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Вестник Томского государственного университета. Философия. Социология. Политология. 2023.
№ 74. С. 66-83.
Tomsk State University Journal of Philosophy, Sociology and Political Science. 2023. 74. pp. 66-83.
Original article УДК 1(091)
doi: 10.17223/1998863Х/74/7
THE MYSTERY OF THE "SIMPLE OBJECT" IN WITTGENSTEIN'S
TRACTATUS
Sofia V. Danko
Independent researcher, Moscow, Russian Federation, danko.sofia@gmail.com
Abstract. The concept of the object in the Tractatus Logico-Philosophicus is still a mystery to scholars. It is yet unclear whether the object is a physical quality, a universal, a Platonic form, an abstract metaphysical construct, etc. There is still no consensus either on how the object relates to the name in the proposition and how the object, while remaining "simple", determines all logically possible events. This is only a small part of the questions that researchers have in connection with this concept. The article proposes a detailed reconstruction of the "logical structure" presented in the Tractatus and puts forward a version of the answer to the question: What is a simple object?
Keywords: Ludwig Wittgenstein, Tractatus Logico-Philosophicus, simple object, atomic fact, logical structure
Acknowledgments: The study was supported by the Russian Foundation for Basic Research, Project No. 20-011-00927: Defining Nothingness: Conceptions of Negativity in Continental Philosophy (2021).
I would like to express my sincere gratitude to Vasily Petrov, Zinaida Sokuler, Yulia Gorbatova and Dmitriy Kanavin for their critical comments, which allowed me to rethink some of the ideas in this work. I would also like to express my gratitude to Dmitry Turko for his professional editing of the text of this article.
For citation: Danko, S.V. (2023) The mystery of the "simple object" in Wittgenstein's Tractatus. Vestnik Tomskogo gosudarstvennogo universiteta. Filosofiya. Sotsiologiya. Politologiya - Tomsk State University Journal of Philosophy, Sociology and Political Science. 74. pp. 66-83. (In Russian). doi: 10.17223/1998863Х/74/7
Научная статья
ЗАГАДКА «ПРОСТОГО ОБЪЕКТА» В ЛОГИКО-ФИЛОСОФСКОМ ТРАКТАТЕ Л. ВИТГЕНШТЕЙНА
Софья Владимировна Данько
Независимый исследователь, Москва, Россия, danko.sofia@gmail.com
Аннотация. Концепт «объекта» в «Логико-философском трактате» до сих пор остается загадкой для исследователей. Все еще неясно, является ли «объект» физическим качеством, универсалией, платоновским эйдосом, абстрактным метафизическим конструктом и т.п. Все еще нет единого мнения, каким образом объект соотносится с именем в предложении, каким образом объект, оставаясь «простым», определяет собой все логически возможные события, и это только малая часть вопросов, возникающих у исследователей в связи с данным концептом. В статье предлагается детальная реконструкция представленной в Трактате «логической структуры» и выдвигается версия ответа на вопрос: «Что такое простой объект?»
Ключевые слова: Людвиг Витгенштейн, Логико-философский трактат, простой объект, атомарный факт, логическая структура
© S.V. Danko, 2023
Благодарности: Исследование подготовлено в рамках гранта РФФИ «Определение Ничто: концепции негативности в континентальной философии»; 20-011-00927 в 2021 году.
Выражаю искреннюю благодарность Василию Петрову, Зинаиде Сокулер, Юлии Горбатовой и Дмитрию Канавину за критические замечания, позволившие переосмыслить некоторые изложенные здесь идеи. Сердечно благодарю Дмитрия Турко за профессиональное редактирование текста этой статьи.
Для цитирования: Danko S.V. The mystery of the "simple object" in Wittgenstein's Tractatus // Вестник Томского государственного университета. Философия. Социология. Политология. 2023. № 74. С. 66-83. doi: 10.17223/1998863Х/74/7
Introduction
The "object" as a concept in Wittgenstein's Tractatus has intrigued early Wittgenstein scholars for many decades. This topic continues to provoke heated debates. Researchers discuss Wittgenstein's inheritance of Russell's main ideas [1-3] and ontological status of simple objects (see, for instance, [4; 5]); they criticize Wittgenstein's claim that the object and the substance of the world are identical (see [6; 7]); they put forward more and more new assumptions about the metaphysical premises of the Tractatus [8. P. 99; 9; 10]. They consider, among other things, the assumption that Wittgenstein himself did not really understand what he meant by the object [11]. Some say that "the failure of the doctrine of simple objects was built into that doctrine from its inception and that its deconstruction is already apparent in the final passages of the Tractatus" [8. P. 116], etc.
