Philosophy of Logical Atomism | Bertrand Russell | Modern, Philosophy | English | 1/3
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the philosophy of logical atomism by Bertrand Russell this is a librivox recording all librivox recordings are in the public domain for more information or to volunteer please visit librivox.org recording by landon DCL kind at the University of Iowa and Iowa City Iowa the following articles are the first two lectures of a course of eight lectures delivered in London in the first months of 1918 and are very largely concerned with explaining certain ideas which I learned from my friend and former pupil Ludvig bacon Stein I've had no opportunity of knowing his views since August 1914 and I do not even know whether he is alive or dead he has therefore no responsibility for what is said in these lectures beyond that of having originally supplied many of the theories contained in them the six other lectures will appear in the three following numbers of the monist BR lecture 1 facts and propositions this course of lectures which I'm now beginning I have called the philosophy of logical atomism perhaps I had better began by saying a word or two as to what I understand by that title the kind of philosophy that I wish to advocate which I call logical atom ISM is one which has forced itself upon me in the course of thinking about the philosophy of mathematics although I should find it hard to say exactly how far there is a definite logical connection between the two the things I am going to say in these lectures are mainly my own personal opinions and I do not claim that they are more than that as I have attempted to prove in the principles of mathematics when we analyze mathematics we bring it all back to logic it all comes back to logic in the strictest and most formal sense in the present lectures I shall try to set forth in a sort of outline rather briefly and rather unsatisfactorily a kind of logical doctrine which seems to me to result from the philosophy of mathematics not exactly logically but as what emerges as one reflects a certain kind of logical doctrine and on the basis of this a certain kind of metaphysic the logic which I shall advocate is atomistic as opposed to the monastic logic of the people who more or less follow Hegel when I say that my logic is atomistic I mean that I share the common sense belief that there are many separate things I do not regard the apparent multiplicity of the world as consisting merely in phases and unreal divisions of a single indivisible reality it results from that that a considerable part of what one would have to do to justify the sort of philosophy I wish to advocate would consist in justifying the process of analysis one is often told that the process of analysis is falsification that when you analyze any given concrete hole you falsify it and that the results of analysis are not true I do not think that is a right view I do not mean to say of course and nobody would maintain that when you have analyzed you keep everything that you had before you analyzed if you did you would never attain anything in analysing I do not propose to meet the views that I disagree with by controversy by arguing against those views but rather by positively setting forth what I believe to be the truth about the matter and endeavouring all the way through to make the views that I advocate result inevitably from absolutely undeniable data when I talk of undeniable data that is not to be regarded as synonymous with true data because undeniable is a psychological term and true is not when I say that something is undeniable I mean that it is not the sort of thing that anybody is going to deny it does not follow from that that it is true though does follow that we shall all think it true and that is as near to truth as we seem able to get when you are considering any sort of theory of knowledge you are more or less tied to a certain unavoidable subjectivity because you are not concerned simply with the question what is true of the world but what can I know of the world you always have to start any kind of argument from something which appears to you to be true if it appears to you to be true there is no more to be done you cannot go outside yourself and consider abstractly whether the things that appear to you to be true are true you may do this in a particular case where one of your beliefs is changed in consequence of others among your beliefs the reason that I call my doctrine logical atomism is because the atoms that I wish to arrive at as the sort of last residue in analysis our logical atoms and not physical atoms some of them will be what I call particulars such things as little patches of color or sounds momentary things and some of them will be predicates or relations and so on the point is that the atom I wish to arrive at is the atom of logical analysis not the atom of physical analysis it is a rather curious fact in philosophy that the data which are undeniable to start with are always rather vague and ambiguous you can for instance say there are a number of people in this room at this moment that is obviously in some sense undeniable but when you come to try and define what this room is and what it is for a person to be in a room and how you're going to distinguish one person from another and so forth you find that what you have said is most fearfully vague and that you really do not know what you meant that is a rather singular fact that everything you are really sure of right off is something that you do not oh the meaning of and the moment you get a precise statement you will not be sure whether it is true or false at least write off the process of sound philosophizing to my mind consists mainly in passing from those obvious vague ambiguous things that we feel quite sure of to something precise clear definite which by reflection and analysis we find is involved in the vague thing that we start from and is so to speak the real truth of which that vague thing is a sort of shadow I should like if time were longer and if I knew more than I do to spend a whole lecture on the conception of vagueness I think vagueness is very much more important in the theory of knowledge then you would judge it to be from the writings of most people everything is vague to a degree you do not realize till you have tried to make it precise and everything precise is so remote from everything that we normally think that you cannot for a moment suppose that is what we really mean when we say what we think when you pass from the vague to the precise by the method of analysis and reflection that I'm speaking of you always run a certain risk of error if I start with a statement that there are so and so many people in this room and then set to work to make that statement precise I shall run a great many risks and it will be extremely likely that any precise statement I make will be something not true at all so you cannot very easily or simply get from these vague undeniable things to precise things which are going to retain the undeniable T of the starting point the precise propositions that you arrive at may be logically premises to the system that you build up upon the basis of them but they are not premises for the theory of knowledge it is important to realize the difference between that from which your knowledge is in fact derived and that from which if you already had complete knowledge you would deduce it those are quite different things the sort of premise that a logician will take for a science will not be the sort of thing which is first known or easiest known it will be a proposition having great deductive power great cogent see and exactitude quite a different thing from the actual premise that your knowledge started from when you were talking of the premise for theory of knowledge you're not talking of anything objective but of something that will vary from man to man because the premises of one man's theory of knowledge will not be the same as those of another man's there is a great tendency among a very large school to suppose that when you are trying to philosophize about what you know you ought to carry back your premises further and further into the region of the inexact and vague beyond the point where you yourself are right back to the child or monkey and that anything whatsoever that you seem to know but that the psychologist recognizes as being the product of previous thought and analysis and reflection on your part cannot really be taken as a premise in your own knowledge that I say is a theory which is very widely held and which is used against the kind of analytic outlook which I wish to urge it seems to me that when your object is not simply to study the history or development of mind but to ascertain the nature of the world you do not want to go any further back then you are already yourself you do not want to go back to the vagueness of the child or monkey because you will find that quite sufficient difficulty is raised by your own vagueness but there one is confronted by one of those difficulties that occur constantly in philosophy where you have two ultimate prejudices conflicting and where argument ceases there is the type of mind which considers that what is called primitive experience must be a better guide to wisdom than the experience of reflective persons and there is the type of mind which takes exactly the opposite view on that point I cannot see any argument what however it is quite clear that a highly educated person sees hears feels does everything in a very different way from a young child or animal and that this whole matter of experiencing the world and of thinking about the world is very much more analytic than that of a more primitive experience the things we have got to take as premises in any kind of work of analysis are the things which appear to us undeniable to us here and now as we are and I think on the whole that the sort of method adopted by decart is right that you should set to work to doubt things and retain only what you cannot doubt because of its clearness and distinctness not because you are sure not to be induced into error for there does not exist a method which will safeguard you against the possibility of error the wish for perfect security is one of those snares we are always falling into and is just as untenable in the realm of knowledge as in everything else nevertheless granting all this I think that des cartes method is on the whole a sound one for the starting point I propose therefore always to begin any argument that I have to make by appealing to data which will be quite ludicrously obvious any philosophical skill that is required will consist in the selection of those which are capable of yielding a good deal of reflection and analysis and in the reflection and analysis themselves what I've said so far is by way of introduction the first truism to which I wish to draw your attention and I hope you will agree with me of these things I call truisms are so obvious that it is almost laughable to mention them is that the world contains facts which are what they are whatever we may choose to think about them and that there are also beliefs which have reference to facts and by reference to facts are either true or false I will try first of all to give you a preliminary explanation of what I mean by when I speak of a fact I do not propose to attempt an exact definition but an explanation so that you