 Dear learners, today we are going to discuss B.S. 2nd semester's logic 2 papers unit 11 that is nature and kinds of induction. First, we will have to know the definitions of inductive inferences. Now, we studied from the viewpoint of J.S.Mill, what J.S.Mill have said about inductive inference. J.S.Mill, he has defined induction as the operation of discovering and proving general proposition. Now, J.S.Mill also says that induction is the name given to the operation of the mind by which we infer that what we know to be true in particular cases or cases will be true in any other cases or cases of a similar kind. Francis Bacon, another philosopher, he says that so far as induction is concerned, induction is something which tries to discover the forms or causes of things, Bacon also adopted the method of elimination. Now, see whenever we are saying about induction, what is actually induction? We know that there are two kinds of inferences, one is the deductive inference, another is the inductive inference. Now, so far as deduction is concerned, in deduction what we do? We always come to a particular conclusion with the help of general premise or premises. That is why, so far as deduction is concerned, its conclusion is always correct or valid. But so far as inductive inferences are concerned, in inductive inferences with the help of experience and observation, we come to a particular proposition, the conclusion is a general proposition and the premise or premises are particular propositions. So, sometimes we had to eliminate many things and sometimes we had to observe and experience many things and on the basis of those observation and experiences and elimination, finally, we come to a general conclusion. Now, in so far as western logic is concerned, in western logic induction is something which is used to mean both process and product of induction. On the other hand, so far as Indian logic is concerned, you will find that in Indian logic, the what reasoning? It is used to mean process of reasoning not to the product. So, with the help of reasoning, we cannot get any product according to Indian logic. Now, we will go to characteristics of inductive inferences. What are the characteristics of inductive inferences? First we will go through of it and now then we will discuss about it. First, it is said that inductive inference is essentially based on the observation of particular facts of experience, observation and experiments supply its premises. Secondly, in induction, a general conclusion is established on the basis of particular facts of experience, which is called generalization. Generalization is an important characteristics of induction. Induction is a process of arriving at the universal conclusion from facts about particular samples. A very important and unique characteristic of induction is the involvement of the inductive leaf or leaf in the dirt. Inductive leaf is a leaf or jump from the known to the yet unknown or from the cases of so far to the yet observed cases. It is a jump from certainty to uncertainty. Through the inductive leaf, we will try to gain a new knowledge. Now see, I have already said that so far as induction is concerned in induction, observation and experiment. These two things are very important. The premises are drawn with the help of observation and experiment. That means, with the help of premises, we finally come to the conclusion and we have already said that so far as inductive inferences are concerned in inductive inferences. The premises are always particular and on the basis of those particular premises, finally, we have come to a general conclusion. And what technique we use, the technique what we use, inductive inferences is observation and another technique which we used to use here is the experiment. That means, observation and experiments are the two techniques with the help of which we can come to a general proposition. Now, another important thing is that so far as generalization is concerned, for generalization, we have to take the help of inductive leaf. Now, what is inductive leaf? I am just giving one example. Suppose, we have observed some of the instances like Ram's model, Hari's model, Jadu's model, Madhu's model. And on the basis of those facts, on the basis of those facts, finally, we have come to a conclusion that all men are mortal. See, it is not possible for anyone to observe and experience the mortality of each and every individual of this universe because before my existence, that means, before I was born also, there are individual who were died and after my, when I die, after that also individuals, human beings were born and they will also die, but it is not my capacity to take the experience of those people. But because of the observation and experience which I have carried, on the basis of that, finally, we have drawn a general conclusion that all men are mortal. That means, from some to all, we had to jump. From some to all, we had to jump. And that jump is called inductive leaf. With the help of inductive leaf only, we can come to a general proposition from the particular premises. Now, we will discuss some other characteristics. See what other characteristics of induction has said. The conclusion of inductive inferences is more probable or less probable, but it can never be certain. But inductive argument will provide stronger probabilistic support and worse inductive argument will provide weaker probabilistic support for their conclusion. The conclusion of induction goes beyond the premises. The basis of going beyond the premises lies in two presuppositions, the law of uniformity of nature and the law of causation. These two principles currently the formal truth of induction and they are called formal grounds of scientific induction. Inductive inference is a non-monotonic. This is because new informations can change the strength of the inductive argument. The importance