 Hi and welcome back. This is week four of the philosophy course and this week we're going to move on to questions of logic and we're going to focus this week on formal logic. Now up to now we've largely just been discussing materialism and different questions related to it, but Marx's philosophy isn't just materialist it's also dialectical materialism and elements of this we have touched upon in previous weeks that is true for example when we discussed the problems of skepticism in bourgeois philosophy and doubt about the existence of an external world I pointed out that that was related partly to problems of thought associated with formal logic with a tendency to sort of isolate different things but we haven't gone into it properly and of course logic is very important to philosophy so it is important that we begin to discuss this and before we discuss dialectical logic we're going to discuss as I said formal logic which Marxism is critical of shall we say and so yeah well let's just start on a discussion of that so logic what is logic for us logic are are laws of thought really or an attempt to describe what the laws of thought are now for materialists these laws of thought are derived from the real laws of the material world the general features of the material world which governs ultimately our thoughts you know for example we can say that there is a logical principle because it's the case that in the real world objects have certain relations or regularities with one another they can't contradict one another or you know certain types of things exist in relations in certain kinds of relations to other things and from these general features we draw certain principles like you know the idea of of different kinds of species for example and that's something must be must belong to one thing and not to another thing this reflects the the the most general features of the material world and if it contradicted it then it would ultimately have to be illogical however for many philosophers especially for formal logicians shall we say logic really has nothing to do with the material world it's merely a set of rules for how we should think irrelevant of what the world is like and for them these rules are sort of self-sufficient they are you know they they only refer to themselves they don't come from anywhere else and they are self-evidence you know like the idea of two plus two equals four and so there's no there's no need to say anything or to prove their origin in the material world for them now for us as I said that is the opposite of the truth and logic is not really a set of rules for thought in the sense of you don't need to have studied logic to be able to think properly because as I said it really reflects the general principles that we have extracted from the world Hegel ironically put this when he said that logic the study of logic no more teaches you how to think than the study of digestion teaches you how to digest you you're still able to digest regardless of whether or not you have studied that formal logic started out as a discipline if you like with Aristotle the ancient Greek philosopher who codified it really into a set of and he was the first one to really sort of propose you know logic has a sort of distinct discipline with a set of rules and so he codified it in a sense and its most famous and sensual rule is the law of non-contradiction and of identity so basically he stated it is that A equals A and does not equal B you know so you can't say that an object doesn't equal itself you can't say that a person is some other person and yet not themselves they can only be themselves and they can't be somebody else and this of course is a very useful although extremely basic and kind of obvious thing to say and our criticism of it is that ultimately is very one-sided and kind of empty really but nevertheless it is an important insight it is based really on the principle of abstraction so human thought really is all about abstraction and what is abstraction well when we abstract something we we isolate certain features of itself we talk about we have the the abstract concept of sharpness right so we find objects that are sharp and we sort of we abstract that characteristic from them and then talk about that as if it exists independently of those of that object and also by abstracting we we we tend to sort of concentrate on a specific object so we might discuss you know a certain species of animal and we concentrate on its features right we we isolate it in a sense and that's what abstraction is all about it's about sort of concentrating on certain things simplifying them and thereby gaining an understanding of them and this is an absolutely vital ability if we we couldn't do this then we wouldn't actually be able to think at all and Lenin says the following he says thoughts proceeding from the concrete to the abstract provided it is correct and of course it's possible to make a false abstraction does not get away from the truth but comes closer to it the abstraction of matter or law of nature the abstraction of value etc in short all scientific or correct abstractions reflect nature more deeply truly and completely from living perception to abstract thoughts and from this to practice such as the dialectical path of the cognition of truth of the cognition of objective reality so for us as Marxists we don't say that this is useless this formal logic which is based on abstraction it is absolutely essential and by abstracting something in a sense you do arrive at a profounder truth then merely you know seeing the thing that is in front of you and treating it as a one-off object you you discover its general properties basically so it's an enormously powerful tool really and that's really the secret to the power of humanity but there is also ultimately a one-sided falseness to abstraction and therefore to formal logic as well both formal logic and abstraction are dangerous for this reason because by tearing something out of its context and concentrating on it and simplifying it we are in a sense saying something that is also untrue on the one hand it is as I've said it's a deeper truth it's also on the same at the same time kind of untrue because of course that feature such as sharpness you know or as Lenin says matter these are never really exist as such and they always exist in a far more complex and changing reality than what our abstraction really is about so yes it allows us to isolate certain details and come to understand them but there's a limit to this it kind of kills the object in a sense it rips it out of its real context in real nature it removes the the sense of fluidity that is true that is real in any given object everything changes everything exists in a complex web of interrelations and abstraction essentially loses this although in a certain sense it also understands it because by giving something a general property like sharpness you are also bringing in relation of course to all other things that are sharp or or things that aren't sharp but nevertheless in the main what you're tending to do is to take things out of their context to concentrate on this object and ignoring its real history and interconnections and dependencies and so the danger of this approach is that