will know what I'm talking about I mean the kind of thing that makes a proposition true or false if I say it is raining what I say is true in a certain condition of weather and is false in other conditions of weather the condition of weather that makes my statement true or false as the case may be is what I should call a fact if I say Socrates is dead my statement will be true owing to a certain Xia logical occurrence which happened in Athens long ago if I say gravitation varies inversely as the square of the distance my statement is rendered true by astronomical fact if I say two and two are four it is arithmetic effect that makes my statement true on the other hand if I say Socrates is alive or gravitation varies directly as the distance or two and two or five the very same facts which made my previous statements true show that these new statements are false I want you to realize that when I speak of a fact I do not mean a particular existing thing such as Socrates or the rain or the Sun Socrates himself does not render any statement true or false you might be inclined to suppose that all by himself he would give truth to the statement socrates existed but as a matter of fact that is a mistake it is due to a confusion which I shall try to explain in the sixth lecture of this course when I come to deal with the notion of existence Socrates himself or any particular thing just by itself does not make any proposition true or false footnote I'm here for the moment treating Socrates as a particular but we shall see shortly that this view requires modification and a footnote Socrates is dead and Socrates is alive are both of them statements about Socrates one is true and the other false what I call fact is the sort of thing that is expressed by a whole sentence not by a single name like Socrates when a single word does come to express a fact like fire or wolf it is always due to an unexpressed context and the full expression of a fact will always involve a sentence we express a fact for example when we say that a certain thing has a certain property or that it has a certain relation to another thing but the thing which has the property or relation is not what I call a fact it is important to observe that facts belong to the objective world they're not created by our thoughts or beliefs except in special cases that is one of the sort of things which I should set up as an obvious truism but of course one is aware the moment one has read any philosophy at all how very much there is to be said before such a statement as that can become the kind of position that you want the first thing I want to emphasize is that the outer world the world so to speak which knowledge is aiming at knowing is not completely described by a lot of particulars but that you must also take account of these things that I call facts which are the sort of things that you express by a sentence and that these just as much as particular chairs and tables are part of the real world except in psychology most of our statements are not intended merely to express our condition of mind but that is often all that they succeed in doing they are intended to express facts which except when they are psychological facts will be about the outer world there are such facts involved equally when we speak truly and when we speak falsely when we speak falsely it is an objective fact that makes what we say false and it is an objective fact which makes what we say true when we speak truly there are great many different kinds of facts and we shall be concerned in later lectures with a certain amount of classification of facts I will just point out a few kinds of facts to begin with so that you may not imagine that facts are all very much alike there are particular facts such as this is white then there are general facts such as all men are mortal of course the distinction between particular facts and general facts is one of the most important there again it would be a very great mistake to suppose that you could describe the world completely by means of particular facts alone suppose that you had succeeded in chronicling every single particular fact throughout the universe and that there did not exist a single particular fact of any sort anywhere that you had not chronicled you still would not have got a complete description of the universe unless you also added these that I have chronicled are all the particular facts there are so you cannot hope to describe the world completely without having general facts as well as particular facts another distinction which is perhaps a little more difficult to make is between positive facts and negative facts such as Socrates was alive a positive fact and Socrates is not alive you might say a negative fact footnote negative facts are further discussed in a later lecture end of footnote but the distinction is difficult to make precise then there are facts concerning particular things or particular qualities or relations and apart from them the completely general facts of the sort that you have in logic where there is no mention of any constituent whatever of the actual world no mention of any particular thing or particular quality or particular relation indeed strictly you may say no mention of anything that is one of the characteristics of logical propositions that they mention nothing such a proposition is if one class is part of another a term which is a member of the one is also a member of the other all those words that come in the statement of a pure logical proposition are words really belonging to syntax they are words merely expressing for or connection not mentioning any particular constituent of the proposition in which they occur this is of course a theme that wants to be proved I'm not laying it down as self-evident then there are facts about the properties of single things and facts about the relations between two things three things and so on and any number of different classifications of some of the facts in the world which are important for different purposes it is obvious that there is not a dualism of true and false facts there are only just facts it would be a mistake of course to say that all facts are true that would be mistake because true and false are correlatives and you would only save a thing that it was not true if it was the sort of thing that might be false a fact cannot be either true or false that brings us on to the question of statements or propositions or judgments all those things that do have the duality of truth and falsehood for the purposes of logic though not I think for the purposes of theory of knowledge it is natural to concentrate upon the proposition as the thing which is going to be our typical vehicle on the duality of truth and falsehood a proposition one may say is a sentence in the indicative a sentence asserting something not questioning or commanding or wishing it may also be a sentence of that sort preceded by the word that for example that Socrates is alive that two and two are for that two and two or five anything of that sort will be a proposition a proposition is just a symbol it is a complex symbol in the sense that it has parts which are also symbols a symbol may be defined as complex when it has parts that are symbols in a sentence containing several words the several words are each symbols and the sentence composing them is therefore a complex symbol in that sense there is a good deal of importance philosophy in the theory of symbolism a good deal more then at one time I thought I think the importance is almost entirely negative ie the importance lies in the fact that unless you are fairly self conscious about symbols unless you are fairly aware of the relation of the symbol to what it symbolizes you will find yourself attributing to the thing properties which only belong to the symbol that of course is especially likely in very abstract studies such as philosophical logic because the subject matter that you are supposed to be thinking of is so exceedingly difficult and elusive that any person who has ever tried to think about it knows you do not think about it except perhaps once in six months for half a minute the rest of the time you think about the symbols because they are tangible but the thing you are supposed to be thinking about is fearfully difficult and one does not often manage to think about it the really good philosopher is the one who does once in six months think about it for a minute bad philosophers never do that is why the theory of symbolism has a certain importance because otherwise you are so certain to mistake the properties of the symbolism for the properties of the thing it has other interesting sides to it too there are different kinds of symbols different kinds of relation between symbol and what is symbolized and very important fallacies arise from not realizing this the sort of contradictions about which I shall be speaking in connection with types in a later lecture all arise from mistakes in symbolism from putting one sort of symbol in the place where another sort of symbol ought to be some of the notions that have been thought absolutely fundamental in philosophy have arisen I believe entirely through mistakes as to symbolism eg the notion of existence or if you like reality those two words stand for a great deal that has been discussed in philosophy there has been the theory about every proposition being really a description of reality as a whole and so on and altogether these notions of reality and existence have played a very prominent part in philosophy now my own belief is that as they have occurred in philosophy they have been entirely the outcome of a muddle about symbolism and that when you cleared up that muddle you find that practically everything that has been said about existence is sheer and simple mistake and that is all you can say about it I shall go into that in a later lecture but it is an example of the way in which symbolism is important perhaps I ought to say a word or two about what I'm understanding by symbolism because I think some people think you only mean mathematical symbols when you talk about symbolism I'm using it in a sense to include all language of every sort and kind so that every word is a symbol in every sentence and so forth when I speak of a symbol I simply mean something that means something else and as to what I mean by meaning I'm not prepared to tell you I will in the course of time and numerate a strictly infinite number of different things that meaning may mean but I shall not consider that I've exhausted the discussion by doing that I think that the notion of meaning is always more or less psychological and that it is not possible to get a pure logical theory of meaning nor therefore of symbolism I think that it is of the very essence of the explanation of what you mean by a symbol to take account of such things as knowing of cognitive relations and probably also of Association at any rate I am pretty clear that the theory of symbolism and the use of symbolism is not a thing that can be explained in pure logic without taking account of the various cognitive relations that you may have two things as to what one means by meaning I will give a few illustrations for instance the word Socrates you will say means a certain man the word mortal means a certain quality and the sentence Socrates is more means a certain fact but these three sorts of meaning are entirely distinct and you will get