The Politics of Logic: Chapter 5 Notes and Comments

You can find the previous chapter notes here.

Wittgenstein and Parmenides

Livingston begins with a comparison of two statements by Wittgenstein and Parmenides.

• Wittgenstein: “What we cannot speak about we must pass over in silence.”
• Parmenides: “You could not know what is not–that cannot be done–nor indicate it.”

The context of Parmenides statement is the following: A traveler journeys to the place of a goddess and is offered a choice between two paths. One is of persuasion, truth, and being. The other path is of non-being, error, and illusion. The goddess here restricts though to the choice of what is and what is not. This choice is a model for rational/logical thought throughout Western thought. The goddess connects being and thinking into a unity. This is the ground for the eternal, changeless One of all that is. This is the institution of the combination of consistency and completeness and the origin of the onto-theological thought that has since governed Western thinking. There is a subtlety in the story though. The goddess is recommending the first and proscribing the second. By claiming the second path as indiscernible and not-being, how can she indicate it? And if the first path is being and the One, how can there even be an alternative to it? Livingston suggests that this ambiguous structure is exhibited by Wittgenstein’s thinking as well.

In the Tractatus, Wittgenstein provides an argument for the necessary existence of simple objects which Livingston says is reminiscent of Paramenides’ argument for the necessary existence of the One:

• 2.02 The object is simple.
• 2.0201 Every statement about complexes can be analyzed into a statement about their constituent parts, and into those propositions that completely describe the complexes.
• 2.021 Objects form the substance of the world. Therefore they cannot be compound.
• 2.0211 If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.
• 2.0212 It would then be impossible to sketch out a picture of the world (true or false).

The premise of this argument is based on the determinacy of sense, the possibility of saying true or false propositions. This restricts reality to two alternatives: true or false. They key point, Livingston says, is that if some of the terms that function as simple names in language could fail to refer, then it would be possible for the propositions that use them to fail to be true in two different ways.

1. The proposition could be false because the object it names isn’t accurate with respect to the actual state of affairs
2. It could fail to be true because the simple names fail to refer to anything at all.

If two is true then the sense of the proposition depends on the truth of other propositions which makes it impossible to determinately correlate the propositions with the state of affairs at all. So, if sense is to be determinate then there must be a fundamental ontological distinction between simple objects and the complexes. Both Socrates and Wittgenstein suggest that if it were possible to describe rather than name the simple objects, when whether a proposition that had simple names had sense would still depend on the truth or falsity of other propositions (the ones describing objects). Sense would then still be indeterminate. This means that for the possibility of sense it is a transcendental condition that it is impossible to saying anything about the simple objects. Even saying a particular simple sign has an object violates this condition. So, the Tractatus suggests, the necessity of simple objects composing the structure of the world must be shown rather than said meaning it is impossible to both assert or deny them.

It must always be possible to rationally decompose the complex state of affairs into its simple parts which correlate with simple names. This is due to the rational structure of language and the world. The prohibition of non-being in the Tractatus is evidence of the unity of logical structure or form that aligns language and the world (logical atomism). Prohibiting the contradictory makes sure the logical order and determines the boundaries of language and sense. Wittgenstein says the temptation to philosophical error comes when one sign is used in different ways. To avoid this the clarifying the logical syntax is necessary: the correlation of each syntactic sign with only one rules of use. This also shows the totality of what there is. So, Livingston argues, both Wittgenstein and Parmenides prohibit inconsistency which limits the One of all that is. This limits speech and provides the position of mystical insight into what cannot be said. The combination of the One with a prohibition of the inconsistent is the origin of the onto-theological and constructivist positions. The prohibition of non-being and the prescription of being are both overdetermined.

Early to Late Wittgenstein

Later, Wittgenstein recognized that the prohibition is overdetermined in that what is ruled out as impossible is also proscribed by the rules that allow for the possibility of logical analysis. Wittgenstein’s later Typescript gives the sense that we cannot see language as a whole as an instrument or tool for accomplishing specific purposes. There is no specific task that we aim for when speaking. If there was a task then grammar would simply be like traffic rules. Instead, explicitly stated grammatical rules must be impossible to not follow and still speak the language. Any expression of the grammatical rule that might cause us to reconsider the sense of one of our remarks must be seen in a paradoxical fashion: the crossing of the constitutive with the descriptive.

Wittgenstein takes his argument from the Tractatus that claims that there is something like a definitive and necessary connection between what can be named and what can exist at all in a different direction. He suggests a transfigured understanding of its sense that liberates us from its force. The questions of rational standards are not just about making sense of moments of institution or origin but questioning the force of their regular and routine application. This is the problem Wittgenstein addresses in his Philosophical Investigations, the question of how signs get their applications, how they are used, and what it means to learn, use, and follow these rules.

As is clear from the rest of the book thus far, the answer is not in the arbitrary standard institution of these signs and rules. The standard, such as the meter stick, holds a position that is neither inside nor outside the language game it constitutes. This position cannot be resolved simply by making a distinction between the perspectives which are internal and external to our language games. The position of the standard is in neither of these two perspectives. From the outside, the standard is just another particular, undifferentiated from any other particular. From inside, the standard does not exist as an object at all, it is just a reference to the law generally and is clothed with the mystical aura of necessity and seems to have must always already been in place.

The Tractatus‘ position was a form of constructivism or criteriology. Like these projects it had an underlying attempt to delimit sense through a univocal and non-contradictory tracing of the boundaries of meaningful language. This attempt to delimit sense was the origin for the arguments for the metaphysical simples and for the necessity of logical structures linking language and world. It is also connected to the Tractatus‘ prohibition of self-membership and self-reference. The Tractatus had the same goal: adducing structural principles to prevent the paradox from arising.