Michael Beaney: The Analytic Revolution (Royal Institute of Philosophy)

thank you thank you very much and thanks very much for the invitation to talk in this series one sometimes thinks that analytic philosophy is a historical Sidney Rosen in a historical way and doesn't really have a history and one thing that I perhaps of anything I've been trying to show in my own work is just how historical analytic philosophy is and try and trace the development of analytic philosophy so I've called the the talk slightly provocatively some people might disagree the analytic revolution I want to suggest that there was something distinctive came into existence when analytic philosophy arose and try and give you an answer as to what's particularly distinctive of analytic philosophy certainly one central strand in analytic philosophy and that's the strand that originates in the work of Frager and Russel so here's the plan I mean you've got a got a handout so if you can't read what's on here you can look at the handout if you fall asleep for five minutes you can perhaps pick up from the hand and that way where we're at and this is the plan fairly straightforward I should say the first half is about Frager introducing his ideas about logic and the use that he put that logic in his project called logis ISM and then I'll turn to Bertrand Russell the other important figure as far as the development of this particular kind of philosophy is concerned then I'll consider some general questions about the nature of analysis and then I'll conclude so there's this other than this slide there's 15 slides so three to four minutes on each one and I'll try and conclude in about 50 to 55 minutes to have time for discussion okay so you know we're where we're at okay so a few words of introduction then analytic philosophy as we know it today I think one would have to say is a very complex tradition there's lots of different if you like sub traditions strands within it some of them reinforce one another some of them are actually in conflict so one con said there is you want can't give necessary and sufficient conditions for what it is to be analytic processes safely not today sometimes certainly if one goes back 20 30 years people will have said the analytic tradition arose in the rebellion by Bertrand Russell and G Moore against British idealism British idealism was the dominant tradition in Britain especially in Oxford in the last two decades in the 19th century and Russell and more came along there from Cambridge so of course they wanted to criticise the octave philosophy and they rejected it and that then started the development of analytic philosophy of course that's a gross simplification as people started to understand the ideas especially of Russell and even more especially of Vik and Stein they realised the importance of Gottlob Frager okay so now I think most people would say that got logged Prager together with Russell Moore and Vik and Stein are the cofounders of analytic philosophy okay why was fragrant fragrant because he created what we now know is modern logic quantificational logic and he used that logic to engage in a project of analysis okay and that influenced Russell the questions that Frager asked about that generated by thinking through his ideas in turn provoked Pitkin Stein so Prager is very much at the center at the root of of ideas that Russell on one hand and Viktor shine in particular on the other developed so one should go back to the fragran if there's one thing I'd like to convince you of is the importance of Frager okay so as Anton said it's not just a story of British philosophy Frager as we'll see him in a minute was German okay so um Russell was influenced by Frager both Prague and Russel was so-called Lodge assists and a Lodge assist is someone who thinks that mathematics or arithmetic just arithmetic in the case of Frager is reducible to logic so friggin Russell had the similar project nevertheless their conceptions of that project was slightly different so there are differences as we'll see that we'll come to and in particular perhaps the most famous and I'm sure a lot of you here will know of this Russell's theory of descriptions is often called a paradigm of analysis by that partly developed against the background of Russell's concern with logis ISM okay now just a stress I don't want to deny that more and Vic and Stein are equally important in the development of analytic philosophy as that in fact the more complex story I tell about the history of analytic philosophy involves two strands the Frager Russell stress more concerned with logic and idea languages and the so called ordinary language strand which comes from or through Vic and Stein and into Oxford in the 1950s but I'm not going to tell that that story that's a little bit later I want to focus on if you like the origins of what we now recognize as analytic philosophy and in particular the strand that originates in the work of Frager and Russell okay so actually on each of these slide for those who do want to take a brief nap I've highlighted the key sentence or passage in red so if you if you haven't followed what I said just focus in on the red bit that's the key bit on each slide okay a single out one particular sentence each time so keeping fragran Russell's work then is at the heart of what I've called here from this talk the analytic revolution ok so a couple of words just by way of introducing Frager he was a mathematician logician and then through his work on logic and mathematics started being interested in in fossa fee I've chosen here a nice picture of him the standard picture you might see rather older Frager after he'd got his project had been destroyed by Russell as well see you slightly grumpier figure but actually this is quite a nice friendly figure I like it was nice bushy beard so that's the figure right that's the picture I prefer he spent his entire academic career with the exception of study for a couple of years in getting at University of llena from 1874 to 1917 when he retired on the writer his main works so the ones that I'll say something about his his main books which is the burglar shrift of 1879 the foundations of arithmetic in 1884 and the basic laws of arithmetic 1893 1903 that's where he develops his logis ISM his views that arithmetic can be reduced to logic in between he developed his philosophical ideas to support his logit ism and his most famous