Apparently, the concept of object is still considered problematic: as Eric Lemaire [12] writes, "The important point is that there is absolutely no consensus about Wittgenstein's view of simple objects in the scientific community. The difficulty with this problem is that there is no textual evidence to support one of the possible solutions". "It is hard to resist the conclusion that Wittgenstein never supplied an adequate way of recognizing when a proposition is fully analyzed, and consequently that he failed to specify a means for recognizing something as a Tractarian object".
We can agree that Wittgenstein never indicated a reliable way of recognizing an object. It is possible that he deliberately evaded the task of defining this simplest element of his logical structure: "<...> He believes that logically demonstrating the need for such objects is enough" [13. P. 38].
Wittgenstein famously replied to Malcolm that, at the time of writing the Tractatus, he considered himself a logician and did not think it necessary to provide specific examples [14. P. 86]. Hintikka believes that "Wittgenstein is not always a completely reliable witness concerning his earlier views" [1. P. 129]. Carruthers also notes that "writing of the Tractatus seems to have been highly intuitive, with much apparently going unsaid, even in Wittgenstein's own thoughts" [15. P. xiii].
In this context, it seems to me useful to focus on the most problematic questions about the object and try to find the answers.
Particular emphasis will be placed on the unthinkability of logical possibility. In my opinion, in the Tractatus scholarship this important circumstance has not been taken into account in due measure. I will show that paying attention to this detail allows us to better understand what a simple object is, what place it occupies in the logical structure and how it relates to the observable picture of the world.
1. Difficulties in reading the Tractatus
According to the Tractatus, the world consists of "atomic facts" (TLP 1, 1.2, 2), while atomic facts consist of "objects" (entities, things) (TLP 2.01), which are the indivisible "substance of the world". Objects correspond to names, and facts correspond to propositions. Objects, like their names, are "simple" and indivisible (TLP 2.02). Facts, like propositions, are logically independent: "Any one can either be the case or not be the case, and everything else remain the same" (TLP 1.21). There is "no order of things a priori" (TLP 5.634), "Everything we see could also be otherwise" (TLP 5.634).
Such a picture seems paradoxical and raises many questions: if the world consists of facts, and the facts of objects (things), then the simplest elements of the world should be objects. Then why is it the "world is the totality of facts, not of things" (TLP 1.1)? And why are objects (entities, things) simple? All the things we know, obviously, have many features that preclude them from being simple. As Hidé Ishiguro notes, "The tiny fleck of snow on my palm is made of H2O; it fell at a particular time in January 1968 in a particular spot in London, etc. etc." [16]. Moreover, it is completely unclear how these things can be "other", and be other in all respects at that. In some ways, of course, they can change, but, obviously, not in any way. If, for example, the chemical formula of water changed, on what grounds would we continue to consider it water? Are names like "water", "oxygen", etc. not the names of simple objects? In this case, what exactly "could be otherwise"? And what is meant by "name" in the Tractatus?
It is also unclear how it is possible to formulate an "elementary proposition" describing an atomic fact: any fact known to us, according to the Tractatus, must be considered "complex" since it inevitably includes compound, composite things that have many different qualities.
Is there a chance to discover "atomic facts" and "simple objects" in the observable picture of the world, or are those purely theoretical concepts that nothing in the world corresponds to?
Let us try to understand all these questions better.
2. Main points on the "simple object" in the Tractatus
2.1. The necessity of simple substances
According to the Tractatus, objects are a necessary condition for the meaningfulness of language and the certainty of the world itself"Objects form the substance of the world. Therefore, they cannot be compound" (TLP 2.021). "If
1 According to the Tractatus, the world consists of facts. The language consists of propositions isomorphic to facts. Facts and propositions are isomorphic by their logical form: propositions create conceivable images of facts (TLP 3.141. 2.141). The conceivable "image" of what is happening is the meaning of the proposition; the image is also the thought (TLP 3). The proposition "shows" how things are: "to think" means to imagine a state of affairs - an apple is red, a cat is on a rug, ice is cold, etc. (TLP 4.031). A proposition creates an image of a possible state of affairs (TLP 4.0311), and, in order to establish its truth or falsity, this image should be compared with observed facts (TLP 2.222, 2223) Everything that can be observed must also be conceivable (as an image or "picture" of what is happening), and everything that is conceivable must be accessible to observation or imaginative representation (TLP 2.11, 2.17). The isomorphism of facts and propositions corresponds to the isomorphism of their elements - "simple objects" and their "names" (TLP 3.22, 4.0311). In the following, I will not specifically dwell on the distinction between "simple objects" and their "names" and I will talk about them while keeping their interchangeability in mind. The same applies to "facts" and "propositions".
