1. Inductive / Deductive reasoning
Dr. Bowman

2. Deductive argument
A deductive argument is an argument that is intended by the arguer to be deductively valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument's premises are true.
In other words -- if the premises are true, it would be impossible for the conclusion to be false – this is what we call a (deductively) valid argument
As long as its premises are true, the argument is sound.

3. Example – Deductive argument
It's sunny in Singapore.
If it's sunny in Singapore, then he won't be carrying an umbrella.
So, he won't be carrying an umbrella.
Here, the argument’s conclusion follows the word "So." The two premises of this argument would, if true, guarantee the truth of the conclusion. However, we have been given no information that would enable us to decide whether the two premises are both true, so we cannot assess whether the argument is deductively sound. It is one or the other, but we do not know which. If it turns out that the argument has a false premise and so is unsound, this won't change the fact that it is valid.

4. Inductive Argument
An inductive argument is an argument that is intended by the arguer to be strong enough that, if the premises were to be true, then it would be unlikely that the conclusion is false. Its success or strength is a matter of degree.
There is no standard term for a successful inductive argument, though one can call it "strong." Inductive arguments that are not strong are said to be “weak;” there is no sharp line between strong and weak.

5. Example – Inductive Argument
An inductive argument can be affected by acquiring new premises (evidence), but a deductive argument cannot be. For example, this is a reasonably strong inductive argument:
Today, John said he likes Romona. So, John likes Romona today.
but its strength is changed radically if we add this premise:
John told Felipé today that he didn’t really like Romona.

6. Telling them apart
The distinction between deductive and inductive argumentation was first noticed by Aristotle ( B.C.E.) in ancient Greece.
The difference between deductive and inductive arguments does not lie in the words used within the arguments, but rather in the intentions of the arguer.
If the arguer believes that the truth of the premises definitely establishes the truth of the conclusion, then the argument is deductive.  
If the arguer believes that the truth of the premises provides only good reasons to believe the conclusion is probably true, then the argument is inductive.
If we who are assessing the quality of the argument have no information about the intentions of the arguer, then we check for both. That is, we assess the argument to see whether it is deductively valid and whether it is inductively strong.

7. Deductive validity
Below are five different definitions of the same concept of validity:
An argument is valid if the premises can’t all be true without the conclusion also being true.
An argument is valid if the truth of all its premises forces the conclusion to be true.
An argument is valid if it would be inconsistent for all its premises to be true and its conclusion to be false.
An argument is valid if its conclusion follows with certainty from its premises.
An argument is valid if it has no counterexample, that is, a possible situation that makes all the premises true and the conclusion false.

8. Telling them apart – Cont’D.
Although inductive strength is a matter of degree, deductive validity and deductive soundness are not. In this sense, deductive reasoning is much more cut and dried than inductive reasoning. Nevertheless, inductive strength is not a matter of personal preference; it is a matter of whether the premise ought to promote a higher degree of belief in the conclusion.
* Deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises. If the argument is a sound one, then we say the conclusion is "contained within" the premises; that is, the conclusion does not go beyond what the premises implicitly require. Think of sound deductive arguments as squeezing the conclusion out of the premises within which it is hidden.

9. Example – Deductive arguments
Consider how the rules of formal logic apply to this deductive argument:
John is ill. If John is ill, then he won't be able to attend our meeting today. Therefore, John won't be able to attend our meeting today.
That argument is valid due to its formal or logical structure. To see why, notice that if the word 'ill' were replaced with 'happy', the argument would still be valid because it would retain its special logical structure (called modus ponens by logicians).

10. Modus Ponens
Here is the form of any argument having the structure of modus ponens: P
If P, then Q
So, Q
The capital letters are variables that can be replaced with declarative sentences, or statements, or propositions (items that are true or false).

11. Examples – Inductive Arguments
Inductive arguments can take very wide-ranging forms. Some have the form of making a claim about a population or set based only on information from a sample of that population, a subset. Other inductive arguments draw conclusions by appeal to evidence, or authority, or causal relationships.
There are other forms. Here is a somewhat strong inductive argument having the form of an argument based on authority:
The police said John committed the murder.
So, John committed the murder.

12. Examples – Inductive Arugments
Here is an inductive argument based on evidence:
The witness said John committed the murder. So, John committed the murder.
Here is a stronger inductive argument based on better evidence:
Two independent witnesses claimed John committed the murder. John's fingerprints are on the murder weapon. John confessed to the crime. So, John committed the murder.
This last argument, if its premises are known to be true, is no doubt good enough for a jury to convict John, but none of these three arguments about John committing the murder is strong enough to be called "valid," at least not in the technical sense of deductively valid. This requires critical thinking.

13. Telling them apart
It is worth noting that some dictionaries and texts define "deduction" as reasoning from the general to specific and define "induction" as reasoning from the specific to the general. However, there are many inductive arguments that do not have that form, for example, "I saw her kiss him, really kiss him, so I'm sure she's having an affair."
Because the difference between inductive and deductive arguments involves the strength of evidence which the author believes the premises provide for the conclusion, inductive and deductive arguments differ with regard to the standards of evaluation that are applicable to them. The difference does not have to do with the content or subject matter of the argument, nor with the presence or absence of any particular word.

14. Telling them apart
 Another complication in our discussion of deduction and induction is that the arguer might intend the premises to justify the conclusion when in fact the premises provide no justification at all. Here is an example:
All odd numbers are integers.
All even numbers are integers.
Therefore, all odd numbers are even numbers.
This argument is invalid because the premises provide no support whatsoever for the conclusion.
However, if this argument were ever seriously advanced, we must assume that the author would believe that the truth of the premises guarantees the truth of the conclusion. Therefore, this argument is still deductive. It is not inductive.