Legal reasoning as a concept is a process of thinking which helps a researcher to come to decision relating to law. Law is a tool of social control that attempts to resolve conflicts in the society, to direct current activity while maintaining continuity with the past, and to control the future by laying down procedures, approaches and theories. Every decision must be guided and followed by a logical reasoning which takes into account the past decisions and statutes, the present position of the parties to the cases, and its own impact on future activity. In this article, we shall discuss deductive reasoning used in logic.

Logic is the science of reasoning. Logic as a discipline trains a person in certain methods, devices, tools and techniques that help in differentiating right reasoning from wrong ones. Reason/Reasoning is used to form inferences; conclusions drawn from propositions or assumptions that are supposed to be true. A piece of reasoning involves argument that is a relational arrangement of premises (evidences, facts, assumptions) and conclusion. There are two forms of reasoning- inductive and deductive and corresponding two types of logic. Inductive logic deals with inductive arguments and deductive logic deals with deductive arguments.

Deductive reasoning is the process in which conclusions are drawn with logical certainty from given premises. This type of reasoning is used in mathematical proofs or when dealing with formal systems.

In inductive reasoning one draws the “best” conclusion suggested by the set of observations/ experiential statements. Here observations used as evidence are always incomplete and insufficient to support a definitive conclusion, therefore one can never be certain of the conclusions one makes.

Deductive Reasoning:

Deductive reasoning or Deduction is the most common type of logic. In legal studies and judicial proceedings, logical deduction is often used to evaluate evidence, form arguments, and arrive at verdicts. Both lawyers and judges use it in their reasoning and decision making.

The basic aim of deductive reasoning is to start with some assumption or premise and reach to a logical conclusion.  The method of studying a phenomenon by taking some assumptions and deducting conclusions from these assumptions is known as the deductive method. It is that method of logical reasoning that goes from the general premises assumed to be true to a specific conclusion. In other words, Deduction is the process of deriving conclusion from the premises that are assumed to be true. Thus, deduction is a process of reasoning from the general to particular or from the universe to individual, from given premises to necessary conclusions i.e., conclusion necessarily follows from premises. In other words, premises offer conclusive ground for conclusion. Conclusive ground means evidences are complete and sufficient enough to support the conclusion. Acceptance of premises leaves no room for any reasonable or meaningful doubt about acceptance of conclusion. Thus, deductive arguments assert that the conclusion is arrived at, necessarily from the truth of the premises.

Let us take an example:

Argument 1:

P1: All men are mortal

P2: Ramesh is a man

C: Therefore, Ramesh is mortal

The conclusion “Ramesh is mortal” is already contained in the premises. What is already contained in the premises in implicit form, reasoning just makes it explicit in conclusion. There is no novelty. No new information is given in the conclusion. So, in any valid deductive argument it can never be the case that false conclusion is drawn from all true premises. If we have assumed

This method is also known as analytical, abstract and a priori method. It has an abstract approach to the study of science. Deductive method is a part of the scientific method. In deductive reasoning, we don’t go beyond what is stated in the set of premises. In legal arguments, this process is called applying the law to the facts.

Example 1:

to qualify as a victim of rape under criminal law there must

(1) be sexual intercourse with a women;

(2) the intercourse must be without her will. (Major premise; states a rule of law.)

Here, the woman had consensual sex. (Minor premise; makes a statement of fact.) Therefore, the plaintiff cannot be a “victim” of rape under criminal law. (Conclusion; correctly applies the law to the facts.)

Example 2:

Lombroso, an Italian, observed peculiar physical features among the criminals and by using the logical deductive thinking formulated the following propositions by taking his observations into consideration :

(1) Criminals are by birth a distinct type of persons;

(2) They can be recognized by stigma or anomalies such as a symmetrical cranium, long lower jaw, flattened nose, scanty beard and low sensitivity to pains;

(3) These physical anomalies identify the personality which is predisposed criminal behaviour; and

(4) Such persons cannot refrain from committing crime unless the circumstances of life are generally favoured.

Example 3:

“All teachers are human. Some human are excellent racers. Therefore, some teachers are excellent racers.”

