# Something New

What Kinds of Things Are Natural

This is a short note arguing that the Lewisian picture works much more smoothly if you take the things that are more or less natural to be functions from objects to magnitudes rather than properties. It’s indebted heavily to soon to be published work of John Hawthorne’s. Daniel Nolan tells me that Jack Smart has a similar view somewhere, but I haven’t been able to chase down the reference for that yet. So this probably isn’t an original view, but then again I’m much happier defending views of Smart’s than original views of my own!

## 4 Replies to “Something New”

1. Greg Frost-Arnold says:

I’m thoroughly sympathetic to the main point of this short note, but I did want to pick one nit. Brian writes (p.1) that “fundamental physics for centuries… been in the business of discovering magnitudes, not properties.”

It seems to me that fundamental physics does discover properties as well as magnitudes. For example, we can reasonably take Newton’s primary discovery in his Principia to be that every bit of matter in the universe attracts every other bit of matter in the universe, according to the inverse-square law.

2. Stephan Leuenberger says:

I think that proposal is very Lewisian in spirit.

However, two questions arise as to how to translate things that Lewis says about natural properties and relations into the function-idiom. First, for a given world, he makes a distinction between natural properties that are in that world and those that are absent from it, or alien to it (for the definition of HS, of materialism, etc.). For this purpose, one could maybe use partial functions, and say that a property is alien to world w if it is not defined for any individual in w. (This raises the question what the difference is between mass(x) = 0 and mass(x) undefined; maybe the range of the of partial mass-function should be only the positive reals.) Or one could designate one value as the “lacks-the-property” value. For mass, this would be 0. But there might be natural properties with no privileged zero point. For those, maybe an arbitrary “lacks-the-property” value could be chosen.

Lewis also thought that perfectly natural properties (since he arguably identified them with the fundamental properties) obey a principle of recombination, and relatedly, that they form a MINIMAL supervenience base for everything (ignoring worries about infinite descent). Since clearly the different mass-functions are not recombinable, i.e. since their values are not able to vary independently, those claims could only be true about functions if one of the many mass-functions Brian mentions counts as natural. Functions do seem to have too much structure for the job.

Thus the entities that are natural are maybe equivalence classes of partial functions.

3. Brian Weatherson says:

Thanks both for the nice comments.

On Greg’s point, I agree that physics discovers properties of the world, or perhaps properties of properties, but I don’t think physics discovers fundamental physical properties as Lewis says. It discovers fundamental magnitudes, and discovers what properties they have.

Stephan’s first point seems right – I should distinguish between value 0 and no value. I was thinking value 0 should be thought of as not having the property, but maybe that’s wrong.

The point about recombination seems right. If there are two mass functions that are scalar multiples of one another, then we certainly don’t want to say that they can be recombined. Maybe what I should say is that it is indeterminate which of the mass functions is the perfectly natural mass function, but it is (super)true that one of them is. This is tricky and I need to think about it more.

4. V. Alan White says:

This concise attempt to state what is natural in terms of functions rather than properties is fascinating—my hat’s off. It led me to rethink some claims by Marc Lange (in his Introduction to Philosophy of Physics text (2002) and especially “The Most Famous Equation” in the JP (2001)). He specifically argues (in the latter) that while both mass and energy have clearly mapped functions of relativistic transformation and equivalence between systems, only “rest-mass” (Lange rejects this term for “Lorentz-invariant mass”) is an invariant property—and as opposed to relativistic mass or so-called mass-energy transformations—and thus real. So Lange posits invariance—the results from a certain subset of transformation functions—as a marker for the reality of properties. What your piece made me realize is that I can now conceive of Lange’s central thesis as also making a sharp distinction between the invariance of a function and the invariance of a function’s output as a magnitude. So Lange’s thesis now seems to me to be also expressible in terms of recognizing that while all familiar relativistic relations are invariant as functions, only some produce invariant magnitudes that are themselves candidates for being objectively real or natural properties. I don’t certainly wish to speak for either you or Lange—but it just seems to me that your argument is thus compatible with a view like his.

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