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Are There Laws in the Physical Sciences? February 14, 2009

Posted by jts3034 in Philosophy of physics.
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What is a Law?

What does it mean to be a physical law? One simple definition is to say that laws are generalizations that describe the world around us. This seems to be a little overly simple though. For example, it would be accurate to say something like, ‘there are no spheres of gold greater than a mile in diameter’. While this statement is a generalization of the state of nature, it doesn’t seem to be what we would consider a law. There is nothing about the nature of gold that prevents the formation of a gold sphere of this size. It simply just doesn’t exist. On the other hand, we could make the generalization that there are no spheres of uranium one mile in diameter. Uranium does have something in its nature that prevents this though. Using the concepts of radioactive decay and critical mass, there is no physical way to construct this object. In this case, the generalization about uranium spheres seems to be a law, or at least lawlike. Thus a stricter definition of law is needed.

Philosophers have tried to build a more explicit way to define law. One way is by equating the universe with a deductive system of logic. Deductive systems can have two qualities associated with them: strength and simplicity. A strong system will take many things into consideration. A simple system will require a minimum number of axioms. In the systems view, a law is any axiom of the system that has the best combination of strength and simplicity. The sphere of gold would add complexity while not adding strength and thus it is excluded as a law. The sphere of uranium adds needed strength and thus is a called a law. Critics of this system argue that this way of thinking causes laws to be mind dependent. What counts as simple or necessary is determined by those who are doing physics. However, laws should be independent of human consciousness.

Another way to view laws is as relationships between universals. For example, if I were to say ‘All F’s are G’s’, then the universals in this case would be F and G and the law would be the relation. Critics of this theory will argue that the relationship is very vague and is not necessarily the best way of describing the law. In the case of the uranium sphere, the law isn’t really that there are no uranium spheres of a mile diameter. That relation is a byproduct of the actual laws of critical mass and radioactive decay.

One other way philosophers talk about laws is to say that they don’t really exist. This is an anti-realist perspective. They will argue that the universe does not have to follow any certain rules. There is no exact way to describe the way things work and every law we have is just really an approximation. Looking back on almost all previous laws shows that much of what we have determined to be laws turned out to be false. The realist would argue that even though previous laws have been shown to only approximate reality, scientists are clearly getting better at describing the universe and we will eventually have some sort of complete understanding.

There is then the issue of what Physicists are actually trying to discover. There is a distinction between strict generalizations and ceteris paribus generalizations. Strict generalizations are those that exactly describe the world. Ceteris paribus generalizations that are only valid under certain circumstances. Ceteris paribus is Latin for other things equal. An example of a ceteris paribus generalization would be Newton’s Laws. These ‘laws’ only hold under the condition that gravity is not extremely large and objects are moving at low relativistic speeds. Some philosophers, such as Nancy Cartwright, argue that physicists only try to discover ceteris paribus generalizations and that there really are no strict generalizations to be found.

The Problem of Induction

 

It is the case that our Laws, considered as generalizations strict or ceteris paribus, must be derived from observations – a process we call induction. Ignoring any epistemological issues with assuming that what we sense accurately represents the universe, the need for induction in forming our Laws, by the nature of induction, precludes logically thinking that they will hold true universally. Explicitly stated, it need not be true that future events will follow the trends we observe, and there is no way to prove whether they will or will not before they occur. The only manner in which one can prove a statement drawn from induction is to perform an infinite number of tests – a task that is clearly impossible. A classic example is that of the “Law of Gravity.” In our experience, in the absence of other forces, objects fall down (or toward the Earth, if you must). Claiming that we can prove the Law by observing it many times – or even claiming that because we have observed it many times, it is likely to hold true universally – is illogical.

A further disadvantage of induction is the uncertainty it breeds. For a given set of observations, a number of conclusions can often be drawn, depending on the drawer’s past observations, experiences, etc. How is one to judge the quality of differing inductive claims? Surely those that are absurd – not following in a recognizable way from observations – can be discounted, as can those that are disprovable by a conflicting observation. Aside from similarly easy cases, judgment seems difficult – this is likely a useful area in which to apply Occam’s razor.

Is it rational to believe that inductively inferred Laws hold throughout the universe? According to the Skeptic’s Field Guide, it is. The author, defining a rational belief as one that is well reasoned and does not contradict itself, makes the following argument. Using an idea from Daniel Dennett, it is both physically and logically possible that the universe is described by a set of laws. According to the author, such an explanation is the simplest one, so by Occam’s razor we should accept the truth of Laws (or at least the ability of Laws to describe the universe). Obviously, this is not a logical argument, as it requires us to accept Occam’s razor. But by his standards, which seem reasonable to me, it is rational.

The truly important question is whether we can accept using inductively inferred laws to complete everyday (and not so everyday) tasks. If we cannot be certain that the aerodynamics principles we’ve established will always hold true, how can we feel safe riding in a plane? The Stanford Encyclopedia of Philosophy claims that we can simply because that is what we are used to. Everything we’ve observed has lead us to believe that induction is a good way to analyze the world, so in everyday life, we do. And as long as the planes keep flying, that’s alright with me.

Another issue with laws are that they have the possibility to be too simple to describe reality.  Sometimes there are other factors in reality that change how things work that differ from what the laws state.  One of those is the example of gravity and how two particles interact.  There is a law of gravity that states that the attraction between two bodies is directly related to the size of those particles and distance between those two.  The trouble is sometimes those particles are charged and this adds additional attraction or repulsion.  The question came up that if you say this then are forces just a human construct and not even reality so can say that these formulas don’t even try to describe reality?

References:

http://plato.stanford.edu/entries/induction-problem/

http://plato.stanford.edu/entries/laws-of-nature/

http://www.skepticsfieldguide.net/2006/11/problem-of-dismissing-induction.html

Nancy Cartwright. How the Laws of Physics Lie. Oxford University Press, USA . 1983

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