Thursday, February 14, 2013

Presentism and simplicity of laws

Consider the following toy example of a law of nature: All electrons are charged. On an eternalist theory of time, the following expression correctly captures the logical structure of this law.

  1. ∀x(Ex→Cx)
On the other hand, on presentism, (1) would only say that all the present electrons are charged. To correctly capture the logical structure of the law that all electrons are charged on presentism, we would need something like:
  1. ∀x(Ex→Cx) & ∀t[P(t)→Wast(∀x(Ex→Cx))] & ∀t[F(t)→Willt(∀x(Ex→Cx))],
where P(t) and F(t) say that t is past or future, respectively, and the Was and Will operators say what was or will be the case at a particular time. There may be ways of slightly simplifying (2), but whatever we do we need to say that all electrons are charged, all electrons were charged and all electrons will be charged. Presumably, this will also come along with a story on which when a physicist says "All electrons are charged", she is using a locution that should be analyzed as something like a triple conjunction, though she may not realize this.

This should be at least a little embarrassing to the presentist. That all electrons are charged seems to be is a very simple law. But (2) is far from simple. Moreover, the analyses may sometimes be even more complex. Consider a putative fairly simple law that makes reference to two different times, say that

  1. exposure to V tends to cause a disease D.
The presentist needs to say something like this:
  1. exposure to V will tend to cause D, and past cases of exposure to V tended to have caused, be causing or be about to be causing D, and future cases of exposure to V will tend to cause D.

But the concern is not merely esthetic (though I do think beauty is a guide to truth). Suppose that our evidence is equally well explained by two general claims, one of which is both (a) significantly simpler and (b) significantly logically weaker. Then we should not have much confidence in the explanation that is both more complex and stronger. For instance, suppose that all observed ravens are black. This is equally well explained by two general claims: That all ravens are black and that all ravens and geese are black. The claim that all ravens are black is both significantly simpler and significally weaker. We should not go for the more complex explanation that all ravens and geese are black. (If we have no other evidence, though, we might cautiously accept the explanation that all birds are black, because while it's logically stronger, it's no more complex.)

Very well. Now, what is my evidence about electrons? Let's oversimplify the evidence by saying that the evidence is that all the electrons we've observed carefully enough have been charged. This observation can be equally well explained either by (2) or by:

  1. ∀t[P(t)→Wast(∀x(Ex→Cx))].
But notice that (5) is significantly simpler than (2) and also significantly logically weaker. So we should no more accept (2) than we should accept the claim that all ravens and geese are black on the basis of observation of ravens alone.

In other words, Presentism combined with a plausible thesis about which explanation one should not accept leads to inductive scepticism.

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6 comments:

  1. Jonathan D. JacobsFebruary 14, 2013 at 11:09 PM

    Why should the presentist or eternalist think that 1 captures the form of laws of nature? That's a regularity theory. But it's certainly open to the presentist to think it's independently plausible that laws are that which explains 1. And that which explains 1 is going to be in some sense necessary. Hence it's the theory of modality, not time, that will be doing the work in laws of nature. (And, hence, presentists need not worry on *that* score, it seems to me. Of course, if the presentists are also Aristotelians, rather than Platonists, that will make their job of giving a theory of *modality* more difficult.)

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  2. Jeremy PierceFebruary 14, 2013 at 11:29 PM

    A regularity theory claims that the regularity's occurrence explains (and is all that is true) to say that something causes something else. That's not what (1) is doing here. What (1) is doing is setting up a law that everything (1) says will happen. The law makes it happen. It's the opposite of a regularity theory. The regularity theory and the realist about laws will both insist that (1) is true. But the regularity theorist thinks the law consists only of the truth of (1). The realists insists that the law declaring (1) to be true ensures that (1) will be true.

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  3. Alexander R PrussFebruary 14, 2013 at 11:55 PM

    We need to distinguish between two propositions: the law and the proposition attributing lawhood to the law.

