Philosophy of Logical Atomism | Bertrand Russell | Modern, Philosophy | Sound Book | English | 2/3
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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 in Iowa City Iowa lecture for propositions and facts with more than one verb beliefs etc you will remember that after speaking about atomic propositions I pointed out to more complicated forms of propositions which arise immediately on proceeding further than that the first which I called molecular propositions which I dealt with last time involving such words as or and if and the second involving two or more verbs such as believing wishing willing and so forth in the case of molecular propositions it was not clear that we had to deal with any new form of fact but only within a form of proposition ie if you have a disjunctive proposition such as P or Q it does not seem very plausible to say that there is in the world a disjunctive fact corresponding to P or Q but merely that there is a fact corresponding to P and a fact corresponding to Q and the disjunctive proposition derives its truth or falsehood from those two separate facts therefore in that case one was dealing only with a new form of proposition and not with a new form of fact today we have to deal with a new form of fact I think one might describe philosophical logic the philosophical portion of logic which is the portion that I concerned with in these lectures since Christmas 1917 as an inventory or if you like a more humble word a zoo containing all the different forms that facts may have I should prefer to say forms of facts rather than forms of propositions to apply back to the case of molecular propositions which dealt with last time if one were pursuing this analysis of the forms of facts it would be belief in a molecular proposition that one would deal with rather than with the molecular proposition itself in accordance with the sort of realistic bias that I should put into all study of metaphysics I should always wish to be engaged in the investigation of some actual fact or set of facts and it seems to me that that is so in logic just as much as it is in zoology in logic you are concerned with the forms of facts with getting hold of the different sorts of facts different logical sorts of facts that there are in the world now I want to point out today that the facts that occur when one believes or wishes or wills have a different logical form from the atomic facts containing a single verb which I dealt with in my second lecture there are of course a good many forms that facts may have a strictly infinite number and I do not wish you to suppose that I pretend to deal with all of them suppose you take any actual occurrence of a belief I want you to understand that I'm not talking about beliefs in the sort of way in which judgment is spoken of in theory of knowledge in which you would say there is the judgment that two and two are four I'm talking of the actual occurrence of a belief in a particular person's mind at a particular moment and discussing what sort of fact that is if I say what day of the week is this and you say Tuesday there occurs in your mind at that moment the belief that this is Tuesday the thing I want to deal with today is the question what is the form of the fact which occurs when a person has a belief of course you see that the sort of obvious first notion that what would naturally arrive at would be that a belief is a relation to the proposition I believe the proposition P I believe that today is Tuesday I believe that two and two are for something like that it seems on the face of it as if you had there relation of the believing subject to a proposition that you won't do for various reasons which I shall go into but you have therefore got to have a theory of belief which is not exactly that take any sort of proposition say I believe Socrates is mortal suppose that that belief does actually occur the statement that it occurs is a statement of fact you have there two verbs you may have more than two verbs you may have any number greater than one I may believe that Jones is of the opinion that Socrates is mortal there you have more than two verbs you may have any number but you cannot have less than two you will perceive that it is not only the proposition that has the two verbs but also the fact which is expressed by the proposition has two constituents corresponding to verbs I shall call those constituents of verbs for the sake of shortness as it is very difficult to find any word to describe all those objects which one denotes by verbs of course that is strictly using the word verb in two different senses but I do not think it can lead to any confusion if you understand that it is being so used this fact the belief is one fact it is not like what you had in molecular propositions where you had say P or Q it is just one single fact that you have a belief that is obvious from the fact that you can believe a falsehood it is obvious from the fact of false belief that you cannot cut off one part you cannot have I believe cut off from Socrates is mortal there are certain questions that arise about such facts and the first that arises is are the undeniable facts or can you reduce them in some way to relations of other facts is it really necessary to suppose that there are irreducible facts of which that sort of thing is a verbal expression on that question until fairly lately I should certainly not have supposed that any doubt could arise it had not really seemed to me until fairly lately that that was a debatable point I still believe that there are facts of that form but I see that it is a substantial question that needs to be discussed one our beliefs etc irreducible facts etc covers understanding a proposition that covers desiring willing any other attitude of that sort that you may think of that involves a proposition it seems natural to say one believes a proposition and unnatural to say one desires a proposition but as a matter of fact that is only a prejudice while you believe in what you desire are of exactly the same nature you may desire to get some sugar tomorrow and of course you may possibly believe that you will I am not sure that the logical form is the same in the case of will I'm inclined to think that the case of will is more analogous to that of perception and going direct to the facts and excluding the possibility of falsehood in any case desire and belief are of exactly the same form logically pragmatists in some of the american realists the school whom one calls neutral monists deny altogether that there is such a phenomenon as belief in the sense i'm dealing with they do not deny it in words they do not use the same sort of language than I'm using and that makes it difficult to compare their views with the views I'm speaking about one has really to translate what they say into language more or less analogous to ours before one can make out where the points of contact or difference are if you take the works of James in his essays and radical empiricism or Dewey in his essay is an experimental logic you will find that they are denying all together but there is such a phenomenon as belief in the sense I'm talking of they use the word believe but they need something different you come to the view called behaviorism according to which you mean if you say a person believes a thing then he behaves in a certain fashion and that hangs together with James's pragmatism James and Dewey would say when I believe in proposition that means that I act in a certain fashion that my behavior has certain characteristics and my belief is a true one if the behavior leads to the desired result and is a false one if it does not that if it is true makes their pragmatism a perfectly rational account of truth and falsehood if you do accept their view that belief as an isolated phenomenon does not occur that is therefore the first thing one has to consider it would take me too far from logic to consider that subject as it deserves to be considered because it is a subject belonging to psychology and it is only relevant to logic in this one way that it raises a doubt whether there are any facts having the logical form that I am speaking of in the question of this logical form that involves two or more verbs you have a curious interlacing of logic with empirical studies and of course that may occur elsewhere in this way that an empirical study gives you an example of a thing having a certain logical form and you cannot really be sure that there are things having a given logical form except by finding an example and the finding of an example is itself empirical therefore in that way empirical facts are relevant to logic at certain points I think theoretically one might know that there are were those forms without knowing any instance of them but practically situated as we are that does not seem to occur practically unless you can find an example of the form you won't know that there is that form if I cannot find an example containing two or more verbs you will not have reason to believe in the theory that such a form occurs when you read the works of people like James and Dewey on the subject of belief one thing that strikes you at once is that the sort of thing they are thinking of as the object of belief is quite different from the sort of thing I'm thinking of they think of it always as a thing they think you believe in God or Homer you believe in an object that is the picture they have in their mom it is common enough in common parlance to talk that way and they would say the first crude approximation that they would suggest would be that you believe truly when there is such an object and that you believe falsely when there is not I do not mean they would say that exactly but that be the crude view from which they would start they do not seem to have grasped the fact that the objective side and belief is better expressed by a proposition than by a single word in that I think has a great deal to do with their whole outlook on the matter of what belief consists of the object of belief in their view is generally not relations between things or things having qualities or whatnot but just single things which may or may not exist that view seems to me radically and absolutely mistaken in the first place there are great many judgments you cannot possibly fit into that scheme and in the second place it cannot possibly give any explanation to false beliefs because when you believe that a thing exists and it does not exist the thing is not there it is nothing and it cannot be the right analysis of false belief to regard it as a relation to what is really nothing this is an objection to supposing that belief consists simply in relation to the object it is obvious that if you say I believe in homer and there was no such person as Homer your belief cannot be a relation to Homer says there is no Homer every fact that occurs in the world must be composed entirely of constituents that there are and not a constituents that there are not therefore when you say I believe in Homer it cannot be the right analysis of a thing to put it like that what the right analysis is I shall come on to in the theory of descriptions I come back now to the