In this example, each of these statements is true. Teachers are indeed human. Some human (e.g. athletes) are excellent racers. And as it happens, some teachers are also good racers. But this argument is not valid. The fact that teachers are humans and that some humans are excellent racers does not prove anything about the racing ability of teachers. Based on the information we’re given in the premises, it is logically possible that no teacher of the world has ever stepped foot in field for running. Because it is logically possible for the premises to be true and the conclusion to be false, this argument is not logically valid. Thus it is a fallacious argument.

Guidelines for Logical and Valid Deduction:

• All premises must be true.
• All expressions used in the premises must be clearly and consistently defined.
• The first idea of the major premise must reappear in some form as the second idea in the specific case.
• No valid deductive argument can have two negative premises.
• No new idea can be introduced in the conclusion.

For Example:

Free access to public education is a key factor in the success of industrialized nations like the United States. (major premise) India is working to become a successful, industrialized nation. (specific case) Therefore, India should provide free access to public education for its citizens. (conclusion)

Assessment of Deductive Reasoning:

Arrangement 1: True Premises, True Conclusion, Valid Argument

Example:

P1: All mammals are animals.

P2: All cats are mammals.

C: Therefore, all cats are animals.

In this argument, all the propositions are known to be true. The premises conclusively establish the conclusion; therefore, making the argument “valid”.

Arrangement 2: False Premises, False Conclusion, Valid Argument

Example:

P1: All mammals are six legged animals.

P2: All Ostriches are mammals.

C: Therefore, all Ostriches are six legged animals.

In this argument, all the propositions are known to be false. But here the premises conclusively establish the conclusion, because if the premises were actually true, the conclusion would have been certainly true. Therefore, this argument is also valid.

Arrangement 3: True Premises, True Conclusion, Invalid Argument

Example:

P1: If I won the KBC Show, I would be a millionaire.

P2: I did not win the KBC show.

C: Therefore, I am not a millionaire.

The premises and conclusion here are true, the argument is invalid because the conclusion does not necessarily follow from the premises. This will be further clear from the next example.

Arrangement 4: True Premises, False Conclusion, Invalid Argument

Example:

P1: If Ratan Tata won the KBC Show, he would be a millionaire.

P2: Ratan Tata doesn’t win the KBC show.

C: Therefore, Ratan Tata is not a millionaire.

In this argument the premises are true, but the conclusion is false in reality. Mr. Tata till now didn’t participate in KBC show, but he is one of the richest persons in India. The argument is invalid because the premises don’t conclusively establish the conclusion.

Arrangement 5: False Premises, True Conclusion, Valid Argument

Example:

P1: All Fishes are mammals.

P2: All dolphins are fishes.

C: Therefore, all dolphins are mammals.

The conclusion here is true in reality, but the premises are unquestionably false. However, since there is a logically necessary connection between the premises and the conclusion, because of which the premises conclusively support the conclusion, the argument is valid.

Arrangement 6: False Premises, True Conclusion, Invalid Argument

Example:

P1: All mammals have wings.

P2: All dolphins have wings.

C: Therefore, all dolphins are mammals.

This argument has two false premises and still the conclusion is true. However, the argument is invalid, because the conclusion is not conclusively supported by the premises. We know that by examining the form of the argument. Here, in the second premise the group “all dolphins” belongs to the group “wings”, and in first premise, the group “all mammals” belong to the group “wings”, and these don’t prove whether the group “all dolphins” belong to the group “mammals”

Arrangement 7: False Premises, False Conclusion, Invalid Argument

Example:

P1: All mammals have wings.

P2: All dolphins have wings.

C: Therefore, all mammals are dolphins.

In this argument both premises and conclusion are false. And the argument is invalid. Because the conclusion is not supported by the premises. Like Arrangement 6 above, here also in the second premise the group “all dolphins” belongs to the group “wings”, and in first premise, the group “all mammals” belong to the group “wings”, and these don’t prove whether the group “all mammals” belong to the group dolphins”

Arrangement 8: True Premises, False Conclusion, Valid Argument

Example: Nil

By definition, in a deductively valid argument if the premises are true, it is impossible for the conclusion to be false. If the conclusion is false, when premises are true, that means the conclusion is not conclusively supported by the premises. Therefore, the argument will be always invalid. That is why there is no example of Arrangement 8.

All possible combinations of the connection between truth- falsity of the statements of the argument and validity- invalidity of that argument can be summarized as shown in the table below.

