 In the last lecture we saw the distinction between deductive and inductive arguments. One of the fundamental most important distinction that we found is that in the case of deductive arguments the conclusion necessarily follows from the premises and it is truth preserving and there is no absolutely there is no new information in the conclusion which is not stated in the premises and other thing is that it is not open ended argument. On the other hand inductive arguments conclusion probably follows from the premises it has variable strength the argument has variable strength and whatever is stated in the conclusion it goes beyond what is stated in the premises and then they are all open ended arguments. So now the next question that arises is this that where do we come across deductive and inductive arguments in general before that you know what I would like to say is that these are the two types of arguments that you come across in logic that is deductive and inductive kind of arguments. So now the next question that arises is where do we come across these deductive arguments how do you identify that this particular argument is a deductive argument etc. So in this lecture what I will be doing is that we will talk about where do we come across this deductive arguments and inductive arguments with some examples and then if we have time then we will go into the details of validity of a deductive argument or invalidity of a deductive argument and then in the case of inductive arguments we can only talk about the strength of the argument. So we can say that a given inductive argument is a weak argument or a strong kind of argument to begin with we will come to the deductive arguments which we usually come that come across these kinds of arguments in the field of mathematics because mathematics seek some kind of certainty so especially when you come across some kind of valid forms so what do we mean by a valid forms and all. So the first commonly found kind of valid form in the logic any logic course is this that is called as modus ponens and all. So according to modus ponens it is like this if a implies b is the case that means this is an antecedent this is a conditional statement out of which a is considered to be an antecedent and b is called as consequent suppose if a then b and then a is the case then b follows from these two. So this is considered to be a valid form so how do we know that it is a valid form and all it is a different question which we will answer it little bit later. So in logic there are some kinds of valid forms and all so this since it has exhibit some kind of pattern which is come under the category of valid forms and the argument is also corresponding argument is also valid argument. So if you say that if the grass is wet then usually we say that it rained and all last night the grass is indeed wet then you say that it rained last night. So the better way of putting this argument is this that if it rains then the grass is wet and it rained then the grass is wet and all unfortunately I mean I put it in a reverse way but it does not matter much and all but this also serves our purpose. If the grass is wet then it rained last night the grass is wet so it rained last night it is in this form a implies b and then a then b. So if it is not used in some kind of valid form then it will become like this a implies b and then b then suppose if you infer a this is an invalid kind of argument because it has invalid form and all. So forget about I am already talking about validity, invalidity etc. and all I did not talk much about what we mean by validity etc. and all but my intention is that where do we come across this deductive arguments under this whenever you have this valid forms and all then you say that it is a deductive kind of argument why it is a deductive argument if these premises are let us say this is premise 1, premise 2 and then this is the conclusion and all if the premises are accepted to be true and the conclusion cannot be false and all. You cannot come up with a single instance where these two are true and this is false and all. So this has to be ruled out and all you cannot cook up any counter example in which your premises are true and the conclusion is false. So the conclusion follows necessarily from the premises that satisfies the case of deductive argument and then there is no new information in the conclusion so whatever is stated in the premises is already in the conclusion that is the second thing which is serving our purpose of deductive arguments and the third thing is this that it is not an open ended argument so there is no new information in the conclusion which is not stated in the premises and then if these two are absolutely true then conclusion also has to be true and all. You buy these two things you will get it free of cost so you have to subscribe to this one also the conclusion also necessarily follows from the premises. So usually when you come across commonly valid forms and all if you come across in logic course all these arguments are they come under the category of deductive argument another commonly the argument which you commonly come across in this is this is called as modus ponens and the other argument which will come across is modus tolens. So this says that if A implies B is the case then you deny the consequent so this is the antecedent and this is the consequent you deny the consequence and you need