theory of behaviorism which I spoke of a moment ago suppose eg that you are said to believe that there is a train at 10:25 this means we are told they start for the station at a certain time we the station you see it is 1024 and you run that behavior constitutes your belief that there is a train at that time if you catch your train by running your belief was true if the train went at 10:23 you miss it and your belief was false that is the sort of thing that they would say it constitutes belief there is not a single state of mind which consists in contemplating this eternal Verity that the train starts at 10:25 they would apply that even to the most abstract things I do not myself feel that that view of things is tenable it is a difficult one to refute because it goes very deep and one has the feeling that perhaps if one thought about long enough and became sufficiently aware of all of its implications one might find after all that it was a feasible deal but yet I do not feel it feasible it hangs together of course with the theory of neutral monism with the theory that the material constituting the mental is the same as the material constituting the physical just like the post office directory which gives you people arranged geographically and alphabetically this whole theory hangs together with that I do not mean necessarily that all the people that profess the one profess the other but that the two do essentially belong together if you are going to take that view you have to explain away belief in desire because things of that sort do seem to be mental phenomena they do seem rather far removed from the sort of thing that happens in the physical world therefore people will set to work to explain away such things as belief and reduce them to bodily behavior and your belief in a certain proposition will consist in the behavior of your body in the crudest terms that is what that view amounts to it doesn't able you to get on very well without mind truth and falsehood in that case consists in the relation of your bodily behavior to a certain fact the sort of distant fact which is the purpose of your bodily behavior as it were and when your behavior is satisfactory in regard to that fact your belief is true and when your behavior is unsatisfactory in regard to that fact your belief is false the logical essence in that view will be a relation between two facts having the same sort of form as a causal relation ie on the one hand there will be your bodily behavior which is one fact and on the other hand the fact that the train starts at such-and-such a time which is another fact and out of a relation of those two the whole phenomenon is constituted the thing you will get will be logically at the same form as you having cause where you have this fact causes that fact it is quite a different logical form from the facts containing two verbs that I'm talking of today I have naturally a bias in favor of the theory of neutral monism because it exemplifies Occam's razor I always wish to get on in philosophy with the smallest possible apparatus partly because it diminishes the risk of error because it is not necessary to deny the entities you do not assert and therefore you run less risk of error the fewer entities you assume the other reason perhaps a somewhat frivolous one is that every de munition in the number of entities increases the amount of work for mathematical logic to do in building up things that look like the entities you used to assume therefore the whole theory of neutral monism is pleasing to me but I do find so far very great difficulty in believing it you will find a discussion of the whole question and some articles I wrote in the monist especially in July 1914 and the two previous numbers also I should really want to rewrite them rather because I think some of the arguments I used against neutral monism are not valid I place most reliance on the argument about emphatic particulars this I all that class of words that pick out certain particulars from the universe by their relation to oneself and by the fact that I think that they for particulars related to them our present to you at the moment of speaking this of course is what I call an emphatic particular it is simply a proper name for the present object of attention a proper name meaning nothing it is ambiguous because of course the object of attention is always changing from moment to moment and from person to person I think it is extremely difficult if you get rid of consciousness altogether to explain what you mean by such a word as this what it is that makes the absence of impartiality you would say that in a purely physical world there would be a complete impartiality all parts of time and all regions of space would seem equally emphatic but what really happens is that we pick out certain facts past and future and all that sort of thing they all radiate out from this and I have not myself seen how one can deal with the notion of this on the basis of neutral monism I do not lay that down dogmatically only I do not see how it can be done I shall assume for the rest of this lecture that there are such facts as beliefs and wishes and so forth it would take me really the whole of my course to go into the question fully thus we come back to more purely logical questions from this excursion into psychology for which I apologise to what is the status of P in I believe P you cannot say that you believe facts because your beliefs are sometimes wrong you can say that you perceive facts because perceiving is not liable to error wherever it is facts alone that are involved error is impossible therefore you cannot say you believe facts you have to say that you believe propositions the awkwardness of that is that obviously propositions are nothing therefore that cannot be the true account of the matter when I say obviously propositions are nothing it is not perhaps quite obvious time was when I thought there were propositions but it does not seem to me very plausible to say that in addition to Bax there are also these curious shadowy things going about such as that today's Wednesday when in fact it is Tuesday I cannot believe they go about the real world it is more than one can manage to believe and I do think no person with a vivid sense of reality can imagine it one of the difficulties of the study of logic is that it is an exceedingly abstract study dealing with the most abstract things imaginable and yet you cannot pursue it properly unless you have a vivid instinct as to what is real you must have that instinct rather well developed in logic I think otherwise you'll get into fantastic things I think my tongue is rather deficient in just that instinct for reality mine own maintains that there is such an object as the round square only it does not exist and it does not even subsist but nevertheless there is such an object and when you say the round square is a fiction he takes it that there is an object the round square and there is a predicate fiction knowing what the sense of reality would so analyze that proposition he would see that the proposition wants analyzing in such a way that you won't have to regard the round square as a constituent of that proposition to suppose that in the actual world of nature there is a whole set of false propositions going about is to my mind monstrous I cannot bring myself to suppose it I cannot believe that they are there in the sense in which facts are there there seems to me something about the fact that today is Tuesday on a different level of reality from the supposition that today is Wednesday when I speak of the proposition that today is Wednesday I do not mean the occurrence in future of a state of mind in which do you think it is Wednesday but I'm talking about the theory that there is something quite logical something not involving mind in any way and such a thing as that I do not think you can take a false proposition to be I think a false proposition must wherever to kurz be subject to analyses be taken to pieces pulled to bits and shown to be simply separate pieces of one fact in which the false proposition has been analyzed away I say that simply on the ground of what I should call an instinct of reality I ought to say a word or two about reality it is a vague word and most of its uses are improper when I talk of reality as I am now doing I can best explain what I mean by saying that I mean everything you would have to mention in a complete description of the world that will convey to you what I mean now I do not think that false propositions would have to be mentioned in a complete description of the world false beliefs would of course false opposition's would and desires for what does not come to pass but not false propositions all alone and therefore when you as one says believe a false proposition that cannot be an accurate account of what occurs it is not accurate to say I believe the proposition P and regard the occurrence as a two-fold relation between me and P the logical form is just the same whether you believe a false or a true proposition therefore in all cases you are not to regard belief as a two term relation between yourself and a proposition and you have to analyze up the proposition and treat your belief differently therefore the belief does not really contain a proposition as a constituent but only contains the constituents of the propositions as constituents you cannot say when you believe what is it that you believe there is no answer to that question ie there is not a single thing that you are believing I believe that today is Tuesday you must not suppose that that today's Tuesday is a single object which I am believing that would be an error that is not the right way to analyze the occurrence although that analysis is linguistically convenient and one may keep it provided one knows that it is not the truth three we describe the logical form of a belief I want to try to get an account of the way that a belief is made up that is not an easy question at all you cannot make what I should call a map in space of a belief you can make a map of an atomic fact but not of a belief for the simple reason that space relations always are at the atomic sort for complications of the atomic sort I will try to illustrate what I mean the point is in connection with there being two verbs in the judgment and with the fact that both verbs have to occur as verbs because if the thing is a verb it cannot occur otherwise than as a verb suppose I take a believes that B loves see a fellow believes that Desdemona loves Cassio there you have a false belief you have this odd state of affairs that the verb loves occurs in that proposition and seems to occur as relating Desdemona to Cassio whereas in fact it does not do so but yet it does occur as a verb it does occur in a sort of way that a verb should do I mean that when a believes that B loves C you have to have a verb in the place where loves occurs you cannot put a substantive in its place therefore it is clear that the subordinate verb ie the verb other than believing is functioning as a verb and seems to be relating to terms but as a matter of fact does not when the judgment happens to be false that is what constitutes the puzzle about the nature of