of additional importance. Information is always a relevant consideration in inductive reasoning. Now, see, I have already said it. That so far as induction is concerned, it always, based on, it is always take the help of some particular proposition. And here we always jump from some to all. And that is why the conclusion of an inductive inference can never be certain. It is always provable in nature. If we'll be able to provide more facts, then its degree of probability will be less. And if we'll be able to provide only some facts with the help of our experience, then its risk of probability will become high. No, but whatever may be the condition, its degrees will be differ. But the quality or its main characteristic will always remain uncertain and provable. It cannot be certain. Now, so far as the conclusion is concerned, what induction actually do? It takes the help of two laws. They are the law of uniformity of nature and the law of causation. What is law of uniformity of nature? According to law of uniformity of nature, nature behaves in the similar way under similar circumstances. And what is law of causation? Law of causation says that every cause has an effect. So, on the basis of these two laws, finally, induction tries to come to a general conclusion. Now, what are the stages of induction? We'll find that there are four stages of induction. Observation, formation of hypothesis, generalization and verification. Now, what is observation? Observation is well-defined perception for a certain definite purpose. But it supplies the materials of induction. It involves analysis and elimination. Now, with the help of observation only, we can see what are the materials of the particular argument or particular induction. And on the basis of observation only, we can eliminate some facts and we can accept some facts. Now, second is the formation of hypothesis. What is the formation of hypothesis? A hypothesis means a provisional supposition. Suppose we take something. Suppose we take that this is true. Now, why we have considered that this is true? Because we already have some experiences. On the basis of those experiences, finally, we give the conclusion that this is true. Now, when hypothesis is there, we will have to try to make the hypothesis correct or we'll have to prove the hypothesis. If we will be able to prove the hypothesis to be true, then the statement will be a law. It will be correct forever. And if we will not be able to prove the hypothesis or it will be proved as wrong, then that particular statement will be dismissed. Now, another one is generalization. Another stage is generalization. Now, what is generalization? Generalization is a process of arriving at general proposition on the observation of particular facts. What the things we have, which I have already discussed these things earlier that in induction, induction what we do? We arrive to a general statement with the help of particular statement. With the help of particular statement and with the help of inductively, finally, we come to a general statement and this process is called generalization. Another thing is verification. Verification means examining by appealing to facts whether the general proposition which is arrived as it is really true or not true. Whenever we are referring an induction, the conclusion of induction and the premises are actually materially true. One of the important point is that they should be materially true because we always give importance to observation and experience. But so far as deduction was there, in the case of deduction what happened? In the case of deduction, we only give importance to formal truth and not the material truth. But in the induction, you always give importance to material truth. The subjective conditions of inductive inferences are freedom from prejudice, patience and preservation, belief in the uniformity of nature and the law of possession. The points we have whatever we have discussed earlier from the basis of those, finally, these points can be derived. Freedom from prejudices, patience and preservations, beliefs in the uniformity of nature and the law of possession. Now we will discuss about the problem of induction. What is the problem of induction? Induction seeks to establish the material truth of universal real proposition and the premises of induction are derived from experience. The problem of induction does refer to the question as to how it is possible for induction to arrived at the universal real proposition on the basis of observation of particular facts. The main problem which is arised in induction is how from the particular proposition will be able to come to a general proposition. Because we can observe for experience only some points, but it is not possible for us to discuss or experience all the particular points about the particular instance. Now what is the solution the philosopher has provided for this problem? The solution to this problem is the lies in the fact that in passing from the particular to general induction, induction relies on two fundamental laws. They are the laws of uniformity of nature and the laws of possession. I have already told you according to uniformity law of uniformity of nature, nature behaves in a similar circumstances, a similar way and the similar circumstances. So if we have observed that, suppose we have observed 100 of instances and they are behaving in the same way, then on the basis of that by applying the law of uniformity of nature finally we will be able to come to the conclusion that this particular instance or in future also this particular under these circumstances that particular point will discuss in the similar way. And other is the law, other is the law of causation, law of causation says that every cause has an effect without having or every event has a cause. Without having a cause nothing can happen. If something is happening because of