the world had no substance, then whether a proposition had sense would depend on whether another proposition was true" (TLP 2.0211). "It would then be impossible to form a picture of the world (true or false)" (TLP 2.0212).
Indeed, if a proposition makes sense, then we can establish its truth or falsity1. If names that make up a certain proposition are not simple, these names imply further propositions (in a compressed form). Then the truth or falsity of the first proposition will depend on the truth value of all further propositions included in the first proposition. If there are no simple names, such a reduction will have to be continued indefinitely. In this case, we will never be able to establish the truth value of the first proposition (as well as all new propositions included in it). Accordingly, no proposition will be meaningful.
In a word, if there are no simple names, then all propositions will be infinitely complex and therefore will not have a truth value. Consequently, all propositions will turn out to be meaningless, i.e., not a single proposition will contribute to a true or false "picture of what is happening". No proposition will tell us what is "happening" or "not happening". In this case, it will really be impossible to build any "picture of the world".
However, it is obvious that native speakers are able to establish the truth or falsity of the propositions used in their language. They have quite definite pictures of ongoing events (pictures of the world). It follows that at some stage all propositions can be reduced to simple propositions consisting of further indivisible simple names2. Simple propositions create a picture of "atomic facts" which is made up of indivisible objects (simple objects). Simple objects correspond to simple names in propositions: "In the proposition the name represents the object" {TLP 3.22).
The argument from the "certainty of the world" (in other words, from the certainty of the pictures of what is happening) does not convince everyone (see [7]), but most scholars admit its validity (see [17; 18]).
I think we can accept the argument offered by Wittgenstein and agree that simple names and simple objects must exist3. However, we do not yet know what exactly is meant by "simple objects" and what names in the language can be considered "simple".
2.2. The object's occurrence in a fact. The constancy of logical possibilities
The key feature of a simple object is its ability to "occur in a fact", that is, to acquire some physical quality or to relate to other objects. Facts are described by propositions, for example, "grass is green", "the book is on the table", etc. At the same time, the meaning of any proposition is completely exhausted by the picture of the fact the proposition describes (we can imagine what it looks like).
1 The Tractatus belongs to the tradition, according to which all meaningful propositions must have a truth value (be true or false).
2 Wittgenstein does not use the expression "simple name" in the Tractatus, but he speaks of replacing a simple object with a name in a proposition, from which we can conclude that names associated with objects are also simple (i.e., they cannot be broken down into further propositions).
3 I will show later that the "existence" of objects means their presence in the logical structure, not their existence in the physical world or metaphysical reality. The logical structure itself is "transcendental", it creates a condition for discussing the existing, while the question whether the logical structure itself exists is meaningless.
Simple objects do not exist in isolation from their possibilities to occur in a fact. All their possibilities are predetermined in the logical structure: "In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing" (TLP 2.012). "If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context" (TLP 2.0121). Let me emphasize that the space of logical possibilities is determined not by what happens, but by what can happen. For example, the proposition "the table is by the window" reports what is happening, and therefore it can be either true or false (what is happening may or may not occur). The very logical possibility for the table "to be by the window" cannot really be ruled out because then this circumstance ("to be by the window") would turn out to be logically impossible for the table. If a table can be by the window, if it is logically possible, then the table cannot be conceived apart from this possibility.
But the table, like any other physical thing, is obviously not a simple object due to its many different qualities. Then what object can be considered simple, and what possibilities are implied for it?
2.3. The object's logical form
Without specifying what simple objects are, Wittgenstein gives examples of their "logical form" that predetermines the ways in which objects can occur in facts1: "The possibility of its occurrence in atomic facts is the form of the object" (TLP 2.0141).
"A spatial object must lie in infinite space <...>" (TLP 2.0131). "A speck in a visual field need not be red, but it must have a colour; it has, so to speak, a colour space round it. A tone must have a pitch, the object of the sense of touch a hardness, etc." (TLP 2.0131). "Space, time and colour (colouredness) are forms of objects" (TLP 2.0251).
