inductive and deductive reasoning

Valid argue structure-A valid structure is the way in which an argument is put together that assures it will pass the test of logical strength.
Deductive-In deductive arguments, the speaker asserts that her premises are true and, therefore, her conclusion must be accepted. Remember that in a deductive argument, logical strength does not depend on the literal truth of the premises. When we test for logical strength, we assume the premises are true. Once we determine that the argument is logically valid, we can then look at the actual – not presumed – truth of the premises.
Inductive-In inductive arguments, the speaker presents evidence that she claims support the probable truth of her conclusion – that her conclusion is the most likely true – and so you should accept it.

*****When evaluating arguments, we have two main questions to ask:
1. Do the premises provide enough logical support for the conclusion?
2. Are the premises true?
In this segment, we’ll discuss how to answer the first question. As we mentioned, the answer to this question depends on whether the argument is deductive or non-deductive.
Validity applies to deductive arguments, strength applies to non-deductive arguments.
Let’s start with deductive arguments and validity.
· Definition: A valid argument is a deductive argument that succeeds in providing decisive logical support.
A valid argument is thus a deductive argument – an argument that attempts to establish conclusive support for its conclusion – that succeeds.
· Definition: An invalid argument is a deductive argument that fails in providing conclusive support.
For deductive arguments, you answer “yes” to the question “Do the premises provide enough logical support for the conclusion?” if the argument is valid, and you answer “no” if otherwise.

Deductive example-“Tightening laws restricting the use and possession of firearms does not protect average law-abiding citizens; it only puts them at greater risk. Enforcing licensing restrictions, trigger locks, and waiting periods makes it more difficult for law-abiding citizens to defend themselves, and, as a result, encourages criminal activity. Only criminals benefit when ordinary citizens are deprived of their right to own a firearm and protect themselves, their homes, and their families” (Lott, 2000, p. 169)
Lott, J., (2000). More guns, less crime: Understanding crime and gun-control laws. University of Chicago Press.
The argument boils down to this:
· s that are obeyed by ordinary citizens and not obeyed by criminals are laws that put ordinary citizens at risk.
· Tight gun laws are laws that are obeyed only by ordinary citizens.
· Tight gun laws put ordinary citizens at risk.
However, the argument itself is composed of three intertwined syllogisms:
Only ordinary citizens are persons who respect tight gun laws.
Criminal persons are not ordinary citizens.
Therefore, criminals do not respect tight gun laws.
Tight gun laws restrict only ordinary citizens.
No criminal is an ordinary citizen.
No criminal is restricted by tight gun laws.
s that disfavor the good are laws that favor the bad.
Tight gun laws favor the bad.
Therefore, tight gun laws disfavor the good. 
Notice that you cannot remove any of the “legs” and maintain the claim. Notice, also, that the reasons are closely connected and depend on or follow from each other. Notice, also, that the first premise (called the major premise) must be accepted as true or the entire argument fails.

Inductive example-The United States is too dependent upon foreign oil. According to the U.S. Department of Energy, we rely on imported foreign oil for about 45% of our needs. Of the imported oil, most comes from Canada, but 22% comes from countries in the Middle East. Undeniably, this dependence shapes our foreign policy. We have vast oil reserves that could make us energy-independent. Development of these resources would produce much-needed jobs, many of them in areas of the country suffering most from the recession. We should be developing an energy policy that makes us energy independent.
· Reason: We import 45% of our oil.
· Reason: Middle East oil imports shape our foreign policy.
· Reason: Our vast oil reserves could make us energy independent.
· Reason: Development of oil reserves could produce much needed jobs.
· Conclusion: For any or all of the above, independent reasons, we should become energy independent.
Notice that any one of these reasons, standing alone, could support the conclusions; they are not logically related to one another as they would be in a syllogism.

LESSON

Infant Reasoning
This week we take up the study of the two major ways in which we exercise reasoning – inductive reasoning and deductive reasoning.
We use inductive and deductive reasoning to arrive at decisions about everything in our lives from selecting a marriage partner to buying a loaf of bread. We arrive at these decisions by forming arguments – not the red-faced pound-the-table kind of argument, but the form of reasoning that uses evidence to support the reasonableness of the decisions we reach.
You have been reasoning this way all of your life. Watch the following video for an example of how infants reason:
Inferences & Assumptions
Watch the following video on inferences and assumption. The examples will show how we make logical leaps and when to be careful of assumptions.
 
We see that assumptions are something we take for granted, without proof. Unwarranted assumptions lead to erroneous generalizations
. For more on that, see the text on the fallacies that relate to inferences and assumptions
So should we never assume? Well, if we never assume, we could be in a lot of trouble.
When Hitler began to persecute Jews in Germany, the Jews living there were much better off if they assumed it would be best to leave the country.
James Holmes, who shot and killed 12 people at a theater in Aurora, Colorado, told police his apartment was booby-trapped. Police assumed he was telling the truth and used bomb-squads to enter his apartment.
If the weather forecast calls for 90 degree heat for the next five days, you will probably make sure your air conditioner is working.
Should we never make value assumptions?

I have shopped at Whale Market for six months. Each time I bought fruit there, it was green, and I would end up throwing it away. I assume Whale Market does not have a good fruit buyer, and I’m not buying fruit there anymore.
What about hidden assumptions?

If you invite me to your house for dinner, I assume you won’t ask me to pay. That works.
If you assume your wife isn’t angry that you never do the dishes because doing dishes is women’s work, so she must be okay with it – you are operating on both a value assumption (women’s work) and the hidden assumption that she agrees with you.
Warranted assumptions have a logical connection between what we know from experience and what we observe – they have a reasonable degree of probability that they are true.
Unwarranted assumptions lead to fallacies; they have little or no connection to what we know and observe. They are often the result of value assumptions or hidden assumptions.