 Welcome back, in the last few lectures we given in any English language passage, we tried to identify the argument, so we said that whenever there is a premise and conclusion indicator, then we said that you know there seems to be some kind of argument present in a English language passage or may be while you are reading a text book, scientific text book etcetera you know or may be a newspaper or something else. So how to identify an argument was the first important task for us, then we started recognizing the, once we started recognizing the argument and we distinguished it from non-arguments, non-arguments in a sense that reports, piece of advice, suggestions, warnings etcetera and all, all these things comes under non-arguments in a sense that they are all non-inferential passages in all, so there is no inferential claim involved in those kinds of passages in all that is why that passage does not contain any argument. So once we recognize the argument in all, so the next question comes to us is what kind of argument it is, so there are two kinds of argument which we usually come across in introductory logic course or in logic at least two kinds of arguments which we come across, one is inductive argument, another one is deductive argument, based upon, based on how the conclusion follows from the premises, we are saying that it is a deductive argument or it is an inductive argument in all, if the conclusion necessarily follows from the premises then it is called as kind of deductive argument, if the conclusion probably follows from the premises then it is called as an inductive argument and also we said that in the case of deductive argument there is no new information in the conclusion which is not there in the premises, whatever is there in the premises we are trying to make it explicit in the conclusion whereas in the case of inductive arguments the conclusion goes beyond what is stated in the premises. So inductive arguments are in general they are defeasible in nature that means addition of new information might invalidate the old conclusions that you have drawn earlier, in the case of deductive arguments it is called as monotonic it is not non defeasible, so there even if you add more information in all your old conclusion will still follow. So this is what we have done so far, so now once we identify recognize the arguments and identified that this is an inductive argument and this is a deductive argument then the next question comes to us is what we mean by validity of deductive arguments and what we mean by the strength of a given inductive argument. In this class what I am going to talk about are these things, so first I will talk about what we mean by truth and it is a relationship with the validity and I will consider few examples and then it is not enough that the arguments are valid and then it has to be one extra condition we will impose that is what we call it as sound lesson. So this is the case for the deductive arguments a deductive argument can be valid or invalid a valid deductive argument can be sound or unsoundable. In the case of inductive arguments you can only talk about the strength of the argument, so you can say that a given inductive argument is either weak or strong. If it is a strong inductive argument the next question comes to us is whether it is a cogent or uncogent argument. A cogent inductive argument is a one in which it has probably true premises and all whereas an uncogent argument is a one in which at least it has one false premise. So these are the things which will be explaining in detail and there is one important method which is kind of common sensical method it is not a formal method etc and all we will be using other formal decision procedures little bit later but since we are considering everything from the scratch the basic concepts. So we will be talking about a specific method which is very interesting in all so that method is called as counter example method if time permits we will go into the details of this one. So now the most important thing which we will be asking ourselves is what we mean by truth. So this is the most difficult question to answer it is a million dollar kind of question it is not easy to come up with an answer and so but as far as possible we are trying to define what we truth or at least the definition of truth that seems to be acceptable to us for some time being. So there are we are all thinking beings we think a lot so there are some thoughts and then the thoughts corresponding to some kind of reality reality of the world or external world etc and all when thoughts refer to some kind of object that exists actually in the world it is a mapping between your thought and the actual object which is existing in the world then we say that there is a correspondence between whatever you think and then whatever actually exists there suppose if I show something that you know for example if I say that this is a pen then this corresponds to one of the objects that exist right in front of me so that is why the statement is true suppose if I say that this is a donkey and then no one will be in a position to believe that this is a donkey it is not referring to the actual facts etc that exist in the world. So there are various theories of truth which I am not going into the details of these things so there are debates between these theories of truth and all but the most widely used or you can say default theory of truth is the correspondence theory of truth. So what is this correspondence theory of truth I am not going to the details of these things but I will briefly mention that you know here are three theories of truth which we commonly use so mostly we will be using correspondence and coherence theory of truth there is another theory of truth which is due to pragmatist that is pragmatic theory of truth which I will talk about it little bit later. So the correspondence of correspondence theory of truth is as follows so according to the correspondence theory a claim that