Possible Worlds and Laws of Nature

In class, I suggested that possible worlds are helpful in all sorts of ways. One of the ways I mentioned was the laws of nature (LN). While nothing I said was false, nothing I said was all that clear either. Hopefully, this brief post clears up some of the confusion I may have created. 

To understand the issue, we need two things: laws of nature and counterfactuals. 

Laws of Nature
The simplest and easiest way to think about a law of nature is to think of them as universal generalizations. A universal generalization is exactly what it sounds like—it is a statement that is universal and general. For example, the statement [all dogs are brown] is universal and general with respect to dogs. The statement [some dogs are brown] is not universal. Laws of nature are often (and in there most basic forms) thought to be just like that. As universal generalizations, they are about something that holds universally (if true they tell us something about every member of the subject). 

For example, Newton’s three laws of motion can all be expressed as universal generalizations. They each tell us something about everything they talk about:

            1. The first tells us something about all instances of uniform motion
 2. The second tells us something about all instances of force
            3. The third tells us something about all physical actions

So, LN are, at bottom (at least the most basic ones), universal generalizations. But not all universal generalizations are LN. The laws of motion (granting that they are in fact laws of nature) are different from other, true universal generalizations such as:

            4. All the coins in my pocket are dimes
            5. All gold spheres are less than a mile in diameter
            6. All bald people are less than 8 ft tall 

One way to see a difference between the above universal generalizations and LN is to think about whether it is physically possible for each of 4-6 to be false. In other words, while it is true that all the coins in my pocket are dimes, all gold spheres are less than a mile in diameter, and all bald people are less than 8 ft tall (does not really matter if this is false; if it is, just get rid of the bald person(s) who is 8 ft tall and it is now true ), these universal generalizations could have been false in our world. It is not as if my pocket somehow turns coins into dimes so that if you tried to put a penny in my pocket it would transform into a dime. 

            If you tried to put a penny in my pocket it would transform into a dime

That is false. That would not happen. And that fact (which it seems we can know without actually performing the experiment) is enough, it seems, to show that the statement [all coins in my pocket are dimes] is not a LN. While it is a true statement is fails to support the relevant counterfactual statement:

            If you tried to put a penny in my pocket it would transform into a dime

The same is true of the above statement about gold spheres and 8 ft tall bald people. While 5 is true now, always has been true, and presumably will continue to be true in the future, it too is not a LN. Why? Well, there is nothing about the nature of gold that precludes it from being formed into a sphere that is a mile or more in diameter (there is something about the nature of other elements that precludes this). In other words, it is possible for a sphere of gold to be a mile or more in diameter. Even though there never has been or probably never will be such a sphere the statement above is not a LN because it too fails to support the relevant counterfactual statement:

            If a hunk of gold were molded into a sphere it could not be a mile in diameter

But the laws of motion (again, assuming they are laws for present purposes) do support their relevant counterfactuals. Take something, x, at rest and even if x is never set in motion it is still true of x that:

            If x were set in motion, then x would remain in motion (unless, bluh bluh bluh)

So, LN seem to differ from some other universal generalizations in that LN support counterfactuals whereas these other universal generalizations do not. And to see that we implicitly relied on possible worlds! Without even trying that hard you easily imagined what it would be like for a penny to enter my pocket, for a hunk of gold to be shaped into a sphere, for an object at rest to be put into motion, even though none of those things really occurred. And you went on to evaluate all of the statements involved even though the events described never happened and may never happen in the future. You imagined a possible state of affairs, a possible world, in which the events described either occur or fail to occur. All of that is what helped you see the difference between a real LN and a fake LN. 


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