into the most hopeless contradictions if you think the word meaning has the same meaning in each of these three cases it is very important not to suppose that there is just one thing which is meant by meaning and that therefore there is just one relation of the symbol to what is symbolized a name would be a proper symbol to use for a person a sentence or proposition is the proper symbol for a fact a belief or statement has duality of truth and falsehood which the fact does not have a belief or statement always involves a proposition you say that a man believes that so-and-so is the case a man believes that Socrates is dead what he believes is a proposition on the face of it and for formal purposes and this can be in to take the proposition as the essential thing having the duality of truth and falsehood it is very important to realize such things for instance as that propositions are not names for facts it is quite obvious as soon as it is pointed out to you but as a matter of fact I never had realized it until it was pointed out to me by former pupil of mine viggen Stein it is perfectly evident as soon as you think of it that a proposition is not a name for a fact from the mere circumstance that there are two propositions corresponding to each fact suppose it is a fact that Socrates is dead you have two propositions Socrates is dead and Socrates is not dead in those two propositions corresponding to the same fact there is one fact in the world which makes one true and one false that is not accidental and illustrates how the relation of proposition to fact is a totally different one from the relation of name to the thing named for each fact there are two propositions one true and one false and there is nothing in the nature of the symbol to show us which is the and which is the false one if there were you could ascertain the truth about the world by examining propositions without looking around you there are two different relations as you see that a proposition may have to affect the one the relation that you may call being true to the fact and the other being false to the fact both are equally essentially logical relations which may subsist between the two whereas in the case of a name there is only one relation that it can have two what it names a name can just name a particular or if it does not it is not a name at all it is a noise it cannot be a name without having just that one particular relation of naming a certain thing whereas a proposition does not cease to be a proposition if it is false it has these two ways of being true and being false which together correspond to the property of being a name just as a word may be a name or be not a name but just a meaningless noise so a phrase which is apparently a proposition may be either true or false or may be meaningless but the true and false belong together as against the meaningless that shows of course but the formal logical characteristics of propositions are quite different from those of names and at the relations they have to facts are quite different and therefore propositions are not names for facts you must not run away with the idea that you can name facts in any other way you cannot you cannot name them at all you cannot properly name a fact the only thing you can do is to assert it or deny it or desire it or will it or wish it or question it but all those are things involving the whole proposition you can never put the sort of thing that makes a proposition to be true or false in the position of a logical subject you can only have it there is something to be asserted or to or something of that sort but not something to be named discussion question do you take your starting points that there are many things as a postulate which is to be carried along all through or has to be proved afterward mr. Russell no neither the one nor the other I do not take it as a postulate that there are many things I should take it that insofar as it can be proved the proof is empirical and that the dis proofs that have been offered are a priori the empirical person would naturally say there are many things the monistic philosopher attempts to show that there are not I should propose to refute his a priori arguments I do not consider there is any logical necessity for there to be many things nor for there not to be many things question I mean in making a start whether you start with the empirical or the AA priori philosophy do you make your statement just at the beginning and come back to prove it or do you never come back to the proof of it mr. Russell no you never come back it is like the Acorn to the oak you never get back to the Acorn in the oak I should like a statement which would be rough and vague and have that sort of obvious Ness that belongs to things of which you never know what they mean but I should never get back to that statement I should say here is a thing we seem somehow convinced that there is truth buried in this thing somewhere we will look at it inside and out until we have extracted something and can say now that is true it will not really be the same as the thing we started from because it will be so much more analytic and precise question does it not look as though you could name a fact by a date mr. Russell you can't apparently name facts but I do not think you can really you always find that if you set out the whole thing fully it was not so suppose you say the death of Socrates you might say that is a name the fact that Socrates died but it obviously is not you can see that the moment you take account of truth and falsehood supposing that he had not died the phrase would still be just as significant although there could not be than anything you could name but supposing he had never lived the sound Socrates would not be named at all you can see it in another way you can say the death of Socrates is a fiction suppose you had read in the paper the Kaiser had been assassinated and it turned out not to be true you could then say the death of the Kaiser is a fiction it is clear that there is no such thing in the world as a fiction and yet that statement is a perfectly sound statement from this it follows that the death of the Kaiser is not a name end of lecture one the philosophy of logical atomism by Bertrand Russell this is a librivox recording all librivox recordings are in the public domain for more information or to volunteer please visit librivox.org recording by land and DC Elkind at the University of Iowa in Iowa City Iowa lecture to particulars predicates and relations I propose to begin today the analysis of facts and propositions for an away the chief thesis that I have to maintain is the legitimacy of analysis because if one goes into what I call logical atomism that means that one does believe the world can be analysed into a number of separate things with relations and so forth and that the sort of arguments that many philosophers use against analysis are not justifiable in a philosophy of logical atomism one might suppose that the first thing to do would be to discover the kinds of atoms out of which logical structures are composed but I do not think that is quite the first thing it is one of the early things but not quite the first there are two other questions that one has to consider and one of these at least is prior you have to consider one are the things that look like logically complex entities really complex – are they really entities the second question we can put off in fact I shall not deal with it fully until my last lecture the first question whether they are really complex is one that you have to consider at the start neither these questions is as it stands a very precise question I do not pretend to start with precise questions I do not think you can start with anything precise you have to achieve such precision as you can as you go along each of these two questions however is capable of a precise meaning and each is really important there is another question which comes still earlier namely what shall we take as prima facie examples of logically complex entities that really is the first question of all to start with what sort of things shall we regard as prima facie complex of course all the ordinary objects of daily life are apparently complex entities such things as tables and chairs loaves and fishes persons and principalities and powers they are all on the face of it complex entities all the kinds of things to which we have Italy give proper names are on the face of them complex entities Socrates piccadilly Romania Twelfth Night or anything you like to think of to which you give a proper name they are all apparently complex entities they seem to be complex systems bound together into some kind of a unity that sort of a unity that leads to the bestowal of a single appellation I think it is the contemplation of this sort of apparent unity which has very largely led to the philosophy of monism and to the suggestion that the universe as a whole is a single complex entity more or less in the sense in which these things are that I have been talking about for my part I do not believe in complex entities of this kind and it is not such things as these that I'm going to take as the prima facie examples of complex entities my reasons will appear more and more plainly as I go on but I cannot give them all today but I can more or less explain what I mean in a preliminary way suppose for example that you were to analyze what appears to be a fact about two piccadilly suppose you made any statement about Piccadilly such as Piccadilly is a pleasant Street if you analyze a statement of that sort correctly I believe you will find that the fact corresponding to your statement does not contain any constituent corresponding to the piccadilly the word Piccadilly will form part of many significant propositions but the facts corresponding to these propositions do not contain any single constituent whether simple or complex corresponding to the word Piccadilly that is to say if you take language as a guide in your analysis of the fact expressed you will be led astray in a statement of that sort the reasons for that I shall give at length in lecture 6 and partly also in lecture 7 but I could say in a preliminary way certain things that would make you understand what I mean Piccadilly on the face of it is the name for a certain portion of the Earth's surface and I suppose if you wanted to define it you would have to define it as a series of classes of material entities namely those which at varying times occupy that portion of the Earth's surface so that you would find that the logical status of piccadilly is bound up with the logical status of series and classes and if you're going to hold Piccadilly as real you must hold that series of classes are real and whatever sort of metaphysical status you assigned to them you must assign to it as you know I believe that series and classes are the nature of logical fictions therefore that thesis if it can't be maintained will dissolve piccadilly into a fiction exactly similar remarks will apply to other instances Rumania Twelfth Night and Socrates Socrates perhaps raises some special questions because the question what constitutes a person has special difficulties in it but for the sake of argument one might identify Socrates with the series of his experiences he would be really a series of classes because one has many experiences simultaneously therefore he comes to be very like