means it can be a conclusion or we will be claiming lots of things and all so a claim is considered to be true mostly it is a conclusion in an argument if it corresponds to what it is so that means it refers to some kind of facts reality etc and all if it is not referring to the facts of matter or the reality that exists in the world etc and all the sentence is false and all. So if it does not correspond to what it is so then that is considered to be a false statement and all suppose if I say that this is a cat then it is not referring to the cat and all so it is referring to some kind of pen etc so if I say that this is a pen and this is corresponding to the actual pen that exists in the world and all so it corresponds to the actual world that exists in the world and all. So that is why the sentence is true suppose if I say that this is a cat or donkey or something else then that particular kind of statement is false and all it is as simple as that there should be some kind of correspondence with the reality or actual matters of fact that we commonly encounter in day to day discourse. So for example if you say snow is white just in case snow is actually white and all suppose if snow is black in color then whatever you are saying is considered to be false and all actually that is not the case so that is why it is false and all is as simple as that and most of the scientist etc they are all comfortable with this kind of theory of truth so we are not going to the depth of these theories to what extent these theories works etc and all at this moment we are just briefly mentioning what we mean by truth so since truth has this connection to the validity so that is why we need to talk about some minimal kind of things about the truth and all. So we will gradually discuss in greater detail when we talk about truth in prepositional logic and truth in predicate logic etc and all. So there is another theory of truth which is slightly different from the correspondence theory of truth correspondence theory of truth tells us that you know there should be some correspondence between whatever you are saying in the actual world actual object that exist in the world and all. So coherence theory of truth according to the coherence theory of truth a statement is true if it is logically consistent with other beliefs that are already held to be true and all we are all having some kind of belief system we accept so many beliefs to be true etc and all. So something is logically consistent with our existence beliefs and all then that particular kind of belief is coherent with the beliefs that you already have at this moment. So a belief is false if it is inconsistent or contradicts with other beliefs that are held to be true earlier. So for example if you say that we do not believe the dinosaurs currently exist because they all got extinct long back some material it fell on earth and all dinosaurs got extinct as that is what we know actual matter of fact is that. So we do not believe that dinosaurs currently exist primarily because it contradicts so many of our other scientific beliefs and all. So we know that it got extinct etc and all so it is inconsistent with what we believe at this point of time. So any belief which is inconsistent with the existence belief is what we call it as incoherent and all. So what is important here is that there should not be any need not be any correspondence between whatever you think and the actual object that exist in the world and all but here there should be we should maintain some kind of logical consistency and all. So if you believe P are not P then the other belief such as for example if you come across any belief such as P and not P which is a contradiction and which goes against P or not P and all. So this is not logically consistent with that particular kind of thing so it is not coherent with that particular kind of thing. So this is what we mean by coherence theory of truth and it has its own problems which I am not going into the details of that one. So there are many beliefs there are some issues with respect to coherence theory of truth which I am not going into the details of that particular kind of thing. So there is another kind of theory of truth which is called as pragmatic theory of truth which is due to famous American philosopher William James. So according to the pragmatic theory of truth any statement is a sentence which can be spoken as either true or false and all. So that statement is true if it allows you to interact effectively and efficiently with your external world and all cosmos that is what we are calling it as. So according to this the less true a belief is the less it facilitates the kind of interaction that we are talking about. So that means a belief is false if it is it facilitates no possible interaction and all in that case it is false and all. If it facilitates interaction then it is considered to be true and this is a little bit difficult and abstract to abstract concept to understand and all. So there are for example to put it in simple terms for example if you say that my belief that inanimate objects objects does not have any life except try and all for example a pen which is in front of me do not spontaneously get up and move about etc and all we do not believe such kind of thing to be true and all because it makes my world more predictable and thus easier to live in. So my belief that inanimate objects do not spontaneously get up and move about is true because it makes my world more predictable and thus easier to live in and all. We believe that the world behaves in a certain way and all and we do not expect that all of a sudden rocks will fly and or rocks will float on water picks will fly etc and all because that does not work in the universe behaves in such a way that it does not work and all. So what matters here matters the most here is what works and all what works at the end of the day is what matters the most in the case of pragmatic theory of true. So the belief that inanimate