to deny the antecedent also. So one mistakenly you can write this modus tolens in this way suppose A implies B is the case and you deny the antecedent and you deny the consequent this is an invalid kind of argument when I talk about the validity or invalidity of deductive arguments I will come back to this particular kind of example. So what I am trying to say at this moment is that whenever you come across some kind of valid forms etc like this then you can say that there is some kind of deductive argument present in that particular kind of arguments. So the first one is modus ponens which I expanded there and the second one is modus tolens these are all deductive arguments why these are deductive arguments this serves our four criteria that four criteria which we have discussed earlier or you can ask four different questions and based on your answers you can judge whether they are deductive or inductive kind of arguments. In the last lecture I spoke about these four questions so whenever you come across hypothetical syllogism like if A then B if B then C then if A then C also comes under a valid form and all obviously is also comes under the category of deductive arguments. Disjunctive syllogism A or B and then not A then obviously it has to be B one excludes another one and A is not the case and obviously what is left out is B only that is what is disjunctive syllogism is clearly a deductive argument if the premises are true the conclusion cannot be false you cannot come up with a single counter example in which A or B is true not A is true but at B is false you know so it is in that sense the conclusion necessarily follows from the premises. So this argument is also a deductive kind of argument in the same way valid forms that you come across like A or B and not B so A and all these are another instance of disjunctive syllogism and there are some other complex kinds of arguments which exhibit some specific valid forms and all they come under the category of constructive dilemma and all it is like this that if either A or B if A then C if B then D then so either C or D and all. So this all the valid forms which come under the category of deductive kind of arguments and all because the conclusion necessarily follows from the premises and all. So they are absolutely true if the premises are true then the conclusion is also necessarily true and all. So these are the different types of deductive arguments which you come across in day to day discourse or even while reading a mathematics text or maybe reading some other books and all. So basically arguments based on mathematics because you know mathematical facts are certain and all 100% true and all in mathematics you do not say that 2 plus 2 is equal to 4 is true with some 90% true etc and all there is no degree of truth involved in these kinds of prepositions and all. So arguments based on mathematics the conclusion depends upon some purely arithmetic or geometrical computation or measurement these kinds of things come under the category of deductive arguments and all. There are arguments based on definition that is the conclusion is claimed to depend merely on some definition or some word or phrase and all for example if you say Ram is bachelor implies that Ram is unmarried and all. So unmarriedness is already there in the word bachelor and all there is nothing no new information that you are stating in the conclusion but you might ask what is so great about these deductive arguments and all there is no new information they are not open ended arguments you are not able to strengthen or weaken the argument or once you accept some conclusion to be true it has to be true forever despite the case that you add all the new premises etc and all what is so great about these deductive arguments and all. I might ask but these are some of the important features or characteristics of deductive argument which has its own advantages when it comes to mathematical reason. So we already spoke about disjunctive syllogisms when you talk about Aristotelian logics we go into the details of what we mean by syllogisms what we mean by categorical syllogism what are the rules for knowing the validity of the syllogisms etc we will talk about when we especially discuss about Aristotelian theory of syllogism. So but at this moment when you come across categorical syllogisms like you know syllogism is an argument with two or premises with specially formed in such a way that all the prepositions in the premises begin with all some are no etc these are the phrases with which all the prepositions begin. So you begin with two such kind of prepositions and then your conclusion is going to be another kind of categorical preposition and all if it is so formed then it is called as a categorical syllogism and all categorical syllogism is a kind of argument in which involves categorical prepositions. So these are also some of the arguments which come under the category of deductive arguments again this criteria is same and all the conclusion necessarily follows from the premises truth preserving absolutely conclusion necessarily follows from the premises and not open ended arguments etc and all. So when it comes to hypothetical syllogism which we talked about earlier distinctive syllogisms all these things come under the category of deductive arguments here are some of the examples for example if you say if pain exists God does not exist so therefore