Critical thinking is an important part of out daily life. It helps us take decisions regarding varoius things like what to spend on, which move is going to headstart my career, how to solve a mathematical proble, and so one.

## What is reasoning?

Reasoning is a logical approach of figuring things out with the help of scientific steps. There are two types of reasoning: deductive and inductive.

Deductive reasoning is where one reaches specific conclusions from general premises. Reasoning is a branch of philosophy as well as mathematics. It is what is also known as ‘top-down’ reasoning.

To understand reasoning better, we need first to be associated with terms that come with it like deductive, inductive, premise, argument, conclusion, and so on.

You can find more information and examples on various math pages, which delve into these concepts in detail.

## Common Reasoning Terms and Their Meaning (Quick Recap)

### Reasoning

It is a logical way of analysing data and coming to conclusions. There are two main types of reasoning: inductive reasoning and deductive reasoning.

### Proposition

A statement in logical reasoning that is either true, or false, but cannot be both. It is generally a declarative sentence and the truthfulness of it may be unknown but not non existent. The word statement and proposition may be used interchangeably.

### Inference

Inference are the logical steps in reaching conclusion in logical reasoning. To infer something, is to draw conclusions. A “rule of inference” is called modus ponens, which means “method of affirming”. It is used to infer conclusions from premises: if K is false, and K is equal to P, then P is false.

In such a case, we should also know about modus tollens, which is, “method of denying”, that, is, deductive inference through contradiction.

### Premise

Premises are statements or propositions used to form a conclusion in deductive reasoning. Premises cannot be less than two. Premise is part of argument.

### Argument

An argument is a philosophical term; it does not mean a quarrel, at least here.

An argument is a cluster of propositions (two statements or more) that determine the validity of the same and where they follow the other.

“For every possible inference there is a corresponding argument.”

### Conclusion

The final idea that is found after analysis of an argument’s premises. It is what premises are trying to prove. Conclusion is true when premises are true. It cannot happen other way round.

### Syllogism

The structure of two or more statements to come that uses deductive inferences to come to a conclusion.

Oxford Learner’s Dictionary defines syllogism as “a way of arguing in which two statements are used to prove that a third statement is true”.

## Truth, Validity, and Soundness in Reasoning

Truth caters to the statements, while validity caters to arguments and their structure. The question of validity rises only in case of deductive arguments and **not** inductive arguments. Because in inductive reasoning, we move from specific conclusions to general ideas.

For example, if we see that friend A has borrowed money and not returned, and see that friend B, C, and G have also done the same, we can form a conclusion that friends do not return money borrowed to them. We do not see the validity of an argument here because it does not follow from general premises.

In case of deductive arguments we cannot infer the same. We move from a general idea, that friends do not return money that has been borrowed to them, to a specific conclusion, that G is a friend, therefore friend G will not return the money that has been borrowed to them.

Then there comes soundness. Some arguments can be sound, some can be absurd. To follow logic, one must first keep aside the absurdity and see what logic brings to the table.

Take this argument for example.

All flowers are green.

Hibiscus is a flower.

Therefore hibiscus is green.

However absurd and unsound the particular premises are, the conclusion that follows are true to the argument.

“Validity of any deductive argument, if they were all true, would provide conclusive grounds for the truth of its conclusion. Such an argument is said ot be valid. Validity is a formal characteristic; it applies only to arguments, as distinguished from truth, which applies to propositions.” (Introduction to Logic, Routledge)

Valid deductive arguments can be valid or invalid. If the premises are true, the conclusion based on those premises has to be true. An argument can be deductively valid if the conclusion follows from the premises. True premises do not gurantee true conclusion unless the premises provide for the conclusion itself.

All drinks are sweet. (false)

Red Bull is a drink. (true)

Red Bull is sweet. (true)

The first premise is false, but the other premises are true (in this case, only one). Hence the conclusion based on the false premise is false, but valid.

## What Are The Types Of Reasoning?

There are approximately seven types of reasoning:

### Deductive Reasoning

Deductive reasonging draws logical conclusion from valid arguments.

This is a top down logic scenario.