we lose you know we can we end up actually misunderstanding the nature of reality and yes so so abstraction by abstracting we categorize things we tend to put things in boxes and say that you know this species is this species and that species is that species and this species has x characteristics right and therefore we are using the law of non-contradiction that I mentioned earlier we are saying that this you know for example how do we describe a given species well we say that x species has y characteristics and therefore if you find that animal that has all of y characteristics then it must be x species and in doing so of course you have gained some very real knowledge but you've also you've sort of compartmentalized the thing you've frozen it so that you don't understand and there's no ability in this way of thinking to understand why that kind of animal came about in the first place where it came from you know you can't understand any of these things and you've you've sort of killed it again so again this is the danger of of formal logic the limitation shall we say of formal logic um now this this this basic principle that it's based upon the law of non-contradiction seems obviously true a a equals a obviously how could it not um but actually is it as true what as it appears well actually it isn't and Hegel pointed this out quite brilliantly before Marx um he pointed out that it's essentially a tautology and a tautology is when you say that something is itself and which is of course what to say a equals a is and the trouble with the tautology is first of all it's kind of empty and unuseless you know if you ask somebody ask you how tall you are and you say well I'm as tall as I am nothing is no real knowledge is gained of course um now if we take an example so we say a dog is a dog which again is a tautology it may appear that we're talking about a dog but actually you haven't said anything whatsoever about a dog or dogs and the only reason that you in discussing this have perhaps a picture of a dog in your mind is because you have experience of dogs this statement saying a dog is a dog doesn't tell you anything about the nature of a dog at all you wouldn't give you a picture of a dog right and so actually not only is it kind of empty but it's actually false in a sense it's nothing really it's not it isn't you're not describing a dog you're not understanding a dog at all um hey describe there's a brilliant passage in in in the logic of his books where he says that uh he takes up the idea of pure existence which is again that really the same thing as saying a dog is a dog since that isn't actually talking about dogs in any real way you're just talking about existence really abstract existence and he points out that this is the same as nothing if you want to talk about anything that is real any actual object any actual thing you have to define it you have to determine it you have to say that it's this and not that you know it's yellow and not red you know it's it's hard it's not soft it's tall and it's not short whatever you're defining it and therefore you're limiting it and you're bringing it in relation to other things you're giving it determinant qualities as hate would say uh but of course these determinant qualities also have to exist in time because let's take the example of being yellow something can only be yellow over time what is it to be yellow it's to reflect uh yellow wavelengths of photons basically wavelengths of light that's why we call something yellow but you can only do that over time it's not something that happens outside of time in a pure instance so any specific quality that something has uh can only exist it can only be expressed in time and therefore through change ultimately therefore everything is always changing and the truth of something is in the fact that it changes um and therefore aid is not equally and i'd like to give a quotation from Trotsky a very famous passage uh from the abc of materials dialectics where he takes up this apparent obvious truth and he says but in reality a is not equal to a this is easy to prove if we observe that these two letters under a lens they're if we observe these two letters under a lens they're quite different from each other but one can object the question is not the size or the form of the letters since they're only symbols but um for symbols for equal quantities for instance a pound of sugar the objection is beside the point in reality a pound of sugar is never equal to a pound of sugar a more delicate scale will always disclose a difference but again one can object a pound of sugar is equal to itself neither is this true though all bodies change uninterruptedly in size weights color etc they're never equal to themselves a sophist will respond that a pound of sugar is equal to itself at any given moment aside from the extremely dubious practical value of this axiom it does not withstand theoretical criticism either how should we really conceive the word moment if it is an infinitesimal interval of time then a pound of sugar is subjected during the course of that moment to inevitable changes or is the moment a purely mathematical abstraction that is a zero of time but everything exists in time and existence itself is an uninterrupted process of transformation time is consequently a fundamental element of existence thus the axiom a is equal to a signifies that a thing is equal to itself if it does not change if it therefore does not exist so apologies for that well long quotation but it is a very very good argument and I think it puts it very clearly so change therefore and everything changes all the time change means that something is and is not and that might seem paradoxical more ridiculous than saying a equals a but actually it is the most fundamental truth of how things are things are here and there at the same time again that might sound ridiculous but take zeno's paradox zeno's paradox was is a famous paradox that basically asserts that change is impossible because it says that for something to get from point a to point c it must in the meantime pass through point b but to pass but before it can get even to point b it must also pass through another point and therefore it can never really arrive at point c because it's always stuck at the interval you know it's always but before it can get there it has to get there before it can get there it has to get to this other shore to a point and then you can always break it down further and further and it's inexplicable however actually gets to see because there's always further points that has to traverse and essentially what he's arguing is that space can be divided up infinitely and every single part of that traverse that that span of space has to be passed and if you can divide it even further still then there's even more points that you have to pass and you can never get through this infinite number of points essentially and this is a very very famous in philosophy is a very famous objection of course it's absurd because we all know that things can move and can get from point a to point c um the problem with this and again it's a problem of formal logic is that it assumes that uh that space is made up of discrete you know uh just infinite number of discrete kind of points