objects all of a sudden starts flying etc will not work and all so it goes against the principles of nature etc and all. So the pragmatic theory of truth invites one problem of this one is that it invites the notion that there are degrees of truth and all since it is involves some kind of degrees of truth for the statements and all that means it allows for let us say 70% true 50% true etc and all the prepositions of statements. So some beliefs might be in that sense effective then the others and thus involves us to reject one of the important fundamental laws of logic that is law of non-contradiction law of non-contradiction says that a statement cannot be both true and both false and all. But if you allow for the degrees of truth then you can very well say that a sentence can be true a sentence can be false as well for example a sentence is 0.5 true and the other sentence is 0.5 false etc. So a sentence can be both true and both false as well. So this leads to the rejection of law of non-contradiction then if you reject the law of non-contradiction we will be doing some different kinds of logic initially we said that the logic that we will be following in this course will obey perfectly obey the three fundamental laws of logic. Law of identity law of which says that p is p law of excluded middle which says that p are not p and the law of non-contradiction a statement cannot be both true and both false simultaneously at the same time. So if you allow for pragmatic theory of truth then we need to get away from law of non-contradiction etc and all. So there are some other issues with respect to pragmatic theory of truth which I am not going to the details of this one but mostly the default theory of truth is the correspondence theory of truth. At this moment what we need to take into consideration is that suppose if I say that this is a pen that means actually referring to the actual pen and all that is why the sentence is true and all. Suppose if I say that this is donkey then it is not referring to the donkey it is referring to actually to the pen so that is why the sentence is false. For example if I say that there are only one two doors in this room and all actually there is only one door here in this room so that is why the statement is false. So it is as simple as that one. So now coming to the concept of validity. So validity is the most important the fundamental concept that one needs to learn in any logic course validity talks about what follows from what. So after all one of the important tasks of logic is to understand what follows from what and all. You have some set of statements in all those statements are leading to another set of statements which we call it as claims. So the word valid is often used to simply indicate once overall approval of an argument something which you accept it to be the final kind of point or something conclusion etc that is considered as you reach to some kind of agreement and all then that is called as a validity and all. In general day to day discourse that is what we mean by validity and all. For example two friends are accepting on certain things and reach some kind of agreement and they will start believing that kind of thing. But in logic in particular an argument is valid if it is impossible for the conclusion to be false given the premises are true and all. So an argument is valid if it would be contradictory or impossible to have all the premises true and the conclusion false and all. An invalid argument is a one in which it is not necessary that if the premises are true the conclusion can be true and all. So what is the most important thing which we need to know is that deductive arguments are truth preserving kind of arguments and all. So that means if you assume the premises to be true there is no way in which you can make your conclusion false and all. So if the premises are true then that guarantees that your conclusion is also true and all. So the most important thing which is important in case of validity is that we need to rule out the possibility that your true premises and a false conclusion and all. You can very well have this particular kind of thing that one of the premises can be false but it you can have a true conclusion it also works and all or both premises can be false but still the conclusion is true that also seems to be okay for us. And in the same way one of the premises is true another premises false and the conclusion is true or false etc then also it is acceptable to us but what we need to rule out completely is this that the premises are true the conclusion cannot be false and all. So that is the case then the argument is called as valid otherwise the argument is invalid. So we need to ensure that if you have two premises and you cannot have false conclusion and all. So that is what we need to keep it in mind. For example if you say if you argue in this way if you oversleep you will be late to the class and of course you are not late to the class that means you did not oversleep that is why you could come to the class on in time. So this argument is an example of modus tolens the first one can be represented as a implies b and not b second one is represented as not b so that is why it is not a. So this argument is valid argument in a sense that even if you try to construct a counter example counter example in a sense that you have two premises and you try to come up with a counter example and all like false conclusion. So then you will yourself will come to know that it is difficult to that is in fact it is impossible to construct a counter example in which the premises are true and the conclusion is false enough. So for constructing a counter example what you need to do is first you need to talk about the form of this argumentation a this is the first one is a implies b and the second one is not b and then this is what is the case if you overslept then you will be late to the class you are not late to the class that means you did not oversleep enough. So that