God does not exist in all it is like modus ponens rule first one is interpreted as a implies not be actually does not exist means not be called exists means be God does not exist is not be enough a implies not be and next one is a so that is why it has to be not be so the first example is like this the first one is interpreted as a implies not be and then a is the case and then not be is the case and so be stands for God does not exist does not exist and then a stands for pain etc if pain is there after all then suppose if you if you say that God does not exist and the pain is obviously there suffering is the thing which remains with us so obviously that means that God does not exist so this is a valid kind of argument you might argue that it is not a sound argument in a sense that one of these premises a implies not be or a one of these things may be false in that sense you can show that it is a unsound argument which will talk about little bit later the second example which come under the category of deductive arguments is this because the triangle a is congruent with triangle b and the triangle a is isosceles and it follows that triangle b is also isosceles so it is based on the definition or it is considered as the inference follows based on definition now arguments based on definition etc the one which we already spoke about John is a bachelor implies that John is unmarried person so there is nothing new no new information present in the conclusion which is not stated in the premises now bachelor is made explicit I mean whatever is implicit in the premises is made explicit in the conclusion in the same way if you say cholesterol is endogenous with humans therefore it is manufactured inside the human body it is not saying anything new except that is making whatever is implicit in the premises explicit in the case of fourth example say either the classical culture originated in Greece or it is originated in Egypt is the two possibilities that we have a or b and we say we are saying that classical culture did not originate in Egypt is also accepted to be suppose if you assume to be 100% true then there is no way in which you can avoid this conclusion that the classical culture is originated in Greece and all it has to be 100% true based on the premises are again 100% true if you say that all plants are living things is this is an example of a syllogism because the statements are beginning with the categorical propositions that is why it is categorical syllogism all plants are living things all trees are plants therefore all trees are living things so you have to note that all come under the category of deductive arguments all deductive arguments are not valid or it may be invalid also or valid arguments can be unsound also so we will talk about those examples a little bit later. So now coming back to inductive reasoning so where do we come across inductive reasoning basically in science we do come across inductive reasoning when the scientist is trying to formulate some kind of law statements what he does is repetitively observe some of the things like let us say metal 1 expands upon heating metal 2 expands upon heating and after doing repeated observations and all with various metals under various circumstances and various situations etc and all then we will come up with generalization which he calls it as inductive generalization which sounds as which is elevated to the status of a law that is moving from particulars to general and all in a certain sense. So as repetitively observed in thousands of experiments etc and all and he formulated this law statement that all metals expands upon heating because of so and so free electrons etc and all. So inductive reasoning is the one which you find it in natural sciences especially when the scientist is trying to draw some kind of inferences based on some kind of repeated observations usually he requires we scientist requires inductive reasoning for formulating law statements we need law statements because you know there are several we need we require law statements gradually they are elevated to some kind of formal kind of theory and all. Inductive reasoning is a method of drawing conclusions based upon limited information we need not have to have complete information and all but yet you can draw some kind of inferences and all especially in a sense the phrase inductive reasoning is sophisticated substitute for a word guessing you know guessing predicting etc they all come under the category of inductive kind of reasoning you know. So usually in our competitive examination you will come across this particular kind of thing 2 4 6 8 10 and guess what is what comes next and all and when you are asked this particular kind of question then you will automatically know that there is some kind of pattern which is the sequence is following then immediately you will predict that the next number that is going to be following this sequence is 12 so I might not mean that you know 12 is going to be the next one and all I might have used in a different sense and all for me you know it might be 14 also but usually you know common sensically we can say that if you are given 2 4 6 8 10 and all they follow certain sequence and all based on that information you can say that 12 is going to be the next number that follows but it might be the case that it may be 14 or it may be 17 or I might have some other thing in my mind which I want