that some cause must have to be there and because of the presence of that particular cause only finally that event has happened. So on the basis of those particular laws finally induction tries to come to a general conclusion. Induction has to rely upon assumptions that the future will uniformly follow the past. For example we assume that the sun will rise tomorrow as it has risen every day in the past. Now what are the kinds of induction? If we will see the kinds of induction then finally we will find that there are two kinds of induction. One is the induction proper and other is the induction improperly so called. What is induction proper? In induction proper what happened? We come to the conclusion with the help of inductive leave. So for induction improperly so called in the case of induction improperly so called we do not come to the conclusion with the help of inductive leave. Now induction proper can be also divided into three points or three kinds there. Scientific induction, unscientific induction and analogy. Now what is scientific induction? Scientific induction is the establishment of a general real proposition. Based on observation of particular instances it relies on the principle of the uniformity of nature and law of causation. By applying or by relying law of uniformity of nature and the law of causation scientific induction always try out with the help of observation scientific induction come to a general proposition. Now what is unscientific induction? Unscientific induction is the establishment of a universal real proposition on the basis of the mere uniform or contradicted experience without any attempt at discovering causal connection. Here only uniformity of nature law of uniformity of nature is taken into consideration but here law of help of law of causation will not take. For example all closer black on the help of for establishing this statement all closer black we cannot take the law of causation the every event has a cause does not apply here ok. So here only law of uniformity of nature will be applied and under is the analogy. Analogy is a kind of induction in which on the basis of observation of resemblance in some particular properties between two things we infer further resemblance in some other property between them. So far as induction improperly so called is concerned it is also divided into three kinds there perfect induction, induction by parity of reasoning and collusion of facts. Now what is perfect induction? Perfect induction is the establishment of a universal proposition on an examination of the particular instances covered by it as for example all known planets move around the sun ok. Here what we do we separately examine each and every instance ok all planets all known planets are moving around the sir all known planets move around the sun ok. For this we have to examine and observe all the different planets and we have by observing those planets we have seen that all the planets are moving around the sun and on the basis of that experience finally we have come to the conclusion that all known planets move around the sun. Now what is induction by parity of reasoning? Induction by parity of reasoning is a process of inference in which we establish a general proposition on the ground that the same reasoning which establishes a particular case will establish every other similar case coming under the same proposition ok. Suppose we have today we are observing cloud and on the basis of that we can say that it will be rain ok. So in future also whenever we will see clouds then on the basis of our observation we will be our experience will be said that it will be rain ok. Another kind is the collusion of facts. Now what is the collusion of fact? James Mill he defines collusion of facts as the mental operation which establishes us to bring a number of actually observed phenomena under a description or which enable us to sum up a number of detail in a similar proposition. He has given one example he said that a navigator while sailing in the ocean discovers a land ok at first he cannot determine whether it is a continent or an island but he coast around it and after a few days he finds he has completely sailed around it. He then brings together observed facts under the conception of an island and declares it is to be an island. Now some fallacies are there in induction. Now what are those fallacies? Inductive fallacies usually why inductive fallacies occur actually. Inductive fallacies occur when the premises of inductive arguments fail to provide the desirable amount of probabilistic support for the conclusion. Inductive fallacies are of two kinds they are inferential and another is the non inferential. Now so far as inferential fallacies are concerned under inferential fallacies there are three kinds of fallacies they are fallacies of causation, fallacies of generalization and fallacies of analogy. That means if we will find one event and it will not support the cause then it will commit fallacy of causation, fallacies of generalization. If enough experience or enough observation will not be able to provide and the general statements will be proved to be wrong then it will be fallacy of generalization and fallacy of analogy when our process of resemblance is not proper then it will become fallacy of analogy. Now in non inferential fallacies also there are two kinds of fallacies, fallacies of observation and fallacies of explanation. Suppose we have failed to observe the facts then on the basis of that if we will draw one conclusion then that will occur fallacy of that will commit fallacy of observation and another is the fallacy of explanation if we will not be able to provide the proper explanation of the conclusion. So this is in brief about the induction the unit call induction and I think you have understood it properly you please go through your SLM and try to understand it again. Thank you.