.
Going backward over the day, I find things of which I am quite certain, other things of which I am almost certain, other things of which I can become certain by thought and by calling up attendant circumstances, and some things of which I am by no means certain.
But this certainty is open to refutation.
One important point about self-evidence is made clear by the case of memory, and that is, that self-evidence has degrees: it is not a quality which is simply present or absent, but a quality which may be more or less present, in gradations ranging from absolute certainty down to an almost imperceptible faintness.
This is true of any predicate even the existential predicate. My cat does not actually exist. But such a creature could exist. Indeed, at this very moment, it may be that a dear friend has just died and left directions that her cat belongs to me. Thus, I could already have a cat. However my fire-breathing dragon can't exist because, as is well known, dragons only belong to ladies with blonde hair and ample bosoms. Once again we see how institutionalized racism in Sunak's Britain is blighting the lives of bleck peeps.
Truth and falsehood are properties of beliefs and statements:
the are predicates, not properties. Following Frege, we say a predicate is a 'verbal phrase' or general term. A property is the 'intension' of a predicate. What is said about a belief or statement is not itself an 'intension' unless it is a 'nominalization' in which case it has an independent existence. Russell disagreed with Frege- who thought there was some separate 'correlate' in such cases- and thus, for him, to say 'x is true' means x is a truth. The problem here is the intensional fallacy. As our knowledge base changes, x may itself change. Liebniz's law of identity ceases to apply. Thus the truth of a truth may be that it is a lie. Indeed, it isn't even itself!
hence a world of mere matter, since it would contain no beliefs or statements,
men are matter. Speech and the making of statements are material things.
would also contain no truth or falsehood.
Speech and statements utilize predicates. But predicates are not properties save in the sense that if the universe is finite then a property is a n-ary predicate. My point is that the intension of epistemic things changes. It may be that everything knowable is finite and 'at the end of mathematical time' there is just one big n-ary predicate by which all things which can be made the subject of a logical calculus have properties such that no intensional fallacies arise
When we speak of philosophy as a criticism of knowledge, it is necessary to impose a certain limitation. If we adopt the attitude of the complete sceptic, placing ourselves wholly outside all knowledge, and asking, from this outside position, to be compelled to return within the circle of knowledge, we are demanding what is impossible, and our scepticism can never be refuted.
Why not be a pragmatic sceptic? Doubt all things but do what you find useful.
For all refutation must begin with some piece of knowledge which the disputants share; from blank doubt, no argument can begin.
But utility would still exist. In any case, better than 'argument' is 'mimetics'. We do what smart peeps are doing. We ignore their claim to be working selflessly for the betterment of the species.
Hence the criticism of knowledge which philosophy employs must not be of this destructive kind, if any result is to be achieved. Against this absolute scepticism, no logical argument can be advanced. But it is not difficult to see that scepticism of this kind is unreasonable.
It is useful enough. A lot of smart and successful people decided that 'love of knowledge' wasn't itself knowledge. They dropped philosophy in favor of doing something useful. Alexander was Aristotle's pupil. But that isn't why Alexandria is named after him.
Descartes’s ‘methodical doubt,’ with which modern philosophy began, is not of this kind, but is rather the kind of criticism which we are asserting to be the essence of philosophy. His ‘methodical doubt’ consisted in doubting whatever seemed doubtful; in pausing, with each apparent piece of knowledge, to ask himself whether, on reflection, he could feel certain that he really knew it. This is the kind of criticism which constitutes philosophy.
People felt what Descartes was doing was useful. After all, like Russell, he was a mathematician.
It is a remarkable fact that Philosophy- which lost prestige when Darwin toppled Aristotelian telos- not to mention what I can only call Mysticism, suddenly gained great salience at the end of the Nineteenth century. Russell and Brouwer and Einstein reversed Plato's dictum that philosophy involves the study of mathematics. Suddenly, it was the mathematicians, and the mathematical physicists, who were rediscovering metaphysics and making it meaningful. Perhaps that was a false dawn. Only pragmatism could triumph because, as the masses gained political power, only what was useful would attract the best minds and thus burgeon.