is what seems to be the case and all this is a valid form and this is a valid argument. Suppose if you have used in this sense the same thing a implies b and then if you say not a and then you infer not b then this argument is invalid because you can come up with an instance where you can make both these premises true and the conclusion false enough. But in this case it is very very it is impossible to construct a counter example enough what we mean by constructing a counter example. So there are certain things which we obviously know these things to be true or obviously you know that the certain things which are false enough for example if we say all cats are mammals that is accepted to be true for us there are obvious things which we know that they are true or if you say all cats are fish then that argument that statement is false enough or if you say that all cats are five legs etc for example sake of fun you can take this into consideration the statement is false enough. So like that you take some true statements and all forget about what a b tells us and all once you extract it into some kind of form and all. So then you substitute for a anything and all cats dogs anything and all or donkeys or anything and then see whether you could come up with a counter example in all counter example in a sense that what needs to be ruled out we have two premises and a false conclusion this has to be ruled out in all suppose if you can cook up a situation where a in place b is the case and then this is also true this is also true then the conclusion is false enough you could come up with such kind of example then this argument is obviously invalid that means you have come up with a counter example coming up with a counter example means it is not necessary that the conclusion follows from the premises in all that means you have shown with an example that you have a true premises and you have a false conclusion so this is what needs to be ruled out in all. So to put in simple terms these are your premises and this is your conclusion so if your premises are true and the conclusion is true there is no problem and all. So if the premises are true and the conclusion is false then this is valid in all these are your premises and this is your conclusion and then we are talking about validity in all. So your conclusion is true then let us talk about this question mark little bit later so when you have true premises and a false conclusion definitely the argument is invalid in all so when you have true premises and a false conclusion the argument is clearly invalid in all but there are three other situations in all where your premises can be true conclusion can be true but validity it may be valid or it may be invalid in all. So you can have both premises false and yet you can have a valid argument or you can have false premises and true conclusion but it can be valid it can be a valid argument. So what I am trying to say is that out of the three four possibilities that I have discussed they are your conclusion can both be true and the conclusion your premises can both be true the conclusion can also be true that seems to be a valid argument no problem for that you can come up with valid arguments in that way or you can also come up with true premises one true premises and this needs to be ruled out in all this is what is the most important thing if you can come across with the two premises in a false conclusion the argument is clearly invalid then in all other cases it is considered as a valid argument you should ensure that you eliminate this particular kind of case this is the decisive factor for knowing that the argument is invalid you come across with the true premise in a false conclusion obviously the argument is invalid so then the other question comes to us is what about this other three cases and all so in that case the question mark indicates that may be valid argument but we can talk about the other features such as soundness etc. So a valid argument which consists of true premises is called as a sound argument which will gradually enter into the details of it. So in the first example if you overslept then you will be late to the PHA one photo to class and you are not late so that is why you do not oversleep that seems to be a valid form it is a valid argument. So another important thing which you need to note is this that in saying that you do not oversleep based on all these assumptions in all first assumption which are constable true we implicitly assume that there is no shift in the meaning of meaning or reference of the terms that you have used hence we must use overslept late the terms which are used here and you etc. and all in the same way throughout this argument and all. So in the case of deductive argument it is taken for granted that there is no shift in the meaning of the words that you have used in the argument and all for example if you say this room is made up of atoms are invisible so that means this room is invisible and all in that case atoms the word atoms is used in two different senses in all there is a shift in meaning from first premise to the second premise so that is not allowed in the case of deductive arguments so it is taken for granted that there is no shift in the meaning of the words that you have used in the argument. So another important thing which you need to note is that for validity things need not have to exist actually in the world in all you can argue in this way that all circles are sorry all squares are circles and all circles are parallelograms so you can say that all squares are parallelograms in all squares are parallelograms that is the conclusion here that is obviously true in all but other way round is not the case all parallelograms are not squares so the conclusion is true but you observe that it has false premises in all so this falls under this particular kind of category so all circles are squares that is false statement all circles are squares all squares are circles that is obviously false