piccadilly considerations of that sort seem to take us away from such prima facia complex entities as we started with two others as being more stubborn and more deserving of oolitic attention namely facts i explained last time what i meant by a fact namely that sort of thing that makes a proposition true or false the sort of thing which is the case when your statement is true and is not the case when your statement is false facts are as I said last time plainly something you have to take account of if you are going to give a complete account of the world you cannot do that by merely enumerated the particular things that are in it you must also mention the relations of these things and their properties and so forth all of which are facts so that fact certainly belonged to an account of the objective world in facts do seem much more clearly complex and much more not capable of being explained away than things like Socrates and Romania however you may explain away the meaning of the word Socrates you will still be left with the truth of that the proposition Socrates is mortal expresses a fact you may not know exactly what Socrates means but it is quite clear that Socrates is mortal does Express a fact there is clearly some valid meaning in saying that the fact expressed by Socrates is mortal is complex the things in the world have various properties and stand in various relations to each other that they have these properties and relations are facts and the things and their qualities or relations are quite clearly in some sense or other components of the facts that have those qualities or relations the analysis of apparently complex things such as we started with can be reduced by various means to the analysis of facts which are apparently about those things therefore it is with the analysis of facts that one's considerations of the problem of complexity must begin not by the analysis of apparently complex things the complexity of a fact is evidenced to begin with by the circumstance that the proposition which asserts a fact consists of several words each of which may occur in other content of course sometimes you get a proposition expressed by a single word but if it is expressed fully it is bound to contain several words the proposition Socrates is mortal may be replaced by Plato is mortal forced by Socrates is human in the first case we alter the subject in the second the predicate it is clear that all the propositions in which the word Socrates occurs have something in common and again all the propositions in which the word mortal occurs have something in common something which they do not have in common with all propositions but only with those which are about Socrates or mortality it is clear I think that the facts corresponding to propositions in which the word Socrates occurs have something in common corresponding to the common word Socrates which occurs in the propositions so that you have that sense of complexity to begin with that in a fact you can get something which it may have in common with other facts just as you may have Socrates as human and Socrates is mortal both of them facts and both having to do with Socrates although Socrates does not constitute the whole of either of these facts it is quite clear that in that sense there is a possibility of cutting up a fact into component parts of which one component may be altered without altering the others and one component may occur in certain other facts though not in all other facts I want to make it clear to begin with that there is a sense in which facts can be analyzed I'm not concerned with all the difficulties of any analysis but only with meeting the prima facie objections of philosophers who think you really cannot analyze at all I'm trying as far as possible again this time as I did last time to start with perfectly plain truisms my desire and wish is that the things I start with should be so obvious that you wonder why I spent my time stating them that is what I aim at because the point of philosophy to start with something so simple as not to seem worth stating and to end with something so paradoxical that no one will believe it one prima facie mark of complexity and propositions is the fact that they are expressed by several words I come now to another point which applies primarily to propositions and that's derivatively to facts you can understand a proposition when you understand the words of which it is composed even though you never heard the proposition before that seems a very humble property but it is a property which marks it as complex and distinguishes it from words whose meaning is simple when you know the vocabulary grammar and syntax of a language you can understand a proposition in that language even though you never saw it before in reading a newspaper for example you become aware of a number of statements which are new to you and they are intelligible to you immediately in spite of the fact that they are new because you understand the words of which they are composed this characteristic that you can understand a proposition through the understanding of its component words is absent from the component words when those words express something simple take the word red for example and suppose as one always has to do that red stands for a particular shade of color you will pardon that assumption but one never can get on otherwise you cannot understand the meaning of the word red except through seeing red things there is no other way in which it can be done it is no use to learn languages or to look up dictionaries none of these things will help you to understand the meaning of the word red in that way it is quite different from the meaning of a proposition of course you can give a definition of the word red and here it is very important to distinguish between a definition and an analysis all analysis is only possible in regard to what is complex and it always depends in the last analysis upon direct acquaintance with the objects we are the meanings of certain simple symbols it is hardly necessary to observe that one does not define a thing but a symbol a simple symbol is a symbol whose parts are not symbols a simple symbol is quite different thing from a simple thing those objects which it is impossible to symbolize otherwise them by simple symbols may be called simple while those which can be symbolized by combination of symbols may be called complex this is of course a preliminary definition and perhaps somewhat circular but that doesn't matter much at this stage I have said that red could not be understood except by seeing red things you might object to that on the ground that you can define red for example as the color with the greatest wavelength that you might say is a definition of red and a person could understand that definition even if he had seen nothing red provided he understood the physical theory of color but that does not really constitute the meaning of the word red in the very slightest if you take such a proposition as this is red and substitute for it this has the color with the greatest wavelength you have a different proposition altogether you can see that at once because a person who knows nothing of the physical theory of color can understand the proposition this is red and can know that it is true but cannot know that this has the color which has the greatest wavelength conversely you might have a hypothetical person who could not see red but who understood the physical theory of color and could apprehend the proposition this has the color with the greatest wavelength but who would not be able to understand the proposition this is red as understood by the normal uneducated person therefore it is clear that if you define red asked the color with the greatest wavelength you're not giving the actual meaning of the word at all you are simply giving a true description which is quite a different thing and the propositions which result are different proposition from those in which the word red occurs in that sense the word red cannot be defined though in the sense in which a correct description constitutes a definition that can be defined in the sense of analysis you cannot define red that is how it is that dictionaries are able to get on because the dictionary professes to define all words in the language by means of words in the language and therefore it is clear that a dictionary must be guilty of a vicious circle somewhere but it manages it by means of correct descriptions I've made it clear then in what sense I should say that the word red is a simple symbol and the phrase this is red a complex symbol the word red can only be understood through acquaintance with the object whereas the phrase roses are red can be understood if you know what red is and what roses are without ever having heard the phrase before that is a clear mark of what is complex it is the mark of a complex symbol and also the mark of the object symbolized by the complex symbol that is to say propositions are complex symbols and the facts they stand for are complex the whole question of the meaning of words is very full of complexities and ambiguities in ordinary language when one person uses a word he does not mean by it the same thing as another person means by it I have often heard it said that that is a misfortune that is a mistake it would be absolutely fatal if people meant the same things by their words it would make all intercourse impossible and language the most hopeless and useless thing imaginable because the meaning you attach to your words must depend on the nature of the objects you are acquainted with and since different people are acquainted with different objects they would not be able to talk to each other unless they attached quite different meanings to their words we should have to talk only about logic a not wholly undesirable result take for example the word Piccadilly we are acquainted with Piccadilly attached quite a different meaning to that word from any which could be attached to it by a person who had never been in London and supposing that you travel in foreign parts and expatiate on Piccadilly you will convey to your hearers entirely different propositions from those in your mind they will know Piccadilly as an important Street in London they may know a lot about it but they will not know just the things one knows when one is walking along it if you were to insist on language which was unambiguous you would be unable to tell people at home what you had seen in foreign parts it would be all together incredibly inconvenient to have an unambiguous language and therefore mercifully we have not got one analysis is not the same thing as definition you can define a term by means of a correct description but that does not constitute an analysis it is analysis not definition that we are concerned with of the present moment so I will come back to the question of analysis we may lay down the following provisional definitions that the components of a proposition are the symbols we must understand in order to understand the proposition that the components of the fact which makes a proposition true or false as the case may be are the meanings of the symbols which we must understand in order to understand the proposition that is not absolutely correct but it will enable you to understand my meaning one reason why it fails of correctness is that it does not apply to words which like or and not are parts of propositions