Arrangement	Premises	Conclusion	Validity
1	True	True	Valid
2	False	False	Valid
3	True	True	Invalid
4	True	False	Invalid
5	False	True	Valid
6	False	True	Invalid
7	False	False	Invalid

This table shows that the validity or invalidity of an argument cannot be determined merely from the truth and falsity of the propositions. Both valid and invalid arguments can have all true propositions or all false propositions, or they can have false premises and a true conclusion.

Sound and Unsound Deductive Arguments:

Depending on its relationship with truth, arguments can be further classified as “sound” and “unsound”. A sound argument is a deductive argument that is valid and it has true premise. It must satisfy two conditions: the argument must be valid, and the premises must be true. If any of this condition is not met, then no valid argument can be termed as sound. Consider the following argument:

P1: All planets of the solar system revolve around the Sun.

P2: The Earth is a planet of the Solar System.

C: Therefore, the Earth revolves around the Sun.

This argument is valid because the logical relation between the propositions are so that if the premises were true, then the conclusion would be certainly true. This argument is valid and in addition, the premises here are actually true. So this is a Sound deductive arguments. In last topic, Arrangement No.1 is sound. All other possible combinations of truth/falsity and validity/invalidity are always unsound.

Significance of Validity in Deductive Logic:

It is obvious from our discussions so far that logicians are interested in the evaluations of arguments, rather than in the evaluation of propositions. The evaluation of deductive arguments is measured in terms of validity and invalidity. Valid and invalid arguments are further evaluated as sound and unsound arguments. Sound arguments are what can be termed as good arguments that can lead us to actually true conclusions with utmost certainty.

In such a situation, one can ask, why logicians do not confine themselves to the study of arguments with true premises only as that may lead us to sound arguments. What is the importance of the non-sound valid arguments? Specially, what is the importance of exploring valid arguments whose premises are not true? Actually the validity of arguments with premises not known to be true are more important than they seem to be. In our day-to-day life, we often need to choose between alternative courses of action where we do not know which alternative is in fact true. What we do is consider consequences of these alternative courses. On considering the consequences, we decide which course of action should be followed. We need to be serious in deciding the consequences of the alternative courses. That is where our training in valid argument with false premises can help us. Because, in case of valid argument with false premise, the logical relation between premises and conclusion is such that if the premises were true, the conclusion would be also true. If we follow a similar valid logical process in deciding the consequences, then we can correctly choose the alternative course of action. According to Irving M. Copi, we “make’ the premises true out of the available alternative courses. But if we deal with only already known true premises, then there will be no point in considering alternative courses, we can accept the one which is true. The purpose of applying logic here will be self-defeating. But the reality is that there will be always alternative courses in life where truth of the alternatives may not be known us.

Steps in Deductive Reasoning:

Step 1. The Exploration of the Problem:

There must be the existence of a definite problem in the mind of the researcher and it must be one of significance for the actual world.

Step 2. Setting up of the Hypothesis from Assumptions:

Researcher has to select the assumptions from which the conclusion will be derived. The assumption must be derived from observation. They must be close to reality. On the basis of suitable assumptions, hypothesis may be formulated. In this step premises or assumptions are identified. These are the statements or facts that you already know or consider to be true. A hypothesis is formulated. This is an initial assumption you make based on the premises, which leads you towards a conclusion.

Step 3. Theoretical Development of the Hypothesis:

The nature and implications of the hypotheses have to be carefully analyzed to formulate a theory. By logical reasoning we have to deduce the consequences. Deductive explanations consist of two parts, The explanandum (conclusion) and explanans (premises). The explanans (premise) explain the explanandum (conclusion) and the explanandum is deduced from the explanans.  The explanandum is the event, problem or thing to be explained and is the conclusion of a deductive argument.

