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I'm an ecology student who's dabbling into philosophy of science. I'm currently writing a term paper on laws of nature (with a focus on ecology as a special science) and try to wrap my mind around Marc Lange's antrireductionist approach on distinguishing laws from mere regularities or accidents.

Lange proposes a concept of nomic stability, stating that

g is a law exactly when g belongs to a stable set

where a set would be a logically closed set of truths. Stability in this context is a sort of extension to nomic preservation:

g is a law if and only if in any context, g would still have held had p obtained, for every p that is logically consistent with every law

The need for this additional concept, as Lange states, arises due to a circularity in nomic preservation: each proposed (non-)law may hold under a certain set of counterfactual suppositions specifically tailored to the set. Aiming to avoid this circularity, he makes use of disjunctive antecedents, stating that if a set includes one accident, it has to include all accidents.

An example he gives to illustrate his argument is the non-law that there is no gold cube larger than one cubic mile (as, theoretically, it would be possible and consistent with modern physics to construct such a cube, just that it has never been done). A set compiled to make the "gold cube accident" a law would also have to include the accident that, e.g., Bill Gates never wanted to build such a cube; which also needed to include the accident that his wive never wanted one being built and so on. This seems quite intuitive to me.

But Lange goes one step further, stating that such a set would in fact have to include all accidents. He gives the example of the accident "all apples on my apple tree are ripe", which so far is not part of the set including the statements on gold cubes. Now disjunctive antecedents come into the picture: the statement

had either some gold cube exceeded one cubic mile or some apple on my tree not been ripe

would be logically consistent with the set, with the gold cube generalization not necessarily taking precedence over the apple generalization in every conversational context. Formulated as a logical expression with P being the gold cube and Q being the apple generalization:

(~P v ~Q) --> P

would not hold.

Now here are my questions:

  1. What is the basic "catch" of this counterfactual supposition? I'm lacking knowledge on logic, so I have a problem grasping that (~P v ~Q) --> P would be a valid (?) logical expression if ~P is not true in the first place. How does this expression as applied to gold cubes and apples distinguish the gold cube accident from, say, the statement that there cannot be a one cubic mile uranium cube (which would be inconsistent with modern physics)?

  2. A friend suggested that the essence of the argument could lie in causal relations between accidents and other accidents, which may be so unlikely that, spoken in terms of modeling, they could only be perceived as stochastic noise. E.g. an unripe apple falling on Ms. Gates' head and due to some unimaginable chain of neurological reactions awakening in her the vision of a one cubic mile gold cube. But Lange's argument explicitly states that a set including accidents would have to include all accidents; given that the set of accidents causally related to the accident of interest would be finite, I don't think this is what Lange meant?

All of the quotes above are taken from this paper. An approach to disjunctive antecedents in a nutshell, i got from this Stanford Encyclopedia article.

As of now, I didn't come up with a satisfying answer to my questions, but at least I found an alternative view on the problems, which eventually may lead to an answer -- or help others to understand my questions better.

Here are some ideas I came up with:

  • I think it's important to understand that the logical expression established by Lange is not meant to provide a tool for "weeding out accidents" and identifying laws in scientific practice. This of course is the task of science itself. The interesting question considered by Lange is what it would take for an established truth to be a law.
  • Lange states that for an established truth statement to make up a law, it needs to be stable, meaning that it has to hold under counterfactual suppositions which are logically consistent with it.
  • The problem now is to identify the set of counterfactual suppositions which are logically consistent with a truth. Take a statement which is considered a law, e.g. "No object can travel faster than the speed of light". Most counterfactuals which would support the opposite would not be logically consistent because it would require severe changes to the set of laws which make up modern physics (not being a physicist, I can only assume that the counterfactuals in question inhabit the realm of science fiction).
  • But what distinguishes the above statement on physical limits to the speed of moving objects from an accident? Let's consider a more intuitive accident than the aforementioned gold cube example, like "I'm the only person in my office" (no need for pity here ;)). This is where Lange states that, if I wanted to generalize this truth and make it a law, I would have to make every accidental truth that can currently be observed, a law. And to prove this, he makes use of disjunctive antecedents.

    • Let P be the truth that I'm the only person in my office and Q the truth that all apples on Mr. Lange's apple tree are ripe. Then, if we say P was TRUE, for P to hold under the counterfactual supposition (~P v ~Q),
      at least some apple on Mr. Lange's apple mustn't be ripe. What seems counterintuitive is that, obviously, the population of my office and Mr. Lange's apple tree have no causal connection whatsoever. But, if I get Lange right, the point is that (from a more linguistic perspective?), both truth statements are equally important and as such should both be members of the set. And, because Q is now a member of the set, just the accident some apple on Mr. Lange's tree isn't ripe would then be logically inconsistent with the set and thus also P would fall.

The question remains: what makes this logical/linguistic "trick" so special, and why is it necessary in the first place? My current impression is that the need for every accident to be part of a set of truth statements that contains an accident and is to be "stable" (i.e. invariant under every counterfactual supposition logically consistent with it), depends heavily on the conversational context. It breaks down to "accidents are puny, laws are special".

  • Just as an aside: The total volume of gold mined is around a hundred thousand times less than you'd need for a cubic mile, and at current prices the cubic mile of gold would cost around 3 quintillion dollars, which exceeds not only Bill Gates' fortune but also the total economic output of humanity over the last hundred thousand years. Of course the price of gold would crash if you could somehow come up with so much, but anyway--your conceptual point stands, but Bill Gates' whims really are irrelevant here. – Rex Kerr Jul 22 '14 at 18:42
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    Wonderful set of questions. Thanks for sharing. I'd like to comment on (1). (¬P ∨ ¬Q) → P is not valid. The antecedent is false only when both P and Q are true, while the consequent is false only when P is false. So pick any truth-assignment where P ≡ 0. Since P is false, ¬P is true, so (¬P ∨ ¬Q) is true. That's the antecedent. Now, since P is false, the consequent is false. That means that the conditional (¬P ∨ ¬Q) → P is falsifiable and is thus not valid. Best of luck on your paper. You'll do a great job I'm sure. – Hunan Rostomyan Jul 23 '14 at 1:27
  • Levent, Which paper of Lange's are you using? (Also, have you looked at any of the other work on ecology and laws?) – ChristopherE Jul 23 '14 at 2:26
  • @RexKerr Thanks for pointing this out; I took the example directly from Lange's paper. It's obviously irrelevant which accident you take as an example, but there may of course be more intuitive ones (like "all coins in my pocket are silver"). – Levent B. Jul 24 '14 at 15:07
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    This is exceedingly long... – Joseph Weissman Dec 30 '15 at 16:44

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