without corresponding to any part of the corresponding facts this is a topic for lecture 3 I call these definitions preliminary because they start from the complexity of the proposition which they define psychologically and proceed to the complexity of the fact whereas it is quite clear that an orderly proper procedure in is the complexity of the fact that you would start from it is also clear that the complexity of the fact cannot be something merely psychological if in astronomical fact the earth moves around the Sun that is genuinely complex it is not that you think it complex it is a sort of genuine objective complexity and therefore one ought in a proper orderly procedure to start from the complexity of the world and arrive at the complexity of the proposition the only reason for going the other way round is that in all abstract matters symbols are easier to grasp I doubt however whether complexity in that fundamental objective sense in which one starts from complexity of a fact is definable at all you cannot analyze what you mean by complexity in that sense you must just apprehend it at least so I'm inclined to think there is nothing one could say about it beyond giving criteria such as I have been giving therefore when you cannot get a real proper analysis of a thing it is generally best to talk round it without professing that you have given an exact definition it might be suggested that complexity is essentially to do with symbols or that it is essentially psychological I do not think it would be possible seriously to maintain either of those views but they are the sort of views that will occur to one the sort of thing that one would try to see whether it would work I do not think they will do at all when we come to the principles of symbolism which I shall deal with in lecture 7 I shall try to persuade you that in a logically correct symbolism there will always be a certain fundamental identity of structure between a fact and the symbol for it and that the complexity of the symbol corresponds very closely with the complexity of the facts symbolized by it also as I said before it is quite directly evident to inspection that the fact for example that two things stand in or a certain relation to one another eg that this is to the left of that is itself objectively complex and not merely that the apprehension of it is complex the fact that two things stand a certain relation to each other for any statement of that sort has a complexity all of its own I shall therefore in future assume that there is an objective complexity in the world and that it is mirrored by the complexity of propositions a moment ago I was speaking about the great advantages that we derive from the logical imperfections of language from the fact that our words are all ambiguous I propose now to consider what sort of language a logically perfect language would be in a logically perfect language the words in a proposition would correspond one by one with the components of the corresponding fact with the exception of such words as or not if then which have a different function in a logically perfect language there will be one word and no more for every simple object and everything that is not simple will be expressed by combination of words by combination derived a course from the words for the simple things that enter in one word for each simple component a language of that sort will be completely analytic and will show at a glance the logical structure of the facts asserted or denied the language which is set forth in Principia Mathematica is intended to be a language of that sort it is a language which has only syntax and no vocabulary whatsoever barring the omission of a vocabulary I maintain that it is quite a nice language it aims at being that sort of language that if you add vocabulary would be a logically perfect language actual languages are not logically perfect in this sense and they cannot possibly be if they are to serve the purposes of daily life a logically perfect language if it could be constructed would not only be in tolerably prolix but as regards its vocabulary would be largely private to one speaker that is to say all the names that it would use would be private to that speaker and could not enter into the language of another speaker it could not use proper names for Socrates or Piccadilly or Romania for the reasons which I went into earlier in the lecture altogether you would find that it would be a very inconvenient language indeed that is one reason why logic is so very backward as a science because the needs of logic are so extraordinarily different from the needs of daily life one wants a language in both and unfortunately it is logic that has to give way not daily life I shall however assume that we have constructed a logically perfect language and that we are going on state occasions to use it and I will now come back to the question which I intended to start with namely the analysis of facts the simplest imaginable facts are those which consist in the possession of equality by some particular thing such facts say as this is white they have to be taken in a very sophisticated sense I do not want you to think about the piece of chalk I'm holding but of what you see when you look at the chalk if one says this is white it will do for about a simple effect as you can get hold of the next simplest would be those in which you have a relation between two facts such as this is to the left of that next you come to though this where you have at triadic relation between three particulars an instance which royce gives is a gives B to C so you get relations which require as their minimum three terms those which we call triatic relations and those which require four terms which we call tetrad ik and so on there you have a whole infinite hierarchy of facts facts in which you have a thing in equality two things under relation three things into relation four things into relation and so on that whole hierarchy constitutes what I call atomic facts and they are the simplest sort of fact you can distinguish among them some simpler than others because the ones containing equality are simpler than those in which you have say a pent attic relation and so on the whole lot of them taken together are as facts go very simple and are what I call atomic facts the propositions expressing them are what I call atomic propositions in every atomic fact there is one component which is naturally expressed by a verb or in the case of quality it may be expressed by a predicate by an adjective this one component is a quality or dyadic or triadic for tetrad ik and so on relation it would be very convenient for purposes of talking about these matters to call a quality a monadic relation and I shall do so it saves a great deal of circumlocution in that case you can say that all atomic propositions assert relations of varying orders atomic facts contain besides the relation the terms of the relation one term if it is a monadic relation to if it is dyadic and so on these terms which come into the atomic facts i define as particulars particulars are defined to be terms of relations and atomic facts this is the definition of particulars and I want to emphasize it because the definition of a particular is something purely logical the question whether this or that is a particular is a question to be decided in terms of that logical definition in order to understand the definition it is not necessary to know beforehand this is a particular or that is a particular it remains to be investigated what particulars you can find in the world if any the whole question of what particulars you actually find in the world is a purely empirical one which does not interest the logician as such the logician as such never gives instances because it is one of the tests of a logical proposition that you need not know anything whatsoever about the real world in order to understand it passing from atomic facts to atomic propositions the word expressing a monadic relation or quality is called a predicate and the word expressing a relation of any higher order would generally be a verb sometimes a single verb sometimes a whole phrase at any rate the verb gives the essential nerve as it were of the relation the other words that occur in the atomic propositions the words that are not the predicate or verb may be called the subjects of the proposition there will be one subject in a monadic proposition two in a dyadic one and so on the subjects in a proposition will be the words expressing the terms of the relation which is expressed by the proposition the only kind of word that is theoretically capable of standing for a particular is a proper name and the whole matter of proper names is rather curious proper names are defined to be words for particulars I've put that down although as far as common language goes it is obviously false it is true that if you try to think how you are to talk about particulars you will see that you cannot ever talk about a particular particular except by means of a proper name you cannot use general words except by way of description how are you to express in words an atomic proposition an atomic proposition is one which doesn't mention actual particulars not merely describe them but actually name them and you can only name them by means of names you can see at once for yourself therefore that every other part of speech except proper names is obviously quite incapable of standing for a particular yet it does seem a little odd if having made a dot on the blackboard I call it John you would be surprised and yet how are you to know otherwise what it is that I'm speaking of if I say the dot that is on the right hand side is white that is a proposition if I say this is white that is quite a different proposition this will do very well while we are all here and can see it but if I wanted to talk about it tomorrow it would be convenient to have christened it and called it John there is no other way in which you can mention it you cannot really mention it itself except by means of a name what pass for names in language like Socrates Plato and so forth were originally intended to fulfill this function of standing for particulars and we do accept an ordinary life as particulars all sorts of things that really are not so the names that we commonly use like Socrates are really abbreviations for descriptions not only that but what they described are not particulars the complicated systems of classes or series a name in the narrow logical sense of a word whose meaning is a particular can only be applied to a particular with which the speaker is acquainted because you cannot name anything you are not acquainted with you remember when Adam named the beasts they came before him one by one and he became acquainted with them and named them we are not acquainted with Socrates and therefore cannot name him when we use the word Socrates we are really using a description our thought may be rendered by some such phrase as the master of Plato or the philosopher who drank the hemlock or the person whom logicians assert to be mortal but we certainly do not use the name as a name in the proper sense of the word that makes it very difficult to get any instance of a name at all in the strict logical sense of the word the only words one does use as names in the logical sense are words like this or that one can use this as a name to stand for a particular with which one