ones a function and concept on sense and reference and on concept and object I'll say something some of the ideas in particularly function concept and on concept an object I'll talk about today and then finally his other most famous papers much much later is or thought from 1918 but I won't actually say anything about that today okay that's just a paid brief introduction to to Frager um okay so let's let's turn then to what I call here the logical revolution that Frager inaugurated and one can contain that revolution quite precisely 1879 that's when frege's first book was published called the Griff shrift sober Griffith means concept script and was the name that fragrance logical system okay and in that book he creates the first system of what we now know as quantificational logic so for those if you don't know what his I'll explain a little bit in a minute about what quantification logic was but basically it's a far more powerful logic than has ever been developed up to that point okay so as I put it here it sort of opened up a whole host of opened up the semantic machinery as I put it here of a whole host of sentences that couldn't be effectively analyzed before by traditional particularly Aristotelian logic ok so it's a far more powerful tool to understand the logical relationships between sentences and that was really important for Frager because when you look at mathematics you actually have quite complicated sentences so you need a more powerful logic in order to analyze mathematical sentences okay so that that's what Frager teve din in the bagua shrift the absolute key so here's the red bit wake up for just this bit and you go back to sleep if you want the absolutely key bit is the use that Frager made a function argument analysis extending it from mathematics to logic okay so this should be familiar from your sort of high school mathematics so we could represent a line in analytic geometry for example as y equals ax plus b where a is the gradient and b is the point where the line intersects the y-axis and we would say that y is a function of X so if you take the equation y equals 2x plus 3 for example and you put in X is 1 you get 5 okay and so on so you exhibit Y is a function of X ok that seems to apply nicely to equations mathematical equations the essence of frege's revolution if you like is to generalize that to all sentences he suggested all sentences can be represented as in function argument form okay so let's take a really simple sentence got love is human okay which traditionally in traditional logic you'd analyze this in subject predicate form so s is P okay in frege's new logic you know in logic you write it as FA where a represents the argument in this case the so called argument in this case Gottlob and FX would represent in this case the function X is human so the idea is you plug in Gottlob into there and out pops your sentence okay so you're representing sentences as functions of arguments and you've got object names and concept or function names okay so that's the basic idea there might not seem to be much difference at this level between the traditional subject predicate analysis ssp and function argument analysis FA it becomes significant when we consider more complex sentences so the next kind of sentence you might consider is relational sentences so if I say got log is shorter than Bertrand which is it's true that you'd analyze that as a function of two arguments which you'd represent as are a B and you can extend it indefinitely so if I said York is between London and Edinburgh that would be a function of three arguments okay so frege's logic already gives you a more unified account of relational sentences but okay okay so that was the key thing on this slide but where the power of function argument analysis really comes in is when you have sentences involving what are called quantifier terms like all some in particular most even though sometimes seen as a as a quantify term terms that quantify how many of something there is okay Aristotelian logic did have a system of logic looked at the relationship between all A's in some A's and some ways always be some ways a B and so on but what frege's new logic can do is consider cases where you have very complex sentences with multiple quantify terms but let's let's just stick to the simplest kind okay for those who've done logic this will be utterly familiar but hopefully some further down the line you'll see what the philosophical significance is and terms of some of the philosophical ideas that Frager and Russell had so we take the sentence all logicians are human okay we represent that in logic is flawed X if X is a logician then X is human okay so we're seeing this in function argument terms you put in a value for X whatever you take if it's a logician then it's human that has a much more complex as we put it logical for than it's simple grammatical form grammatically all magicians the human might seem rather like got love is human it's just that you switch from a name for a single object to a name for a collection of objects okay frege's say actually the logic the logical form of the the sentence or logicians of a human is much more complex than its grammatical form might suggest okay it has this form that will be reveals in the logic which we might express by saying if anything is in a if anything is a logician then it's human for all X if something is a logician then it's human so you have two functional expressions X is L X as a logician X is human connected by a propositional connective if then and banned by the quantifier so it's much more complex okay something similar applies to the sentence some magicians are human here you use the so called existential quantifier and you have that says there are some things that are both logicians and humans okay so the key the key thing is then these sentences are much more complex than their grammatical form might suggest and logic is a tool as it were to open up the complexity of that sentence so one way to put it using a term that Russell later uses in his theory descriptions is that the subject terms or logician song magicians are analyzed away okay in their logic or formalization and there as a word English paraphrase of that the term all logicians some magicians doesn't appear it disappears okay we just have a term for the concept magician and the concept human that's the key bit that I'll come back to in a minute okay