all circles are parallelograms that is also considered to be false so but it is considered to be a valid argument for the sake of assumption you can take some of the premises to be true and you have to see whether the conclusion is false or not if the conclusion is false then the argument is invalid but in this case the conclusion is obviously true and all so in a way it is preserving the truth and all in a sense that you assume that all all squares are circles is true so this is only for our assumption actually we know that it is it goes against the principles of mathematics that you know a square cannot be a circle and all its counter intuitive to us so but what we have seen here in this case in this situation is that you have false premises but still you have a true conclusion but at the argument is valid and all but it is impossible for us to come up with an argument in which your true premises and obviously false conclusion so that seems to be ruled out and all so this kind of argument it is an invalid kind of argument you can come up with any counter example in which you can show that these two are true then you can show that this conclusion this is false for example if you say if it rains then the grass is wet it did not rain the grass is not wet and all of course it did not rain and all but the grass can still be wet and all in several different ways for example a sprinkler might be on or maybe somebody poured some water there etc so that means you could come up with an instance where you would come up with a counter example in which your true premises and a false conclusion so so the other examples which you commonly come across to strengthen our point that you cannot come across is very difficult to cook up an example where you have true premises and a false for a valid kind of argument but yet you can say that it is a valid argument so that argument has to be invalid and all suppose if you say if you are in Kanpur you are obviously in Uttar Pradesh because Kanpur is a part of Uttar Pradesh of course if you are not in Uttar Pradesh then you should not be in Kanpur and all so it is pretty straight forward thing and all so you can ask suppose I do not know anything about Kanpur Uttar Pradesh or anything and all how do we know that this argument is valid or invalid so just transform this thing into an appropriate form so this is what you come across if you are in Kanpur you are in Uttar Pradesh you are not in Uttar Pradesh then that means you are also not in Kanpur you are somewhere else in India so this seems to be the case since a valid form obviously this is a valid kind of argument. The next one is the one which we already discussed in greater detail all squares are circles all circles are squares so that is why all squares are parallelograms so you have false premises but you have a true conclusion and all so that is also permitted it is also a valid kind of perfectly valid kind of argument but you might ask how suppose if I accept these particular kinds of things I mean does it make any sense to us or not so for that you need to invoke another kind of property which is give emphasis on some of the extra features of logic that is the soundness and all if you incorporate soundness into consideration then we can rule out this particular kind of argument by saying that this argument is not sound it is not sound in a sense that one of the premises is false of course in this case both premises are false so obviously it is a unsound kind of argument so there are some arguments in which I told in the last few classes that there is no way in which you can analyze that these arguments are valid or invalid and all unless until you there seems to be some mistakes in this argument and all but it is very difficult to recognize it unless until you analyze the content carefully and all. So the argument goes like this happiness is end of life that is what we are trying to achieve so everyone will be trying for happiness at least at the end of the day or maybe end of his life etc and we know that end of life is obviously death etc and therefore if you say that happiness is death then nobody will be in a position to believe that this follows from the those two things because in the in this argument what we have done is happiness end of life is used in two different senses so one is for achieving something that is the main purpose which is used happiness and then the second one it is used in a different sense that is end of life in end of breath etc and all that leads to death and all. So there is a shift in the meaning of the word or phrase that you use that is the end of life is used in two different senses so that is why this argument has some kind of mistake when we talk about fallacies and we will talk about these kinds of arguments you know otherwise at the first instance if you observe these kinds of argument it looks as if that they are valid arguments you know like a implies b, b implies c and a implies c is the case you know. So what is the connection between validity and true premises and all which we already discussed in greater detail there are four cases which I have mentioned so the only thing which would focus your attention is on this thing your premises are true and the conclusion is false then obviously the argument is invalid that is the second case which we shown it on the board in all other cases the argument can still be valid so we can rightly conclude that an argument is valid simply on the grounds that your premises are all true we cannot guarantee that particular kind of thing you know you can have true premises but still your argument may be invalid and all let us consider a simple example like this some Indians are women suppose if you say that there is a case you say some all not all will can be women and all with some Indians are women let us say for famous Bollywood actor Hithig Roshan is an Indian so therefore Hithig Roshan is a woman for example if you say that particular kind of thing then this argument is