Deduction and Induction

What is an Argument?

An argument is a set of statements. One statement is the conclusion of the argument. The others are the premises. The premises give support to the conclusion.
Deductive arguments and Inductive arguments are two types of logically correct arguments.

#What are the characteristics of a deductive argument?

A Deductive Argument is:

1. Non-Ampliative: In a valid deductive argument, all of the content of the conclusion is already present in the premises.

2. Valid arguments are necessarily truth preserving: If the premises are true, the conclusion must be true.

3. Valid Arguments are Erosion proof. If new premises are added, the argument remains valid.

4. Deductive validity is an all-or-nothing issue: A deductive argument is either valid or invalid.

#What are the characteristics of an inductive argument?

An Inductive argument is:

1. Ampliative: The conclusion has content that goes beyond the content of the premises.

2. Inductive arguments are not necessarily truth preserving: A correct inductive argument may have true premises and a false conclusion.

3. Inductive arguments are not erosion proof: new premises may undermine the argument.

4. Inductie arguments have different degrees of strength. In some inductive arguments the premises support the conclusion more or less strongly than in other inductive arguments.


An Example of Deductive argument

(1) All Italians are beautiful
Matteo is an Italian
________________________
Matteo is beautiful

This argument is a valid deduction. It is nonampliative: when we say that all Italians are beautiful, we also say that Matteo is beautiful, given that he is Italian. It is necessarily truh-preserving: If the premises express something true, the conclusion must also express something true - given that the conclusion doesn't express anything which is not already expressed in the premises. Even if new premises are added, e.g. Ruth is Italian, the argument remains valid. The premises support totally, not up to a certain degree, the conclusion.


An Example of Inductive Argument:

(2) All observed Scots like beer­
=========================
All Scots like beer


This argument is ampliative: The premise is only about the Scots that have been observed so far. The conclusion is about all Scots (also those to be observed). It is not necessarily truth preserving. Possibly, there is, was, orwill be a Scot who dislikes beer. The argument is not erosion proof: it suffices to observe Andy, who is a Scot who dislikes beer, to undermine the argument. The strength of this argument is also a question of degree. If you have observed millions of Scots in different ages of history and places your argument would be stronger than an argument whose premise rely only on the observation of few Scots gathered at the pub one Saturday night.


NOTE

Deductive validity and Inductive correctedness only concern the logical relation between premises and conclusion. They enable us to give an answer to this question:
Does the conclusion of the argument really follow (deductively), or is supported (inductively), from the premises?

A separate issue is: Are the premises of the argument true and worthy of our belief?

A Valid Deduction may have true premises and true conclusion (in this case the deduction is sound):

(3) All humans have a brain.
Ruth is human.
­­­_______________________
Ruth has a brain.

BUT A Valid deduction may also have false premises and true conclusion:

(4) All soccer players are American
Obama is a soccer player­­­
________________________
Obama is American

... and a valid deduction may also have false premises and false conclusion:

(5) All Humans play soccer for Liverpool
Mickey Mouse is human
­­­________________________________
Mickey Mouse play soccer for Liverpool

- When we say that a valid deduction is necessariy truth preserving, we mean that there cannot be a valid deduction with true premises and a false conclusion.

- Instead when we say that an inductive argument is correct we mean that if the premises are true (and relevant to the conclusion), then the conclusion is probable.