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# What are deductive and inductive reasoning?

First, we will talk about deductive logic. Deductive reasoning is a tool to connect premises with a conclusion. Deductive reasoning is also called as deductive logic and logical deduction. It is opposite to inductive reasoning. Deductive reasoning uses top-down logic (while inductive uses down-top logic) to solve tasks where general trend is well known to find some specific details. One of the most popular examples where someone uses deductive reasoning is a story about Sherlock Holmes – famous private detective. He used deductive reasoning to find some important details and to solve the crime. However, not only detectives use deductive thinking – it is used much wider. This way or another we all use it to solve our daily tasks and not only.

There is a simple example of a deductive argument:

• First assertion – all dogs love meat
• Second assertion – Pluto is a dog
• Final conclusion - Pluto loves meat.

If we are talking about deductive logic, we also have to say about law of detachment, law of syllogism and law of contrapositive. Law of detachment is the first form of logical deduction. It is also known as Modus ponens and affirming the antecedent logic. Imagine that one conditional statement was made. We also have a hypothesis (for example, it will be «P»). In this case we need to deduct the conclusion from the hypothesis and the statement. The most basic form for the law of detachment will be:

• P → Q (we have a conditional statement)
• P (hypothesis stated based on a conditional statement)
• Q (conclusion deduced based on a conditional statement and the hypothesis).

Thereby, in deductive logic we have two basic steps – to make a hypothesis and to deduce a conclusion. We can use the law of detachment to conclude Q (final conclusion) from P (hypothesis). The example of using the law of detachment will be:

• If we have and angle that is greater than 90° and less than 180° we can than assume that this angle is obtuse
• We get an information that our angle is 120°
• We can conclude from the hypothesis that our angle is obtuse.

The law of detachment doesn’t work in the other direction. In other words, if we will know the conclusion that our angle is obtuse, we cannot deduce from that, that our angle is 120°, for example.

The law of syllogism is a specific way of thinking in logic of deduction. It uses two conditional statements. This law combines the hypothesis from one statement with the conclusion of another to get needed result – to make a final conclusion. The example of the law of syllogism can be shown in this way:

• P → Q
• Q → R
• Therefore, P → R.

Where P and Q are a hypothesis and a conditional statement, respectively; R is a final conclusion/conditional statement. Here is an example of deductive logic using the law of syllogism:

• If Harry is sick, then he will be absent
• If Harry is absent, then he will miss his sport class
• Therefore, if Harry is sick, then he will miss his basketball game.

The last one – the law of contrapositive used to deduce that if conclusion is false that the hypothesis must be false too. This is a scheme that can describe the law of contrapositive within the deductive logic:

• P → Q
• ~Q
• Therefore, we can conclude ~P.

Here is an example of logic of deduction with use of the law of contrapositive:

• If it is dark outside, then there is no sun in the sky
• There is a sun in the sky
• Thus, it is not dark outside.

One of the oldest mentions about the logic of deduction was made in the 4th century BC by Aristotle.

## What is an inductive reasoning?

Inductive reasoning is an example of down-top logic. That means that with a help of inductive logic we can discover a general trend based on many different specific details. There are such types of inductive reasoning as:

• Generalization
• Statistical syllogism
• Simple induction
• Argument from analogy
• Casual inference
• Prediction

Generalization or inductive generalization is used to make a conclusion about the population from the premise about a sample. Generalization within inductive reasoning can be described in this scheme:

• The proportion Q of the sample has attribute A
• Therefore:
• The proportion Q of the population has attribute A.

The example of the generalization will be:

• In an urn we have 20 balls — either black or white
• We draw a sample of eight balls and find that six are black and two are white.
• Now we can make a generalization - there must be fifteen black and five white balls in the urn.

There is one feature of this method - it may not be precise. The premises’ degree of compliance to a conclusion depends on such factors:

• The number of units in the sample group
• The number of units in the population
• The degree to which the sample represents the population (the more random sample we will take the more it will represent the population).

Statistical syllogism is aimed to proceed from a generalization to a conclusion about some individual. An example of statistical syllogism within inductive reasoning can be like this:

• For example the proportion Q of population P has attribute A
• An individual T is a member of P
• Therefore, we can say that there is a probability which corresponds to Q that T has A.

Simple induction within inductive logic is aimed to produce a conclusion about another individual from a premise about a sample group. Here is an example of simple induction:

• Proportion R of the known instances of population P has attribute X
• Individual K is another member of P
• Therefore, we can assume that there is a probability corresponding to R that K has X.

You can notice, that simple induction is a combination of statistical syllogism and generalization; it takes conclusion from generalization, while a first premise is taken from the statistical syllogism.

Argument from analogy is another thing from the world of the inductive reasoning. Analogical conclusion (inference) is based on searching and noticing sharing properties of two or more things and giving a conclusion based on that, that these things will also have some other properties shared in future. An example of argument from analogy will be:

• R and T are similar in respect to properties x, y, and z
• Object R has been observed to have further property g
• Therefore, we can assume that T probably has property g also.

Analogical reasoning is widely used in philosophy, science, humanities, common sense. However, people use it only as an auxiliary method, because it is a big share of conjectures in this logic. More advanced (refined) approach of analogical reasoning is case-based reasoning.

The other two methods in inductive logic are prediction and casual inference. First is aimed to draw a conclusion about a future individual based on a past sample, while casual inference takes the conditions of the occurrence of an effect and draws a conclusion about a casual connection.

Inductive and deductive reasoning are two important logical tools. We cannot say that one of them is more important that other – they just perform different functions which constitute one powerful tool. Inductive and deductive logic are aimed to solve different tasks. Inductive logic is an example of down-top logic. That means that it uses information about some properties of units in a sample to make a conclusion in general. And vice versa, deductive logic is an example of top-down logic. Logical deduction can help you to make a conclusion about some specific details in sample based on general information about whole sample. Learn these two types of logic and you will know basic information about how to work with sample and how use top-down and down-top logic.

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