Tuesday 10/2

Tractatus Logico-Philosophicus, 6.13-6.3751

Discussion Questions

First Question: Mathematics Pure and Applied

Wittgenstein asserts at 6.211 that "...in real life a mathematical proposition is never what we want. Rather, we make use of mathematical propositions only in inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics." What might be some concrete examples that would help explain precisely what he has in mind here?

Second Question: Scientific Theory

Our excitement at discovering Wittgenstein providing an example can be tempered a great deal by the difficulty of grasping the point his examples are intended to illuminate. Consider 6.341:

Newtonian mechanics, for example, imposes a unified form on the description of the world. Let us imagine a white surface with irregular black spots on it. We then say that whatever kind of picture these make, I can always approximate as closely as I wish to the description of it by covering the surface with a sufficiently fine square mesh, and then saying of every square whether it is black or white. In this way I shall have imposed a unified form on the description of the surface. The form is optional, since I could have achieved the same result by using a net with a triangular or hexagonal mesh. Possibly the use of a triangular mesh would have made the description simpler: that is to say, it might be that we could describe the surface more accurately with a coarse triangular mesh than with a fine square mesh (or conversely), and so on. The different nets correspond to different systems for describing the world. Mechanics determines one form of description of the world by saying that all propositions used in the description of the world must be obtained in a given way from a given set of propositions—the axioms of mechanics. It thus supplies the bricks for building the edifice of science, and it says, ‘Any building that you want to erect, whatever it may be, must somehow be constructed with these bricks, and with these alone.’

In this case, what is the example he is giving here, and what is the point he thinks this example gets across?

Third Question: Laws of Nature

At 6.371, Wittgenstein claims that "[t]he whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena." He goes on in 6.372 to conclude that "[t]hus people today stop at the laws of nature, treating them as something inviolable, just as God and Fate were treated in past ages."

If natural laws are not explanatory, then what use are they? What work do they do in scientific theory, if any at all?

Fourth Question: Willing

Why is "[t]he world... independent of my will"? (6.373)