belief you will notice that wherever one gets to really close quarters with the theory of error one has the puzzle of how to deal with error without assuming the existence of the non-existent I mean that every theory of error sooner or later wrecks itself by assuming the existence of the non-existent as when I say Desdemona loves Cassio it seems that you have a non-existent love between Desdemona and Cassio but that is just as wrong as a non-existent unicorn so you have to explain the whole theory judgment in some other way I come now to this question of a map suppose you try such a map as this a fellow's belief is pointing towards Desdemona's loving Cassio this question of making a map is not so strange as you might suppose because it is part of the whole theory of symbolism it is important to realize where and how a symbolism of that sort would be wrong we aren't how it is wrong is that in a symbol you have this relationship relating these two things and in the fact it doesn't really relate them you cannot get in space any occurrence which is logically of the same form as belief when I say logically of the same form I mean one that can be obtained from the other by replacing the constituents of the one by the new terms if I say Desdemona loves Cassio that is of the same form as a is to the right of B those are of the same form and I say that nothing that occurs in space is of the same form as belief I have got on here to a new sort of thing a new beast for our zoo not another member of our former species but a new species the discovery of this fact is due to mr. Vick enstein there is a great deal that is odd about belief from a logical point of view one of the things that are odd is that you can believe propositions of all sorts of forms I can believe that this is white in that two and two or four they are quite different forms yet one can believe both the actual currents can hardly be of exactly the same logical form in those two cases because of the great difference in the forms of the propositions believed therefore it would seem that belief cannot strictly be logically one in all different cases but must be distinguished according to the nature of the proposition that you believe if you have I believe P and I believe Q those two facts if P and Q are not of the same logical form and are not of the same chuckle form in the sense I was speaking of a moment ago that is in the sense that from I believe P you can derive I believe Q by replacing the constituents of one by the constituents of the other that means that belief itself cannot be treated as being a proper sort of single term belief will really have to have different logical forms according to the nature of what is believed so that the apparent sameness of believing in different cases is more or less illusory there are really two main things that one wants to notice in this matter that I am treating out just now the first is the impossibility of treating the proposition believed as an independent entity entering as a unit into the occurrence of the belief and the other is the impossibility of putting the subordinate verb on a level with its terms as an object term in the belief that is a point in which I think that the theory of judgment which I set forth once in print some years ago was a little unduly simple because I did then treat the object verb as if one could put it as just an object like the terms as if one could put loves on a level with Desdemona and Cassio as a term for the relation belief that is why I have been laying such an emphasis in this lecture today on the fact that there are two verbs at least I hope you will forgive the fact that so much of what I say today is tentative and consists of pointing out difficulties the subject is not very easy and it has not been much dealt with or discussed practically nobody has until quite lately begun to consider the problem of the nature of belief with anything like a proper logical apparatus and therefore one has very little to help one in any discussion and so one has to be content on many points at present with pointing out difficulties rather than laying down quite clear solutions for the question of nomenclature what sort of name shall we give to verbs like believe and wish and so forth I should be inclined call them propositional verbs this is merely a suggested name for convenience because they are verbs which have the form of relating an object to a proposition as I have been explaining that is not what they really do but it is convenient to call them propositional verbs of course you might call them attitudes but I should not like that because it is a psychological term and although all the instances in our experience are psychological there is no reason to suppose that all the verbs I am talking of are psychological there is never any reason to suppose that sort of thing one should always remember Spinoza's infinite attributes of deity it is quite likely that there are in the world the analogs of His infinite attributes we have no acquaintance with them but there is no reason to suppose that the mental and the physical exhausted the whole universe so one can never say that all the instances of any logical sort of thing are of such-and-such a nature which is not a logical nature you do not know enough about the world for that therefore I should not suggest that all the verbs that have the form exemplified by believing and willing are psychological I can only say all I know are I noticed that in my syllabus I said I was going to deal with truth and falsehood today but there is not much time to say about them specifically as they are coming in all the time the thing one first thinks of as true or false is a proposition any proposition is nothing but a belief is true or false in the same way as a proposition is so that you do have facts in the world that are true or false I said a while back that there was no distinction of true and false among facts but as regards that special class of facts that we call beliefs there is in that sense that a belief which occurs may be true or false though it is equally a fact in either case one might call wishes false in the same sense when one wishes something that does not happen the truth or falsity pends upon the proposition that enters in I'm inclined to think that perception as opposed to belief go straight to the fact and not through the proposition when you perceive the fact you do not of course have error coming in because the moment it is a fact that is your object error is excluded I think that verification in the last resort would always reduce itself to the perception of facts therefore the logical form of perception will be different from the logical form of believing just because of that circumstance that it is a fact that comes in that raises also a number of logical difficulties which I do not propose to go into but I think you can see for yourself that perceiving would also involve two verbs just as believing does lyin inclined to think that volition differs from desire logically in a way strictly analogous to that in which perception differs from belief but it would take us too far from logic to discuss this view end of lecture for the philosophy of logical Adam isn't 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 5 general propositions and existence I'm going to speak today about general propositions and existence the two subjects really belong together they are the same topic although it might not have seemed so at the first glance the propositions and facts that I've been talking about hitherto have all been such as involved only perfectly definite particulars or relations or qualities or things of that sort never involved the sort of indefinite things one alludes to by such words as all some a any and it is propositions and facts of that sort that I'm coming on to today really all the propositions of this sort that I mean to talk of today collect themselves into two groups the first that are about all and the second they're about some these two sorts belong together they are each other's negations if you say for instance all men are mortal that is the negative of some men are not mortal in regard to general propositions the distinction of affirmative and negative is arbitrary whether you're going to regard the propositions about all as the affirmative ones and the propositions about some as the negative ones or vice-versa is purely a matter of taste for example if I say I meant no one as I came along that on the face of it you would think is a negative proposition of course that is really a proposition about all I e all men are among those whom I did not meet if on the other hand I say I met a man as I came along that would strike you as affirmative whereas it is the negative of all men are among those I did not meet as I came along if you consider such propositions as all men are mortal and some men are not mortal you might say was more natural to take the general propositions as the affirmative and the existence propositions as the negative but simply because it is quite arbitrary which one is to choose it is better to forget these words and to speak only of general propositions and propositions asserting existence all general propositions deny the existence of something or other if you say all men are mortal that denies the existence of an immortal man and so on I want to say emphatically that general propositions are to be interpreted as not involving existence when I say for instance all Greeks or men I do not want you to suppose but that implies that there are Greeks it is to be considered emphatically as not implying that that would have to be added as a separate proposition if you want to interpret it in that sense you will have to add the further statement and there are Greeks that is for purposes of practical convenience if you include the fact that there are Greeks you are rolling two propositions into one and it causes unnecessary confusion in your logic because the sorts of propositions that you want are those that do assert the existence of something and general propositions which do not assert existence if it happened that there were no Greeks both the proposition that all Greeks are men and the proposition that no Greeks are men would be true the proposition no Greeks are men is of course the proposition all Greeks are not men both propositions will be true simultaneously if it happens that there are no Greeks all statements about all the members of a class that has no members are true because the contradictory of any general statement does assert existence and is therefore false in this case this notion of course of general propositions not involving existence is one which is not in the traditional doctrine of the syllogism in the traditional doc the syllogism it was assumed that when you have such a statement as all Greeks or men that implies that there are Greeks and this produced fallacies for instance all chimeras are animals in all chimeras breath flame therefore some animals breathe flame this is a syllogism and are opti but that mood of the syllogism is fallacious as this instance shows that was a point by the way which had a certain historical interest because it impeded Leibniz in his