if you like that must each of which have to be occupied before you can get to the next one because in reality space is not made up of little discrete points in reality it is continuous and you don't sort of perfectly inhabit one space one absolute point and then suddenly pop into the next one and then the next one and then the next one in reality you are flowing through a continuous span of space rather than there being just so many discrete points um and and therefore to comprehend this you have to be able to comprehend that not only does everything change but the change involves contradiction it involves the idea of being here and there being you know in more than one point because in reality there isn't such a thing as a single point but a continuous flow of space um but uh formal logic can't really understand that's because it does want to divide things up into these discrete moments um now formal logic also and i mentioned before that formal people who practice formal logic treat it as not derived from the material world as independent from the material world and just a set of rules self-contained rules for thought um and in treated in this way it is indifferent to content it's just a set of abstract rule and the advantage of this is supposed to be that these abstract rules can apply to anything you know they are universal they're very clear and they're just absolutely objective it's it's true or it isn't true um and it's supposed to be very therefore very clear basically um and it eliminates contradiction apparently that's the another advantage that it has um but is that true and can that be true well let's take a famous example um what is known as the syllogism which is the the statement uh if a then b a therefore b that is considered in formal logic a perfectly valid statement right and an example of it would be you know uh if a famous example if it rains the streets are wet and then you say it is raining therefore the streets are wet that is a valid statement it you know kind of ticks all the boxes essentially um but according to formal logic doesn't matter what the actual premises are so long as you complete that sort of cycle so you can also say if it rains the streets are on fire it is raining therefore the streets are on fire according to formal logic that is as valid as saying if it rains the streets are wet it rains therefore the streets are wet because it's a ridiculous thing to say uh and there's no connection between the the principle of rain and fire that is that you can understand it doesn't just is complete nonsense it's incomprehensible um now it is according to formal logic false to flip the um the syllogism so in other words to say if a then b b therefore a so to go back to our example that would be if it rains the streets are wet the streets are wet therefore it is raining now that is considered false and it is false it's true because why because obviously there are plenty of other things that could cause the streets to be wet maybe a fire engine you know um was putting out a fire and it sprayed some water somewhere and therefore the streets are wet so the the mere fact that the streets are wet does not prove that it's raining but how do we know that that is true that that it's true that in other words how do we know that it's false to say it to put the syllogism in the other way around as I just given only because of real world experience right so that's the only thing that can tell us anything about uh the fact that there can be other causes of streets getting wet or any other particular thing you care to mention it's only knowledge of the real world and the manifold causation that there can be the things that the fact that one thing can be caused by many different things such as the streets being wet can be caused not only by rain but but could potentially be caused by a whole host of other things obviously involves the understanding of what water is etc it only makes sense because we have real knowledge real experience of the principles of the objective world otherwise if we had absolutely no experience that how and what what how would any of these terms have any meaning whatsoever now in 20th century philosophy where formal logic was adhered to still it really has held philosophy back um for example you have what is known as propositional calculus which is taught in a lot of universities today and again this has zero content it's not about the content it's not about the actual material things you're supposed to be talking about it's a set of abstract rules that are supposed to apply perfectly and you just need to learn them and it's sort of always presented as like almost in a mathematical kind of algebraic way very sort of appears very scientific but again it says nothing about the world it seems to comprehend nothing about real human language for example if you study if you study it you will learn that it can only deal with yes or no answers ambiguities you know gray areas other kinds of answers to things are not uh comprehended in this system uh and also you will learn that but is the same as and so but is eliminated so any sentence that you want to put into propositional calculus that includes the word but you get rid of that and you put and in because it means the same thing but but does not mean the same as and it is a related term it has something in common but there's a gradation of meaning and it and it's it's important to have that you were to tell that to someone who practices proposition calculus they would accept that but does mean something that they would say well that doesn't matter that's not really what we're dealing with and that shows you that propositional calculus and formal logic in general has become this kind of rigid dogma totally abstract and unable to comprehend the real meanings of human language and thoughts and of course of the real world and therefore barren really um so if if human thought were to stick and if philosophy does stick to this dogma or a formal logic it inevitably becomes entangled in contradictions it's true that formal logic expresses a truth which we do need to to comprehend and that is that you know things do stay the same in other words it would be absurd to insist on calling your friend a different name every minute because they've shed some cells and they've grown some other cells somewhere else that would be ludicrous they have fundamentally stayed the same um and that of course applies to all kinds of objects that's what formal logic bases itself upon and that's very important we don't go around throwing names and concepts out and out because the the objects has changed in some infinitesimal way um so one side it expresses one side of the truth shall we say but if we stick to that one side we'll get entangled in contradictions we won't be able to understand the deeper um questions of change of systems of interconnection you know and of basically the fund of contradiction and the transformation of one thing into something other than itself and that is really the most profound way of understanding the world how do things change what are the systems that govern change in the universe to understand those questions we all need formal logic which is what we're going to come on to discuss in the next few weeks