The nondepictability of pictorial form in any state of affairs

In Tractatus Logico-Philosophicus, Ludwig Wittgenstein argues that pictorial form cannot be depicted. First, I explain the ontology, the picture theory of meaning, and the show-say distinction in the Tractatus before interpreting Wittgenstein’s argument. As his conclusion may be interpreted in multiple ways, I argue for the formulation “a picture cannot depict any state of affairs involving its pictorial form.” I show that his argument is similar to that of David Hume against the idea of the self, considering one possible objection.

Ontology

The ontology is about what is in reality, while the picture theory is about the depicting or displaying of things in reality. First, a brief explanation of the ontology. Objects form the ontological basis of the world. (2.02, Pears and McGuinness translation) They are things that exist necessarily and do not change. (2.027) A state of affairs is a particular arrangement of objects that is possible (non-existent) or actual (existent). (2.01, 2.031) A state of affairs is not an object itself because it doesn’t have to exist. (2.06) Still, existing states of affairs are in reality as they consist of objects being arranged a certain way.

‘Form’ is a word used in different concepts of the ontology and the picture theory. The form of an object is “the possibility of its occurring in states of affairs.” (2.0141) The form is within an object rather than without, since “in logic nothing is accidental.” (2.012) Every object has embedded information about which possible states of affairs it could be in. So given any set of objects, the objects alone determine their possible arrangements, i.e. the possible states of affairs that consist of them.

Show-say distinction

There are two possible modes of conveying meaning: depicting and displaying. Reading the Tractatus, I interpret ‘depict’ to be synonymous with ‘say’ and ‘present’, and ‘display’ to be synonymous with ‘show’ where context permits. Depicting seems to involve providing meaningful content through language, while displaying is more of a mysterious and futile gesture. What can be displayed cannot be depicted, (4.1212) and what can be depicted cannot be displayed. (3.262) Depicting is substantially more fruitful than displaying, as “what we cannot speak about we must pass over in silence.” (7)

Picture theory of meaning

The picture theory relates the above to logic and thought. Let’s focus on distinguishing between a picture, its pictorial form, and its representational form. This distinction is crucial to my interpretation.

First, a picture depicts an existent or non-existent state of affairs. (2.11) So a picture depicts some actual or possible arrangements of objects. The objects are accounted for by corresponding elements in the picture. (2.131) The structure of the picture is in some way isomorphic to the arrangement of the objects in the state of affairs.

Second, the pictorial form of a picture is the possibility that the state of affairs it depicts exists. (2.151) The pictorial form is what the picture has in common with reality. (2.17) [This makes intuitive sense only if the picture is distinct from reality and the state of affairs it depicts. Hence, the picture isn't in reality, but is a model of it. (2.12)] The pictorial form connects the two like a dull mirror reflection in which “only the end-points of the graduating lines actually touch the object that is to be measured.” (2.15121) Examples include spatial form and coloured form. (2.171) I interpret that the pictorial form of a picture consists of not only one possibility, but a set of infinitely many possibilities. Aside from the objects depicted by the elements of the picture, there is a plethora of other objects in the world that could be arranged in every which way. Since states of affairs are mutually independent, (2.061) there are infinitely many states of affairs aside from the desired state of affairs, each of which could be existent or non-existent.

Third, a picture’s representational form is the standpoint from which it depicts the state of affairs. Given this definition in 2.173 right after statements about pictorial form, a picture’s pictorial form and its representational form are evidently distinct. The former relates a picture to reality, (2.17) like a finger, while the latter is the picture’s one-sided perspective only, (2.173) like an eye. (Here I am not depicting accurately how the representational form relates to the pictorial form, but I am trying to display it.)

While commentators have interpreted pictorial form and representational form as synonymous, (O’Grady, 302) that shall not be done in this essay. The Ogden translation of the Tractatus translates them both as ‘form of representation’, but this introduces a discrepancy between 2.17 (“What the picture must have in common with reality… is its form of representation.”) and 2.173 (“The picture represents its object from without (its standpoint is its form of representation).”). These two are analytically not the same concept.

Using the concepts above, relationships can be drawn between the ontology and the picture theory. A picture corresponds to states of affairs as the former depicts the latter. An element of a picture corresponds to an object as the former depicts the latter. Pictorial form may seem to correspond to form of objects as they both concern the possibility of a match between something and reality. However, since form of objects applies to individual objects and not an arrangement of objects, I take pictorial form to correspond instead to the possibility of the structure of states of affairs. If they match, then the picture depicts the state of affairs as a whole.

Interpretation of “a picture cannot depict its pictorial form”

In 2.172, Wittgenstein writes that a picture cannot depict its pictorial form. Let’s analyze what this means before moving on to his argument for it. These four formulations for the meaning of 2.172 should exhaust all possibilities:

  • (a) No element of a picture can correspond to the picture’s pictorial form.
  • (b) A picture cannot depict that it has its pictorial form.
  • (c) A picture cannot depict that any picture has its pictorial form.
  • (d) A picture cannot depict any state of affairs involving its pictorial form.