attempts to construct a mathematical logic he was always engaged in trying to construct such a mathematical logic as we have now or rather such a one as boule constructed and he was always failing because of his respect for Aristotle whenever he invented a really good system as he did several times it always brought out that such moods as dartie are fallacious if you say all a is B and all a is C therefore some B is C if you say this you incur a fallacy but he could not bring himself to believe that it was fallacious so he began again that shows you that you should not have too much respect for distinguished men footnote C F Gujarat the logic Delaney's end of footnote now when you come to ask what really is asserted in a general proposition such as all Greeks are men for instance you find that what is asserted is the truth value of all values of what I call a propositional function a propositional function is simply any expression containing an undetermined constituent or several undetermined constituents and becoming a proposition as soon as the undetermined constituents are determined if I say X is a man or n is a number that is a propositional function so is any formula of algebra say the product of X plus y and X minus y is equal to x squared minus y squared a propositional function is nothing but like most of the things one wants to talk about in logic it does not lose its importance through that fact the only thing really that you can do with a propositional function is to assert either that it is always true or that it is sometimes true or that it is never true if you take if X is a man X is mortal that is always true just as much when X is not a man as when X is a man if you take X as a man that is sometimes true if you take X as a unicorn that is never true one may call a propositional function necessary when it is always true possible when it is sometimes true impossible when it is never true much false philosophy has arisen out of confusing propositional functions and propositions there is a great deal in ordinary traditional philosophy which consists simply in attributing two propositions the predicates which only apply to propositional functions and still worse sometimes in attributing to individuals predicates which merely apply to propositional functions this case of necessary possible impossible is a case in point in all traditional philosophy that comes a heading of modality which discusses necessary possible and impossible as properties of propositions whereas in fact they are properties of propositional functions propositions are only true or false if you take X as X that is a propositional function which is true whatever X may be ie a necessary propositional function if you take X as a man that is a possible one if you take X as a unicorn that is an impossible one propositions can only be true or false the propositional functions have these three possibilities it is important I think to realize that the whole doctrine of modal only applies to propositional functions not to propositions propositional functions are involved in ordinary language in a great many cases where one does not usually realize them in such a statement as I met a man you can understand my statement perfectly well without knowing whom I met and the actual person is not a constituent of the proposition you are really asserting there that a certain propositional function is sometimes true namely the propositional function I met X and X is human there is at least one value of x for which that is true and that therefore is a possible propositional function whenever you get such words as a sum all every it is always a mark of the presence of a propositional function so that these things are not so to speak remote or recondite they are obvious and familiar a propositional function comes in again in such a statement as Socrates is mortal because to be mortal means to die at some time or other you mean there is a time at which Socrates dies and that again involves a propositional function namely that T is a time and Socrates dies at T is possible if you say Socrates is immortal that also will involve a propositional function that means that if T is any time whatever Socrates is ally at time T if we take immortality as involving existence throughout the whole of the past as well as throughout the whole of the future but if we take immortality as only involving existence throughout the whole of the future the interpretation of Socrates is immortal becomes more complete vis there is a time T such that if T prime is any time later than T Socrates is alive at T prime thus when you come to write out properly what one means by a great many ordinary statements it turns out a little complicated Socrates is mortal and Socrates is immortal are not each other's contradictory because they both imply that Socrates exists in time otherwise he would not be either mortal or immortal one says there is a time at which he dies and the other says whatever time you take he is alive at that time whereas the contradictory of Socrates is mortal would be true if there is not a time at which he lives an undetermined constituent in a propositional function is called a variable existence when you take any propositional function and assert of it that it is possible then this sometimes true that gives you the fundamental meaning of existence you may express it by saying that there is at least one value of x for which that propositional function is true take X as a man there is at least one value of x for which this is true that is what one means by saying that there are men or that men exist existence is essentially a property of a propositional function it means that that propositional function is true in at least one instance if you say there are unicorns that will mean that there is an X such that X is a unicorn that is written in phrasing which is unduly approximated to ordinary language but the proper way to put it would be X is a unicorn is possible we have got to have some idea that we do not define and one takes the idea of always true or if sometimes true as one's undefined idea in this matter and then you can define the other as the negative of that in some ways it is better to take them both as undefined for reasons which I shall not go into at present it will be out of this notion of some x which is the same as the notion of possible then we get the notion of existence to say that unicorns exist is simply to say that X is a unicorn is possible it is perfectly clear that when you say unicorns exist you are not saying anything that would apply to any unicorns there might happen to be because as a matter they're not any and therefore if what you had to say had any application to the actual individuals it could not possibly be significant unless it were true you can consider the proposition unicorns exist and can see that it is false it is not nonsense of course if the proposition went through the general conception of the unicorn to the individual it could not even be significant unless there were unicorns therefore when you say unicorns exist you are not saying anything about any individual things and the same applies when you say men exist if you say that men exist and Socrates is a man therefore Socrates exists that is exactly the same sort of fallacy as it would be if you said men are numerous Socrates is a man therefore Socrates is numerous because existence is a predicate of a propositional function or derivatively of a class when you say of a propositional function that it is numerous you will mean that there are several values of x that will satisfy it that there are more than one or if you like to take numerous in a larger sense more than ten or more than twenty or whatever number you think fitting if x y and z all satisfy a propositional function you may say that that proposition is numerous but x and y and z severally are not numerous exactly the same applies to existence that is to say that the actual things that there are in the world do not exist or at least that is putting it too strongly because that is utter nonsense to say that they do not exist is strictly nonsense but to say that they do exist is also strictly nonsense it is a propositional functions that you can assert or deny existence you must not run away with the idea that this entails consequences that it does not entail if I say the things that there are in the world exist that is a perfectly correct statement because I'm there saying something about a sir class of things I say it in the same sense in which I say men exist but I must not go on to this is a thing in the world and therefore this exists it is there the fallacy comes in and it is simply as you see a fallacy of transferring to the individual that satisfies a propositional function a predicate which only applies to a propositional function you can see this in various ways for instance you sometimes know the truth of an existence proposition without knowing any instance of it you know that there are people in Timbuktu but I doubt if any of you could give me an instance of one therefore you clearly can no existence propositions without knowing any individual that makes them true existence propositions do not say anything about the actual individual but only about the class or function it is exceedingly difficult to make this point clear as long as one adheres to ordinary language because ordinary language is rooted in a certain feeling about logic a certain feeling that our primal ancestors had and as long as you keep to ordinary language you find it very difficult to get away from the bias which is imposed upon you by language when I say eg there is a X such that X as a man that is not the sort of phrase one would like to use there is an X is meaningless what is an X anyhow there is not such a thing the only way you can really state it correctly is by inventing a new language ad hoc and making the statement apply straight off to X as a man as when one says X is a man is possible or invent a special symbol for it the statement that X is a man is sometimes true I've dwelt on this point because it really is a very fundamental importance I shall come back to existence in my next lecture existence as it applies to descriptions which is a slightly more complicated case than I am discussing here I think an almost unbelievable amount of false philosophy has arisen through realizing what existence means as I was saying a moment ago a propositional function in itself is nothing it is merely a schema therefore in the inventory of the world which is what I am trying to get at one comes to the question what is there really in the world that corresponds with these things of course it is clear that we have general propositions in the same sense in which we have atomic propositions for the moment I will include existence propositions with general propositions we have such propositions as all men are mortal and some men are Greeks but you have not only such propositions you have also such facts and that of course is where you get back to the inventory of the world that in addition to particular facts which I've been talking about in previous lectures there are also general facts and existence facts that is to say there