that's simple this is a simple sentence with just one quantify term where for like quantification logic really comes into its own is where you have complex sentences sentences involving two or more quantifiers so here's just a standard example to illustrate the importance of the idea here so if I were to say every philosopher respects some magician okay you've got to quantify terms every and some that sentence is actually ambiguous right you can either mean take any philosopher there's some magician not necessarily the same one boom they respect or could mean there is some one magician that every philosopher respects okay they have two different meanings you can display that meaning there's two different meanings really nicely in quantificational logic we don't worry this is unfamiliar but this is the idea for X if X is a philosopher then there's some Y such that Y is a logician such that X respects Y okay that's the first reading and the second reading there is some magician someone magician that all philosophers respect okay so you can capture that difference really nicely using quantifier notation and then you can prove for example that that implies that but not the other way round okay and thinking that that implies that is what's called the quantifier shift fallacy and actually you can detect the quantifier shift fallacy in philosophical and even mathematical arguments okay so identifying as it were the ambiguity and pinpoint note as were clarifying it by means of the logic can actually provide useful service to all of us who engage in thinking okay so that's just an example of the power of quantificational logic and the the possibility that it has of representing complex propositions okay so how'd then did Frager use his logic his lodge yeah used his logic sorry used the possibilities of analysis opened up by this in actually explaining his logical ideas and then in the next section you will consider how he used his logical analysis in his logic this project his phosphated mathematics ok so here's what Frager says he says as we've just noted God lobbies human all logicians a human have different logical forms okay he puts that by saying there are two different logical relations involved the first is called subsumption you subsume an object under a concept okay the second is subordination and that's the relationship between one concept and another concept on the same level we'll come back to that idea in a minute okay so two different logical relations are involved when we say that Gottlob is human we're subsuming an object under a concept as we when we say all humans as or logicians the humans which is the relationship between the two concepts logician and human okay so here's then what one says logical analysis it aims to do is to reveal the logical form of sentences not just for its own sake but to solve philosophical problems okay that's crucial in as well the development of analytic philosophy it gives you the tools to reveal the logical form to solve certain philosophical problems so here's a really simple example to illustrate the basic idea and again we'll come back to the strategies you hear later on so I say unicorns do not exist okay that's true if we analyze that in subject-predicate for we might be what's the subject unicorns and what's the predicate sort of do not exist or words we might want to put it non existent so we might express that by saying unicorns are non-existent okay everything well how do we understand that what are these unicorns that have this property of non-existence if there aren't any you of course and then you know how can how can that be true okay looks like this is a puzzle the puzzle of negative existential statements okay analyzing in traditional subject predicate terms sort of makes one thing well what are these are these unicorns and some philosophers most notably and famously someone called Alexis my norms suggested well you've got to suppose they exist somehow let's call it subsistence rather than an existence in order to be the subject term of such sentences okay now how do we formalize this representing logic we do so using the existential quantifier so to say that unicorns do not exist is just to say there is nothing it's not the case that there are some X such that X as a unicorn okay so here - the subject term unicorns is analyzed away okay what does this mean as we're interpreting it back into a ordinary language it may the concept unicorn is is not instantiated the concept eunuch doesn't have any instances okay so there if you know all you're committed to is the concept of a unicorn you can give an account of that it's you know concept that's made up composed of the concept of a horse and the concept of horn so we you know we don't have a problem with the concept of the unicorn okay so when we claim that unicorns do not exist we're not claiming that there are these mysterious entities that have the property of non-existence we're just claiming something about a concept namely that the concept is not instantiated okay what Frager says is the then draws a distinction first level and second level concepts so what we're saying when we say unicorn do not exist is that the first level concept which is a concept under which objects can fall if they do falls within just a single from falling under a second level concept so when we say the concept unicorn is not instantiated we're saying a first level concept forthwith in the second level concept is not instantiated okay so these quantifiers the existential and the universal quantifier are seen as second level concepts okay and that's that's crucial as well okay so you where you can see the sophistication of the understanding of the way the logic works here but also doing some philosophical work okay so no we don't we haven't got to suppose that the unicorn some have subsists to make sense the sentence all we need to suppose is that the relevant concept somehow exists and what we claim is it has no instances okay so that's one one one good example okay let me start to unpack some of what's going on here by distinguishing to I think quite important conceptions of analysis okay interpretive and decompositional okay so the message of what we just said is that logical analysis seems can do genuine philosophical work if we understand the logical structure of logical form of our sentences we get a better sense of some of the philosophical problems that might