I just wanted to add several points to this discussion. (01)
1. When talking about ontology, it's important to distinguish the
claims we are making about what exists, and the language (formal
or informal) that we use to characterize what exists. (02)
2. The planet Venus is something that people have observed long
before they had any written language or formal logic for
talking about it. They didn't have any conceptions about
modern sets, classes, mereological sums, etc. Some may have
had two different concepts (morning star vs evening star) and
others may have identified it with a god or goddess. Those ways
of talking did not change the nature of the thing in the sky. (03)
3. It is indeed unusual to talk about Venus as a singular set
or class. But one could, if desired for some reason, develop
a formal ontology with that feature. But that feature would
be an artifact of the formalism and the conventions for using it. (04)
4. The distinction between intensions and extensions can be used
for individuals as well as for sets, relations, functions, and
classes. The basic point is that the extension is something
in the world (or a model of the world), and the intension is
a definition that is used to characterize and identify the
thing or things in the world (or some model of the world). (05)
Please note that Frege used the example of the morning star
vs the evening star to illustrate his distinction between Sinn
vs Bedeutung. (06)
The terms Sinn and Bedeutung name two points on the meaning triangle.
In German, they are Zeichen, Sinn, Bedeutung -- usually translated
as sign, sense, and reference. (07)
Those terms are related to intensions & extensions, but they
are not quite the same. For other terms used to label the
three vertices of the meaning triangle, see Slides 88 to 90
of http://www.jfsowa.com/talks/kdptut.pdf (08)
John (09)
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