Deductive Reasoning vs. Inductive Reasoning

During the scientific process, deductive reasoning is used to reach a logical true conclusion. Another type of reasoning, inductive, is also used. Often, people confuse deductive reasoning with inductive reasoning, and vice versa. It is important to learn the meaning of each type of reasoning so that proper logic can be identified.

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 the University of California.

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 the University of California, 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.

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.

Another form of scientific reasoning that doesn't fit in with inductive or deductive reasoning is abductive. Abductive reasoning usually starts with an incomplete set of observations and proceeds to the likeliest possible explanation for the group of observations, according to Butte College.

It is based on making and testing hypotheses using the best information available. It often entails making an educated guess after observing a phenomenon for which there is no clear explanation.

For example, a person walks into their living room and finds torn up papers all over the floor. The person's dog has been alone in the room all day. The person concludes that the dog tore up the papers because it is the most likely scenario. Now, the person's sister may have brought by his niece and she may have torn up the papers, or it may have been done by the landlord, but the dog theory is the more likely conclusion.

Abductive reasoning is useful for forming hypotheses to be tested. Abductive reasoning is often used by doctors who make a diagnosis based on test results and by jurors who make decisions based on the evidence presented to them.

Guess the author (if you can read the whole thing)

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Apparently, our discussion which took place a long time ago, and which, as I was pleased to learn, has not been forgotten by you, has nevertheless not cleared up this matter in your mind. I will attempt to do so now, in writing, which imposes both brevity and other limitations. I trust, however, that the following remarks will serve our purpose.

Basically the problem has its roots in a misconception of the scientific method or, simply, of what science is. We must distinguish between empirical or experimental science dealing with, and confined to, describing and classifying observable phenomena, and speculative science, dealing with unknown phenomena, sometimes phenomena that cannot be duplicated in the laboratory. Scientific speculation is actually a terminological incongruity; for science, strictly speaking, means knowledge, while no speculation can be called knowledge in the strict sense of the word. At best, science can only speak in terms of theories inferred from certain known facts and applied in the realm of the unknown. Here science has two general methods of inference;
(a) The method of interpolation (as distinguished from extrapolation), whereby, knowing the reaction under two extremes, we attempt to infer what the reaction might be at any point between the two.
(b) The method of extrapolation, whereby inferences are made beyond a known range, on the basis of certain variables within the known range. For example, suppose we know the variables of a certain element within a temperature range of 0 to 100, and on the basis of this we estimate what the reaction might be at 101, 200, or 2000.

Of the two methods, the second (extrapolation) is clearly the more uncertain. Moreover, the uncertainty increases with the distance away from the known range and with the decrease of this range. Thus, if the known range is between 0 and 100, our inference at 101 has a greater probability than at 1001.

Let us note at once, that all speculation regarding the origin and age of the world comes within the second and weaker method, that of extrapolation. The weakness becomes more apparent if we bear in mind that a generalization inferred from a known consequent to an unknown antecedent is more speculative than an inference from an antecedent to consequent.

That an inference from consequent to antecedent is more speculative than an inference from antecedent to consequent can be demonstrated very simply:

Four divided by two equals two. Here the antecedent is represented by the divided and divisor, and the consequent - by the quotient. Knowing the antecedent in this case, gives us one possible result - the quotient (the number 2).

However, if we know only the end result, namely, the number 2, and we ask ourselves, how can we arrive at the number 2, The answer permits several possibilities, arrived at by means of different methods: (a) 1 plus 1 equals 2; (b) 4-2 equals 2; (c) 1 x 2 equals 2; (d) 4 2 equals 2. Note that if other numbers are to come into play, the number of possibilities giving us the same result is infinite (since 5 - 3 also equals 2; 6 3 equals 2 etc. ad infinitum).

Add to this another difficulty, which is prevalent in all methods of induction. Conclusions based on certain known data, when they are ampliative in nature, i.e. when they are extended to unknown areas, can have any validity at all on the assumption of everything else being equal, that is to say on an identity of prevailing conditions, and their action and counter-action upon each other. If we cannot be sure that the variations or changes would bear at least a close relationship to the existing variables in degree; if we cannot be sure that the changes would bear any resemblance in kind; if, furthermore, we cannot be sure that there were not other factors involved - such conclusions of inferences are absolutely valueless!

For further illustration, I will refer to one of the points which I believe I mentioned during our conversation. In a chemical reaction, whether fissional or fusional, the introduction of a new catalyzer into the process, however minute the quantity of this new catalyzer may be, may change the whole tempo and form of the chemical process, or start an entirely new process.

We are not yet through with the difficulties inherent in all so-called scientific theories concerning the origin of the world. Let us remember that the whole structure of science is based on observances of reactions and processes in the behavior of atoms in their present state, as they now exist in nature. Scientists deal with conglomerations of billions of atoms as these are already bound together, and as these relate to other existing conglomerations of atoms. Scientists know very little of the atoms in their pristine state; of how one single atom may react on another single atom in a state of separateness; much less of how parts of a single atom may react on other parts of the same or other atoms. One thing science considers certain - to the extent that any science can be certain, namely that the reactions of single atoms upon each other is totally different from the reactions of one conglomeration of atoms to another.

We may now summarize the weaknesses, nay, hopelessness, of all so-called scientific theories regarding the origin and age of our universe:

(a) These theories have been advanced on the basis of observable data during a relatively short period of time, of only a number of decades, and at any rate not more than a couple of centuries.

(b) On the basis of such a relatively small range of known (though by no means perfectly) data, scientists venture to build theories by the weak method of extrapolation, and from the consequent to the antecedent, extending to many thousands (according to them, to millions and billions) of years!

(c) In advancing such theories, they blithely disregard factors universally admitted by all scientists, namely, that in the initial period of the birth of the universe, conditions of temperature, atmospheric pressure, radioactivity, and a host of other cataclystic factors, were totally different from those existing in the present state of the universe.

(d) The consensus of scientific opinion is that there must have been many radioactive elements in the initial stage which now no longer exist, or exist only in minimal quantities; some of them - elements that cataclystic potency of which is known even in minimal doses.

(e) The formation of the world, if we are to accept these theories, began with a process of colligation (of binding together) of single atoms or the components of the atom and their conglomeration and consolidation, involving totally unknown processes and variables.

In short, of all the weak scientific theories, those which deal with the origin of the cosmos and with its dating are (admittedly by the scientists themselves) the weakest of the weak.

It is small wonder (and this, incidentally, is one of the obvious refutations of these theories) that the various scientific theories concerning the age of the universe not only contradict each other, but some of them are quite incompatible and mutually exclusive, since the maximum date of one theory is less than the minimum date of another.

If anyone accepts such a theory uncritically, it can only lead him into fallacious and inconsequential reasoning. Consider, for example, the so-called evolutionary theory of the origin of the world, which is based on the assumption that the universe evolved out of existing atomic and subatomic particles which, by an evolutionary process, combined to form the physical universe and our planet, on which organic life somehow developed also by an evolutionary process, until homo-sapiens emerged. It is hard to understand why one should readily accept the creation of atomic and subatomic particles in a state which is admittedly unknowable and inconceivable, yet should be reluctant to accept the creation of planets, or organisms, or a human being, as we know these to exist.

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