Strictly speaking, and in simplest terms, there are two arguments, and these two or more statements lead to another statement. The two given premises support the final statement, hence the whole argument has deductive validity.

### Inductive Reasoning

Inductive reasoning makes logically sound conclusion from specific ideas. It is also a conditional reasoning where an inductive argument is formed and conclusions are inferred on the basis of “if” and “then”.

If the cat is orange, then it is more aggressive.

This is a conditional statement.

More on deductive and inductive reasoning and how deductive arguments differ from inductive reasoning can be found below.

### Analogical Reasoning

It a kind of reasoning that makes correct conclusion by finding a valid argument between two or more kind of things.

### Abductive Reasoning

Similar to inductive reasoning, but here one makes an educated guess. Abductive inferences seek to simplify a given set of competing hypotheses.

Abductive reasoning was established by Charles Sanders Pierce in the end of the nineteenth century.

### Causal Reasoning

In philosophy, causality is the relation between two “temporally simultaneous or successive events” when one event is followed by the other event (cause and effect).

### Decompositional Reasoning

When an idea is two big, several factors affect it. In such scenarios it becomes difficult to pin down cause and effect of things. Therefore to make the logical system and correct reasoning, one must break down all the premises to come to the intended conclusion.

## What is the Meaning of Deductive Reasoning?

Every argument claims that the conclusion that proceeds have been given ground by the same argument itself. In other words,

Deductive reasoning definition as per Oxford Reference is, “Reasoning from the general to the particular, for example by developing a hypothesis based on theory and then testing it from an examination of facts. Also known as deduction.”

A commonly used example of deductive reasoning that we have all come across in our school Mathematics book:

If A = B, and B = C, then, A = C.

This is a fair example of deductive reasoning.

In deductive reasoning, there are generally two premises with one conclusion. A conclusion that does not follow the given premise will make it an invalid deductive reasoning.

Let us take a complicated example. The following argument was published in The New York Times when Babe Ruth hit his seven hundredth home run in 1934:

“A record that promises to endure for all time was attained on Navin Field today when Babe Ruth smashed his seven-hundredth home run in a lifetime career. It promises to live, first because few players in the history have enjoyed the longevity, on the diamond of the immortal Bambino, and, second because only two other players in the history of baseball have hit more than 300 home runs.”

In this paragraph, the conclusion is followed by justifications numbered as “first” and “second”. The conclusion however turns out to be factually false now (but then true), since Hank Aaron made the same record some forty years later. The deductive inference from this is that the argument had a logical conclusion for a given period of time.

## What are Deductive Reasoning Examples?

Let us see how deductive logic help us reach conclusions based on given premises:

*All plants perform photosynthesis. Snakeplant is a plant. Therefore, snakeplant performs photosynthesis.*

All planets are round. Earth is a planet. Therefore Earth is round.

All toys are made of plastic. Barbie is a toy. Therefore barbie is made of plastic.

To apply for college, one has to take SATs. Sheila is applying for college. Therefore, Sheila has to take SATs.

One cannot learn algebra without knowledge of basic arithmetic. I want to learn

All animals hunt. Tiger is an animal. Therefore, tigers hunt.

All cats are cute. I am a cat. Therefore I am cute.

All dogs give birth. Max is a male dog. Max gives birth.

All premises are true. Conclusion is a premise. Therefore conclusion is true.

## What Is the Difference Between Deductive and Inductive Reasoning?

How deductive reasoning and inductive reasoning works are totally opposite. Inductive and deductive reasoning are polar opposites and work in different scenarios. Deductive logic moves from general to specific and inductive reasoning general conclusions are drawn from particular.

“An inductive argument claims that its premises give only some degree of probability, but not certainly, to its conclusion.” (Introduction to Logic, Routledge)

Examples of inductive reasoning goes something like this:

Every winter roses bloom in my garden. Therefore I will see roses this winter in my garden.

Inductive reasoning follows a bottom up logic and aims for a general conclusion.

Summary

Deductive reasoning begins from general ideas to particular conclusions. False premises makes the conclusion false. Deductive and inductive approaches are important in everyday reasonging and learning them makes our life a lot easier.