The shapes of objects put a limit on what is conceivable and expressible in language. For example, propositions like "green is wider than blue", "B-flat is darker than C-sharp", "the face has lost all color" can, of course, be used as metaphors, but their literal sense is missing. We cannot imagine what they would look like (as opposed to situations such as "this rabbit is white", "there is a glass on the table", etc.).
2.4. Internal and external qualities of the object
The list of logical forms mentioned in the Tractatus is obviously incomplete. However, it is clear that every form of an object a priori and invariably contains all the possibilities of its occurrence in a fact. In a sense, all these possibilities are known: "If all objects are given, then thereby are all possible atomic facts also given" (TLP 2.0124). "Objects contain the possibility of all states of affairs" (TLP 2.014).
In other words, a simple object's form presupposes all the possibilities of its occurrence in a fact. These possibilities imply all the possible qualities (and relations) that the object will acquire if it occurs in a fact. Wittgenstein calls the
1 One can learn about the requirements of logical form only "from within" the language. Because some language constructs are meaningless, it is impossible to imagine what it is like that they communicate ("depict").
qualities or relations possible for an object "internal". If they are actualized in reality, they become "external". Since all possible occurrences of the object in a fact are known, all its "internal qualities" (which determine each possibility) are known. If a quality possible for an object becomes real, we get an "atomic fact" in which the object is represented in its "external qualities". Each of the "external qualities" defines a specific material property, or, in other words, an occupied place in the space of logical possibilities: "A spatial object must lie in infinite space. (A point in space is a place for an argument.)" (TLP 2.0131).
Every fact that has taken place is logically possible, but no fact is logically necessary. Because "external qualities" are logically undetermined, logic does not prescribe which of the possible facts "will be the case". Only the general necessity for an object to have some kind of material quality in accordance with the requirements of the "logical space" is logically determined (TLP 2.0131, 3.4, 3.42).
In particular, an extended object1 must necessarily occupy some space (logic "knows" every such possibility and every "internal quality"). But there is no logical necessity for it to occupy this and not some other place. Which specific place will be occupied (which specific possibility will be realized) will manifest in the "external quality". Besides, logic "does not know" at which point in space the "extended" object will be located, what specific density the "object of the sense of touch" will have, which color will be realized for the object "in a visual field" (out of the whole spectrum of logically possible colors), etc. "In order to know an object, I must know not its external but all its internal qualities" (TLP 2.01231).
As evident, all internal qualities of an object are extremely specific (see [11]). Every fraction of any dimension is taken into account in the space of logical possibilities; therefore, any physical quality (any shade of color, any density, etc.) is basically logical (for details, see section 10 below).
The specific possibility of an object's occurrence in one or another atomic fact may never be realized (for every logical space, "I can think2 of this space as empty" [TLP 2.013]). In this respect, logical possibility is precisely possibility and not necessity (that something material will actualize in the world). However, in the very possibility of what can happen there is no longer any arbitrariness or variability: any logical possibility is always already present: "<...> A new possibility cannot subsequently be found" (TLP 2.0123).
So, according to the Tractatus, simple objects must exist and they can occur in facts. Logic presupposes all their "internal qualities", i.e., all possible occurrences of objects in facts, but not "external qualities". Logic does not predetermine which possibilities will be realized.
However, the simple object itself is still shrouded in mystery. It is possible to shed light on it by clarifying the specifics of logical possibility.
3. Key to the "simple object": logical possibility cannot be conceived
According to the Tractatus, any thought is an imaginable picture of what is happening. "To think" means to imagine a concrete picture of a fact: "The logical
1 The capacity to have spatial coordinates is some object's logical form that objects of a different form lack. For example, a sound (tone) has a "pitch" and does not have a spatial position (unlike spatial vibrations of the membrane that accompany the sound).
2 "Logical space", of course, cannot be "thought": only facts can be thought, but metaphorically he speaks here "of this space as empty", i.e., logical space is a region of unrealized logical possibilities.
picture of the facts is the thought" (TLP 3). Accordingly, it is not the possibilities themselves that are imaginable and expressible in propositions, but only their material realizations, i.e., imaginable, material images of facts. In these facts objects have already been determined in their external qualities. The possibilities themselves remain unimaginable, and therefore unthinkable.