    The law will often be an ordinary unmodalized proposition p, like that E=mc2, or that F=ma, or that all electrons are charged.

    Then there is a further proposition that p is a law.

    So far everything I said is neutral between many accounts of laws, including regularity, divine will, and natural necessity ones. The differences between these come in when we ask what grounds the proposition that p is a law.

    Note also that if Presentism is true, (1) could in principle be "in some sense necessary", even if electrons didn't use to be charged. For while what is metaphysically necessary can't change (though I don't know for sure whether presentists who are opponents of S5 will agree), it is not clear that what is naturally necessary couldn't change over time. (Imagine, for instance, a force whose intensity varies with time.)

    Jonathan's suggestion may work if laws aren't just "in some sense necessary" but are actually metaphysically necessary. However, then that my argument can be made not for what one might call "real laws", but also for other law-like claims, like that all life on earth derives from a single ancestor, or that increase in demand with no change in supply leads to increase of price. Such metaphysically contingent law-like claims can figure in genuine scientific theories just as much as uncontroversially real laws do, and are also subject to simplicity constraints. Many will say that they are laws, but I am not going to push that now.

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  4. Alexander R PrussFebruary 14, 2013 at 11:56 PM

    By the way, the argument of this post is a tweak of the argument of this paper.

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  5. Dagmara LizlovsFebruary 19, 2013 at 8:22 PM

    "For instance, suppose that all observed ravens are black. This is equally well explained by two general claims: That all ravens are black and that all ravens and geese are black. The claim that all ravens are black is both significantly simpler and significally weaker. We should not go for the more complex explanation that all ravens and geese are black. (If we have no other evidence, though, we might cautiously accept the explanation that all birds are black, because while it's logically stronger, it's no more complex.)"

    Looks like here I go again. All ravens are not black. There are some rare white ravens out there. They are not albinos, but are leucistic. Yes, they have been observed by people. So they are more than just a myth. White ravens are special to the Haida people of the Pacific Northwest. According to their legends the world was created by a White Raven who underwent challenges and sacrifices to bring about the better good of his people. See this article:

    http://digitaljournal.com/article/294246

    and

    http://detectivedeathmachine.tumblr.com/post/37403164380/fairy-wren-leucistic-common-raven-photos-by

    I particularily like the caption which reads "Fear is the little death."

    Now lets get on to those black geese. The term "black goose" covers several species that come under the genus "branta" this includes the Canada Goose (tastes very good when cooked in a soup), the Cackling Goose (a smaller version of the Canda Goose), Brant Goose, Black Brant etc. These geese are not entirely black, but have significant areas of black and usually have white underbellies and have legs and feet which are black or very dark grey. More on them here:

    http://en.wikipedia.org/wiki/Branta


    Here is what looks like a melanistic snow goose although snow geese do not fall under the category of black geese, snow geese are under the genus "Anser":

    http://www.taxidermy.net/forum/index.php?topic=294012.0

    Snow geese are typically white, are considered pests on the Eastern Shore in Maryland. They move in huge flocks from field to field and when they get up out of a field they picked clean they look like a white tornado. We have a special Snow Goose conservation season this time of year with no bag limits and no limits on how many shells we can have in a shotgun. Decoying them is hard because you need hundreds of decoys in a spot you know they will use. This can be accomplished by using diapers (cerrtainly cheaper than $10,000 worth of decoys). There is another color varient in the snow goose with blue grey feathers, and this goose is called a blue goose. Last year while out hunting, I tried to bag a blue goose, but missed.

    As for electrons being negatively charge and positrons being positively charged what about antimatter?

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  6. Dagmara LizlovsFebruary 19, 2013 at 8:51 PM

    More on electrons, postrons and antimatter. The video clip on this link here is quite cool:

    http://www.nasa.gov/mission_pages/GLAST/news/fermi-thunderstorms.html

    Now that has me all charged up!

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