arise from misinterpreting them okay but analysis here doesn't just mean decomposition if you ask people today what we know what his analysis mean they often say well it means breaking something down into its it's doesn't it okay so one thing I've really been trying to do my work partly by going right back to the ancient Greeks and elaborating on different conceptions of analysis is that that isn't the only conception of analysis okay maybe it's a conception that is suggested by traditional subject-predicate analysis so you take got labas human what's the analysis well you break it into its bits got lob is inhuman okay but as we've just seen in function argument analysis who are who are suggesting there are quite different constituents okay all logicians are human for example is if anything is a logician then it's human okay so you're not breaking it down into all and logicians are and human but into something else so that suggests you need to distinguish interpreting the sentence into its logical form then you do the decomposition okay so go back to the unicorns not exist we're not decomposing into unicorns and the property of non-existence but into the concept unicorn and the second level property is not instantiated okay so you interpret unicorns do not exist as the concept unicorn is not instantiated that's interpretive analysis then you can perhaps do your decompositional analysis and say we know we should be committed to the concept unicorn existing and the second level property is not instantiated okay so you need to separate out these two elements in the analysis the interpretation which is often encoded in the logical representation and then the decomposition comes in to sort of directly to what's really out there in the world okay so again if you wanted in a slogan in logical analysis there's no decomposition without interpretation we're going to see how that works in more in more detail in the rest of this talk okay so a few words then about frege's lodges this project I'm going to try and explain about too much technicality and just to give you a flavor of what frege's doing so as I mentioned that the three main books that he wrote Arbor Griffith 1879 the foundations of arithmetic 1884 and the basic laws of arithmetic 1893 and 99 1903 in the first book we're sure he gives you his new logic he also provides using that logic a logical analysis of mathematical induction which is an important form of reasoning in mathematics ok so it made it you know these plausible that maybe his claim that arithmetic is reducible to logic could you know it could could work one can give a logical analysis and mathematical induction on his own system of logic was actually quite complicated and I'm not using it here no one uses it now and because he was very complicated people didn't understand what he was doing so his book got rather bad reviews so someone suggested to him that he ought to write his ideas more informally before doing the formal proofs the result was the foundations of arithmetic in 1884 which is an absolute masterpiece and if there's one book you should read to understand what analytic philosophy generally is about and certainly Frager it's that book ok I'm going to say something about that in a minute and then the formal proofs were offered in his his magnum opus really the basic laws of arithmetic but I shall concentrate on the key idea of the foundations and this is the claim so this is a bit in red number statements are assertions about concepts ok so what is Frager mean by say number statements or assertions about concepts well we were ready in a position to see what it means number statements are just like existential statements existential statements in fact are a type of number statement when we say that something doesn't exist we mean that the concept has no instances when we say that something does exist we mean that the concept has at least one instance okay so existential stems are a kind of number statement and what is an existential statement it's an assertion about a concept when we say that unic or not exist we're making a claim about the concept unicorn namely that it doesn't have any instances okay so a simple idea so here's an example Prager gives Jupiter has four moons and every day claim we might make Jupiter has four moons well if we analyze this in traditional subject-predicate terms we'd say well the subject is Jupiter and then has this property has four moons what is this property having four moons how can we analyze that further it's not clear how we would how we would go okay well what Frager suggests is since this is this should be understood as a an assertion about a concept it's an assertion about the concept of Jupiter so when we say Jupiter has four moons we mean the concept moon of Jupiter has four instances okay so it's an assertion about a concept okay now here's a little kind of sketch of how one might might then define that logically okay this is the kind of thing that frame Freddie it does so when we say that the concept moon has four instances recently mean there are objects VW x and y such that each of them is a moon of Jupiter and none of them are identical with one another so they're distinct and if there's anything else there was a moon of Jupiter it'll be equipment to one or other those okay so it said there are four objects that are moons of Jupiter that are distinct and there were no others okay so this now looks extremely complicated right logically but it captures the idea that's involved here so this is if you like a representation of the logical form using quantifiers it has a much more complex logical form than that would suggest but the idea is this reveals what's really meant or going on when we say that Jupiter has four moons what we mean we mean there are four objects that have the property of being moon of Jupiter and no others and that's what's expressed expressed here okay so that's that's the idea one generalizes the idea frege's trying to give an account of all kinds of sentences that involve number terms now number here is being used adjective early for moons we also talked about the number four for example so let me just say briefly give you an idea about how free Frager defines the natural numbers themselves okay so here we need to introduce another important idea the idea of an extension of a concept or a class so the idea is that for every concept you have a set of things that