In my opinion, this obvious circumstance is often blurred by the unconscious identification of a fact's possibility with a possible fact's material image. When we talk about the possibility of some fact, we usually imagine it in the form of a material picture-image (otherwise we cannot think of anything). There is a risk to mistakenly see in this mental image the logical possibility itself For example, we say "it may be cloudy tomorrow", imagining a colored picture of a cloudy day as an unrealized possibility. The mistake is that such a picture is no longer a pure possibility. This is due to the fact that any image for the senses should be understood as a material fact, as a realized sensual image (even if it was realized only in the imagination).
Accordingly, it is permissible to speak of a "realized" possibility only conventionally. One can just as conventionally say about the "realized" possibility that it "is the case" now. Conventionality is due to the fact that at the level of "realized" possibility which is "the case", one does not think of a possibility itself (which is unthinkable), but only of its material realization, i.e., one thinks not of a fact's possibility, but of a possible material fact, and only in relation to that possible fact it will be true to say that it is "either the case or not the case".
In other words, one should be aware of the unbridgeable gap that lies between the possibility of a fact and a possible fact. Even if the possibility, relatively speaking, is "realized" in the world of material facts, in itself it remains only a possibility, ethereal and unthinkable.
It is clear that the "unbridgeable gap" concerns only the difference in "ways" (modes) of the fact's and its possibility's existence. The other aspect of this gap is their organic correlation: every possibility is always the possibility of a fact (thought, meaning, proposition), while the fact exists only in correlation with its possibility.
Let me explain why I consider paying attention to this topic so important. We really tend to somehow imagine everything we talk about, in one way or another. Therefore, the moment we mention possibilities, imaginative thinking comes into force. For example, the possibility for a table to be by the window is immediately presented as a picture of a table being by the window. However, this imaginary picture is obviously "complex" since it includes many specific properties (color, shape, etc.). Accordingly, any "possibilities" will inevitably be imagined in the form of compound pictures of what is happening, including things familiar to us in all their concreteness and qualitative complexity. In this case, even in our assumptions we will never break through to "simple objects" and their elementary ("atomic") possibilities: in any imagined picture, we will deal only with compound things and with complexes made up of various situations (and not with one specific elementary situation). Therefore, there is a danger of taking a concrete physical thing (a table, a tree, a hare, etc.) for an object, and then unsuccessfully looking for simplicity in it. Another danger lies in the identification of a simple object with an abstract idea of homogeneous physical things (in the spirit of Platonic forms). There are no grounds for that in the Tractatus: all logical possibilities are equal,
since they are all logically independent, therefore "<...> There is no order of things a priori" (TLP 5.634).
If we take into account the unthinkability of logical possibility, it will be much easier to distance ourselves from an imaginable picture of the world and "line up" elementary logical possibilities, each of which is unthinkable, unimaginable and unobservable. Accordingly, it will become clear that a simple object of logical possibilities is also unobservable and unthinkable. Further, it will be shown that the object remains like this at all levels, including in the case of its actual occurrence in material facts. This will help us understand what exactly remains behind the scenes, that is, to understand what a "simple object" is. But first, let us see how we are to conceive logical possibility if it is unthinkable.
4. How to approach unthinkable possibilities
A particular difficulty here is that an unthinkable logical possibility has to be introduced through the conceivable: if it is conceivable for an object to have color, then it is unthinkable that it does not have this possibility. This is how we introduced this concept here, using the material situation as an example: if it is conceivable that a table can be by the window, then it is unthinkable that it does not have this possibility. Wittgenstein himself says in the Tractatus: "<...> If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context" (TLP 2.0121). It is as if he suggests conceiving possibilities themselves, possibilities that the object necessarily has.
This should not mislead: indeed, in order to testify to the possibility of a situation, one must first have this situation in mind (i.e., think, imagine it). Then one must move on to the fact that this situation is only possible (which means that it does not exist yet). It turns out that in order to conceive only the possibility of a situation, one must conceive or imagine its absence, which, of course, is impossible: the absence of a situation does not look like anything. Nevertheless, it is precisely this yet unrealized possibility that must be kept in mind in order to finally understand the concept of a simple object. To do this, one must adhere to such an understanding of the possibility that does not allow its negation, since any conceivable, imaginable (if only in the imagination) fact does allow negation. Even this is not enough: obviously, in the Tractatus Wittgenstein is talking about elementary logical possibilities that can be realized in the form of an object occurring in an atomic fact. This means that in order to proceed to unimaginable, unthinkable elementary possibilities, one must first conceive of an atomic fact and then "imagine" that it has not yet taken place. However, here a new difficulty awaits us: an atomic fact in itself is unimaginable and unthinkable; all conceivable facts are always compound (like our "table" example). Even the most "primitive" fact, it would seem, like an object's having a color, is also always presented as a complex. We are unable to conceive or observe the spot color without imagining the outline of this spot (even if this spot occupies all our visual field, we still refer to the extension of the visual field). Therefore, even at the level of pure possibility all conceivable facts will refer us to a complex of logical possibilities and not to a single possibility.