to replace it with 12 or I can write 6 plus 6 or something like that. So we make our answer based on the first five terms and all repeated observations until we actually see the six term it is a kind of guess and all. So this kind of conjectures repetitions etc there are already used by Fermat the great mathematician he used inductive reasoning especially in formulating some kind of conjectures and all. So the mathematics conjecture is a one which is not a proved kind of theorems and all. So there are many conjectures which you will find in mathematics like gold box conjecture is one kind of conjecture even till to date it is not yet resolved and all it is not yet proved. So something is proved means every theorem has to be proved to be true and all. So there should not be any theorem which is not proved not provable etc and all. A theorem has to be proved and all it has to be true first it has to be proved also. So Fermat used this inductive reasoning especially to conjecture that every prime number every number of the form 2 to the power of n plus 1 is a prime number whenever n is power of 2. So he says that conjecture that so why I am talking about this particular kind of thing is that arguments based on predictions guesses conjectures etc they all come under the category of inductive kind of arguments and all. Fermat has used this kind of inductive reasoning in mathematics in a different way and all. Suppose if you say that 2 to the power of n plus 1 for example if you have 2 square plus 1 then that is going to be 5 is a prime number 2 to the power of 3 plus 1 this is 9 and 2 to the power of 4 plus 1 etc is 16 plus 1 17 etc and all. So he formulated this conjecture that every number of the form 2 to the power of n plus 1 is a prime number whenever n is a power of 2 the next power of 2 in the first column of the table the table is not there here it should be 35 and all 32 that is 2 to the power of 5 2 to the power of 5 is 32 plus 1 is 33 and all. So like that you go on and on and all etc and then suppose if you say 2 to the power of 32 plus 1 and all so that happens to be a big number 4, 2, 9, 4, 9, 6, 7, 2, 9, 7 it is there in the slide and all. So 2 to the power of 32 plus 1 is going to be this particular kind of number and all. So what is that a Fermat is trying to do yes formulated this conjecture that any number of this format 2 to the power of n plus 1 has to be a prime number and all especially when n is a power of 2 and all. So 2 to the power of 4 plus 1 is a prime number 2 to the power of 5 plus 1 that is 33 it is also frame number like that you know go on and on and all 2 to the power of 32 plus 1 can predict that that is also a prime number and all based on repeated observations and all. So he has used it in this particular kind of thing and all but this conjecture whether it is proved or not it is not I am not sure about it. So Euler is also used a similar kind of thing Euler proved that the number especially 4, 2, 9, 4, 9, 6, 7, 2, 9, 7 unfortunately this number is not a prime number a prime number is a one which is divisible by itself or by one and all. So Euler came to this conclusion that this number contemporary of Fermat and all he came he showed that 4, 2, 9, 4, 9, 6, 7 the big number which is stated here is unfortunately it is divisible by some number 641 and all. So what is the case is that and consequently he proved that it is not a prime number because it is divisible divided by 641 and all the prime number is a one which is divided by itself or at least by 1 and all but it is divided by 641 and all and he showed that it is not a prime number and all. As a result the conjecture that resulted from Fermat's use of inductive reasoning is turned out to be false and all. So we can use this particular kind of conjectures etcetera conjectures can be proved false also can be proved true we can be proved as false also. So what is the thing which we learn from this particular kind of thing is that Fermat has also used some kind of inductive reasoning in guessing the thing and all 2 to the power of n plus 1 is a prime number then he guess that you know based on that he calculated that 2 to the power of 32 plus 1 is a prime number but Euler has proved that this is not prime number etcetera and all that means he proved that his guess is wrong. So with repeated observations till 2 to the power of 5 4 plus 1 2 to the power of 5 4 plus 1 or gut feeling says that it is true and gut feeling says that that is prime number and all but yet you know it may not be conclusion is not guaranteed by whatever is there earlier and all. The conclusion probably follows from the premises but it may turn out to be the case that the conclusion may be false and all. So all the guesses based on predictions etcetera the conclusion goes beyond what is stated in the premises and all. So other kinds of deductive again we come back to the deductive arguments and all deductive arguments are based on some kind of valid forms a factual claims if any if it is there well and good and all. So although inductive reasoning can sometimes lead to false conclusion the one which we have seen our guess work may be false and all it can often be useful first step to the process of applying deductive reasoning to determine whether the conclusion is true true. So based on your observations you use inductive reasoning to conclude that the product of even natural of an even natural number with the