obviously invalid because it may be the case that Hithig Roshan is a man rather than a woman and all the first premise says that only some Indians are women and all but if you replace this argument in a different way for example all Indian are women and all it is which goes beyond our belief that you know it can be the case and all but hypothetically you imagine a situation in which only people you will come across are women in India the imaginary situation is assumed to be true and all then Hithig Roshan is an Indian then in that case the first sentence which is which we have used all Indians are women which has no exception and all that means there is no case in which you know somebody is a woman and all. So there are no exceptions for that universal generalization in that case Hithig Roshan has to be a woman so but in this case some Indians are women Hithig Roshan is an Indian both are true but still the argument is invalid and all. So we cannot judge only with the help of true premises and all that you know the argument is valid and all but here is an instance you have true premises but still you have an invalid kind of argument and all so but validity preserves the degrees preserves the truth and all so the truth preserving kind of thing suppose if you assume these two arguments to be true the conclusion cannot be false and all. So in the first case some Indians are women means the Indians are not women is also the true and all which we have not taken into consideration here in this particular kind of argument some X or Y means some Ys are X also so the same as that particular some X are not Y also. So the other instance is this that if you have true premises and a true conclusion but still the argument may be invalid some Indians work in movie industry for example Aishwarya Rai is an Indian again hence Aishwarya Rai works in movie industry and all. So the premise says that only some Indians are movie industry and all Aishwarya Rai is an Indian so obviously the second premise you cannot make it false and all so the only way in which Aishwarya Rai works in the movie industry just because she is an Indian that does not seem to follow from this thing all are true but it the argument seems to be not acceptable to us. If you had said that all Indians work in the movie industry then the Aishwarya Rai is an Indian then it might be the case that Aishwarya Rai has to work in the movie industry and all but here it says that some Indians work in movie industry and all only some it says about some and all some does not work in the movie industry and all what happens if Aishwarya Rai is an Indian but still she does not come under the category of some Indians who does not work in the movie industry. In that case you could come up with a counter example in which your true premises in a false conclusion Aishwarya Rai does not work in the movie industry. So what is important in all these examples from all these examples is that validity is what we is the one which we use to preserve the truth and all. If you start with the truth and reason in a valid fashion that means if you have formed so valid then we will always end up with truth and all. Your true premises and you will not end up with a false conclusion and all. So that is what is the thing which we need to take into consideration. The next important feature which we will be knowing in greater detail is that it is not enough that your arguments are valid but it has to be sound enough and all. So what is this extra feature that we are trying to add for an argument for an argument so an argument is sound if it is valid first of all it has to be valid and all that means the conclusion necessarily follows from the premises and the extra thing which it has to be extra feature that it has should have is that it should have one of the premises to be true also not one of the premises every premise has to be true and all it so happens that you know our argument the argument is valid but it has true premises as well. So how do we know that these premises are true or false etc and all again you know it is not the job of a logician to look into or verify the facts etc and all it is job of someone else and all maybe scientist might verify these facts to be true etc and all. So then based on the evidence that you got a scientist have verified it and then two statements you could come up with and how it is leading to the other statement now is the one which you are trying to talk about. So now if you want to know that the argument is sound then it has to be valid that means it is impossible for the conclusion to be false given the premises which are you which you are accepting it to be true the first thing that is a valid kind of argument and the second thing which you need to see is that whether all the premises are actually true or not. So again you can say how do we know that the thing is true and all we use the default theory of truth which we have discussed in the beginning of this class that you know a sentence is true which if it is corresponding to the actual world a corresponding to the object in the actual world which exist you know. So we try to show that either that one of the premises is false or that the conclusion does not follow in either cases you can show that it is a unsound argument and argument could be sound in either of these two ways you know for example sometimes some somebody convinces you with this kind of argument that it looks as if that for example a simple example which I already taken into consideration all squares are all circles are squares all squares are circles and all circles are parallelograms all squares are circles in all squares are parallelograms so that is the one which we discussed in the last few minutes. So if your friend comes and tells you this particular kind of thing then you cannot question the validity of the argument now if I assume that the first two premises are true then since it is a deductive argument so it preserves the truth and all there is no way in