Part of a Series of Excerpts from Prof. Sundar Sarukkai’s Book, ‘What is Science?’

Dr. Sarukkai introduces logic to the reader in the following manner-

” We are endowed with sensory organs that allow us to experience the world. Our knowledge of the objects in the world is derived from these experiences. But quite mysteriously, we also seem to have knowledge of that of which we have no direct experience. For example, we are able to predict that it will rain by seeing dark clouds. This predictive knowledge does not come from experience because what we predict has not happened as yet. Also, from a few pieces of information we are able to know new information without being told about it. We seem to know – without any direct experience – that if an object is smaller than another then the second object is bigger than the first. We often derive knowledge through a process of reasoning.”

” It is this process of reasoning that is referred to as logic. Reasoning is a simple process of connecting two sentences together, two thoughts together, and then arriving at a conclusion. For example, suppose we have two sentences: ‘This fruit is red’ and ‘All red fruits are sweet’. Given these two sentences, if we conclude that ‘This fruit is not sweet’, then we seem to be making a mistake. Given these two sentences, it seems to be the case that only one correct conclusion is possible for any of us. This is the statement that ‘This fruit is sweet’. The process of inferring in this manner is referred to as deductive inference. There is a certainty to this process of reasoning. Another way of saying this is to say that from two true sentences you cannot deduce a false sentence. The inference we make in generalization is most often inductive inference, where from a few samples we generalize to new situations.”

(Page 55)

” Logic is a study of such inferences. It is an analysis of arguments of these kinds. Logic allows us to understand under what conditions such inferences are correct, what kinds of mistakes are possible in making these inferences and so on. The human mind is always in the process of making inferences. Three common kinds of inferences are the deductive, inductive and abductive.”

” Consider some common examples of inference which we make in our daily lives. We see smoke over a particular place and we immediately think that there is fire there. Although we do not see the fire with our eyes we are able to infer that there is fire there – no wonder then that inference was equated with the capacity to ‘see’ through the mind’s eye. That is, we come to know of something in the world through a capacity of the mind alone. This in a nutshell is the ‘power’ of logic and is the reason why logic has been privileged within science.”

(Page 56)

” But absolute certainty is not available in all inferences. Inductive inferences, where we generalize from a few cases to many or all, is one such example. An example from the Indian logical school, Nyaya, is illustrative: if we find that one grain of rice is cooked in a vessel then we infer that all the grains of rice are cooked. There is really no certainty in such an inference. It is possible that one of the grains may not be cooked when we check all the grains. Now, a very important part of logic has to do with probability and not with certainty. In particular, for science, it is these probabilistic logics that are useful.”

(Page 57)
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