is acquainted at the moment we say this is white if you agree that this is white meaning that this that you see you are using this as a proper name but if you try to apprehend the proposition that I am expressing when I say this is white you cannot do it if you mean this piece of chalk as a physical object then you are not using a proper name it is only when you use this quite strictly to stand for an actual object of sense that is really a proper name and in that it has a very odd property for a proper namely that it seldom means the same thing to moments running and does not mean the same thing to the speaker and to the hearer it is an ambiguous proper name but it is really a proper name all the same and it is almost the only thing I can think of that is used properly and logically in the sense that I was talking of for a proper name the importance of proper names in the sense of which I am talking is in the sense of logic not of daily life you can see why it is that in the logical language set forth in principia mathematica there are not any names because there we are not interested in particular particulars but only in general particulars if I may be allowed such a phrase particulars have this peculiarity among the sort of objects that you have to take account of in an inventory of the world that each of them stands up entirely alone and is completely self-subsistent it has that sort of self subsistence that used to belong to substance except that it usually only persists through a very short time so far as our experience goes that is to say each particular that there is in the world does not in any way logically depend upon any other particular each one might happen to be the whole universe it is a merely empirical fact that this is not the case there is no reason why you should not have a universe consisting of one particular and nothing else that is a peculiarities of particulars in the same way in order to understand a name for a particular the only thing necessary is to be acquainted with that particular when you are acquainted with that particular you have a full adequate and complete understanding of the name and no further information is required no further information as to the facts that are true of that particular would enable you to have a fuller understanding of the meaning of the name discussion mr. Carr do you think there are simple facts that are not complex our complex is all composed of symbols are not the simples that go into complexes themselves complex mr. Russell no facts are simple as to your second question that is of course a question that might be argued whether when a thing is complex it is necessary that it should in analysis have constituents that are simple I think it is perfectly possible to suppose that complex things are capable of analysis ad infinitum and that you never reach the simple I do not think it is true but it is a thing that one might argue certainly I do myself think that complex is I do not like to talk of complexes are composed of simples but I admit that that is a difficult argument and it might be that analysis could go on forever mr. Carr you do not mean that in calling of the thing complex you have asserted that there really are simples mr. Russell no I do not think that is necessarily implied mr. Neville I do not feel clear but the proposition this is white is in any case a simpler proposition than the proposition this and that have the same color mr. Russell that is one of the things I have not had time for it may be the same as the proposition this and that have the same color it may be that white is defined as the color of this or rather that the proposition this is white means this is identical in color with that the color of that being so to speak the definition of white that may be but there is no special reason to think that it is mr. Neville are there any monadic relations which would be better examples mr. Russell I think not it is perfectly obvious a priori that you can get rid of all monadic relations by that trick one of the things I was going to say if I had had time was that you can get rid of dyadic and reduce to triatic and so on but there is no particular reason to suppose that that is the way the world begins that it begins with relations of order n instead of relations of order one you cannot reduce them downward you can't reduce them upward question if the proper name of a thing of this varies from instant to instant how is it possible to make any argument mr. Russell you can keep this going for about a minute or two I made that dot and talked about it for some time I mean it varies often if you argue quickly you can get some little way before it is finished I think things last for a finite time a matter of some seconds or minutes or whatever it may happen to be question you do not think that air is acting on that and changing it mr. Russell it does not matter about that if it does not alter its appearance enough for you to have a different sense data end of lecture two the philosophy of logical atomism by Bertrand Russell this is a librivox recording all librivox recordings are in the public domain for more information or to volunteer please visit librivox.org recording by landon DCL kind at the University of Iowa in Iowa City Iowa lecture three atomic and molecular propositions I did not quite finish last time the syllabus that I intended for lecture two so I must first to do that I have been speaking at the end of my last lecture on the subject of the self subsistence of particulars how each particular has its being independently of any other and does not depend upon anything else for the pelagic impossibilities of its existence I compared particulars with the old conception of substance that is to say they have the quality of self subsistence that used to belong to substance but not the quality of persistence through time a particular as a rule is apt to last for a very short time indeed not an instant but a very short time in that respect particulars differ from the old substances but in their logical position they do not there is as you know a logical theory which is quite opposed to that view a logical theory according to which if you really understood any one thing you would understand everything I think that rests upon a certain confusion of ideas when you have acquaintance with a particular you understand that particular itself quite fully independently of the fact that there are great many propositions about it that you do not know the propositions concerning the particular are not necessary to be known in order that you may know what the particular itself is it is rather the other way around in order to understand a proposition in which the name of a particular occurs you must already be acquainted with that particular the acquaintance with the simpler is presupposed in the understanding of the more complex but the logic that I should wish to combat maintains that an order thoroughly to no any one thing you must know all its relations and all its qualities all the propositions in fact in which that thing is mentioned and you deduce of course from that that the world is an interdependent whole it is on a basis of that sort that the logic of monism develops generally one supports this theory by talking about the nature of a thing assuming that a thing has something which you call its nature which is generally elaborately confounded and distinguished from the thing so that you can get a comfortable seesaw which enables you to deduce whichever results see at the moment the nature of the thing would come to mean all the true propositions in which the thing is mentioned of course it is clear that since everything has relations to everything else you cannot know all the facts of which a thing is a constituent without having some knowledge of everything in the universe when you realize that what one calls knowing a particular merely means acquaintance with that particular and is presupposed in the understanding of any proposition in which that particular is mentioned I think you will also realize that you cannot take the view that the understanding of the name of the particular presupposes knowledge of all the propositions concerning that particular I should like to say about understanding that that phrase is often used mistakenly people speak of understanding the universe and so on but of course the only thing you can really understand in the strict sense of the word is a symbol and to understand a symbol is to know what it stands for I pass on from particulars to predicates and relations and what we mean by understanding the words that we use for predicates and relations a very great deal of what I am saying in this course of lectures consists of ideas which I derived from my friend dinkenstein but I've had no opportunity of knowing how far his ideas have changed since August 1914 nor whether he is alive or dead so I cannot make anyone but myself responsible for them understanding a predicate is quite a different thing from understanding a name by a predicate as you know I mean the word that is used to designate equality such as red white square round and the understanding of a word like that involves a different kind of act of mind from that which is involved in understanding a name to understand a name you must be acquainted with the particulars of what it is a name and you must know that it is the name of that particular you do not that is to say have any suggestion of the form of a proposition whereas an understanding a predicate you do to understand read for instance is to understand what is meant by saying that a thing is read you have to bring in the form of a proposition you do not have to know concerning any particular this that this is read but you have to know what is the meaning of saying that anything is read you have to understand what one would call being read the importance of that is in connection with the theory of types which I shall come to later on it is in the fact that a predicate can never occur except as a predicate when it seems to occur as a subject the phrase once amplifying and explaining unless of course you're talking about the word itself you may say read is a predicate but then you must have read in inverted commas because you were talking about the word read when you understand read it means that you understand propositions of the form that X is read so that the understanding of a predicate is something a little more complicated than the understanding of a name just because of that exactly the same applies to relations and in fact all those things that are not particulars take eg before in X's before Y you understand before when you understand what that would mean if x and y were given I do not mean you know it is true but you understand the proposition here again the same thing applies a relation can never occur except as a relation never as a subject you will always have to put in hypothetical terms if not real ones such as if I say that X before Y I assert a relation before X and y it isn't this way that you will have to expand such a statement as before is a relation in order to get its meaning the different sorts of words in fact have different sorts of uses and must be kept always to the right use and not to the wrong use and it is fallacies arising from putting symbols to wrong uses that lead to the contradictions concerned with types there is just one more point before I leave