Today, no one believes that the world was created in BC; but not so very long ago skepticism on this point was thought an abominable crime … It is no credit to the orthodox that they do not now believe all the absurdities that were believed years ago. The gradual emasculation of the Christian doctrine has been effected in spite of the most vigorous resistance, and solely as the result of the onslaughts of Freethinkers A, It is intellectual blindness not to recognize the revolutionary import of early Christianity, whatever the contemporary feeling concerning the sacrament of marriage may be, when it set itself like a wall against the tides of boundless sensuality and impressed upon the Roman world the sanctity of human life.
Kayden , 88 Contrary to what was often said about his personal life, it is also worth noting that Russell did not practice or defend a libertine ethic. As Wood also notes, Perhaps the finest tribute to his success is that few people now even realize the nature of the old ideas. Russell, it must be repeated, was fighting a cruel and indefensible state of affairs where sexual ignorance was deliberately fostered, so a boy might think the changes of puberty were signs of some dreadful disease, and a girl might marry without knowing anything of what lay ahead of her on her bridal night; were women were taught to look on sex, not as a source of joy, but of painful matrimonial duty; where prudery went to the extent of covering the legs of pianos in draperies; where artificial mystery evoked morbid curiosity, and where humbug went hand in hand with unhappiness ….
Russell says much the same thing when he notes that Religion has three main aspects. In the second place there is theology. In the third place there is institutionalized religion, i. Schilpp , —6. As Russell explains, Suppose, for instance, your child is ill. Love makes you wish to cure it, and science tells you how to do so. There is not an intermediate stage of ethical theory, where it is demonstrated that your child had better be cured.
Your act springs directly from desire for an end, together with knowledge of means. This is equally true of all acts, whether good or bad. Instead, they are positively frustrated: If theology is thought necessary to virtue and if candid inquirers see no reason to think the theology true, the authorities will set to work to discourage candid inquiry.
In former centuries, they did so by burning the inquirers at the stake. In Russia they still have methods which are little better; but in Western countries the authorities have perfected somewhat milder forms of persuasion. Of these, schools are perhaps the most important: the young must be preserved from hearing the arguments in favour of the opinions which the authorities dislike, and those who nevertheless persist in showing an inquiring disposition will incur social displeasure and, if possible, be made to feel morally reprehensible.
A, Societies as well as individuals, says Russell, need to choose whether the good life is one that is guided by honest inquiry and the weighing of evidence, or by the familiarity of superstition and the comforts of religion.
Partly this is due to our need to understand nature, but equally important is our need to understand each other: The thing, above all, that a teacher should endeavor to produce in his pupils, if democracy is to survive, is the kind of tolerance that springs from an endeavor to understand those who are different from ourselves.
One of the best summaries is given by Alan Wood: Russell sometimes maintained, partly I think out of perverseness, that there was no connection between his philosophical and political opinions. This was perfectly legitimate, and even praiseworthy, in a world which never stays the same, and where changing circumstances continually change the balance of arguments on different sides.
If they are successful, they carry out the behest of Power, becoming themselves as powerful, in terms of Mr. Even though they spread the good life to millions, the more successful they are, the more usurpatious and dangerous. As a young man, he says, he spent part of each day for many weeks reading Georg Cantor, and copying out the gist of him into a notebook. At that time I falsely supposed all his arguments to be fallacious, but I nevertheless went through them all in the minutest detail.
This stood me in good stead when later on I discovered that all the fallacies were mine. Girard, Kansas: Haldeman-Julius Publications, Muirhead ed. Norton, Slater ed. Pears ed. Schapiro, C. Darlington, Francis Watson, W. Aa, Russell on Ethics , London: Routledge. Ab, Russell on Religion , London: Routledge. A, Russell on Metaphysics , London: Routledge. Rempel and John G. Slater eds.
