Abstract
In this chapter I approach Wittgenstein’s Tractatus Logico-Philosophicus as a story about the groundlessness of meaning. More specifically, I discuss how the Tractatus addresses the temptation to avoid the groundlessness of meaning through the idea that meaning can be grounded a priori, before experience, either on objects as empty conditions of sense or on logical syntax. I argue that Wittgenstein’s work offers, instead, an anti-aprioristic view on how signification works that leaves meaning to the use of language and to the application (Anwendung) of logic.
[T]hat all is in flux must lie in the essence of language.
Wittgenstein, Big Typescript
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Notes
- 1.
Unless otherwise stated, throughout the book all references to the Tractatus are from Wittgenstein, L. (1992). Tractatus logico-philosophicus. D. F. Pears and B. F. McGuinness (Trans.) London: Routledge.
- 2.
To the best of my knowledge, there has not been any interpretation of the Tractatus that systematically brings out how the affects it creates influence the reader’s way throughout the book.
- 3.
A similar idea is expressed by Juliet Floyd when she writes that “[t]he Tractatus is a deeply reflective rejection of the traditional a priori” (1998, 81).
- 4.
It is important to clarify that Wittgenstein is not looking to describe any mental activity from the side of the thinking or representing subject; what he is interested in are those characteristics of language, logic , and the world that make representation possible. In the Tractatus a “thought” is a “logical picture” and is distinguished from the Fregean idea of thoughts as entities that we grasp through thinking. Thoughts for Frege are objective entities that can be grasped and are differentiated from thinking. For example, Frege writes: “The grasp of the thought presupposes someone who grasps it, who thinks. He is the owner of the thinking, not the thought. Although the thought does not belong with the contents of the thinker’s consciousness, there must be something in the consciousness that is aimed at the thought. But this should not be confused with the thought itself” (1997, 342). Later on, he adds: “The thinker does not create them but must take them as they are. They can be true without being grasped by a thinker; and they are not wholly unactual even then, at least if they could be grasped and so brought into action ” (1997, 345). Also thoughts are the senses of sentences, so to understand a sentence means to grasp the thought it expresses: “The thought, in itself imperceptible to the senses, gets clothed in the perceptible garb of a sentence, and thereby we are able to grasp it” (1997, 328).
- 5.
By his own admission. See (1937, 282).
- 6.
Frege treats logical constants as truth functions which can be meaningful by being correlated with entities in the world, such as concepts. Russell presupposes some kind of logical objects . As he says: “Such words as or, not, all, some, plainly involve logical notions; and since we can use such words intelligently, we must be acquainted with the logical objects involved.” See Russell (1984, 99).
- 7.
In the Notebooks Wittgenstein wonders if there are other facts besides the positive facts , given that it is easy to confuse what does not take place with what takes place instead. In other words, Wittgenstein sees that there is a philosophical temptation to read -p as q, for example to take a proposition such as “the board is not black” to correspond for example to the proposition “the board is green.” He answers as follows: “the negative proposition excludes reality. It does not include any reality incompatible with that affirmed by the positive proposition” (NB, p. 39). This means that “p” and “-p” have the same representational content. What changes is just the position of the proposition towards reality.
- 8.
The idea that a single connective was sufficient had already been suggested and proved by Henry Sheffer in 1913. This connective was either the Sheffer stroke (p↑ q, or joint denial) or the Sheffer dagger (p|q, alternative denial).
- 9.
Wittgenstein gives us the form [p̄, ξ̄, N(ξ̄)] to establish a connection between the general form of proposition and the logical operation of negation . But in what sense can the general propositional form be related with negation ? To understand this we should pay attention to the fact that if operations and constants are just the logical coordinates of the elementary proposition (the logical space around every proposition) and do not represent anything external to them (they don’t correspond to anything in reality), the logical operation of negation is just what all propositions have in common. In order to better understand how a logical operation can be related to the general propositional form, we will examine something that seems prima facie contradictory to this idea. In 4.5 Wittgenstein writes: “The general form of a proposition is: This is how things stand. How can the logical operation of negation be connected to ‘this is how things stand’”? Anthony Kenny’s (1976) interpretation might be helpful: he chooses to read “this is how things stand” as “this state of affairs exists” so that it can be combined more easily with 4.21 where Wittgenstein says that “an elementary proposition asserts the existence of a state of affairs .” If 6.001 was rewritten accordingly to 4.21, we would get: “every proposition is a result of successive applications of the operation N(ξ) to propositions asserting the existence of a state of affairs .” But according to 5.47, an elementary proposition really contains all logical operations , so Wittgenstein expresses the same thing from two different perspectives. We can also understand this in the following way: if the elementary propositions contain already all logical operations —like a point contains its coordinates—this means that logical operations also belong to (and presuppose) the same possibilities of combination of names of the elementary propositions (and of their correlate objects) (see 1976, 96).