the subjects I meant to have dealt with last time and that is a point which came up in discussion at the conclusion of the last lecture namely that if you like you can get a formal reduction of say monadic relations to die annek or of dyadic to triadic or of all the relations below a certain order to all above that order but the converse reduction is not possible suppose one takes for example red one says this is red that is red and so forth now if anyone is of opinion that there is reason to try and get on without subject predicate propositions all that is necessary is to take some standard red thing and have a relation which one might call color likeness sameness of color which would be a direct relation not consisting in having a certain color you can then define the things which are red as all the things that have color likeness to this standard thing that is practically the treatment that Berkeley and Hume recommended except that they did not recognize that they were reducing qualities to relations the thought they were getting rid of abstract ideas altogether you can perfectly well do in that way a formal reduction of predicates to relations there is no objection to that either empirically or logic cailli if you think it is worthwhile you can proceed in exactly the same way with dyadic relations which you can reduce to triadic royce used to have a great affection for that process for some reason he always liked triadic relations better than dyadic ones he illustrated his preference in his contributions to mathematical logic and the principles of geometry all that is possible I do not myself see any particular point in doing it as soon as you have realized that it is possible I seen a particular reason to suppose that the simplest relations that occur in the world are say of order n but there is no a priori reason against it the converse reduction on the other hand is quite impossible except in certain special cases where the relation has some special properties for example the Attic relations can be reduced to sameness of predicates when they are symmetrical and transitive thus eg the relation of color likeness will have the property that if a has exact color likeness with B and B with C then a has exact color likeness with C and if a has it with B B has it with a but the case is otherwise with asymmetrical relations take for example a is greater than B it is obvious that a is greater than B does not consist in a and B having a common predicate fourth it did it would require that B should also be greater than a it is also obvious that it does not consist merely in there having different predicates because if a has a different predicate from B B has a different predicate from a so that in either case whether of sameness or difference of predicate you get a symmetrical relation for instance if a is of a different color from B B is of a different color from a therefore when you get symmetrical relations you have relations which it is formally possible to reduce to either sameness of predicates or difference of predicates but when you come to asymmetrical relations there is no such ability this impossibility of reducing dyadic relations to sameness or difference of predicates is a matter of a good deal of importance in connection with traditional philosophy because a great deal of traditional philosophy depends upon the assumption that every proposition really is of the subject predicate form and that is certainly not the case that theory dominates a great part of traditional metaphysics and the old idea of substance and a good deal of the theory of the absolute so that that sort of logical outlook which had its imagination dominated by the theory that you could always express a proposition in a subject predicate form has had a very great deal of influence upon traditional metaphysics that is the end of what I ought to have said last time and I come now to the proper topic of today's lecture that is molecular propositions I call them molecular propositions because they contain other propositions which you may call their atoms and by molecular propositions I mean propositions having such words as or if and and so forth if I say either today is Tuesday or we've all made a mistake in being here that is the sort of proposition that I mean that is molecular or if I say if it rains I shall bring my umbrella that again is a molecular proposition because it contains the two parts it rains and I shall bring my umbrella if I say it did rain and I did bring my umbrella that again is a molecular proposition or if I say the supposition of its raining is incompatible with the supposition of my not bringing my umbrella that again is a molecular proposition there are various propositions of that sort which you can complicate ad infinitum they are built up out of propositions related by such words as or if and and so on you remember that I defined an atomic proposition as one which contains a single verb now there are two different lines of complication in proceeding from these two more complex propositions there is the line that I have just been talking about where you proceed to molecular propositions and there is another line which I shall come to in a later lecture where you have not two related propositions but one proposition containing two or more verbs examples are got from believing wishing and so forth I believe Socrates is mortal you have their two verbs believe and is or I wish I were immortal anything like that where you have a wish or a belief or a doubt involves two verbs a lot of psychological attitudes involve two verbs not as it were crystallized out but two verbs within the one unitary proposition but I'm talking today about molecular propositions and you will understand that you can make propositions with or and and and so forth where the Constituent propositions are not atomic but for the moment we can confine ourselves to the case where the Constituent propositions are atomic when you take an atomic proposition for one of those propositions like believing when you take any proposition of that sort there is just one fact which is pointed to by the proposition point it to either truly or falsely the essence of a proposition is that it can correspond in two ways with the fact in what one may call the true way or the false way you might illustrate it in a picture like this in the true case the proposition is directed towards the fact in the false case the proposition is directed away from the fact supposing you have the proposition Socrates is mortal either there would be the fact that Socrates is mortal or there would be the fact that Socrates is not mortal in the one case it corresponds in a way that makes the proposition true in the other case in a way that makes the proposition false that is one way in which a proposition differs from a name there are of course two corresponding to every fact one true and one false there are no false facts so you cannot get one fact for every proposition but only for every pair of propositions all that applies to atomic propositions but when you take such a proposition as P or Q Socrates is mortal or Socrates is living still there you will have two different facts involved in the truth or the falsehood of your proposition P or Q there will be the fact that corresponds to P and there will be the fact that corresponds to Q and both of those facts are relevant in discovering the truth or falsehood of P or Q I do not suppose there is in the world a single disjunctive fact corresponding to P or Q it does not look plausible that in the actual objective world there are facts going about which you could describe as P or Q but I would not lay too much stress on what strikes one as plausible it is not a thing you can rely on altogether for the present I do not think any difficulties will arise from the supposition that the truth or falsehood of this proposition P or Q does not depend upon a single objective fact which is disjunctive but depends on the two facts one of which corresponds to P and the other to Q P will have a fact corresponding to it and Q will have a fact corresponding to it that is to say the truth or falsehood of this proposition P or Q depends upon two facts and not upon one as P does and as Q does generally speaking as regards these things that you make up out of two propositions the whole of what is necessary in order to know their meaning is to know under what circumstances they are true given the truth or falsehood of P and the truth or falsehood of Q that is perfectly obvious you have as a schema for P or Q using true true for P and Q are both true true false for P true and Q false etc true true comes out true true false comes true false true comes out true and false false comes out true where the bottom line states the truth or the falsehood of P or Q you must not look about the real world from object which you can call or and say now look at this this is or there is no such thing and if you try to analyze P or Q in that way you will get into trouble but the meaning of disjunction will be entirely explained by the above schema I call these things truth functions of propositions when the truth or falsehood of the molecular proposition depends only on the truth or falsehood of the propositions that enter into it the same applies to P and Q and if P then Q and P is incompatible with you when I say P is incompatible with Q I simply mean to say that they are not both true I do not mean anymore those sorts of things are called truth functions and these molecular propositions that we are dealing with today are instances of truth functions if P is a proposition the statement that I believe P does not depend for its truth or falsehood simply upon the truth or falsehood of P since I believe some but not all true propositions and some but not all false propositions I just want to give you a little talk about the way these truth functions are built up you can build up all these different sorts of truth functions out of one source namely P is incompatible with Keela meaning by that that they are not both true and that one at least of them is false we will denote P is incompatible with Q by P / Q take for instance p / p IE p is incompatible with itself in that case clearly p will be false so that you can take p / p as meaning p is false ie p / p is defined to be not P the meaning of molecular propositions is entirely determined by their truth schema there is nothing more in it than that so that when you have got two things of the same truth scheme huh you can identify them suppose you want if P then Q that simply means that you cannot have P without having Q so that P is incompatible with the falsehood of Q thus if P then Q is defined to be P's and compatible with Q's and compatibility with Kela when you have that as follows of course at once that if P is true Q is true because you cannot have P true and Q false suppose you want P or Q that means that the falsehood of P is incompatible with the falsehood of Q if P is false Q is not false and vice versa that will be P's and compatibility with P is incompatible with Q's and compatibility with Q suppose you want P and Q are both true that will mean that P is not incompatible with Q when P and Q are both true it is not the case that at least one of them is false thus P and Q are both true is defined to be P's and compatibility with Q is incompatible with P's and compatibility with Q the whole of the logic of