inductive and deductive reasoning

bob -Can you guys give me good definitions of deductive and inductive reasoning with examples? Perhaps with examples illustrating the difference between them. And please, if you could, keep it down to a hundred words or so. Thanks. (it's for my blog)

puiwaihin - Deductive reasoning: Using statements of general facts to prove with absolute certainty the truth of a specific proposition. These are similar to mathematics and follow strict rules. Statements that do not follow the rules are invalid and do not reach a statement of truth. Statements that do follow the rules will be true as long as all the propositions at the start of the reasoning are also true.

Example of good logic-
To be proven: I have skin
Premise1: All healthy human males have skin
P2: All humans have a gender
P3: The only human genders are male and female
P4: I am human
P5: I am not female
P6: I am healthy
Statement1: Since I am human, I have a gender
S2: Since my gender is not female, and the only other gender humans can have are male and female, I must be male
Proved (S3): Since I am a healthy male, I have skin.

As long as all the premisies are true, nothing new outside the premises, and the form of the arguments follow the rules of logic, the conclusion must be true.

Inductive reasoning: Using specific observations to create a general rule. Induction can ascertain absolute truth when every case involved is examined (such as in computer science), but most often the conclusion goes beyond what has been observed. Conclusions reached by inductive reasoning can be shown to be false later when more observation is made.

Example:
1. Every time you wake up the building you went to sleep in is still around you.
2. You conclude that after you go to sleep the building around you will still be there when you wake up.

bob - But what if there is an earth quake?

Danimal - Bob, On some of this, I’m borrowing a bit from a previous post, but with a little editing, it’s basically what I want to say.

Induction:
Induction essentially means noticing a pattern and making a prediction that follows that pattern. Most often an inductive argument makes predictions about future events based on past experiences. For example:

1. The sun has always risen every morning so far.
2. The sun will rise tomorrow (or every morning). [*]

“The sun has always risen,” is the pattern. The conclusion is simply taking that pattern and extending it to the future. It doesn't always have to be about future events, though. For example, if I was conducting an archeological dig and happened upon a Neanderthal, I could say:

1. Neanderthals have always hunted wild animals.
2. This particular Neanderthal hunted wild animals.



Again, the premise sets a pattern: Neanderthals have always hunted wild animals. The conclusion uses this pattern to make a prediction (or probability argument) about the habits of specific Neanderthals.


Deduction:
In deduction, we basically “deduce” the conclusion from the premise(s). A deductively valid argument is one where, if all of it’s premises are true, the conclusion must be true. For example,

1) Only Bush or Kerry will win
2) Bush won
Therefore Kerry lost.

If premises 1 and 2 are true, then there is no possible way for the conclusion to be false.


Specifics on how they are different
What’s unique about inductive arguments is that they lead us to genuinely new beliefs. Whereas with deduction, the conclusion is always contained within the premise, whether it is implicit or explicit.

Unlike deduction, induction is basically a probability argument. All the premises might be true, but the conclusion might still be false. For example, if I was waiting for the subway, I might say,

1) This subway has been on time every day for the last 20 days.
2) This subway will be on time today.

But it is always possible that the subway will not actually be on time, just like it’s true that the sun will not rise every morning for eternity. What has happened in the future may be an indication of what will happen, but past events do not guarantee the truth of future events. Correct premises only increase the probability that a conclusion will be true.

Danimal - bob wrote: But what if there is an earth quake?

Induction is a probability argument. The premises do not guarantee the truth of its conclusion.

Danimal - Quote:

To be proven: I have skin
Premise1: All healthy human males have skin
P2: All humans have a gender
P3: The only human genders are male and female
P4: I am human
P5: I am not female
P6: I am healthy
Statement1: Since I am human, I have a gender
S2: Since my gender is not female, and the only other gender humans can have are male and female, I must be male
Proved (S3): Since I am a healthy male, I have skin.



There’s a much quicker and easier way to prove this:

1: All healthy human males have skin
2. puiwaihin is a healthy human male
Therefore, puiwaihin has skin

bob - So the basic difference between inductive reasoning and deductive reasoning is that deductive reasoning is based upon established fact and points to further factual conclusions that can logically be made based on those facts; while inductive reasoning is based on past knowns and is generally used to make predictions about future events?

I am pretty certain that is what you said but I remember these things better if I write them in my own words.

Thanks guys.

By the way, the earthquake thing was suppossed to be a joke.