- 10.
The truth functions of a given number of elementary propositions can always be set out in a schema of the following kind:
-
(T T T T) (p, q) Tautology (If p then p, and if q then q.) (p ⊃ p ∙ q ⊃ q)
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(F T T T) (p, q) In words: Not both p and q. (∼(p ∙ q))
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(T F T T) (p, q) ,, ,, : If q then p. (q ⊃ p)
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(T T F T) (p, q) ,, ,, : If p then q. (p ⊃ q)
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(T T T F) (p, q) ,, ,, : p or q. (p v q)
-
(F F T T) (p, q) ,, ,, : Not q. (∼q)
-
(F T F T) (p, q) ,, ,, : Not p. (∼p)
-
(F T T F) (p, q) ,, ,, : p or q, but not both. (p ∙ ∼q : v : q ∙ ∼p)
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(T F F T) (p, q) ,, ,, : If p then q, and if q then p. (p ≡ q)
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(T F T F) (p, q) ,, ,, : p
-
(T T F F) (p, q) ,, ,, : q
-
(F F F T) (p, q) ,, ,, : Neither p nor q. (∼P ∙ ∼q or p | q)
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(F F T F) (p, q) ,, ,, : p and not q. (p ∙ ∼q)
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(F T F F) (p, q) ,, ,, : q and not p. (q ∙ ∼p)
-
(T F F F) (p, q) ,, ,, : q and p. (q ∙ p)
-
(F F F F)(p, q) Contradiction (p and not p, and q and not q.) (p ∙ ∼p ∙ q ∙ ∼q)
-
- 11.
For a demonstration of the rest, see Kenny (1976, 87–89).
- 12.
As Aristides Baltas explains: “If a Wittgensteinian ‘object’ is merely the substantive ‘what’ that bears a manifold of logical possibilities , its corresponding ‘name ,’ since it bears exactly the same manifold of logical possibilities , is logically indistinguishable from it. With respect to logical possibility , the object and the name of the object are strictly identical” (2012, 201).
- 13.
For a more contemporary account that prioritizes metaphysical simplicity and argues for the idea that the metaphysical simples are the ultimate atoms of Wittgenstein’s ontology, see Bradley (1992).
- 14.
Two different versions of Russell’s acquaintance are the approach by the Hintikkas and that by Hacker. The Hintikkas approach regards acquaintance as an acquaintance not with objects but with names . They stress that it is through an act of pointing that the relation between an object and a name is recovered, and they give the example of Russell’s own idea that there are “in our language only two logically proper names for particular objects other than oneself, to wit, ‘this’ or ‘that.’ If so, Russellian objects of acquaintance are introduced by displaying them and pointing to them” (Hintikkas in Friedlander, 174). On the other hand, Hacker understands acquaintance with objects either as acquaintance with elements in one’s experience or with their descriptions/elucidations: “knowledge of the correlation between its constituent names and the objects they name […] will be the case either if I have endowed the name-signs with a Bedeutung by correlating them through a mental act with elements in my experience, or alternatively if they have been explained to me by means of elucidations” (1986, 51).
- 15.
I am grateful to Anton Leodolter for bringing this to my attention.
- 16.
See also 5.5563: “In fact , all the propositions of everyday language, just as they stand, are in perfect logical order. That utterly simple thing, which we have to formulate here, is not a likeness of the truth, but the truth itself in its entirety. (Our problems are not abstract, but perhaps the most concrete that there are.)”
- 17.
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Balaska, M. (2019). Groundlessness in the Tractatus. In: Wittgenstein and Lacan at the Limit. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-16939-8_3
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