which all squares are parallelograms can be false and all. So that is a perfectly valid kind of argument the only choice that you have is that you can show that the given argument is unsound by say by stating that one of your premises is false of course in this case both the premises are false. So in that way you can show that this particular argument all circles are all squares are circles all circles are parallelograms and all squares are parallelograms it is false it is an unsound kind of argument. So there are situations in which you have a valid argument might have some kind of false premises and all for example if you say all logicians are millionaires and all. Good codle is of an outstanding logician that is a true statement so good codle is a logician therefore good codle has to be a million year. So this argument is a valid argument but we all of us know that not all actually if you verify the facts etc historical facts etc all logicians cannot be million years if it is a case then well and good but actually unfortunately unfortunately it is not the case. So in this case this is a valid argument but it is an unsound argument because you can very well show that all logicians are million years has this exception or it is one instance where it is not the case. So its conclusion might not follow from the premises for example if you say all billionaires eat well and all they are lot of money rich and etc and all they eat well overeating etc for example Ravi eats well just because Ravi eats well and all you cannot come under the category that is a billionaire and all. So this is kind of invalid kind of what I am trying to say is that in the first argument you can show that one of the premises is false or the other way of showing that the argument is unsound is that you know the conclusion does not follow from the premises I mean you show that it is invalid argument all invalid arguments are automatically unsound arguments. So this is the connection between truth and validity just because your true premises that does not mean that the argument is valid and all you can have true premises and true conclusion but yet the argument may be invalid and all. So for validity what is important is that if you accept the premises to be true the conclusion cannot be false and so that means you are rolling out the possibility of invalidity and all. So an unsound argument you will come across in three different categories and all the first category the argument is valid but it has at least one false premise and all it is one of the premises is false. So category 2 is that obviously it is an invalid argument that means the conclusion does not follow from the premises but all its premises may be true and all not may be they are true and all. In category 3 it can be an invalid argument but it has at least one false premise and all. So in either of this in these three categories we can show that the argument is unsound and all. First of all invalid arguments are all automatically unsound and all. So that means invalid plus false premise for example there are some examples for this kind of thing all trees or animals of course that is a false proposition all bears are animals of course the bears are animals only that is a true statement. So if you say that all bears are trees and all this is a very strange kind of conclusion that you are trying to come of it. First of all all bears are trees does not follow from all trees are animals all bears are animals but you might ask why it is a case that you know it is not a valid kind of argument but the best way of looking at it is by seeing the form of these arguments all x or y all this is like this particular kind of thing I will go into the details of it all trees are animals for example if you all x or y so for example if you say that thing x stands for trees and y stands for animals trees and then this is animals is the first argument and the second argument is all bears are animals in all. So all z z stands for bears all bears are all z are animals in all so this is y so now from this you are concluding that what is that you are concluding so all bears are trees all z that is considered to be bears in all are trees that means x so this is the one which we are trying to get come of it so this is an invalid argument the valid form of this one is this all x are y and all y are z then you say that all x are z so if this is put in this particular kind of format then it can be considered as a valid argument so this is clearly an invalid argument obviously it is a unsound kind of argument suppose if you transform it in such a way that come up with that particular kind of thing the first one this is the right kind of form this is obviously invalid and all this is a valid kind of argument so you came across that particular kind of valid argument but let us say one of the premises falls in all then in that case the argument will become an unsound argument in all so unsoundness arises in three different categories so suppose if your friend presents you some kind of argument which are convincing and there is no way in which you can show that it is invalid kind of thing that means the conclusion seems to be necessarily following from the premises the only way in you can the only choice that you have is that you can show that one of the premises to be falls in all that is the only thing which you can do the conclusion does not follow from the premises although it is correct or you can try to show that one or more premises are very uncertain of course this is another way of saying that you know you make it uncertain in the sense that they are not 100% true in all may be true may be false etc and all then in that case you are converting that argument into some kind of inductive argument in all so it is in the sense that conclusion does not need not necessarily follow from the premises but conclusion only probably follows from the premises in all so that means conclusion only probably follows from the premises means you could