natural number is always an even natural number and all. So we use both reduction induction simultaneously and all based on our convenience and all although we know that in the case of inductive reasoning the conclusion may turn out to be false probably be false but it is for a starting point you can use this inductive reasoning and all to prove certain other thing and all. What are different types of inductive arguments that we come across usually come across in general there are the two there are different kinds of inductive argument four different kinds of inductive arguments which we frequently see in natural sciences or maybe in the day-to-day discourse. So they are arguments from cause to effect arguments based on science inductive generalizations and analogy. So let me explain these things in a while in greater detail. So these are all quite obvious to us and most of the examples are quite familiar to us using day-to-day examples and all but we are trying to put it in this particular kind of category which comes under the category of inductive arguments. Even for judging this whether it is an inductive or deductive argument you need to rely on those four questions and all. Is it an open ended argument? Is it truth preserving? Is it some kind of variable strength present in this particular kind of thing etc. in the argument etc. Whether the conclusion necessarily follows from the premises all these questions you need to ask to judge whether this argument is inductive argument or deductive argument. So arguments based on science is like this the notion it is a notion that certain types of evidence are symptomatic of some wider principle or outcome. However what is marked on a sign does not have to be necessarily true though it is usually seems to be the case in all. So there is a good but not conclusive reason to believe that that particular kind of thing which is stated science is going to be true in all. Let us take an example so that you can explain this thing in a better way. For example smoke is often considered to be a sign of fire and all but it may turn out to be the case that there may be some other reasons for can be shown as sign for fire and all. Rhetical short circuit etc. and all there also fire my break out. So there may not be any smoke etc. and all. Sometimes there may not be any smoke for the fire and all. Some people think that high scores on in the SAT exam are a sign of person who is smart and of course you will do well in the college and all. The same way person who crack JEEA etc. and all will usually say that is a bright student and all. But it may turn out to be the case that he join in IIT might fail in all the courses in IIT also. That may not be an indicator but definitely it is going to be taken into consideration. But again depending upon his background as well as depending upon how he performs in the exams in IITK whether or not he is going to succeed in all depends on all. So just mere great score in the SAT examination does not make him smart and we cannot guess that he will do well in all. The other argument which come under the category of inductive argument is this that argument based on authority and all. So somebody is having some kind of authority. It is not like church has some kind of authority etc. and all. But anyone who is some expertise has some expertise in a particular kind of thing and all. So usually we say that he has some kind of authority and all. For example if the Deputy Ristar announces that if the Deputy Ristar any authority announces that there is no classes tomorrow then we believe that particular kind of thing and all. Somebody some other kind of person who is working somewhere else in IWD or someone announces that there is no class tomorrow then we suspect that particular kind of thing because it is not based on authority. Again the question comes to us is what serves as authority and all. It is a difficult question to answer and all. Usually we make use of common sense to judge that physicists have some kind of authority and some kind of fields. Usually we say that a politician usually you know is expected to have some kind of authority in the politics etc. and all. But suppose all of a sudden he starts prescribing some kind of drugs etc. Drugs in the sense that he tells his voters that you know he should use this particular kind of medicine etc. and all. And people will be suspicious about his claims and all. A politician is expected to have expertise in some area and all not in the medicine etc. and all. So now argument from authority goes like this or any person or sincerely asserts that something is the case S is the case and all. So then that is why that is S is the case and all. Einstein explains that something is the case and all. So that is why it is the thing and all. Where R stands for source of information for example a person or a paper or reference work etc. S stands for any public any kind of statement and all. If R sincerely asserts something is the case that is why it is the so S is the statement. That means this is true or false and it can be taken as as a true or false. So we use arguments from authority when we appeal to usually appeal to dictionary, encyclopedias, maps, experts in particular kind of field and all. So basically these are considered to be having some kind of we say that some kind of authority is there in that particular kind of subject matter. So we rely on