Step 4. Verification of Theories:

1. Applying Deductive Reasoning: Deductive reasoning is applied to the premises. This involves a systematic approach, in essence saying, “If A and B are true, then C must also be true.” In this step laws of logic are applied to your premises and hypothesis. These laws (like Law of Identity, Law of Non-Contradiction, and Law of Excluded Middle) provide a framework for logical reasoning and deduction.
2. Leading to a Necessary Conclusion: From the given premises and using the principles of logic, logical deduction leads to a necessary conclusion. If the premises are true and the reasoning process is correct, this conclusion is irrefutably true.
3. Assurance of Truth Preservation: A crucial aspect of logical deduction is that it’s truth-preserving. This means if the original statements (premises) are true, then the derived statement (conclusion) is also guaranteed to be true.
4. Checks and Balances: The process is rechecked to ensure no leaps of logic have been made. This acts as a confirmation of the conclusion’s validity, reinforcing the confidence in the result of the logical deduction. After deducing a conclusion, it is critical to evaluate your result and reflect on the whole logical deduction process. Verify the conclusion with real-life scenarios or additional data, if possible.

Merits and Demerits of Deductive Reasoning:

Merits of Deductive Reasoning:

• Powerful: Deductive explanation is very powerful because it makes use of a valid form of deductive argument where the explanandum (conclusion) must be true if the explanans (premises) are true.
• Simple method: The process of deductive reasoning is clear and easy to follow, making it easy to understand the reasoning behind a conclusion. This clarity also makes it easier to identify any errors or mistakes in the reasoning process.
• Generality: Deductive reasoning can be used to make general statements and inferences that apply to a wide range of situations. From a few basic facts of human nature, a number of inferences can be drawn by logical reasoning.
• Certainty: Deductive reasoning allows for the creation of logical and certain conclusions based on premises that are assumed to be true. Thus, the deductive method lends for the generalizations which are accurate and exact, provided the premises on which they arc based are true.
• Free of Bias: Deductive reasoning is based on logical principles and does not rely on subjective opinions or biases. This means that deductive reasoning can be used to arrive at objective conclusions that are based on facts and logical principles, rather than on personal opinions or beliefs.
• Validity: If the premises are true and the reasoning is logically valid, the conclusion must also be true. This means that if the conclusion is false, either the premises are false or the reasoning is invalid.
• Testability: Deductive reasoning can be tested by checking the premises and the logical steps used to reach a conclusion, which makes it easy to verify the validity of a conclusion. This allows for the conclusion to be independently tested and verified, which increases the reliability and trustworthiness of the conclusion.
• Substitute for Experimentation: It is not possible for the investigator to conduct controlled experiments with the legal phenomena in a laboratory. He can, therefore, fall back upon deductive reasoning.

Demerits of Deductive Reasoning:

• Limited Scope: The deductive method is based on facts and logical reasoning, which makes it reliable and objective. However, the method may not be suitable for subjects that rely more on personal opinion and subjective interpretation. Thus, the deductive method is most effective in subjects that are based on logical reasoning and mathematical proof, such as mathematics, logic, and science. It may not be as effective in subjects that rely more on intuition, such as literature, art, or history. Thus, deductive method can be applicable to the limited studies only. Deductive reasoning relies on existing knowledge and information to reach a conclusion, and is not useful for discovering new information or exploring uncharted territories.
• Lack of Creativity:  As the deductive method follows a set of rules and procedures, it can be seen as a rigid and inflexible method. Thus it discourages students from thinking outside the box. If the researcher confines only to abstraction, his model may have the elegance and be logically beautiful but it may be far away from real life.
• Limited to Premises: The validity of a deductive argument is dependent on the truth of its premises. If the premises are false, the conclusion is also false, regardless of the logical form of the argument. This means that deductive reasoning is limited by the accuracy of the information and assumptions used as premises. The theories arrived at by deductive reasoning are valid only under assumed conditions. The assumptions must be valid, if the theories are to be hold good.
• Requires High Degree of Logic and Reasoning: Deductive reasoning assumes that the person making the argument has complete knowledge of the subject at hand and all relevant information. In reality, this assumption is often not met, leading to invalid conclusions.Not everyone can use deductive method successfully and even many experienced researchers have been trapped by faulty reasoning.
• Can Overlook Alternatives: Deductive reasoning can lead to overlooking alternative possibilities and perspectives, as it focuses on reaching a single logical conclusion based on given premises.

Conclusion:

Logical deduction is the process of drawing conclusions based on premises or statements that are known or assumed to be true. It involves using reasoning and logical principles to derive new information or insights. The main purpose of logical deduction is to make valid and sound arguments and arrive at accurate conclusions. It helps us to analyze and evaluate information, solve problems, and make informed decisions.