deduction is concerned simply with complications and developments of this idea this idea of incompatibility was first shown to be sufficient for the purpose by mr. Scheffer and there was a good deal of work done subsequently by M the cod it is a good deal simpler when it is done this way then when it is done in the way of principia mathematica where there are two primitive ideas to start with namely or and not here you can get on with only a single premise for deduction I will not develop this subject further because it takes you right into mathematical logic I do not see any reason to suppose that there is a complexity in the facts corresponding to these molecular propositions because as I was saying the correspondence of a molecular proposition with facts is of a different sort from the correspondence of a Tomic proposition with a fact there is one special point that has to be gone into in connection with this that is the question are there negative facts are there such facts as you might call the fact that Socrates is not alive I have assumed in all that I have said hitherto that there are negative facts that for example if you say Socrates is alive there is corresponding to that proposition in the real world the fact that Socrates is not alive one has a certain repugnance to negative facts the same sort of feeling that makes you wish not to have a fact P or Q going about the world you have a feeling that there are only positive facts and that negative propositions have somehow or other got to be expressions of positive facts when I was lecturing on this subject at Harvard I argue that there were negative facts and it nearly produced a riot the class would not hear of there being negative facts at all I'm still inclined to think that there are however one of the men to whom I was lecturing at Harvard mr. demos subsequently wrote an article in mind to explain why there are no negative facts it is in mind for April 1917 I think he makes as good a case as can be made for the view there are no can negatively ask that you should not dogma ties I do not positively say that there are but there may be there are certain things you can notice about negative propositions mr. Delmas points out first of all that a negative proposition is not in any way dependent on a cognitive subject for its definition to this I agree suppose you say when I say Socrates is not alive I'm merely expressing disbelief in the proposition that Socrates is alive you've got to find something or other in the real world to make this disbelief true and the only question is what that is his first point his second is that a negative proposition must not be taken at its face you cannot he says regard the statement Socrates is not alive as being an expression of a fact in the same sort of direct way in which Socrates is human would be an expression of a fact his argument for that is solely that he cannot believe that there are negative facts in the world he maintains that cannot be in the real world such facts as Socrates is not alive taken ie as simple facts and that therefore you've got to find some explanation of negative propositions some interpretation and that they cannot be just as simple as positive propositions I shall come back to that point but on this I do not feel inclined to agree his third point I do not entirely agree with that when the word not occurs it cannot be taken as a qualification of the predicate for instance if you say that this is not read you might attempt to say that not read is a predicate but that of course won't do in the first place because a great many propositions are not expressions of predicates in the second place because the word not applies to the whole proposition the proper expression would be not this is red but not applies to the whole proposition this is red and of course in many cases you can see that quite clearly if you take a case I took in discussing descriptions the present King of France is not bald and if you take not bald as as predicate that would have to be judged false on the ground that there is not a present King of France but it is clear that the proposition the present King of France is bald is a false proposition and therefore the negative of that will have to be a true proposition and that could not be the case if you take not bald as a predicate so that in all cases where a naught comes in that naught has to be taken to apply to the whole proposition not P is the proper formula we come now to the question how are we really to interpret not P and the suggestion offered by mr. demos is that when we assert not P we are really asserting there is some proposition Q which is true and it's incompatible with P an opposite of peas his phrase but I think the meaning is the same that is his suggested definition not P means there is a proposition Q which is true and is incompatible with P as eg if I say this chalk is not red I shall be meaning to assert that there is some proposition which in this case would be the proposition this chalk is white which is consistent with the proposition it is red and that you use these general negative forms because you do not happen to know what the actual proposition is that is true and is incompatible with P or of course you may possibly know what the actual proposition is but you may be more interested in the fact that P is false then you are in the particular example which makes it false as for instance he might be anxious to prove that someone is a liar and you might be very much interested in the falsehood of some proposition which he had asserted he might also be more interested in the general proposition than in the particular case so that if someone had asserted that that chalk was red he might be more interested in the fact that it was not red than in the fact that it was white I find it very difficult to believe that theory of falsehood you will observe that in the first place there is this objection that it makes incompatibility fundamental and an objective fact which is not so very much simpler than allowing for negative facts you've got to have here that P is incompatible with Q in order to reduce not to incompatibility because this has got to be the corresponding fact it is perfectly clear whatever may be the interpretation of not that there is some interpretation which will give you a fact if I say there is not a hippopotamus in this room it is quite clear there is some way of interpreting that statement according to which there is a corresponding fact and the fact can be merely that every part of this room is filled up with something that is not a hippopotamus you would come back to the necessity for some kind or other a fact of the sort that we have been trying to avoid we have been trying to avoid both negative facts and molecular facts and all the succeeds in doing is to substitute molecular facts for negative facts and I do not consider that that is very successful as a means of avoiding paradox especially when you consider this that even if incompatibility is to be taken as a sort of fundamental expression of fact incompatibility is not between facts but between propositions if I say P is incompatible with Q one at least of P and Q has got to be false it is clear that no two facts are incompatible the incompatibility holds between the propositions between the P and the Q and therefore if you are going to take incompatibility as a fundamental fact you have got in explaining negatives to take as your fundamental fact something involving propositions as opposed to facts it is quite clear that propositions are not what you might call real if you were making an inventory of the world propositions would not come in facts would beliefs wishes wills would the propositions would not they do not have being independently so that this incompatibility of propositions taken as an ultimate fact of the real world will want a great deal of treatment a lot of dressing up before will do therefore as a simplification to avoid negative facts I do not think it really is very successful I think you will find that it is simpler to take negative facts as facts to assume that Socrates is not alive is really an objective fact in the same sense in which Socrates as human is a fact this theory of mr. de meses that I have been setting forth here is a development of the one one hits upon at once when one tries to get round negative facts but for the reasons that I given I do not think it really answers to take things that way and I think you will find that it is better to take negative facts as ultimate otherwise you will find it so difficult to say what it is that corresponds to a proposition when eg you have a false positive proposition say Socrates is alive it is false because of a fact in the real world a thing cannot be false except because of a fact so that you find it extremely difficult to say what exactly happens when you make a positive assertion that is false unless you're going to admit negative facts I think all those questions are difficult and there are arguments always to be adduced both ways but I'm a whole I do inclined to believe that there are negative facts and that there are not disjunctive facts but the denial of disjunctive facts leads to certain difficulties which we shall have to consider in connection with general propositions in a later lecture discussion question do you consider that the proposition Socrates is dead is a positive or negative fact mr. Russell it is partly a negative fact to say that a person is dead is complicated it is two statements rolled into one Socrates was alive and Socrates is not alive question does putting that not into it give it a formal character of negative and vice-versa mr. Russell no I think you must go into the meaning of words question I should have thought there was a great difference between saying that Socrates is alive and saying that Socrates is not a living man I think it is possible to have what one might call a negative existence and that things exist of which we cannot take cognizance Socrates undoubtedly did live but he is no longer in the condition of living as a man mr. Russell I was not going into a question of existence after death but simply taking words in their everyday significant question.what is precisely your test as to whether you have got a positive or negative proposition before you mr. Russell there is no formal test question if you had a formal test would it not follow that you would know whether there were negative facts or not mr. Russell no I think not in the perfect logical language that I sketched in theory it would always be obvious at once whether proposition was positive or negative but it would not bear upon how you're going to interpret negative propositions question would the existence of negative facts be anything more than a mere definition mr. Russell yes I think it would it seems to mean that the business of metaphysics is to describe the world and it is in my opinion a real definite question whether in a complete description of the world you would have to mention negative facts or not question how do you define a negative fact mr. Russell you could not give a general definition if it is right that negativeness is an ultimate end of lecture 3 you

Philosophy of Logical Atomism | Bertrand Russell | Modern, Philosophy | English | 1/3

1: [00:00:00] – Lecture 1

2: [00:34:28] – Lecture 2

3: [01:13:08] – Lecture 3

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