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

Dr. Sarukkai addresses the question of where logic is to be found in Science-

“From the ancient Greek tradition to modern logic, logic is presumed to have certain characteristics: it is universal, is not related to the empirical world and is different from empirical knowledge (or knowledge of the world). In contrast, science is fundamentally about the world, it is fundamentally a type of knowledge of our world. Therefore, in principle, science cannot be reduced or even equated with logic.”

(Page 57)

“Another related problem is that there are many types of logic. Logic, like other disciplines, has developed extensively from ancient times. There are now new types of logic which are quite different conceptually from early Greek logic. Another example of a different kind of logic is ‘Indian logic’, which was the logic as described in ancient Indian philosophical traditions. Indian logic is a classic example of logic which is not based on presuppositions that logic is universal, not empirical and not epistemological. Whether it is the Nyaya school or the Buddhists or the Jainas, Indian logic is a rigorous analysis of inferences that we make. For long, because of this empirical and epistemological element explicitly present in Indian logic, many logicians claimed that Indians had no tradition of logic. Given the direction that modern logic has taken today this claim is not so forcefully articulated now. But more importantly, Indian logic shows how science moderates logic and not the other way. Many conceptual ideas that arise in Indian logic resonate strongly with scientific methodology and praxis. This does not in any way imply that Indian logic is ‘doing’ science. What it is doing, however, is expecting logic itself to be scientific, in contrast with the position that science be logical.”

” Among all human activities, science is seen to be the exemplar of logical thought and analysis. This is mainly because the methodology and the results of science are related to ideas such as objectivity, truth, laws, rationality and so on. Science is also explicitly connected with logic through its use of mathematics. In the development of modern logic, the association between mathematics and logic proved to be very important. On the one hand, the shift to symbolic logic meant that logic was being presented in a form similar to mathematics. On the other hand, the belief that mathematics can be entirely reduced to logic, meaning that all mathematical statements can be reduced to logical statements, brought mathematics and logic much closer. This belief called logicism, championed so bravely by Russell, was also based on the belief that mathematics is the exemplar of deductive logic.”

(Page 58)

” The relation of science with logic is also manifested in other ways. While the mathematical component of science is seen to reflect the deductive structure of argument in science, there is much in science which draws upon other forms of argumentation, particularly inductive and abductive inferences. Many of these inferences in science follow the same structure as the common inferences we make, such as the inference of fire from smoke. Thus, the philosophical issues that arise in analysing inferences in science share some common conceptual ground with ‘ordinary’ everyday inferences. Paradoxically, the strong empirical grounding of science places it in potential conflict with the Western tradition of formal logic. Science draws upon observations and reason, and by weaving them together constructs its narratives of the world.”

” Scientists do not do science by asking whether their thoughts are ‘logical’. In their practice and methodology, scientists indulge in activities which are many times merely habits and rituals. In fact, scientific knowledge, like other knowledge systems, has a strong ritual component to it. Being ritualistic is also to be methodological and one of the important characteristics of methodology is that it trains one to do something without much reflection on what they are doing. Scientific methodology shares this trait with various other human activities which are ritualistic in character even as it is distinct from them in other important ways. Habits, creative thinking, serendipity, ‘irrational’ action and such, are placed under the context of discovery. The step of justifying these discoveries and results, where the claims are placed within a larger community for acceptance, is a process that is outwardly not arbitrary, illogical or irrational. It is in this domain that logic makes an obvious entry.”

(Page 59)

” Therefore, it is not surprising that the association of logic in science is primarily found in scientific methodology. After all, much of science is based on ways of thinking which are very similar to what we do in our ordinary lives. Scientists do not infer any differently from non-scientists, although they may subject their inferential conclusions to more rigorous and varied kinds of tests. In most part, what is different in scientific thinking is the kinds of things they think about, the tools they use to analyse, an undercurrent of scepticism in their thinking combined with a strong streak of pragmatism.”

” However, the methodological instinct in science takes commonsense logic to a more refined level. Thus, it is no surprise that the relation between logic and science begins and ends with methodology. For example, Cohen and Nagel make explicit this connection by noting that in essence ‘scientific method is simply the pursuit of truth as determined by logical considerations”

(Page 60)

“… knowing how to frame an appropriate hypothesis is itself part of methodology. However, logic makes its proper appearance when deductive consequences of the hypothesis are explored. Thus, from some hypotheses we make on observing a phenomenon, we deduce possible consequences and if those consequences hold good then the hypothesis is probably right. This, in essence, is the hypothetico-deductive model that has been discussed in great detail in the philosophy of science.”

” Logic is also manifested in the various logical relations between theories and observations. Many scientific statements, including scientific laws, are implications – as manifested in if-then statements. For example, one of Kepler’s laws illustrates a deductive implication: ‘If the attraction between two masses is inversely proportional to the square of the distance between them, and there is a sun with one ambient planet, then the orbits of the planet will be an ellipse with the sun in one focus.’ Such implications are also found in statements related to definitions: ‘If an animal has more than six legs then it is not an insect.’ A large number of scientific descriptions are causal descriptions which also have this structure, as for example, ‘If a piece of litmus is placed in acid then it will turn pink’ (Trusted 1979)”

(Page 61)

” An important principle of implication is that in a conditional of the form ‘If p, then q’, when p is true, q has to be true. So if we look upon theory as p and observation statements as q, then if p is true it implies that q has to be true. Such a logical relation also satisfies the other condition, namely, that if observations are true it does not imply the appropriate theory is true, following from the logical consequence that if q is true, it is not necessary that p must also be true. Moreover, according to a logical principle, if q is not true then p is also not true. In other words, if there is no observation then the theory is wrong. This, in essence, is the principle of falsification. So we can see that falsification has a logical basis.”

” However, science is not possible without the extensive use of inductive inferences. Induction is a type of inference. Consider some common examples: a ball that is thrown up in the air falls down. We see this happening many times and in many places, and we generalize from particular observations to the general claim that whenever a ball is thrown up, it will fall down. This capacity to describe a particular behaviour of the ball in all cases, whether spread over space (wherever) or time (whenever), is a mysterious one. What allows us to talk about these cases with any measure of certainty? We also make inductive inferences when we draw conclusions about all members of a class from some observed members. For example, from tasting one drop of seawater we conclude that all drops of seawater will be salty. Although in normal usage we tend to use the word ‘all’, such generalizations are also expressible through statistical generalizations, such as saying that something is true 60% of the time. Such examples are called induction by enumeration. Analogy is another kind of induction where from observation of some property or properties in one object we infer similar properties in other objects.”

” We can distinguish between deduction and induction in this manner: deduction is nonampliative inference and induction is ampliative inference. In ampliative inference the conclusion contains more than what is in the premises. The uncertainty in such inferences creates a potential conflict for science, and scientific methodology can be seen as a method to try and make such inferences as certain as possible. The approach to induction that is most commonly accepted today is the probabilistic approach, which has also become the backbone of scientific inference.”

(Page 62)

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