fall under that concept fraggles that the extension of the concept now we might talk about it being the class or the set okay classes frege's all work they're a kind of abstract object a kind of logical object okay so what Frager does is define the numbers as classes as extensions of concepts so since he thinks that let's accept this for now that class is a kind of logical object if you can define the numbers as class than you've shown that numbers are effect and in fact logical objects okay so here's his roughly how how it goes in order to find the numbers logically we've got to take logical concepts so take the concept of identity and negation which are accepted as logical concepts okay form the concept then not identical with itself okay we can form the concept not identical itself is a logical concept well nothing says forego is not identical with itself okay so the class of things that fall under the concept not identical itself is Bonnard class okay so the simple view is just define the number 0 as the null class in fact fragrance it is a the class of all classes that have the same number of members of the now class but we can ignore that complication here the basic idea is the number 0 can be defined in terms of the null class which is logically defined well now we have our first object so we can form the concept is identical with this object ok that has 1 object we can use that to define our number 1 now we have two objects so we can define the concept is identical with either naught or one and we can use that to define the number two and so on that's how that's how it goes ok as I put it here starting with a non class then and using the only logical concept we can define all the natural numbers okay so that's that's that's that's the idea ok we'll see why this is important just a second okay so now turning turning to to Burton Russell then the second half of the of the talk probably more familiar to most of you very famous in all sorts of ways I'm also like Frager a mathematician who turned to concern with the foundations of mathematics and developed logic himself to some extent and a fossa fer educated the Cambridge if your father were concerned the key books and events are firstly his rebellion against British idealism partly inspired by Moore's own rebellion that they had slightly different agendas between roughly 1898 in 1902 and I'm not going to say anything in detail about this Brussels main objection to British idealism was it couldn't do justice to mathematics ok it's only when he discovered frege's new logic he had a meeting famous meeting with piano famous Italian magician in 1900 and piano said no you've got to read Frager or gotta understand this new logic and he didn't realize that this was a if you like the tool the key to his own problems about trying to explain mathematics okay then his first attempt was in the principles of mathematics in 1903 okay after that think about just like Frager thinking about the philosophical ideas you have his most famous paper on denoting of 1905 which we'll talk about in a minute and then again like Frager a formal demonstration of his logis ISM with Whitehead who also has become a famous philosopher in his own right principia mathematica 1910 to 1913 if you want the the briefest succinctness and best summary of Russell's philosophy is introduction to mathematical philosophy which you wrote when he was in prison he was imprisoned for during the first world war for objecting to the war and he wrote this book see ya cloud has a silver lining as they say and okay so lot of paradox okay I've said Frager was concerned to demonstrate logis ism he's working very hard at it obsessed by it Russell discovered a paradox now known as Russell's paradox in 1902 and he wrote to Frager telling him about this paradox and fragrance dated he said you've undermined the foundations on which I wanted to build arithmetic when it was sent favorable frege's second volume of his foundation his basic laws of arithmetic was impressed and he tried to respond to the paradox in an appendix but actually he realized soon after that his response doesn't didn't didn't work and actually he ended up giving up his logis ISM because he couldn't solve this this particular problem so it's left to Russell then to take up the mantle of logics ISM and try and find a way to solve the paradox okay and a lot of his work in the succeeding the next decade were an attempt to solve the paradox and develop logic says even though the paradox seemed to be threatening okay so what what is this what is this paradox well there's two kind of assumptions that kind of drive it and remember than what fragrant does is define the numbers as classes in fact the class of classes that are that had the same number of members as a as a given class so actually he allows himself talk of classes of classes as well in his account so one assumption is that for every concept there's a class associated with it the things the class the set the class the extension of things the extension of the concept the set of things that fall under that concept and that classes can be members of other classes and in particular can be members of themselves so take the concept of a class okay that would fall under if you take the class of classes right that class is itself a class so it would be a member of itself okay so with that in mind here's the paradox so I prayed all of this is in red now so you will have to wake up for more and longer than usual on this slide okay so the idea is this we take the class of horses okay the class itself is not a horse okay so that class is not a member of itself okay the class is not a horse so it's not a member of itself but now take the class turn on horses right the class of non horses is itself a non horse yeah so that is a member of itself okay so you can divide all classes into those that the members of themselves and those that aren't members of themselves okay now let's click together the class of classes that are not members themselves and ask is that class a member of itself or not if it is since it's the class of classes they're not members of itself then it is and if it is I've got this right way back and if it isn't since it's the class the classes that are members of themselves it is okay so you've got a contradiction so you've got an object that seemed to exist because it's legitimately well formed okay but it has contradictory