Modality: Metaphysical Necessity and Contingency

I have been working on "An Introduction to Metaphysics" by Carroll and Markosian today, and decided to summarize a few useful points for ya'll! Take note that understanding the following information will greatly enhance your ability to grasp the Cosmological Argument (especially the argument concerning contingency and necessity).

Metaphysical Necessity and Contingency

Let's introduce a term that is probably unfamiliar to most: Metaphysical Necessity.

As for a definition, I will give you a few examples of things that are 'metaphysically necessary.'

1. Larry is a person or Larry is not a person
2. 3 + 3 = 6
3. Green is a color
4. All bachelors are unmarried

Carroll and Markosian point out that it is difficult to give a specific definition for 'necessary.' However, one way that they put it was "About the best we can do is to say that these propositions are metaphysically necessary because they can't be false, because they have to be true." Indeed, if you think about it, if there are three sheep in a pen, and three more walk in, there are now six sheep in the pen. There is no legitimate debate on this. Green is a color. All bachelors are unmarried. These things are true by definition.

To illustrate this further, we will introduce two more terms: 'metaphysically impossible' and 'metaphysically contingent.'

Here are some examples of things that are metaphysically impossible:

1. Larry is a person and Larry is not a person
2. 3 + 3 = 46
3. Green is not a color
4. Not all bachelors are unmarried

Every statement on this list can not be true. It is impossible for them to be true.

And now for some examples of things that are metaphysically contingent:

1. Larry is a person
2. There are three sheep in the pen
3. Green is the color of leaves
4. Los Alamos is full of nerds

Everything on this list can possibly be true or false. It is possible for there to be three sheep in the pen or not. It is possible for leaves to be green or another color. It is possible for Los Alamos to not be full of nerds. It is possible for each of these statements to be true or false.

To summarize (and keep in minds that these definitions are somewhat lacking):
Metaphysically necessary: Something that must be true- it is impossible for it to be false. All bachelors are unmarried.
Metaphysically impossible: The opposite. It must be false. It is impossible for green to not be a color.
Metaphysically contingent: Can be true or false depending on the way the world is.
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 Time for another definition! This one should be easy.

Metaphysically possible: things that are either metaphysically necessary or metaphysically contingent.