are not mainly propositions of that sort but also facts of that sort that is rather an important point to realize you cannot ever arrive at a general fact by inference from particular facts however numerous the old plan of complete induction which used to occur in books which was always supposed to be quite safe and easy as opposed to ordinary induction that plan of complete induction unless it is accompanied by at least one general proposition will not yield you the result that you want suppose for example that you wish to prove in that way that all men are mortal you are supposed to proceed by complete induction and say a is a man that is mortal B is a man that is mortal C is a man that is mortal and so on until you finish you will not be able in that way to arrive at the proposition all men are mortal unless you know when you have finished that is to say that in order to arrive by this road at the general proposition all men are mortal you must already have the general proposition all men are among those I have enumerated you never can arrive at a general proposition by inference from particular propositions you will always have to have at least one general proposition in your premises that illustrates I think various points one which is epistemological is that if there is as there seems to be knowledge of general propositions then there must be primitive knowledge of general propositions I mean by that knowledge of general propositions which is not obtained by inference because if you can never infer a general proposition except from premises of which one at least is general it is clear that you can never have knowledge of such propositions by inference unless there's knowledge of some general propositions which is not by inference I think that the sort of way such knowledge or rather the belief that we have such knowledge comes into ordinary life is probably very odd I mean to say that we do habitually assume general propositions which are exceedingly doubtful as for instance one might if one were counting up the people in this room assume that one could see all of them which is a general proposition and very doubtful as there may be people under the tables but apart from that sort of thing you do have in any empirical verification of general propositions some kind of assumption that amounts to this that what you do not see is not there of course you would not put it so strongly as that but you would assume that with certain limitations in certain qualifications if a thing does not appear to your senses it is not there that is a general proposition and it is only through such propositions that you arrive at the ordinary empirical results that one obtains in ordinary ways if you take a census of the country for instance you assume that the people you do not see are not there provided you search properly and carefully otherwise your census might be wrong it is some assumption of that sort which would underlie what seems purely empirical you could not prove empirically that what you do not perceive is not there because an empirical proof would consist in perceiving and by hypothesis you do not perceive it so that any proposition of that sort if it is accepted has to be accepted on its own evidence I only take that as an illustration there are many other illustrations one could take of the sort of propositions that are commonly assumed many of them with very little justification I come now to a question which concerns logic more nearly namely the reasons for supposing that there are general facts as well as general propositions when we were discussing molecular propositions I threw doubt upon the supposition that there are molecular facts but I do not think one can doubt that there are general facts it is perfectly clear I think that when you have enumerated all the atomic facts in the world it is a further fact about the world that those are all the atomic facts there are about the world and that is just as much an objective fact about the world as any of them are it is clear I think that you must admit general facts as distinct from and over and above particular facts the same thing applies to all men are mortal when you have taken all the particular men that there are and found each one of them severally to be immortal it is definitely a new fact that all men are mortal how new a fact appears from what I said a moment ago that it could not be inferred from the mortality of the several men that there are in the world of course it is not so difficult to admit what I might call existence facts such facts asked there are men there are sheep and so on those I think you will readily admit as separate and distinct facts over and above the atomic facts I spoke of before those facts have got to come into the inventory of the world and in that way of propositional functions come in as involved in the study of general facts I do not profess to know what the right analysis of general facts is it is an exceedingly difficult question in one which I should very much like to see studied I am sure that although the convenient technical treatment is by means of propositional functions that is not the whole of the right analysis beyond that I go there is one point about whether there are molecular facts I think I mentioned when I was saying that I did not think there were disjunctive facts that a certain difficulty does arise in regard to general facts take all men are mortal that means X is a man implies X is immortal whatever X may be you can see at once that it is a hypothetical proposition it does not imply that there are any men nor who are men and who are not it simply says that if you have anything which is a man that thing is mortal as mr. Bradley has pointed out in the second chapter of his principles of logic trespassers will be prosecuted may be true even if no one trespasses since it means merely that if anyone trespasses he will be prosecuted it comes down to this that X is a man implies X as a mortal is always true is a fact it is perhaps a little difficult to see how that can be true if one is going to say that Socrates is a man implies Socrates is a mortal is not itself effect which is what I suggested when I was discussing disjunctive facts I do not feel sure that you could not get round that difficulty I only suggested as a point which should be considered when one is denying that there are molecular facts since if it cannot be got round we shall have to admit molecular facts now I want to come to the subject of completely general propositions and propositional functions by those I mean propositions and propositional functions that contain only variables and nothing else at all this covers the whole of logic every logical proposition consists wholly and solely of variables though it is not true that every proposition consisting wholly and solely of variables is logical you can consider stages of generalization as Socrates loves Plato X loves Plato X loves Y X are Y there you have been going through a process of successive generalization when you have got two X or why you've got a schema consisting only of variables containing no constants at all the pure schema of dual relations and it is clear that any proposition which expresses a dual relation can be derived from X or Y by assigning values to X and r and Y so that that is as you might say the pure form of all those propositions I mean by the form of a proposition that which you get we need for every single one of its constituents you substitute a variable if you want a different definition of the form of a proposition you might be inclined to define it as the class of all those propositions that you can obtain from a given one by substituting other constituents for one or more of the constituents the proposition contains eg in Socrates loves Plato you can substitute somebody else for Socrates somebody else for Plato and some other verb for loves in that way there are a certain number of propositions which you can derive from the proposition Socrates loves Plato by replacing the constituents of that proposition by other constituents so that you have there a certain class of propositions in those propositions all have a certain form and one can if one likes say that the form they all have is the class consisting of all of them that is rather a provisional definition because as a matter of fact the idea of form is more fundamental than the idea of class I should not suggest that as a really good definition but it will do provisionally to explain the sort of thing one means by the form of a proposition the form of a proposition is that which is in common between any two propositions of which the one can be obtained from the other by substituting other constituents for the original ones when you've got down to this formulas that contain only variables like X R Y you are on the way to the sort of thing that you can assert in logic to give an illustration you know what I need by the domain of a relation I mean all the terms that have that relation to something suppose I say xry implies that X belongs to the domain of our that would be a proposition of logic and is one that contains only variables you might think it contains such words as belong and domain but that is an error it is only the habit of using ordinary language that makes those words appear they are not really there that is a proposition of pure logic it does not mention any particular thing at all this is to be understood as being asserted whatever x and r and y may be all the statements of logic are of that sort it is not a very easy thing to see what are the constituents of a logical proposition when one takes Socrates Lux Plato Socrates is a constituent loves is a constituent and Plato is a constituent then you turn Socrates into X loves into R and played-out into y x and r and y are nothing and they are not constituents so it seems as though all the propositions of logic were entirely devoid of constituents I do not think that can be quite true but then the only other thing you can seem to say is that the form is a constituent that propositions of a certain form are always true that may be the right analysis though I very much doubt whether it is there is however just this to observe is that the form of a proposition is never a constituent of that proposition itself if you assert that Socrates lost Plato the form of that proposition is the form of the dual relation but this is not a constituent of the proposition if it were you would have to have that constituent related to other constituents you will make the form much too substantial if you think of it as really one of the things that have that form so that the form of a proposition is certainly not a constituent of the proposition itself nevertheless it may possibly be a constituent of general statements about propositions that have that form so I think it is possible that logical proposition might be interpreted as being about forms I can only say in conclusion as regards the constituents of logical propositions that it is a problem which is rather new there has not been much opportunity to consider it I do not think any literature exists at all which deals with it in any way whatever and it is an interesting problem I just want