encyclopedias, maps etc. Google maps or whatever it is for judging the authority of particular kind of thing and all. Arguments from authority are strong given that authority in Cossini is reliable and more reliable the authority more stronger the argument would be. An inductive argument can be most strong especially in the sense that it is having reliable kind of authority. That means argument based on authority will be having some kind of strength and all. So in his dictionary of philosophy for example Anthony Flu defines logicism as a view that mathematics in particular arithmetic is a part of logic. So that is what logicism is because he is referring to dictionary of philosophy or encyclopedia of philosophy or Stanford encyclopedia of philosophy etc. We consider to be having some kind of authority and all we vest our authority in those kinds of things. Then based on that you know you judge that probably this is what is the standard definition of logicism and all. Suppose if all of a sudden some politician tells us that this is the definition and all and we very well suspect that particular kind of thing and all. So how do we know that this particular kind of argument is having reliable authority or not. Suppose if it is not based on reliable authority and all then there seems to be some kind of mistake in the argumentation when we talk about fallacies we will talk about those particular kinds of mistakes in the argumentation which come under the category of fallacies and all. That fallacy is called as fallacy of weak induction based on unqualified kind of authority and all. So there are the few questions which we need to ask is the authority reliable on the subject issue or not. So Weinstein talks about physics and all it makes some sense and all for example usually common sense says that for example all of a sudden some president of some country talks about prescription of drugs etc. and all and we very well be in some kind of doubt or the Pope all of a sudden tries to talk about prescription of some drugs etc. and all will be suspicious about that particular kind of thing. So are there authorities that assert that S is false is the question which we need to ask whether you want to judge whether it is having reliable authority or not. So the answer is if so or authorities more less equally reliable on a subject issue or not is the one which you need to ask is authority being miscoted or misinterpreted etc. If it is misinterpreted or miscoted then it is considered to be the fallacy of unqualified other when they talk about fallacies I will talk I will go into the details of this particular kind of thing. Again when it is the other kinds of arguments which come under the category of inductive arguments or arguments from analogy. Analogy is the one which we commonly use in day to day discourse when you are trying to compare to similar kind of objects etc. In argument from analogy or analogical arguments which you commonly see in science also natural sciences you are comparing to similar kind of metals and then suppose if you have one metal is having some kind of property then usually you know the metal also behaves in the same way like the other metal then you will say that the second metal is also having a similar kind of property. An argument from analogy or an analogical argument is an argument in which it is inferred from the fact that two or more objects situations or instances are similar in certain ways to a conclusion that there are similar in some other ways also. So let us say A and B are there and then they are similar in two respects and all. Then you will say that the third one the other kind of property that you come across maybe you know you will be under the impression that this the metal B is also having a similar kind of property. So this is like this an example is like this they have this kind of pattern A is similar to B and B has some kind of property P and all. So obviously you will say that since A and B are similar to each other and you probably know you will say that A is also having that particular kind of property B P because A and B are similar they show same kind of things in several different ways. Here is an example which tells us in greater detail Ravi's laptop was manufactured by Apple Inc etc corporation etc and it is very dependable and all that is a property that it has stable operating system etc or desktop all these things. And now you are comparing another statement as is Rani's laptop was also manufactured by Apple that means these two are similar in the sense that they are manufactured by Apple industry. So therefore based on that thing you will infer that B is also having the property P, P is like this Rani's new laptop will also be dependable as well. So again this argument we are going beyond what is stated in the premises so that is why it is an open ended argument if you add more information to it then it will strengthen or weaken this particular kind of argument it is in that sense it is a open ended argument. So there are few other arguments again I will come to the end of this lecture there are some kind of arguments which you commonly come across there are statistical generalizations what is the statistical generalization a statistical generalization is an inductive inference in which an inference is made from the fact that certain percentage or portion of a group bears some kind of property to conclusion that the same