properties so can't exist after all okay now some paradox you say well that shows there can't be such a class the problem is that the defining condition for such a class is seemingly perfectly logically legitimate classes ought to be able to be members of other classes and membership is something that you you can define and looks like some classes come out as not members of themselves okay so that that's that's that's the problem now again without going into the real details of this what was Freya what was Russell's response his response was the so-called theory of types and in essence what he says is there's a hierarchy of objects of things that say things so I'm covering both objects and classes there's objects on the ground level there's classes of those objects there's classes of those classes and so on up the hierarchy its objects classes classes classes classes of classes of classes and so on okay and something can only be a member of the class higher up okay class higher up can't be a member of class low down okay so they can't be a class cannot be a member of itself okay that was the essence of Russell's view it's really more complicated than Frager Fraga thought you could just blithely talk about a domain of all objects including classes and everything else and what Russell's paradox shows is that you can't okay you've got to recognize there's some kind of structure now the interesting question then is what's the status of these classes they're not like ordinary objects but what are they Russell came to believe that they're they're a kind of logical fiction or logical construction so let me just give you an example to illustrate the basic idea here okay so if I would say something like which I think let's say it's true it's not exactly this number who could have another number the average British woman has 1.9 children okay now you analyze this in traditional subject predicate form who is this average average British woman like some imagine some investigative journalist from the BBC you going man who know can we find me this average woman even if there were such an average woman I think you wouldn't find that they had one point nine children okay but we know what we mean when we say that and we can say the such sentences are true what do we mean we just mean that the total number of children of British women divided by the total number British women is 1.9 okay so the average British woman is a kind of logical fiction or a logical construction which you can explain by understanding this proposition is this this sort of um that's what we mean when we say that this is a kind of abbreviated simpler form okay it enables us to say well look you know while the average British woman has 1.9 children the average Chinese woman has 1.6 we can make comparisons more easily across countries by using this kind of notation mine makes it simpler to talk it's a convenient way of talking ok but of course that there is no such person or need be no such person as the average British woman okay so there's a sense in which it's a logical fiction or logical construction okay which doesn't mean that sentences in which the term appears don't have a sense than the truth value okay so let's apply that idea just to give you an idea of what's going on here to talk of classes so we can say things about classes we can say the class of horses is a subclass of the class of animals seems to be true but if you know classes don't really exist because they're they're problematic no what do we mean well we just need anything that falls under the concept horse falls under the concept animal which we can represent very easily in logic okay so if you like this doesn't commit us to the existence of classes just to the existence of concepts and so one could say in a sense talk of classes is constructed out of our talk of concepts okay so that that's that's the idea and I think this is one way of explaining the idea of logical constructions okay so let's turn to Russell Thea descriptions because it's this problem that is in the sense in the background to Russell's theory description which you know may well be familiar to to a lot of a lot of you so the theory of descriptions are concerned with the meaning of definite descriptions that's terms of the form VF and remember a term like the class of classes that are not members of themselves isn't is a definite description so you know we're going to need to understand how definitely descriptions work and how they might still contribute to the meaning of sentences and the truth value of sentences even if they themselves we might want to say don't refer to anything okay so here's Russell's famous example the present King of France is bald again just like we did with unicorns not exist you know if there is no present King of France well what are we talking about doesn't mustn't present King of France subsist somehow in order for us to say anything about him okay if there isn't a king of France how do we understand the sentence is it true or false what it doesn't have a truth value if there's no present King of France looks like lots of questions arise when we puzzle over sentences in which the F doesn't seem to have a referent okay so here's Russell's analysis then the present King of France is bored is a complex sentence made up of a conjunction of three simpler sentences the first is there's at least one King of France which you can represent in logic there's some X such that KX the second is there's at most one King of France which again you can represent like that if you've got two things that look as if they're kings of France actually they're one and the same so that says there's the most one King of France and then the third one whatever is King of France is bald okay if you put all those three together you get the claim that there's one and only one there's unique King of France and whatever was King of France is bald which again simplified you would represent in logic like that there's some x such as x is the King of France and for y if y is a king front then they're the same and X is board okay so again made one main message the logical form of the present King of France is much more complex as a quantificational structure than the original sentence okay now so now working to a bit that even those who might know something about the thorough descriptions might be interested in how would we interpret that bearing in mind what we