now to give you a few illustrations of propositions which can be expressed in the language of pure variables but are not propositions of logic among the propositions that are propositions of logic are included all the propositions of pure mathematics all which cannot only be expressed in logical terms but can also be deduced from the premises of logic and therefore they are logical propositions apart from them there are many that can be expressed in logical terms that cannot be proved from logic and are certainly not propositions that form part of logic suppose you take such a proposition as there is at least one thing in the world that is a proposition that you can express in logical terms it will mean if you like that the propositional function X is identical with X is a possible one that is a proposition therefore that you can express in logical terms but you cannot know from logic whether it is true or false so far as you do know it you know it empirically because there might happen not to be a universe and then it would not be true it is merely an accident so to speak that there is a universe the proposition that there are exactly thirty thousand things in the world can also be expressed in purely logical terms and it's certainly not a proposition of logic but an empirical proposition true or false because a world containing more than thirty thousand things in a world containing fewer than thirty thousand things are both possible so that if it happens that there are exactly thirty thousand things that is what one might call an accident and is not a proposition of logic there are again two prop that one is used to in mathematical logic namely the multiplicative axiom and the axiom of infinity these also can be expressed in logical terms but cannot be proved or disproved by logic in regard to the axiom of infinity the impossibility of logical proof or disproof may be taken as certain but in the case of the multiplicative axiom it is perhaps still open to some degree of doubt everything that is a proposition of logic has got to be in some sense or other like a tautology it has got to be something that has some peculiar quality which I do not know how to define that belongs to logical propositions and not to others examples of typical logical propositions are if P implies Q and Q implies R then P implies R if all A's are B's and all B's are C's then all A's are C's if all A's are B's and X is an A then X is a B those are propositions of logic they have a certain peculiar quality which marks them out from other propositions and enables us to know them a priori but what exactly that characteristic is I am NOT able to tell you although it is a necessary characteristic of logical propositions that they should consist solely of variables ie that they should assert the universal truth or the sometimes truth of a propositional function consisting wholly of variables although that is a necessary characteristic it is not a sufficient one I am sorry that I've had to leave so many problems unsolved I always have to make this apology but the world it really is rather puzzling and I cannot help it discussion question is there any word you would substitute for existence which would give existence to individuals are you applying the word existence to two ideas or do you deny that there are two ideas mr. Russell no there is not an idea that will apply to individuals as regards the actual things are in the world there is nothing at all you can say about them that in any way corresponds to this notion of existence it is a sheer mistake to say that there is anything analogous to existence that you can say about them you get into confusion through language because it is a perfectly correct thing to say all the things in the world exist and it is so easy to pass from this to this exists because it is a thing in the world there is no sort of point in a predicate which could not conceivably be false I mean it is perfectly clear that if there were such a thing as this existence of individuals that we talk of it would be absolutely impossible for it not to apply and that is the characteristic of a mistake end of lecture five 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 6 descriptions and incomplete symbols I am proposing to deal this time with the subject of descriptions in what I call incomplete symbols and the existence of described individuals you will remember that last time I dealt with the existence of kinds of things what you mean by saying there are men or there are Greeks or phrases of that sort where you have an existence which may be plural I'm going to deal today with an existence which is asserted to be singular such as the man with the iron mask existed or some phrase of that sort where you have some object described by the phrase the so-and-so in the singular and I want to discuss the analysis of propositions in which phrases of that kind occur there are of course a great many propositions very familiar in metaphysics which are of that sort I exist or God exists or Homer existed and other such statements are always occurring in metaphysical discussions and are I think treated in ordinary metaphysics in a way which embodies a simple logical mistake that we shall be concerned with today the same sort of mistake that I spoke of last week in connection with the existence of kinds of things one way of examining a proposition of that sort is to ask yourself what would happen if it were false if you take such a proposition as Romulus existed probably most of us think that Romulus did not exist it is obviously a perfectly significant statement whether true or false to say that Romulus existed if Romulus himself entered into our statement it would be plain that the statement that he did not exist would be nonsense because he cannot have a constituent of a proposition which is nothing at all every constituent has got to be there as one of the things in the world and therefore if Romulus himself entered into the propositions that he existed or that he did not exist both these propositions could not only not be true but could not be even significant unless he existed that is obviously not the case and the first conclusion one draws is that although it looks as if Romulus were a constituent of that proposition that is really a mistake Romulus does not occur in the proposition Romulus did not exist suppose you try to make out what you do mean by that proposition you can take say all the things that Livy has to say about Romulus all the properties he ascribes to him including the only one probably that most of us remember namely the fact that he was called Romulus you can put all this together and make it positional functions saying X has such in such properties the property is being those that you find enumerated in living there you have a propositional function and when you say that Romulus did not exist you are simply saying that that propositional function is never true that it is impossible in the sense I was explaining last time ie that there is no value of x that makes it true that reduces the non-existence of Romulus to the sort of non-existence I spoke of last time where we have the non-existence of unicorns but it is not a complete account of this kind of existence or non-existence because there is one other way in which a described individual can fail to exist and that is where the description applies to more than one person you cannot eg speak of the inhabitant of London not because there are none but because there are so many you see therefore that this proposition Romulus existed or Romulus did not exist does introduce a propositional function because the name Romulus is not really a name but a sort of truncated description it stands for a person who did such and such things who killed Remus and founded Rome and so on it is short for that description if you like it is short for the person who was called Romulus if it were really a name the question of existence could not arise because a name has got to name something or it is not a name and if there is no such person as Romulus there cannot be a name for that person who is not there so that this single word Romulus is really a sort of truncated or telescoped description and if you think of it as a name you will get into logical errors when you realize that it is a description you realize therefore that any proposition about Romulus really introduces the propositional function embodying the description as say X was called Romulus that introduces you at once to a propositional function and when you say Romulus did not exist you mean that this propositional function is not true for one value of x there are two sorts of descriptions what one may call ambiguous descriptions when we speak of a so and so and what one may call definite descriptions when we speak of the so-and-so in the singular instances are of an ambiguous description a man a dog a pig a cabinet minister of a definite description the man with the iron mask the last person who came into this room the only Englishman who ever occupied the papal see the number of the inhabitants of London the son of 43 and 34 it is not necessary for a description that it should describe an individual it may describe a predicate or relation or anything else it is phrases of that sort definite descriptions that I want to talk about today I do not want to talk about ambiguous descriptions as what there was to say about them was said last time I want you to realize that the question whether a phrase is a definite description turns only upon its form not upon the question whether there is a definite individual so described for instance I should call the inhabitant of London a definite description although it does not in fact describe any definite individual the first thing to realize about a definite description is that it is not a name we will take the author of Waverly that is a definite description and it is easy to see that it is not a name a name is a simple symbol ie a symbol which does not have any parts that are symbols a simple symbol used to designate a certain particular or by extension an object which is not a particular but is treated for the moment as if it were or is falsely believed to be a particular such as a person this sort of phrase the author of Waverly is not a name because it is a complex symbol it contains parts which are symbols it contains four words and the meanings of those four words are already fixed and they have fixed the meaning of the author of Waverly in the only sense in which that phrase does have any meaning in that sense its meaning is already determinant ie there is nothing arbitrary or conventional about the meaning of that whole phrase when the meanings of the author of and Waverly have already been fixed in that respect it differs from Scott because when you have fixed the meaning of all the other words in a language you've done nothing toward fixing the meaning of the name Scott that is to say if you understand the English language you would understand the meaning of the phrase the author of Waverly if you had never heard it before whereas you would not understand the meaning of Scott if you had never heard the word before because to know the meaning of a name is to