Lewis eds. Moore ed. Rempel, Andrew Brink and Margaret Moran eds. Rempel ed. Lewis and Mark Lippincott eds. Rempel and Beryl Haslam eds. Bone and Michael D. Stevenson eds. Bone ed. Planned Vol. Ayer, A. Irvine ed. Banks, Erik C. Jackson ed. Broad, C. Klemke ed. Chalmers, David J. Collins, Jordan E. Dewey, John, and Horace M. Kallen eds. Eames, Elizabeth R. Eliot, T. Elkind, Landon D. Feinberg, Barry, and Ronald Kasrils eds. Gabbay, Dov M. Gandy, R. Grattan-Guinness, I. Hager, Paul J.
Hardy, Godfrey H. Hylton, Peter W. Irvine, A. Wedeking eds. Breck, eds. Kayden, Eugene M. Klement, Kevin C. Klemke, E. Kroon, Fred W. Bottani and R. Davies eds. Lapointe, Sandra ed. Link, Godehard ed. Monro, D. Nakhnikian, George ed. Nasim, Omar W. Pears, David F. Potter, Michael K. Quine, W. Ramsey, Frank P. Roberts, George W. It is again perhaps better understood as an endorsement of a methodological maxim. Elkind forthcoming. It should be noted, however, that there is significant controversy over whether, in the end, Wittgenstein himself meant to endorse this metaphysics.
In the Tractatus , the world is described as consisting of facts. The objects making up these atomic basics were described as absolutely simple.
Elementary propositions are propositions whose truth depends entirely on the presence of an atomic fact, and other propositions have a determinate and unique analysis in which they can be construed as built up from elementary propositions in truth-functional ways.
Quine , in which it is claimed that it is only a body of scientific theories that can be compared to experience, and not isolated sentences. However, even in later works growing out of this tradition, the influence of Russell can be felt. Ironically, nowhere is this more true than in the later writings of Wittgenstein, especially his Philosophical Investigations Among other things, Wittgenstein there called into question whether a single, unequivocal notion of simplicity or a final state of analysis can be found e.
Debates regarding the nature of simple entities, their interrelations or dependencies between one another, and whether there are any such entities, are still alive and well. Introduction 2. Because Russell believed it impossible for a finite mind to grasp a proposition of infinite complexity, however, Russell rejected a view according to which the false proposition designated by All numbers are odd.
Similarly, the proposition expressed by Some number is odd. PM , 44 As we have seen, at the time of writing Principia Mathematica , Russell believed that an elementary proposition consisting of a single predicate representing an n -place relation along with n names of individuals is true if it corresponds to a complex. Of course, I should be glad to reach the absolutely simple, but I do not believe that that is within human capacity. What I do maintain is that, whenever anything is complex, out knowledge is advanced by discovering constituents of it, even if these constituents themselves are still complex.
SA , 40 According to Russell, analysis proceeds in stages. In a later work, Russell summarized his position as follows: If the world is composed of simples—i. The stuff would consist of all the simples denoted by names, while the structure would depend on relations and qualities for which our minimum vocabulary would have words. Wittgenstein claimed: 4. Wittgenstein , 89 5. Wittgenstein , The lack of any logical relations between atomic propositions goes hand in hand with a similar view about atomic facts ; each atomic fact is metaphysically independent of every other, and any one could obtain or fail to obtain regardless of the obtaining or not of any other.
Russell writes: When some set of supposed entities has neat logical properties, it turns out, in a great many instances, that the supposed entities can be replaced by purely logical constructions composed of entities which have not such neat properties. In that case, in interpreting a body of propositions hitherto believed to be about the supposed entities, we can substitute the logical structures without altering any detail of the body of propositions in question LA , London: Kegan Paul, AMi The Analysis of Mind.
Griffin and A. London: Unwin Hyman, London: Routledge, EA Essays in Analysis , ed. Cambridge: Cambridge University Press, London: W. Norton, Wittgenstein, Tractatus Logico-Philosophicus. LK Logic and Knowledge , ed. London: Longmans, PE Philosophical Essays. PM Principia Mathematica with A. Cambridge: Cambridge University Press, —27 First edition — First edition London: Williams and Norgate, ROM Russell on Metaphysics , ed. Schlipp, ed. The Philosophy of Bertrand Russell. New York: Harper in Row, Eames and K.