said before about Frager okay well what are we saying when we're saying that's putting it back as a were an ordinary language we're saying that the concept King of France is uniquely instantiated is instantiated by one and only one object and whatever instantiates that concept also instantiates the concept bald okay so it's a claim about concepts okay and what this suggests then is that although Russell's third descriptions is often held out as a paradigm of analysis all the materials for this analysis were already in Frager they're already for like embedded in the in the use of quantification or Lodge how might we will rephrase this still further to bring out this idea we might do it like this the concept King of France is uniquely instantiated and is subordinate to the concert board so remember we've already seen frege's analysis of existential statements okay as the instantiation of concept and we've seen as in the case of all magicians of human we've got the subordination so actually what Russell is saying is involved in the claim that the present King of France has brought is an assertion about a concept that a concept is uniquely instantiated and is subordinate to another concept so this sort of solves the problem in the same ways we sort of solved the problem in the case of negative existential statements we haven't got to worry about who with this present King of France is to make sense of it we're just talking about the relevant concepts we're saying that the concept King of France is instantiated uniquely and that concept is subordinate to another concept so if we can give an account of how we understand the concepts and Russell takes for granted we have an understanding of the logical connectors here that's an issue but we have a basic understanding of logic all we need is an understanding the concepts we haven't got to worry about somehow grasping the supposed referent of the terms okay so that's that's his solution and as I say the key thing as far as you might concern with the analytic revolution is that it's the resources made available by frege's new logic that provided the tools for this kind of analysis okay president King of France's Board is understood as interpreted as a claim about concepts not objects okay so find a couple of comments and then then then conclude so what I want to claim then is what's particularly distinctive of analytic philosophy as I say with qualification particularly the kind of Fraggle strand is the role played by interpretive analysis okay solving philosophical problems by translating them in a form such that they're amenable to logical formalization but what's interesting in that is that Frager and Russell use interpretive analysis differently and actually you'll find this then in later analytic philosophy people using this logical analysis and rather different ways for different philosophical purposes in particular one might say Russell uses interpretive analysis in a more eliminative astray not than just reductivist okay so let me just briefly explain the idea here just to contrast the two different methods and Frager us all so go back to our friend Jupiter and its moons Jupiter has four moons which we suggest here's a there's a logical analysis of that okay if that's something like that logical analysis is correct then for the term force is analyzed away it doesn't appear in any way here okay snot a term for four but says Frager this is actually also equivalent to the number of Jupiter's moons is the number four that also seems to be equivalent right so here's frege's thought then he thinks that this then shows that numbers are objects so he thinks his is thinking this if this tape if this is true and this is equivalent to this this must be true a sentence can only be true if the terms in it have meaning but item in his German so the number of Jupiter's moons and the number of four must have meaning but diatom which for him means they must be an object that they refer to that was his thinking so for him interpretive analysis is actually a way to indicate that something must have reference for the sentence of the hotel truth value okay Russell on the other hand precisely used interpreters to show that we don't need to be committed to objects as the reference of terms if we can find some paraphrase that has a word does away with it but you can see how interpretive analysis can actually be used in in different ways okay I myself have more sympathy for Russell the Russell position here but I prefer to talk about logical constructions rather than logical fictions because logical fictions makes you think well you know to say that something is a fiction is to say well it could exist but as a matter of fact doesn't whereas I think there's something misleading about even thinking whether numbers exist or not that's not to say the one can't think of them as in some sense a logical construction okay one can show how one can construct like we've seen in the case of the average British woman in class terms out of other terms okay but anyway that aside the key point then is that interpretive analysis opens up a variety of projects okay we can be more realist or playtest as it sometimes put with Frager or can be more a limb to vist with Russell there are different possibilities but they're all rooted in the possibilities of logical interpretive analysis okay so one final problem then before concluding so here's another paradox we've seen Russell's paradox this was a real threat to Frey get specific Lodge assist project but there's a possible paradox that this seems to threaten the whole idea of analysis especially interpretive analysis so let me make a few comments about that as well so here's one simple way of putting the paradox so we say analyzing a sentence or a concept a as B okay Jupiter has four moons as whatever it is okay then here's the dilemma either a and B have the same meaning or they don't if they had the same meaning then a is B as a trivial identity and doesn't tell us anything okay or maybe don't have the same meaning in which how can the analysis be correct so there's no such thing as an analysis that's both correct and informative okay now there's a lot to say about this paradox and actually Freya himself said something about this paradox and to some extent is he motivated his very famous distinction between sense and reference which I won't talk about today but here's an example to illustrate