Being Critical

Logical errors are, I think, of greater practical importance than many people believe; they enable their perpetrators to hold the comfortable opinion on every subject in turn.

~Bertrand Russell

One of the more confusing concepts found in logic is deductive/inductive reasoning.

A good deductive argument is one whose premises being true would mean the conclusion must be true. For example:

Premise A: All birds can fly
Premise B: Penguins can't fly
Conclusion: Penguins are not birds.

The above argument is considered a valid deductive argument because if the premises were true, the conclusion must be true. But obviously the Premise A isn't true, penguins are considered birds. Nonetheless the deductive logic itself is still valid.

Here is a different example:

Premise A: Cats are mammals
Premise B: All mammals are warm blooded.
Conclusion: Cats are warm blooded.

The example above is a sound deductive argument because it is valid AND its premises ARE all true.

Now, an inductive argument supports rather than proves. In other words, if the premises of a strong inductive argument are true, the conclusion probably is true.

Example of a strong, inductive argument...

Premise A: There are 10 women in the room
Premise B: 9 of those women are brunette
Conclusion: Most likely all the women are brunette.

If Premise B had a lower sample number , the argument would become weaker. But what about this example?

Premise A: Most lights in the sky are UFOs.
Premise B: There are many lights in the sky.
Conclusion: The next light to be seen is probably a UFO.

Now, even though this is a strong inductive argument, premise A is not true. Thus, it is not considered a cogent inductive argument. I cogent inductive argument is a strong argument with the premises being true. So the Brunette Example previously would be considered a cogent inductive argument.

Playing Games with Iran

I came across this when doing some research in game theory. Andreas Blume at the University of Pittsburgh gives an example, through game theory, of what courses of action the US could take with respect to Iran.
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Iran and the West
Iran seeks to go forward with work on uranium enrichment.
The US and Europe are worried that having a uranium enrichment facility will eventually enable Iran to build a nuclear bomb.
A coarse description of their respective strategic options might be as follows:
1. The West can ignore the problem, engage in diplomacy, or act militarily.
2. Iran can give up their nuclear ambition, slowly develop its enrichment capabilities, or opt for rapid development.

Some thoughts about payoffs for the West-Iran Game:

1.We will choose to model the conflict as a zero-sum game. A note of caution: This deliberately ignores that there are numerous dimensions of common interest between Iran and the West.
2. It suffices to keep track of the payoff of only one of players (we’ll choose the West); the other player’s payoffs are the same, except with the opposite sign.
3. If Iran decides to give up its nuclear ambition, then ignoring what they do is a valid option for the West, which will be indicated by a positive payoff, 5, for the West. Recall that Iran’s payoff in this case must be −5.
4. Ignoring Iran’s ambitions is less attractive if Iran chooses slow, indicated by a negative payoff, -2, for the West.
5. The worst outcome for the West is to ignore the problem when Iran proceeds rapidly, indicated by a payoff of -6.
6. The best outcome for the West with diplomacy would be if Iran gave up its ambition. The worst outcome in this case would be if Iran kept slowly developing its enrichment capabilities. In the case that Iran proceeded
rapidly, it would then be possible to convince others, e.g. Russia and China, that diplomacy has been exhausted.
7. Military action, in the game we will set up, is the preferred option only in the event that Iran proceeds rapidly.

Payoff Matrix for West-Iran Game

Iran
Give Up __Slow __Rapid

_____________________________Ignore______ 5__ _-2____-6
__________________West __ Diplomacy _____4 ____-1 ____1
_______________________________Act _____-5 ____-4 ____2

Game III-2

Consider the West’s decision problem first:

Unlike before, assume that the West is afraid that Iran will always discover its strategy choice and that, knowing the West’s strategy, Iran will always try to hold the West’s payoff as low as possible.

One may ask: What is the best strategy against an omniscient opponent who is trying to minimize one’s payoff?

1. Against an omniscient adversary with diametrically opposed interests, the West’s payoff from ignore is -6.
2. Against an omniscient adversary with diametrically opposed interests, the West’s payoff from diplomacy is -1.
3. Against an omniscient adversary with diametrically opposed interests, the West’s payoff from act is -5.

4. In this scenario there is an unambiguously best strategy for the West: Diplomacy.

Observe that the payoff of −1 is the highest payoff that the West can guarantee for itself in this game.

The West secures at least the payoff -1 by adopting the strategy diplomacy.

Assume that Iran is equally afraid that the West will have advance knowledge of Iran’s strategy and will limit Iran’s payoff as much as possible.

We can think of Iran as trying to minimize the West’s payoff. Thus, in our payoff matrix, Iran aims for low values.

One may ask: What is the best strategy for Iran against an omniscient West who is trying to limit Iran’s payoff as much as possible?

In this world, Iran will try to minimize the maximum payoff that the West can achieve against any of Iran’s strategies.

-The West’s highest payoff against Iran’s strategy give up is 5.

-The West’s highest payoff against Iran’s strategy slow is -1.

-The West’s highest payoff against Iran’s strategy rapid is 2.

Recall our assumption that Iran’s goal is to minimize the maximum payoff the West can achieve against Iran’s strategy.

This goal is achieved by adopting the strategy slow.

Iran’s strategy slow guarantees that the West can achieve no higher payoff than -1.

Observe that both the West and Iran can guarantee the payoff -1 in this game.

The West can guarantee that its payoff will be at least -1.

Iran can guarantee that the West’s payoff is no higher than -1.

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It appears as though Diplomacy is the best course of action.

Source: http://www.pitt.edu/~ablume/Game%20Theory%20Principles/game-slides-3.pdf

Obama's Iraq Logic

All be it I don't agree with Obama on the issues, I do think he is a very articulate, intelligent person. That is why I was somewhat surprised when I read this in AP News:

Democratic presidential hopeful Barack Obama said Thursday the United States cannot use its military to solve humanitarian problems and that preventing a potential genocide in Iraq isn't a good enough reason to keep U.S. forces there.

"Well, look, if that's the criteria by which we are making decisions on the deployment of U.S. forces, then by that argument you would have 300,000 troops in the Congo right now — where millions have been slaughtered as a consequence
of ethnic strife — which we haven't done," Obama said in an interview with The Associated Press.

"We would be deploying unilaterally and occupying the Sudan, which we haven't done. Those of us who care about Darfur don't think it would be a good idea," he said.

What Obama did was commit the Tu Quoque fallacy. When confronted with possibility of genocide in Iraq, Obama turns the focus to the uninhibited ethnic strife in the Congo as if it where justification to the outcome of his plan. Here is the simplified version of the argument that Obama is making to help point out the fallacy:

American: If the US pulls out troops in Iraq then ethnic strife and cleansing will occur.
Obama: Yes, but the status quo allows for genocide in the Congo.

See how the argument does not make sense, it doesn't address the issue. In other words, when people claim "Obama's plan will cause genocide", Obama responds "you already allow for genocide." That's not a suitable answer.