know who it is applied to you sometimes find people speaking as if descriptive phrases were names and you will find it suggested eg that such a proposition as Scott is the author of Waverly really asserts that Scott and the author of Waverly are two names for the same person that is an entire delusion first of all because the author of Waverly is not a name and secondly because as he can perfectly well see if that were what is meant the proposition would be one like Scott is Sir Walter it would not depend upon any fact except the person in question was so-called because name is what a man is called as a matter of fact Scot was the author of Waverly at a time when no one called him so when no one knew whether he was or not and the fact that he was the author was a physical fact the fact that he sat down and wrote it with his own hand which does not have anything to do with what he was called it is in no way arbitrary you cannot settle by any choice of Naumann clay Chur whether he is or is not to be the author of Waverly because in actual fact he chose to write it and you cannot help yourself that illustrates how the author of Waverly is quite a different thing from a name you can prove this point very clearly by formal arguments in Scott is the author of Waverly he is of course expresses identity ie the entity whose name is Scott he is identical with the author of Waverly but when I say Scott is mortal the is is the is of predication which is quite different from the is of identity it is a mistake to interpret Scott is mortal as meaning Scott is identical with one among mortals because among other reasons you will not be able to say what mortals are except by means of the propositional function X is mortal which brings back the is of predication you cannot reduce the is of predication to the other is but the is in Scott is the author of Waverly is the is of identity and not a predication footnote the confusion of these two meanings of is is essential to the Hegelian concept of identity in difference end of footnote if you were to try to substitute for the author of Waverly in that proposition any name whatever say see so that the proposition becomes Scott is C then if C is a name for anybody who is not Scott that proposition would become false while if on the other and see is a name for Scott then the proposition will become simply a tautology it is at once obvious that if C were Scott itself Scott is Scott is just a tautology but if you take any other name which is just a name for Scott then if the name is being used as a name and not as a description the proposition will still be a tautology for the name itself is merely a means of pointing to the thing and does not occur and what you are asserting so that if one thing has two names you make exactly the same assertion which ever of the two names you use provided they are really names and not truncated descriptions so there are only two alternatives if C is a name the proposition Scott is C is either false or tautologies but the proposition scott is the author of Waverly is neither and therefore is not the same as any proposition of the form Scott is C where C is a name that is another way of illustrating the fact that a description is quite a different thing from a name I should like to make clear what I was saying just now that if you substitute another name in place of Scott which is also a name of the same individual say Scott is Sir Walter then Scott and Sir Walter are being used as names and not as descriptions your proposition is strictly a tautology if one asserts Scott is Sir Walter the way one would mean it would be that one was using the names as descriptions one would mean that the person called Scott is the person called Sir Walter and the person called Scott is a description and so is the person called Sir Walter so that would not be a tautology it would mean that the person called Scott is identical with the person called Sir Walter but if you are using both as names the matter is quite different you must observe that the name does not occur in that which you assert when you use the name the name is merely that which is a means of expressing what it is you are trying to assert and when I say Scott wrote Waverly the name Scott does not occur in the thing I am asserting the thing I am asserting is about the person not about the name so if I say Scott is Sir Walter using these two names as names neither Scott nor Sir Walter occurs in what I am asserting but only the person who has these names and thus what I am asserting is a pure tautology it is rather important to realize this about the two different uses of names or of any other symbols the one when you are talking about the symbol and the other when you are using it as a symbol as a means of talking about something else normally if you talk about your dinner you're not talking about the word dinner but about what you are going to eat and that is a different thing altogether the ordinary use of words is as a means of getting through two things and when you are using words in that way the statement Scott is Sir Walter is a pure tautology exactly on the same level as Scott is Scott that brings me back to the point that when you take Scott is the author of Waverly and you substitute for the author of Waverly a name in the place of a description you get necessarily either at cetology or a falsehood a tautology if you substitute Scott or some other name for the same person and a falsehood if you substitute anything else but the proposition itself is neither a tautology nor falsehood and that shows you that the proposition Scott is the author of Waverly is a different proposition from any that can be obtained if you substitute a name in the place of the author of Waverly that conclusion is equally true of any other proposition in which the phrase the author of Waverly occurs if you take any proposition in which that phrase occurs and substitute for that phrase a proper name whether that name be Scott or any other you will get a different proposition generally speaking if the name that you substitute is Scott your proposition if it was true before will remain true and if it was false before will remain false but it is a different proposition it is not always true that it will remain true or false as may seen by the example George the fourth wished to know if Scott was the author of Waverly it is not true that George the fourth wish to know if Scott was Scott so it is even the case that the truth or the falsehood of a proposition is sometimes changed when you substitute a name of an object for a description of the same object but in any case it is always a different proposition when you substitute a name for a description identity is a rather puzzling thing at first sight when you say Scott is the author of Waverly you are half tempted to think there are two people one of whom is Scott and the other the author of Waverly and they happen to be the same that is obviously absurd but that is the sort of way one is always tempted to deal with identity when I say Scott is the author of Waverly and that is expresses identity the reason that identity can be asserted there truly and without topology is just the fact that the one is a name and the other a description or they might both be descriptions if I say the author of Waverly is the author of Marvin that of course asserts identity between two descriptions now the next point I want to make clear is that when a description when I say description I mean for the future a definite description occurs in a proposition there is no constituent of that proposition corresponding to that description as a whole in the true analysis of the proposition the description is broken up and disappears that is to say when I say Scot is the author of Waverly it is a wrong analysis of that to suppose that you have their three constituents Scot is and the author of Waverly that of course is the sort of way you might think of analyzing you might admit that the author of Waverly was complex and could be further cut up but you might think the proposition could be split into those three bits to begin with that is an entire mistake the author of Waverly is not a constituent of the proposition at all there is no constituent really there corresponding to the descriptive phrase I will try to prove that to you now the first and most obvious reason is that you can have significant propositions denying the existence of the so and so the Unicorn does not exist the greatest finite number does not exist propositions of that sort are perfectly significant are perfectly sober true decent propositions and that could not possibly be the case if the unicorn were a constituent of the proposition because plainly it could not be a constituent as long as there were not any unicorns because the constituents of propositions of course are the same as the constituents of the corresponding facts and since it is a fact that the unicorn does not exist it is perfectly clear that the unicorn is not a constituent of that fact because if there were any fact of which the unicorn was a constituent there would be a unicorn and it would not be true that it did not exist that applies in this case of descriptions particularly now since it is possible for the so-and-so not to exist and yet four propositions in which the so-and-so occurs to be significant and even true we must try to see what is meant by saying that the so-and-so does exist the occurrence of tents in verbs is an exceedingly Annoying vulgarity due to our preoccupation with practical affairs it would be much more agreeable if they had no tents as I believe is the case in Chinese but I do not know Chinese you ought to be able to say Socrates exists in the past Socrates exists in the present or Socrates exists in the future or simply Socrates exists without any implication of tents but language does not allow that unfortunately nevertheless I'm going to use language in this tense list way when I say the so-and-so exists I am NOT going to mean that it exists in the past or in the present or in the future but simply that it exists without implying anything involving tents the author of Waverly exists there are two things required for that first of all what is the author of Waverly it is the person who wrote Waverly ie we are coming now to this that you have a propositional function involved this X rights Waverly and the author of Waverly is the person who writes Waverly and an order that the person who writes Waverly may exist it is necessary that this propositional function should have two properties one it must be true for at least 1 X 2 it must be true for at most one X if nobody had ever written Waverly the author could not exist and if two people had written int the author could not exist so that you want these two properties the one that it is true for at least one x and the other if that it is true for at most one X both of which are required for existence the property of being true for at least one X is the one we dealt with last time what I expressed by saying that the propositional function is possible then we come on to the second condition that it is true for at most one X and that you can express in this way if x and y wrote wave early