the problem so go back to our all logicians a human represented in logic is 4x alex implies H X so frege's analysis interpretive analysis is saying that's that says the same as always to be interpreted as the concept and logician is subordinate to the concept human now question do those two l1 and l2 have the same meaning can't someone understand what it is for logicians to be human without having any idea of the concept of subordination a lot of you today didn't know what subordination meant okay so how can you claim that that that has the same meaning you surely understood what all logicians a human meant okay now a minimum condition for correctness of analysis is certainly logical equivalence I think we would say well you might not have realized it but if that's true that's true and vice versa certainly if you buy the analysis in fact we want a little bit more than that as well and that's where it gets kind of messy trying to spell out what the suppose notion of sameness to sense as it would be here is let me bypass that question by stressing an important feature of analysis which i think is the way to resolve the paradox and that's the dynamic nature of the process of analysis again I've put this by saying again little slogan here takeaway message an analysis is informative by being transformative so what happens when you're offered in analysis as you understand it in analysis is that you acquire the concept by means of which to Rican sexualize deepen your understanding of what you started from so one thing I hope for those of you didn't know much of this before I might have hoped to understand today is that one can understand that the logical relation in the claim that all logicians are human is a relationship of subordination between concepts okay so I've kind of taught you I've given you the vocabulary in this case the concept of subordination to understand that sentence better when you've grasped that concept you can say oh yes I see that's exactly the same okay so you're brought to recognize the relevant similarity okay and that's because of the transformative dynamic aspect of analysis and not if we just take the a and B and just say well what how do I understand that you've got to recognize that analysis has a informative other has a transformative dimension okay so in general then this is the like that the message of of analytic frosting why I think one would say that it has been a very productive influential root movement in all sorts of different ways manna manna for different kinds of ways analysis provides different conceptual richer conceptual tools to understand something so what frege's new logic opened was a whole set of concepts by means of which to think more clearly about the logic relations between concepts okay we've seen some already subsumption subordination distinction first level and second level concepts etcetera etcetera quantifiers the second level concepts and so on they help us to think more clearly about the way that language works that in turn I think opens up a further set of questions which have also given rise to discussion naming the concepts of meaning sense reference and so on okay so well might then suggest to sort of round out the discussion here that those logical and semantic concepts and relations are themselves a kind of logical construction okay which emerge in our practices of doing analysis okay we get people to understand the relevant notion of meaning sense whatever it might be through taking them through the relevant analyses in the way that I hope I've Illustrated in the talk today ok so then finally conclusion very briefly what is analytic philosophy the obvious answer analytic philosophy is concerned with analysis but then the obvious objection is well analysis has always been involved in certainly Western philosophy from Socrates and Plato onwards okay so that that's not going to say anything that what's distinctive about analytic philosophy okay so what I want to claim is like the take-home message what's especially distinctive of this Frager Russell strand of analytic philosophy is the role played by interpretive analysis formal analysis that draws on the resources as we've seen the powerful new resources of the new quantificational logic okay so that brought with it a whole new set of concepts or maybe crystallized concepts that were there but no we probably didn't quite understand or realize how important they were as I said subordination stood sumption first level second level concepts etc which opened up a further set of questions about what's going on which opens up further issues about meaning sense and so on which are certainly characteristic of analytic philosophy in the later development and interestingly those are the questions that are taken as I put it here in by the next generation of analytic flosses in particular thickens dyeing the logical positivists and con up in particular when the so called linguistic turn was taken okay now that's another story I want to claim nevertheless that even that linguistic turn is ultimately rooted in frege's and Russell's analytic revolution thank you

Channel: RoyIntPhilosophy

Views: 10,512

Rating: 4.8271604 out of 5

Keywords: Analytic Philosophy (Field Of Study), Michael Beaney, Bertrand Russell (Author), Gottlob Frege, philosophy lecture, royal institute of philosophy, history of philosophy

Id: QCwcFC3cfks

Length: 51min 38sec (3098 seconds)

Published: Thu Jan 29 2015

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[u/ADefiniteDescription]

ABSTRACT:

Analytic philosophy, as we recognize it today, has its origins in the work of Gottlob Frege and Bertrand Russell around the turn of the twentieth century. Both were trained as mathematicians and became interested in the foundations of mathematics. In seeking to demonstrate that arithmetic could be derived from logic, they revolutionized logical theory and in the process developed powerful new forms of logical analysis, which they employed in seeking to resolve certain traditional philosophical problems. There were important difference in their approaches, however, and these approaches are still pursued, adapted, and debated today. In this lecture I shall elucidate the origins of analytic philosophy in the work of Frege and Russell and explain the revolutionary significance of their methods of logical analysis.

[u/cclaudian]

It irks me that I can't read the slides off the video :(