For (b) and (c) to be valid, a picture must correspond to some object in reality, which is a debatable assumption. Accepting this requirement, a counterexample to (b) and (c) is that “a spatial picture can depict anything spatial.” (2.171) If a spatial state of affairs is depicted, then there is a spatial structure to the picture, which implies spatial form is its pictorial form. The spatial state of affairs being depicted means that its spatial form is depicted. Since the possibility of the structure of the state of affairs is supposed to match the pictorial form of the picture, the pictorial form is indirectly depicted. Furthermore, in (b) and (c) the picture is supposed to be depicting either itself or another picture, which makes the depiction closer than the characteristic that “only the end-points of the graduating lines actually touch the object that is to be measured.” (2.15121) In the case of (b), this situation resembles much more of a self-reference than a mirror reflection. In the case of (c), the two pictures are intimately related due to my argument before that each pictorial form is a set of infinitely many possible states of affairs. For two infinitely sets to be the same, their generators are intuitively similar.

(a) has limited plausibility because a pictorial form is more akin to structure than it is to any individual object, as I argued above. Even if a pictorial form is an object in reality, it is covered by (d).

(d) does not assume that the picture is an object, nor does it imply that its pictorial form is an object. The pictorial form could be the structure that is somehow involved, probably isomorphically, with some states of affairs. We already know that this relationship between pictorial form and states of affairs is explicitly allowed by the picture theory. Furthermore, the nondepictability of pictorial form is an important result in the Tractatus with consequences for other arguments, and (d) is the broadest formulation. Therefore, I shall consider this formulation.

Humean interpretation of the argument for “a picture cannot depict its pictorial form”

Under this formulation of the conclusion of the argument for the nondepictability of pictorial form, I shall provide an interpretation of the argument. The following are the neighbouring sentences around the concluding sentence 2.172. Although the argumentation format of the Tractatus is not clear, these sentences appear to provide the strongest support for the conclusion.

2.171
A picture can depict any reality whose form it has. A spatial picture can depict anything spatial, a coloured one anything coloured, etc.
2.173
A picture represents its subject from a position outside it. (Its standpoint is its representational form.) That is why a picture represents its subject correctly or incorrectly.
2.174
A picture cannot, however, place itself outside its representational form.
2.172
A picture cannot, however, depict its pictorial form: it displays it.

2.171 is true by definition: what is common between a picture and states of affairs is its pictorial form, and every picture has a pictorial form, so “a picture can depict any reality whose form it has.” Although 2.171 says ‘form’ only, I take it to mean any type of form, including pictorial form, in order to explain its examples of spatial and coloured form. The question remains whether 2.173–4 lead to the conclusion.

2.173–4 provide necessary conditions for the depiction expressed in 2.171. In 2.173, ‘subject’ refers to the states of affairs that the picture is supposed to depict. In this case, the picture is supposed to depict its pictorial form involved in some state of affairs. However, the pictorial form is in the picture in a similar way form is in an object, or structure is in a state of affairs. There is no form outside or beyond an object, and no structure outside a state of affairs, so there is no pictorial form outside a picture. Since the ontology and the picture theory are related in other ways, I find this relation plausible for supporting 2.173. Issues are elaborated in the following reasoning for 2.174.

2.174 sounds like David Hume’s argument against the idea of the self, which says that one cannot be conscious of one’s consciousness from that very consciousness. Analogously, one cannot see one’s point of view from that very point of view. (Dicker, 21) It is not conceivable, and it is commonly held that what is not conceivable is impossible. Maybe Wittgenstein had a similar intention here in that every picture necessarily has a point of view, namely its representational form. However, with its representational form the picture cannot conceivably place itself outside that form in order to depict that very form. However hard it tries to consider itself distinctly, there is conceivably still a little part of itself that is part of that same form. Since placing itself outside its representational form is not conceivable, it is impossible. If it is impossible, then given 2.173, pictorial form cannot be depicted in any state of affairs.

Objection to the Humean interpretation

Recall my interpretation that pictorial form is distinct from representation form. If pictorial form were identical to representational form, then Hume’s argument against the idea of the self would serve as a solid analogy by the above argumentation. Based on my assumption though, one concern is that perhaps the concepts of representational form and pictorial form could be interpreted in such a way as to allow for the pictorial form to be depicted from the representational form without any problems. I argue that this is impossible.

The representational form is the point of view of the picture, serving effectively as an eye. Anything it considers is directed from the picture outward in whichever direction. The representational form is what allows the picture to depict states of affairs. (2.173) The pictorial form is not outside the picture, but inside. So to arrive at the desired conclusion of formulation (d), the representational form must consider the pictorial form, which is inside it. The representational form is forced to look inward and depict the state of affairs it sees. While it may be able to see parts of the picture in some state of affairs, remember that the picture contains this representational form as well. The ‘eye’ cannot see its own point of view, the part that contains the representational form, from that same point of view. So there would always be some missing consideration; the state of affairs under depiction would always be incomplete in its account of pictorial form. Therefore, since it is not conceivable for the picture with its representational form to place itself, the pictorial form cannot be depicted in any state of affairs. If the pictorial form cannot be depicted, and it is not meaningless in the way that I have been referring to it, then it must be displayed instead.

Summary

I began with a discussion of the ontology described in the Tractatus, followed by the display-depict distinction and the distinction between a picture, its pictorial form, and its representational form.

Out of four possible formulations of Wittgenstein’s conclusion of the nondepictability of pictorial form, I decided that rather than being forced to treat either a picture or a pictorial form as corresponding to an object, the conclusion is for the nondepictability of any state of affairs involving pictorial form.

An interpretation similar to Hume’s argument against the idea of the self was put forth. This version of the argument holds even with the assumption that pictorial form is not the same as representational form, due to their complementary functions.