then X is identical with Y whatever x and y maybe that says that at most one wrote it it does not say that anybody wrote Waverly at all because if nobody had written it that statement would still be true it only says that at most one person wrote it the first of these conditions for existence fails in the case of the Unicorn and the second in the case of the inhabitant of London we can put these two conditions together and get a portmanteau expression including the meaning of both you can reduce them both down to this that X wrote Waverly is equivalent to X is C whatever X maybe is possible in respect of C that is as simple I think as you can make the statement you see that means to say that there is some entity C we may not know what it is which is such that when X is C it is true that X will Waverly and when X is not C it is not true that X wrote Waverly which amounts to saying that C is the only person who wrote Waverly and I say there is a value of C which makes that true so that this whole expression which is a propositional function about C is possible in respect of C in the sense explained last time that is what I mean when I say that the author of Waverly exists when I say the author of Waverly exists I mean that there is an entity C such that X wrote Waverly is true when X is C and is false when X is not seen the author of Waverly as a constituent has quite disappeared there so that when I say the author Waverly exists I'm not saying anything about the author of Waverly you have instead this elaborate to do with propositional functions and the author of Waverly has disappeared that is why it is possible to say significantly the author of Waverly did not exist it not be possible if the author of Waverly were a constituent of propositions in his verbal expression this descriptive phrase occurs the fact that you can discuss the proposition God exists is a proof that God as used in that proposition is a description and not a name if God were a name no question as to existence could arise I have now defined what I mean by saying that a thing described exists I still have to explain what I mean by saying that a thing described has a certain property supposing you want to say the author of Waverly was human that will be represented thus X wrote Waverly is equivalent to X is C whatever X may be and C is human is possible with respect to C you will observe that what we gave before as the meaning of the author of Waverly exists is part of this proposition it is part of any proposition in which the author of Waverly has what I call a primary occurrence when I speak of a primary occurrence I mean that you are not having a proposition about the author of Waverly occurring as a part of some larger proposition such as I believe that the author of Waverly was human or I believe that the author of Waverly exists when it is a primary occurrence ie when the proposition concerning it is not just part of a larger proposition the phrase which we defined as the meaning of the author of Waverly exists will be part of that proposition if I say the augur Waverly was human or poet or Scotsman or whatever I say about the author of Waverly in the way of a primary occurrence always this statement of his existence is part of the proposition in that sense all these propositions that I make about the author of Waverly imply that the author of waverly exists so that any statement in which a description has a primary occurrence implies that the described object exists if I say the present King of France is bald that implies the present King of France exists if I say the present King of France has a fine head of hair that also implies that the present King of France exists therefore unless you understand how a proposition containing a description is to be denied he will come to the conclusion that it is not true either that the present King of France is bald or that he is not bald because if you were to enumerate all the things that are bald you would not find him there and if you were to enumerate all the things that are not bald you would not find him there either the only suggestion I have found for dealing with that on conventional lines is to suppose that he wears a wig you can only avoid the hypothesis that he wears a wig by observing that the denial of the proposition the present King of France is bald will not be the present King of France is not bald if you mean by that there is such a person as the king of France and that person is not bald the reason of this is that when you state that the present king of France is bald you say there is a C such that C is now king of France and C is bald and the denial is not there is a C such that C is now king of France and C is not bald it is more complicated it is either there is not a C such that C is now King of France or if there is such a C then C is not bald therefore you see that if you want to deny the proposition the present King of France is bald you can do it by denying that he exists instead of by denying that he is bald in order to deny this statement that the present King of France is bald which is a statement consisting of two parts you can proceed by denying either part you could deny the one part which would lead you to suppose that the present King of France exists but is not bald or the other part which will lead you to the denial that the present King of France exists and either of those two denials will lead you to the falsehood of the proposition the present King of France is fault when you say Scott is human there is no possibility of a double denial the only way you can deny Scott is human is by saying Scott is not human but wear a descriptive phrase occurs you do have the double possibility of denial it is of the utmost importance to realize that the so-and-so does not occur in the analysis of propositions in whose verbal expression it occurs that when I say the author of Waverly is human the author of Waverly is not the subject of that proposition in the sort of way that Scott would be if I said Scott is human using Scott as a name I cannot emphasize sufficiently how important this point is and how much error you get into metaphysics if you do not realize that when I say the author of Waverly is human that is not a proposition of the same form as Scott is human it does not contain a constituent the author of Waverly the importance of that is very great for many reasons and one of them is this question of existence as I pointed out to you last time there is a vast amount of philosophy that rests upon the notion that existence is so to speak a property that you can attribute to things and that the things that exist have the property of existence and the things that do not exist do not that is rubbish whether you take kinds of things or individual things described when I say eg Homer existed I am meaning by Homer some description say the author of the Homeric poems and I am asserting that those poems were written by one man which is a very doubtful proposition but if you could get hold of the actual person who did actually write those poems supposing there was such a person to save him that he existed would be uttering nonsense not a falsehood but nonsense because it is only a person's described that it can be significantly said that they exist last time I pointed out the fallacy of saying men exist Socrates is a man therefore Socrates exists when I say homer exists this is Homer therefore this exists that is a fallacy of the same sort it is an entire mistake to argue this is the author of the Homeric poems and the author of the Homeric poems exists therefore this exists it is only where a propositional function comes in that existence may be significantly asserted you can assert the so-and-so exists meaning that there is just one si which has those properties but when you get hold of a C that has them you cannot say of this see that it exists because that is nonsense it is not false but it has no meaning at all so the individuals that there are in the world do not exist or rather it is nonsense to say that they exist and nonsense to say that they do not exist it is not a thing you can say when you have named them but only when you have described them when you say Homer exists you mean Homer is a description which applies to something a description when it is fully stated is always of the form the so-and-so the sort of things that are like these descriptions and that they occur in words in a proposition but are not an actual fact constituents of the proposition rightly analyzed things of that sort I call incomplete symbols there are a great many sorts of incomplete symbols and logic and they are sources of a great deal of confusion and false philosophy because people get myzel by grammar you think that the proposition scott is mortal and the proposition the author of Waverly is mortal are the same form you think that they are both simple propositions attributing a predicate to a subject that is an entire delusion one of them is or rather might be and one of them is not these things like the author of Waverly which I call incomplete symbols are things that have absolutely no meaning whatsoever in isolation but merely acquire a meaning in a context Scott taken as a name has a meaning all by itself it stands for a certain person and there it is but the author of Waverly is not a name and does not all by itself mean anything at all because when it is rightly used in a propositions those propositions do not contain any constituent corresponding to it there are a great many other sorts of incomplete symbols besides descriptions these are classes which I shall speak of next time and relations taken in extension and so on such aggregations of symbols are really the same thing as what I call logical fictions and they embrace practically all the familiar objects of daily life tables chairs Piccadilly Socrates and so on most of them are either classes or series or series of classes in any case they are all incomplete symbols ie they are aggregations that only have a meaning in use and do not have any meaning in themselves it is important if you want to understand the analysis of the world or the analysis of facts or if you want to have any idea what there really is in the world to realize how much of what there is in phraseology is of the nature of incomplete symbols you can see that very easily in the case of the author of Waverly because the author of Waverly does not stand simply for Scott nor for anything else if it stood for Scott Scott is the author of Waverly would be the same proposition as Scott is Scott which it is not since George the fourth wished to know the truth of the one and did not wish to know the truth of the other if the author of Waverly stood for anything other than Scott Scott is the author of Waverly would be false which it is not hence you have to conclude that the author of Waverly does not in isolation really stand for anything at all and that is the characteristic of incomplete symbols end of lecture six

Philosophy of Logical Atomism | Bertrand Russell | Modern, Philosophy | Sound Book | English | 2/3

4: [00:00:00] – Lecture 4

5: [00:34:34] – Lecture 5

6: [01:11:07] – Lecture 6

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