Question

1. Kepler used the precise observations of the positions and movements of the planets and labored many years to mathematically determine that the orbits of the six planets known at the time were in the shape of ellipses.

Galileo, performed experiments about the motions of objects and looked for patterns in their data. For example, Galileo found that the period of a pendulum was independent of the mass and amplitude but was dependent on the length of the string and gravity.

Albert Einstein's special theory of relativity, which was published in 1905, is a good example of how physicists ask questions and form hypotheses. Einstein never did a single experiment in this field in the laboratory. He used mathematics in his work.

Peter Higgs postulated that the universe was permeated by a field (Higgs field) that contains numerous uniformly distributed particles called Higgs bosons that cluster around other particles moving through the field. The Large Hadron Collider proved the existence of Higgs bosons.

1. Describe deductive reasoning, including an example from one of the scientists above. Be sure to clearly explain your choice.

2. Describe inductive reasoning, including an example from one of the scientists above. Be sure to clearly explain your choice.

Answer 1

Deductive reasoning

Deductive reasoning is a basic form of valid reasoning. Deductive reasoning, or deduction, starts out with a general statement, or hypothesis, and examines the possibilities to reach a specific, logical conclusion, according to California State University. The scientific method uses deduction to test hypotheses and theories. "In deductive inference, we hold a theory and based on it we make a prediction of its consequences. That is, we predict what the observations should be if the theory were correct. We go from the general — the theory — to the specific — the observations," said Dr. Sylvia Wassertheil-Smoller, a researcher and professor emerita at Albert Einstein College of Medicine.

Deductive reasoning usually follows steps. First, there is a premise, then a second premise, and finally an inference. A common form of deductive reasoning is the syllogism, in which two statements — a major premise and a minor premise — reach a logical conclusion. For example, the premise "Every A is B" could be followed by another premise, "This C is A." Those statements would lead to the conclusion "This C is B." Syllogisms are considered a good way to test deductive reasoning to make sure the argument is valid.

For example, "All men are mortal. Harold is a man. Therefore, Harold is mortal." For deductive reasoning to be sound, the hypothesis must be correct. It is assumed that the premises, "All men are mortal" and "Harold is a man" are true. Therefore, the conclusion is logical and true. In deductive reasoning, if something is true of a class of things in general, it is also true for all members of that class.

According to California State University, deductive inference conclusions are certain provided the premises are true. It's possible to come to a logical conclusion even if the generalization is not true. If the generalization is wrong, the conclusion may be logical, but it may also be untrue. For example, the argument, "All bald men are grandfathers. Harold is bald. Therefore, Harold is a grandfather," is valid logically but it is untrue because the original statement is false.

Einstein just used aberration of light and Fizeau’s experiment which were inadequate premises to put forward the principle of relativity and permanent principle of light velocity. The deductive reasoning used by Einstein showed not only his talent, but also the strictness in deduction

Inductive reasoning

Inductive reasoning is the opposite of deductive reasoning. Inductive reasoning makes broad generalizations from specific observations. Basically, there is data, then conclusions are drawn from the data. This is called inductive logic, according to Utah State University.

"In inductive inference, we go from the specific to the general. We make many observations, discern a pattern, make a generalization, and infer an explanation or a theory," Wassertheil-Smoller told Live Science. "In science, there is a constant interplay between inductive inference (based on observations) and deductive inference (based on theory), until we get closer and closer to the 'truth,' which we can only approach but not ascertain with complete certainty."

An example of inductive logic is, "The coin I pulled from the bag is a penny. That coin is a penny. A third coin from the bag is a penny. Therefore, all the coins in the bag are pennies."

Even if all of the premises are true in a statement, inductive reasoning allows for the conclusion to be false. Here's an example: "Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald." The conclusion does not follow logically from the statements.

Inductive reasoning has its place in the scientific method. Scientists use it to form hypotheses and theories. Deductive reasoning allows them to apply the theories to specific situations.

while Galileo uses inductive reasoning, as he does a series of experiences so he can come to a conclusion and establish a general law.