Secondary Literature Austin, J. Sense and Sensibilia , ed. Oxford: Clarendon Press. Ayer, A. Language, Truth and Logic , 2nd ed. Baldwin, Thomas, a. Baldwin, Thomas ed. Bell, John and William Demopoulos, Bostock, David, Bradley, F.
The Principles of Logic , 2 vols. Oxford: Oxford University Press. Carnap, Rudolf, Cartwright, Richard, Cocchiarella, Nino, Elkind, Landon, Elkind, Landon and Gregory Landini, eds. Griffin, Nicholas, Griffin, Nicholas ed. Hager, Paul, Hochberg, Herbert, Hylton, Peter, Klement, Kevin, Philosophy Compass , 5 January , doi Russell , New York: Routledge.
Linsky, Bernard, Livingston, Paul, Lycan, William, Monk, Ray and Anthony Palmer eds. Moore, G. Selected Writings , ed. London: Routledge. Pears, David, Introduction to B. Quine, W. Rorty, Richard ed. Sainsbury, R. Russell , London: Routledge. Simons, Peter, Similarly, that the infinity of the natural numbers is not a mathematical issue follows from the rejection of classes or sets as abstract particulars.
There are many such surprises in Principia Mathematica. Though the conception of Logicism has not changed, it is easy to see that quite a lot happened in the interim between The Principles of Mathematics and Principia Mathematica. For a great many years the interim period has been akin to the dark ages whose role in modern science has only recently come to light.
In this period, Russell worked steadfastly to emulate the impredicative comprehension of cp-Logic in an ingenious substitutional logic of propositional structure. The foundations of the idea to find a substitutional theory to emulate a simple type of universals and thereby classes is already manifest in Appendix B of The Principles of Mathematics itself.
The theory of denoting concepts of The Principles of Mathematics proved to be a quagmire and without the theory of definite descriptions, Russell could not execute the plan for a substitutional theory see, Landini b.
In summary, the whole of Russell philosophical work in mathematical logic may be seen in terms of his trials and tribulations at emulating an impredicative simple-type regimented cp-Logic of universals. Our focus, therefore, is squarely on the evolution of the cp-Logic of Principia Mathematica. When Russell abandoned the propositions of his substitutional theory, he abandoned the idea of a second volume for The Principles of Mathematics.
But he did not abandon hope that an emulation of an impredicative simple-type stratified regimentation of the cp-Logic of universals might still be found. In the introduction to the first edition of Principia Mathematica , Whitehead and Russell propose an informal nominalistic semantic interpretation of the object-language bindable predicate variables. But by , Russell had come to realize that such a nominalistic semantics could not validate impredicative comprehension axioms.
Russell never stopped trying, however. In its second edition, Russell experimented with Wittgensteinian ideas for emulating impredicative comprehension, imagining an altered grammar to accommodate extensionality. Whitehead was not happy with this experiment being included in the new edition since neither he nor Russell intended to advocate it.
Alas, Whitehead was right see, for example, Lowe , Monk Gregory Landini Email: gregory-landini uiowa. Bertrand Russell: Logic For Russell, Aristotelian syllogistic inference does not do justice to the subject of logic. The Substitutional Theory of Propositions pdf 7. References and Further Reading a. John G. Slater London, Routledge, First published in Mind 14 , pp.
Manuscript received by the London Mathematical Society on 24 April First published in The American Journal of Mathematics 30 , pp.
The no-class theory of classes is not quite as straightforward as the theory of classes it replaces. We discuss it in detail in Chapter 3, Section Russell himself does not say that names refer in isolation and predicates do not. Rather, he says that names have meaning in isolation and predicates do not and so are not names and do not refer to objects.
Elsewhere, it means other things for him. This of course is because the no-class theory eliminates classes, not predicates. It is true of some predicates and not of others. But is it true of itself or not? We thus have a contradiction. We can try to use something analogous to the no-class theory to eliminate predicates. For example, we might replace predicates with propositions. Unfortunately there are also similar paradoxes for propositions.
And so on. Fortunately, Russell has another method for avoiding paradoxes called the theory of logical types. Notice that both versions of the Russell paradox arise from self-reference — from allowing a set to be a member of itself or a predicate to apply to itself.
