I wanted to return to the issue of Pluto, which has already been the subject of a number of posts. The International Astronomical Union (IAU) created a rich array of issues and problems when it undertook a definitional change that resulted in the demotion of Pluto to the class of "dwarf planets".
The topic this time is what exactly did the IAU define?
I was watching a PBS special on the status of Pluto a few days ago. It included scenes from a diner where the genial Neil deGrasse Tyson was asking customers what they thought about the new status of Pluto. The reponses varied, but the issue at hand was about whether Pluto was "a planet". The diners all thought that they were dealing with the general concept signfied by the term "planet". Yet there is reason to think they were mistaken.
The IAU resolved (see http://www.iau.org/public_press/news/detail/iau0603/) concerning the following:
"The IAU therefore resolves that planets and other bodies in our Solar System, except satellites, be defined into three distinct categories in the following way:"
So what is being defined? Answer: "planets and other bodies in our Solar System, except satellites".
Not planets in general. But wait a moment - on the web page referred to, it also says "Resolution 5A is the principal definition for the IAU usage of 'planet' and related terms." Yet this is not part of the text of Resolution 5A. It seems to be some extraneous comment of uncertain provenance. It certainly appears to be in conflict with the text of Resolution 5A, which, again, is only dealing with the situation in the Solar System.
So we have: a lot of people thinking that the IAU defined "planet"; and the text of Resolution 5A which is defining "planets and other bodies in our Solar System, except satellites"; and a statement on the IAU web site saying that Resolution 5A is to be used for planets in general.
This is contradictory. The definition is for a "planet in the Solar System" but somehow can be used for a planet not in the Solar System also. In other words, we can substitute the definition for both A and Not-A.
Let's try that with the proposition about one of the extrasolar planets:
"51 Pegasi b is a planet that orbits the star 51 Pegasi".
Substituting the definition presented in Resolution 5A for the term "planet" we get:
"51 Pegasi b is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit that orbits the star 51 Pegasi."
So we have a contradiction. 51 Pegasi b apparently orbits both the Sun and 51 Pegasi.
This contradiction arises from the IAU restricting the definition of "planet" to the Solar System, but pretending that it can be used for any planet. It also shows how Natural Science is dependent on Logic, which is part of Philosophy. But that is a far more controversial topic.