Inductive Reasoning in Science

Inductive Reasoning in Science

While deductive logic is highly accurate in predicting the conclusion, which can never be wrong if the premises are true. However, deductive logic fails to create new knowledge since the premises already contain the conclusion. The inductive argument may not provide a conclusion with absolute certainty, but its utility lies in exploring unknown territory and creating new knowledge.

Inductive logic is the basis of all discoveries in science. Consider the example of Newton discovering gravity. It is said that once, Newton was sitting below an apple tree and saw an apple falling. Billions of people before him must have seen an apple falling from its tree, but they never applied logic to think why apples fall to the ground. However, Newton must have thought that since all apples fall to the ground, the earth must apply some form of force on them.  His thought process can be summarised in the form of the following argument,

• Premises 1: When force is applied to a thing, it moves in the direction of force.
• Premises 2: All apples fall on the ground.
• Conclusion: Therefore,  Ground applies a force of attraction towards the apple.

When Newton observed that not only apples but every material object fell towards the ground, he concluded that the earth exerts a force of attraction, which he later called gravity, on all material things. Later, he found that not only the earth, but every single object applies a force on every other material object, which is proportion to the masses of the object and inversely proportion to the square of the distance between the objects. This is how Newton formulated the universal law of gravity, which can be expressed by the formula F = G(m₁m₂)/R², where F is the magnitude of the attractive force,  G is the gravitational constant, m₁ and m₂) are the masses of the objects, and R is the distance between the two objects.   

However, most of the time, the correlation between two variables is not so evident. For instance, it is well established through numerous studies that ‘smoking causes cancer’. However, such a conclusion is not based on direct observation because many smokers never get cancer, while many nonsmokers get cancer. However, when the data of a large number of smokers and nonsmokers are collected, it is found that smokers are more likely to get cancer as compared to nonsmokers. Hence, smoking does not necessarily lead to cancer but increases the probability of cancer many times. Likewise, through numerous studies, it has been concluded that obesity causes heart problems because obesity increases the likelihood of increasing heart problems.

Inductive arguments are thus the essence of scientific reasoning and investigations, as they attempt to make an inference from a particular case to a general case. The structure of the inductive argument in scientific investigation can be expressed as follows.

Structure of Inductive Argument in Science

• a₁ is B.
• a₂ is B.
• :
• a_n is B.
• Therefore, all A are B

Inductive reasoning is extensively used to find correlations between different variables and develop scientific laws by extending the particular observation to general principles.

Correlation Coefficient (CC)

Correlation is a statistical measure that expresses the extent to which two variables are linearly related. It is measured in terms of a correlation coefficient (CC), which can be positive, negative or zero, having a number between -1 and 1 that tells the strength and direction of a relationship between variables. The relationship may be expressed as follows.

Table: The Relationship between two variables based on the Correlation Coefficient (CC), and

CC	Relationship
1	A perfect positive correlation i.e. when one variable changes, the other variables change in the same direction.
-1	A perfect negative correlation i.e. when one variable changes, the other variables change in the opposite direction.
0	Zero correlation i.e. no relationship between the variables.

The relationship can also be shown in the following graph.

Let us now discuss how the law of inertia was discovered using the inductive method of science.

In the course of the experiment, the scientists found the following results.

1. Acceleration doubled when force doubled (when mass is kept constant, 
2. Acceleration halved when mass was doubled (When the force is kept constant,

In mathematical terms, the relationship can be expressed as follows,

1. Acceleration (a) ∝ Force (F),
2. Acceleration (a) ∝ 1/mass (m)

Combining the two equations, we get a= k F/m (where k is a constant)

The unit of measurement of force F was defined by Newton by taking the value of the constant k=1. This means that the force that leads to the acceleration of a mass of one kg to 1 meter square in a second is defined as one Newton.

Accordingly, we get the formula for the law of inertia as  a=F/m or F=ma.

in this case, the correlation between force and acceleration also gives causation because we can change a particle’s acceleration (effect) by changing the two causes (variables), i.e., by doubling the force or dividing the mass into half. It is essential to understand that all other variables must be kept constant to find perfect correlations between two variables.

Inductive Reasoning in Logic and Science

“Induction” is defined differently in science than in logic. In science, the inductive argument moves from specific to general, while in logic, the inductive argument is valid in all cases. For instance, if the argument proceeds from general to specific, it is not considered to be a valid inductive argument for science despite being a strong argument for the purpose of logic.

Accordingly, the following logic shall be considered invalid in science.

Argument

• 90% of humans are right-handed.
• John is a human.
• Therefore, John is right-handed.

This argument is strong according to logic since the probability of John being right-handed is 90%.  However, the arguments are not valid according to scientific reasoning since they proceed from general to particular. The inductive logic in science must always proceed from a specific instance to draw a general conclusion. For instance, according to a study conducted by the Centers of Disease Control and Prevention (CDC) USA, smokers are 15 to 30 times more likely to get lung cancer or die from lung cancer than nonsmokers.

In this case, we find that many smokers don’t get cancer, while many nonsmokers get cancer. Hence, the claims of scientists that ‘smoking causes cancer’ is not a valid argument since, in many cases, ‘smoking does not cause cancer’ is not valid, and many people get cancer despite never smoking. However, the claim shall be treated as valid for the purpose of science since smoking increases the probability of cancer multiple times. Many people fail to understand the role of probability in scientific prediction and reject scientific conclusions.

Fallibility of Science

Only the disciplines like mathematics, computer science, and logic follow deductive logic, which is intended to be valid. However, deductive logic is not very useful in the creation of new pieces of knowledge. Science deals with inductive reasoning, which aims to be strong rather than valid. Hence, no scientific law is valid in all situations, and many scientific laws fail in the micro and macro world, i.e. at very small and very large dimensions.  Accordingly, the laws discovered in science using inductive reasoning are considered to be fallible since a general principle is made applicable to all merely based on a limited number of observable facts, and a scneitific law will fail, even if one single observation is found to be contrary to the stated law.

It is said that once Einstein was shown a German newspaper that claimed, “One hundred German physicists claim Einsteins theory of relativity is wrong.” Einsteins replied, “If I were wrong, it would only take one.”

In our day-to-day lives, numerous people try to convince us of their ideas, points of view, ideologies, and beliefs. Unfortunately, most of the ideas are false and not logically tenable. One of the most important functions of critical thinking is to develop a deep understanding of logical fallacies, which enables us to see through the logic and find out whether or not this logic is valid. Critical thinkers must accept only valid or strong logic and reject invalid or weak arguments.