percentage of the entire group bears some particular kind of property. So again with an example this gets clear and all what it says is certain percentage or portion of a group bears some kind of property P and all let us say 30 40 percentage of a particular kind of portion of a group has this particular kind of property then with that you generalize and say that the same percentage of the entire group also bears this particular kind of property with an example concrete example substrate idea will get simpler we say that usually in this example 65% of the adult citizens in India who pulled a proof of the job that dagger Manmohan Singh is doing what Manmohan Singh is doing as the premist of India therefore 65% of all adult citizens of India approve of the job that Manmohan Singh is doing as a premist is honest and all these things and they are also approving this particular kind of thing in short what is case here is that Dr. Manmohan Singh is enjoying 65% of the approval rating as the prime minister of India. So there are some other examples which come under the category of inductive arguments they are arguments inductive arguments by enumeration. Suppose if some so and so percentage of a sample of A or B is so we say that approximately some percentage of A or B is enough. So what we do in the case of enumerative induction is that we argue from the premises about some members of a group to generalization about the entire group and all and some questions we need to ask for judging whether it is an argument based on enumeration inductive argument based induction based on enumeration is a sample size is random is a sample is of an appropriate size sufficient size is there or not which we need to question is a sample is inaccurate due to psychological factors there are some of the questions which we need to ask. The final argument that you come across in day to day discourse or may be one in the natural sciences is one of the most important inductive arguments that is the arguments from cause and effect. So this is an inference inference is a some kind of mental process in which we move from some particular premises to another kind of statement which is called as a conclusion. Inference moves from cause to effect or sometimes even moves from effects to cause in smoke to fire etc. Or maybe you observed some kind of fire and then you will infer some of the other things arguing that something is the direct result of something else example because so many women are working long hours outside the home kids today are more violent and dangerous enough. So since women are working coming late from the office and all there is nobody to take care of the kids etc maybe the conclusion probably follows that you know kids today are more violent and dangerous enough it appears that one is causing the other one. But again whether it is a good argument or not ultimately the logic what we try to come up with is that whether it is a good argument or a bad argument. So how do we judge that it is a good or bad argument that means the argument based on cause and effect here are some of the questions that we will be asking ourselves does one thing really cause the other one or not or it is a due to some spurious cause or it is a correlation or it is confused as correlation etc. And all the one which we need to ask ourselves are there merely correlated and all is there any other larger cause or series of causes that better explains the effect that is in question and all. If your answer is yes then you can this argument can be improved further. So with this you know I will close this lecture so what we spoke about is this that in we have talked about various instances where we come across deductive and inductive arguments relative arguments usually come across in arguments based on mathematics arguments based on definition etc. Then whereas inductive arguments usually arguments based on science arguments based on otherity arguments based usually based on cause and effect etc. They are all come under the category of inductive argument. How did we judge that these are inductive and deductive argument again our four basic questions that we asked ourselves is it truth preserving is the argument truth preserving or in the argument whether the conclusion necessarily follows from the premises or is this argument is there any new information present in the argument these are some of the questions that we asked and based on that we judge that the given argument is deductive or inductive. In the next lecture I will be talking about special important property of logic that is validity. Validity tells us that suppose if you are given two statements and all how it follows in a leads to some other kind of statement that we are calling it as a conclusion how the premises are leading to the conclusion the link between the premises and the conclusion how they are leading to the conclusion is known by the concept of validity. So once we talk about validity then we talk about soundness of deductive argument in the case of inductive and deductive arguments we can only talk about the strength of the inductive argument that means we can only say that a given inductive argument is strong or weak and if it is strong then we can ask ourselves whether it is a cogent argument or a uncogent argument based on the premises are probably true etc. So then in the next class we talk about the validity of deductive arguments.