There are several different types of logic, but probably the two most common are deductive and inductive. Both of these play a vital role in science, but we use them for different purposes. Therefore, it is my intention to explain the differences between these types of logic and when and how we use both of them in science.

Deductive logic
This is the most powerful form of reasoning. It is the type of logic that results in logical proofs. It goes from general concepts and/or specific observations to a focused conclusion. For example,

1. The sum of the angles of any triangle equals 180 degrees (general concept)
2. Angle A of triangle ABC = 45 degrees (specific observation)
3. Angle B of triangle ABC = 90 degrees (specific observation)
4. Therefore angle C of triangle ABC = 45 degrees (focused conclusion).

Notice that the conclusion is a certainty. This is the power of deductive logic, it tells you what absolutely must be true (assuming that your premises are true).

To give another famous example:

1. All men are mortals (general concept)
2. Socrates is a man (specific observation)
3. Therefore, Socrates is a mortal (focused conclusion)

I used this example to bring up a very important point about deductive logic. Deductive syllogisms often include a premise that was arrived at via inductive logic, this will become important in the next section.

In science, deductive logic is typically what is used at to arrive at facts. In other words, we use it to determine the results of specific experiments. For example:

1. I stomach flushed turtle A
2. Its stomach contained the remains of a fish
3. Therefore, turtle A ate a fish

So in short, deductive logic always gives a specific, focused conclusion and is used in science to determine facts and the outcomes of individual experiments.

Inductive logic

In contrast to deductive logic, inductive logic always results in a general conclusion and can be used to construct theories. It should be noted, that it is impossible to use deductive logic to arrive at a theory. Theories only come from inductive logic.

Inductive logic works somewhat backwards from deductive logic. It starts with specific observations and works towards a general conclusion (note: both types of logic start with observations and work to a conclusion). For example, think back to the Socrates example in the deductive logic section. How do we know that all men are mortals? Well, we know that from inductive logic,

1. Every man that we have “tested” (observed) has been mortal (collection of specific observations)
2. There is no reason to think that an immortal man could exist (logical statement)
3. Therefore, all men are mortals (general conclusion)

Notice, an inductive conclusion is not as strong as a deductive conclusion, but it is still often very powerful. Technically speaking, it is true that I cannot be completely certain that there is not an immortal walking around pretending to be mortal, but there is simply no reason to think that such a person exists, so the conclusion is clearly valid. It should be noted, however, that not all inductive conclusions are equal. For example, if I said that, “I have liked every Christopher Nolen film so far, therefore, I like all Christopher Nolen films (present and future)” my conclusion is clearly dubious. There are so many variables involved in making a film that it is absurd to think that he will never make one that I don’t like. This is generally not the case in science. In science, we use inductive logic with as few variables as possible, and we generally support our conclusions with mathematical models. Also, the consistency of the physical universe adds an extra level of support to our inductive conclusions.

Additionally, because of the law of large numbers, the strength of an inductive conclusion increases as the number of observations used to form the conclusion increases. If I measure the rate of something once, it would be absurd to say that it always moves at that rate. If I measure it 100 times, however, it becomes more certain. If I measure it 1,000 times, it becomes even more certain.

Perhaps the greatest support of an inductive conclusion is, however, its ability to predict other events/make things work. Suppose that I build a device that would only work if the aforementioned rate was constant, and, when I turn the device on, it works. That would be extremely strong evidence that my inductive conclusion was correct. In fact, predictive power is the benchmark that we use to measure the strength and validity of theories.

This brings me to the restatement of a very important point about all scientific theories. They all rely on inductive logic. This is inherent in the nature of a theory (i.e., it is a general framework based on observations and used to explain other observations), but, something only gets promoted to the status of theory after it has been shown to have a high predictive power. For example:

1. Every physical body with mass that we have tested has produced gravity and been acted upon by gravity.
2. There is no logical reason to think that gravity wouldn’t be constant, and there are strong mathematical/logical reasons to think that gravity is a constant
3. Numerous functional devices and calculations rely on the concept that gravity is constant
4. Therefore all physical bodies with mass produce gravity and are acted upon by gravity (i.e., the universal theory of gravity).

Notice, technically, I cannot be 100% certain of the conclusion. I have not tested every physical body in the universe, but virtually everyone will agree that the conclusion is valid.

I explained in a previous post that laws are synonymous with theories, allow me to demonstrate this by showing that the second law of thermodynamics was also arrived at using inductive logic.

1. Every closed system that we have ever observed has increased in entropy
2. There is no logical reason to think that a closed system could decrease in entropy, and there are strong mathematical/logical reasons to think that entropy must always increase
3. Numerous devices/experiments only work because all closed systems increase in entropy
4. Therefore, all closed systems increase in entropy (i.e., the second law of thermodynamics)

To summarize, scientists generally use deductive logic to determine the outcomes of specific experiments (sometimes inductive logic is also required depending on the nature of the experiment), and we use inductive logic to generalize from those experiments and form laws and theories. This is true for all laws/theories, whether we are talking about the laws of thermodynamics or the theory of gravity.