If our dreams, night after night, were as coherent one with another as our days, we should hardly know whether to believe the dreams or the waking life.
Many people don't remember their dreams. It may be that some people dream coherently. Indeed, some scientists claim to have found the solution to difficult problems in their dreams. Freud, at around this time, was suggesting that dreams were a 'royal road' into the unconscious. Perhaps 'neuroses' could be cured by talking to a therapist about your dreams. What is certain is this created a lucrative profession.
As it is, the test of coherence condemns the dreams and confirms the waking life.
Only utility matters. If I had nice dreams about dragons I could have made a lot of money- like the guy who wrote 'Game of Thrones'.
But this test, though it increases probability where it is successful, never gives absolute certainty, unless there is certainty already at some point in the coherent system.
That certainty would be arbitrary. I suppose Russell, the logicist, and Godel, the Platonist, sought, in their different ways, for an 'absolute proof'. For Brouwer, perhaps a 'creating subject' was good enough. Everything useful might have good enough 'univalent foundations' but an existential utilitarianism our species may never shake off till scarcity ends or we become 'as Gods'. The Biblical reference is to those who serve on juries. If you are not called on to do so, then 'judge not lest ye be judged'. What is certain, for most of us, is that if we were judged on our deserts, we wouldn't escape whipping.
Russell, however, was an optimist. Human judgment could be perfected because Humanity was perfectible. But perfect justice would be a property of a Paradise on Earth. Mathematical logic would play a part in bringing about this Utopia.
This, at any rate, was what he wrote just before the Great War
The problems of the continuum are closely connected with the problems of the infinite and their solution is effected by the same means.
Russell met Godel around the time he showed the negation of CH was inconsistent with ZF (or ZFC equivalent set theories) and Cohen showed it was independent. Interestingly, both Godel, a Platonist, and Cohen, a formalist, thought CH was false. On the other hand Godel's 'fundamental theorem' (which implies that CH holds for constructible sets) was motivated by Russell's axiom's of reducibility. Godel wrote 'I should also like to mention that the fundamental theorem constitutes the corrected core of the so-called Russellian axiom of reducibility. After all, as was mentioned a while ago, Russell had previously given a construction similar to that of the Mα, but had restricted himself to finite orders. His axiom of reducibility then says that the orders of the sets of every type are bounded by a fixed finite number. He was evidently far from being able to prove that. But it now turns out that if the construction of the orders is continued into the transfinite, the existence of certain transfinite bounds actually becomes provable. That is the content of the fundamental theorem.' Interestingly, Godel considered the early Russell to be a Platonist on the basis of his remark that Logic was in the world like zoology. Did this meant there is a pure and perfect 'not' up in Heaven? Russell attributed this view to Godel. It seems even the disputes of the Logicians can only be resolved at the Court of the Almighty!
The paradoxes of Zeno the Eleatic and the difficulties in the analysis of space, of time, and of motion, are all completely explained by means of the modern theory of continuity. This is because a non-contradictory theory has been found, according to which the continuum is composed of an infinity of distinct elements; and this formerly appeared impossible. The elements cannot all be reached by continual dichotomy; but it does not follow that these elements do not exist.
The problem here is that the continuum hypothesis (CH) hasn't been proved and thus existence proofs which rely on the Axiom of Choice may not actually mean anything. Indeed, its use in specific fields- e.g. Mathematical Econ- may cause hypertrophying intensional fallacies. Social Choice theory, which is as bien pensant as Russell himself, consists of nothing but proofs that all cats are dogs who are also Dictators. To paraphrase Chesterton, proving God doesn't exist opens the door to proving everything is the cat which is the dog which is secretly controlling your mind.
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