come up with a counter example in which your premises are true the conclusion is falls even if you come up with one single instance and that is good enough to say that the argument is invalid even if you suppose if you have 100 tomatoes in all the tomato that you picked up is a rotten tomato then that is good enough to show that the basket that the tomato it contains has a rotten tomatoes and all so here is an interesting kind of dilemma I mean which is slightly different from what we are trying to discuss in all so this dilemma goes like this is a very important kind of problem which arises in the prepositional logic in particular so gradually we will go into the details of this particular kind of thing so the story goes like this a crocodile steals a son from his father but the crocodile is a little bit kind enough or generous he gives some kind of options in all he is not just eat away the it away son and all but he promises to return the child suppose if he is asking his father to guess certain kinds of things in all you guess whether I am going to return your child or not that is what you know but the intention of a crocodile is either to eat or return the baby and baby or kid here so a crocodile steals a son from his father and promises to return the child if the father can correctly guess what the crocodile is going to do and suppose crocodile intends to eat and all if the father guesses that he is going to return the baby so then he will the father's guess is wrong so he is not going to return the baby so he will eat crocodile will simply eat the child so if it goes against what the crocodile is intending to do then the father's guess is obviously wrong and all then he is not going to return the baby so either the crocodile has two options in all either he will eat or he will return the child and all the father guesses correctly in all that means it goes exactly in accordance with the intentions of the crocodile then you will return the baby otherwise you will eat the baby what happens if the father guesses that the child will not be written to him in all suppose if that is the case in all then what is going to happen so for this particular kind of problem this is a kind of unsolvable kind of problem in all because there is no solution for this problem if the crocodile keeps the child then he violates his rule because the father has predicted correctly in all the rule that he has violated is he has to return the baby but his actual intention is that he will so hungry and all you will eat away eat the baby in all so since the father predicted correctly he has to return the baby but he has eaten the baby in all so he cannot return so that seems to be a problem if the crocodile returns the child in all then it still violates his rule rule in the sense that you know if you predicted correctly I will return the baby if you predicted wrongly and all I will eat the baby in so if the crocodile returns the child in all then he still violates his rule as father's prediction was wrong is father's prediction was wrong and he has to eat the baby cannot return the baby in all so it is like it is like some kind of paradoxical situation or it is not a paradoxical situation is crocodile is in some kind of dilemma whether to eat or return the baby in all so this problem gets unsolved and this is this problem can be written in the formal terms like this so this can be considered as a valid kind of argument and all but one can show that it can be unsolved etc so this problem is simply written as this thing P implies Q and R implies CS and PRS then it will be either Q or SN so it is like in the case of crocodiles dilemma either to eat or return the baby is the one which is easy is in some kind of dilemma if he returns the baby there is a problem and if he eats the baby then also you cannot return the baby you cannot return the baby then also there is a problem so he is in a dilemma what to do in all so if the father's guess is correct then he is going to return the baby and if the father's guess is false he is going to eat the baby so now the father can only guess either true or false there is no middle value between these things it has to be true it has to be false it is guess has to be correct I guess has to be false if it goes exactly according to the intentions of the crocodile and the guess is correct otherwise suppose for example crocodile intend to eat in all father says you are going to return the baby so then it goes against that one inconsistent with that one so that is false so now from this crocodile has only so these two things so this is seems to be a perfectly valid kind of argument and all so this is what is crocodile has to say and this is father and then crocodile and then father will respond in certain way suppose if you say is not going to return the baby so then it leads to crocodile will it puts crocodile into some kind of dilemma and actually crocodile is intend to eat the baby is so hungry and so now there is no solution in particular in this sense that if the crocodile keeps the child then he violates his rule as a father predicted correctly and all the father predicted correctly and he has to return the baby but he actually has eaten the baby if the crocodile returns the child and then that means still violates his rule that father's prediction was wrong and all so in this case his problem gets unsolved and all so we will we will stop here and then we will move on to the strength of inductive arguments in the next class so what we have simply said was is that we started with different theories of truth and then we talked about the relationship between truth and validity and all it is not just enough that you know your premises are true the conclusion just based just based on the premises are true we cannot say that the argument is valid so for the validity what is important here is that if the premises are true the conclusion cannot be false so we will continue with the strength of the inductive arguments in the next class.