Many other similar paradoxes also arise from self-reference, by allowing sets to be members of themselves, predicates to apply to themselves, propositions to be about themselves, and so forth. The theory of types prevents such paradoxes from arising by banning self-reference. This rule is the theory of logical types.
And the theory of logical types is justified by the vicious circle principle , which says that any sentence formed by a set taking itself as a member or predicate taking itself as an argument is meaningless. By adopting the rule that is justified by this principle, namely, the theory of types, the paradoxes for both sets and predicates do not arise. The theory of types works like this: If sets cannot meaningfully be members of themselves and predicates cannot meaningfully refer to themselves, we end up with a hierarchy of different types, or levels, of sets or of predicates, their level depending on what types of things they can meaningfully take as members or arguments, and also depending on what sets or predicates can meaningfully take them as members or arguments.
At the first level in the hierarchy are individuals. This is the zero-order. Then, there are predicates that apply to individuals. These are called first-order predicates. Anything we call an object is an individual — cars, people, molecules, mountains, what have you. They also cannot apply to other first-order predicates. To say something about any predicate, you need a higher-order predicate. Predicates that apply to first-order predicates are called second-order predicates.
First-order predicates, as well as not being able to apply to themselves or to other first-order predicates, cannot apply to higher-order predicates. Sets are structured similarly with individuals again at the zero-order. Sets that take individuals as members are first-order sets, sets that take sets that take individuals as members are second-order sets, and so on.
And propositions about objects are first-order propositions, those about first-order propositions are second-order propositions, and so on. This is the basic idea. The actual theory of types is a few steps more complicated than this and will be explained in full in Chapter 3. But as you can see, stratifying sets and the things they can take as members, or predicates and the things they can apply to, prevents them from being self-referential, so the self-referential paradoxes of logic and set theory cannot arise.
Notice though that both the no-class theory of classes and the theory of logical types are used to avoid the paradoxes of class theory and logic. Why both methods? First, the no-class theory gets rid of sets by converting them to predicates.
But since paradoxes also arise for predicates, the theory of types is needed to stratify predicates and prevent paradoxes for predicates from arising. There are also predicates that apply to sets, but since the no-class theory transforms these sets into predicates, there is no need to create a separate hierarchy for them. This keeps the theory of types from getting any more complex than it already is. There are also philosophical problems with stratifying predicates that apply to sets.
By converting the sets to predicates, the philosophical problems are avoided. These problems are described in Chapter 3. Notice also that there is still a hierarchy for sets in type theory.
They still need stratifying in order to be used, even though we know they are really predicates. And because there are self-referential paradoxes that arise for propositions, the hierarchy of propositions is included in the theory of types as well.
One last point: notice that the paradoxes for set theory only arise from some sets. But the no-class theory eliminates all sets. This is clearly overkill. Why do it? Answer: As well as needing to avoid the set-theoretic paradoxes, Russell has separate philosophical reasons for wanting to eliminate classes from his logic altogether, for example, to avoid the ancient problem of the one and the many.
Roughly the problem is this: sometimes symbols for sets are treated as representing many things its members , other times they are treated as representing one thing the set itself. But it cannot be both. Because of this and other such philosophical puzzles, as well as in order to simplify the theory of types, Russell eliminates all classes from his logic using the no-class theory and the idea of logical fictions to define them away.
We have seen that Russell uses several different kinds of analysis in his mathematical philosophies. He also applies these methods outside of mathematics to answer philosophical questions about the world at large. We have already seen four varieties of analysis: the general kind that seeks the most basic concepts and principles, the theory of descriptions and its use in defining away mathematical functions, the no-class theory of classes, and the theory of logical types. His analysis of the first four of these physical points, moments in time, mental phenomena, and matter will be introduced in the following section and discussed at greater length in Chapter 4.
In them, a defense of analysis is part of his view of reality. They feel that the nature of objects is determined by the role they play in larger wholes, and that analyzing wholes into parts leaves out these larger connections. And if the nature of an object lies in the role it plays in a whole, and the nature of that whole lies in the role it plays in some larger whole, reality is ultimately one undivided whole — the plurality we experience is an illusion.
He believes that logic and grammar reveal the nature of reality.
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