First of all, I'd like to identify Induction for y'all. Induction is pretty much a generalization of events. It comes in two forms: I've seen alot of green emeralds, therefore all emeralds are green; The sun will rise tomorrow because it's risen every day.

In addition, I'd like to identify what Deduction is. It is the use of logic and tautologies such that the conclusion *has* to be true if the premisses are true.

Alot of our decisions and knowledge are based upon Induction; it is what we do naturally. Hume saw a problem with Induction, and what he saw is pretty damaging. His arguement was that Induction was not rational, and that would mean that almost everything we know is not justified, and we would then know next to nothing. Basically, his two arguements go like this:

Proof 1: The Principal of the Uniformity of Nature

1. All Inductions have as a hidden premiss that the universe is uniform (aka, the future will resemble the past at time...known as "the Principle of the Uniformity of Nature", henceforth said as PUN).

2. In order to be rational, an arguement must have all its premisses be rational.

3. In order for induction to be rational, PUN must also be rational.

4. If PUN is rational, then it can be rationalized with either deduction or induction.

5. PUN cannot be proven with Induction because it would be circular reasoning \ begging the question.

6. PUN cannot be proven with Deduction because the universe is not, by definition or by logic, required to be uniform.

7. Therefore, PUN is not rational.

8. Therefore, Induction is not rational.

Proof 2: Reliability

1. Induction can be rationally justified if it is shown to be reliable.

2. To show it is reliable, you must provide an inductive or deductive arguement for the reliability.

3. Induction cannot be argued for reliability with Induction, again because of the question-begging.

4. Induction cannot be argued for reliability with logic and definitions

5. Therefore, Induction cannot be shown to be reliable.

6. Therefore, Induction cannot be rationally justified.

So, this leaves us in a weird place. Are we able to counter both of these proofs?

Well, Strawson argued that Induction is, by definition, a rational activity. He says that this doesn't save Induction from reliability, but it's still rational. Sober's (the author of the textbook) arguement against this is the example of a recipe: if you have a recipe for a cake that you argue is an excellent (rational) recipe, yet you have no reason for thinking that the recipe would result in a nice cake (reliablitiy), that would sound silly.

I would argue that Induction is, by definition, a rational activity. It is the rational use of PUN. But this doesn't change the fact that the results are dependant on PUN and the knowledge is gone, so that kind of leads to a dead end.

Next, Max Black argued that it wouldn't be question begging to prove induction with induction. He says that:

1. Induction has been highly reliable in the past.

2. Therefore, Induction will be highly reliable now.

is a valid proof of it. The problem with this is it opens the way for non-sensical proofs. Take the example of counter-induction. It works the opposite way Induction does. Here's a proof of counter-induction using counter-induction:

1. Counter-Induction has been highly unreliable in the past.

2. Therefore, counter-Induction will be highly reliable now.

Quite problematic, eh? Well, after thinking about this some, I've wondered if there is any merit to analyzing why Counter-Induction would be flawed in a way that induction wasn't. A couple of ideas I've had are:

1. In order to prove and disprove Counter-Induction using Counter-Induction, the opposite condition must first be true. In other words, Counter-Induction seems to be self-contradicting.

2. The arguement for counter-induction has that counter-induction is both true and false. This shows contradictions that would allow you to assume anything you want.

3. Counter-Induction cannot work with PUN, so perhaps it works with the Prinicpal of the dis-uniformity of nature? One potential problem with this, though, is that by being dis-uniform, it would become uniform in that sense. So, counter-induction either has no supporting principals, or it has a component that can be considered inductive, which is contradictory to the definition of counter-induction.

To end, Sober offers some of his own ideas. To begin with, he talks about background assumptions. If you assume that the universe is uniform then there's no problem with induction. You can also assume in-between inductions to solve this problem. When talking to somebody, if you are looking to construct a rational arguement for another person, you are free to use whatever the both of you hold to be true.

Also, Sober discusses how Hume is trying to disconnect beliefs about the future with beliefs about the present and how it is similar to Descartes' attempt to connect indubitable beliefs with present and past observations. If you believe these connections are deductive, you are lead to skepticism. So, you're forced to believe in your own connections between them.

Anywho, I've got to go to class, so thoughts\comments\arguements\etc...