It turns out that a simple object is hidden in two "kinds of unthinkability" simultaneously: in addition to the unthinkability of the logical possibility itself, the simple object is hidden by the very elementarity of the logical possibility which
does not allow one to start from the atomic fact as its material correlate and move from a conceivable situation to its unthinkable possibility.
Apparently, it is impossible to conceive the way leading to the simple object. This way can only be considered indirectly, by analogy with what we are able to conceive. That is why Wittgenstein spoke about how all propositions of the Tractatus are meaningless, calling them the sketches of a "weak draughtsman": in order to show how propositions of a language can be meaningful, it is necessary to show the unthinkable logical background of any thought. The language does not have any legitimate means to achieve that task. All "normal" propositions of the language depict something conceivable, visible, tangible, and therefore compound.
4.1. On terminology in the Tractatus: some examples
Wittgenstein does not explicitly state the unthinkability of logical possibilities, nor does he say that no natural language proposition is an elementary proposition and no observable thing is a simple object. Besides, many phrases of the Tractatus can be misleading, for example: "...Logic treats of every possibility, and all possibilities are its facts" (TLP 2.0121). This part apparently says that all possible facts are already implied in logic. However, the same part does not preclude a reading in which logical possibilities themselves are understood as facts. The inaccuracy of such a reading is clearly evidenced by the existence of the part that says logical possibility cannot be denied (TLP 2.0121), which means that it cannot be a fact that may not be the case (TLP 1.21) (the last two aspects figure as the "essence" of the Tractatus, and, apparently, we should be guided by them).
Here is another example of a "dangerous" aphorism: "The substance of the world can only determine a form and not any material properties. For these are represented by the propositions formed by the configuration of the objects" (TLP 2.0231). This thesis explains well the relationship between a logical possibility and a material fact, but even here it must be taken into account that not a single sentence of a natural language "depicts" separate "configurations of objects": each configuration is an atomic fact that can only be described by an elementary proposition, the image of which is inaccessible to us: "not a single proposition of ordinary language seems to be elementary" [19. P. 157].
The following remark should also be approached with caution: " 'An atomic fact is thinkable' means: we can imagine it" (TLP 3.001). This remark emphasizes that every fact is a thinkable fact, and every thought necessarily presupposes an articulated image of the fact. Nevertheless, atomic facts cannot be literally considered thinkable. Since their images are given in thought only as parts of compounds, they cannot be "observed" separately.
Similar difficulties are associated with most of the Tractatus' theses, the discussion of which is a subject for another research.
5. What is a simple object? ("form of dependence" and "form of independence" of a simple object)
Since the object of pure possibility does not yet possess any actual quality, it can apparently be considered "simple", i.e., devoid of qualities. However, does the very possibility of having some quality not provide complexity to an object? The answer lies in the aphorisms that distinguish between the "form of dependence" and the "form of independence" of a simple object:
"The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connexion with the atomic fact, a form of dependence. <...>" (TLP 2.0122)
"The thing" here apparently means the same as "simple object". Its "dependence" consists in the fact that it does not exist "separately" from its logical possibilities: if something is possible for an object, it cannot be "imagined" that it does not have such a possibility. At the same time, an object (thing) is not bound to any specific possibilities. It can have any color, any density, etc., and this is a "form of its independence"1.
Of course, if we consider logical possibilities as images held in the imagination, then objects will always be endowed with some qualities, i.e., they will inevitably have some form, some color, etc. In this case, it will be extremely difficult to understand how an object can be simple. If we discard conceivable images, then we can turn to an object that does not yet have any actual qualities. The next step is to understand that no possible quality is logically necessary for the object. If the object had logically necessary qualities, they would immediately make it compound, since it could occur in facts only together with these qualities. However, the object does not have any logically necessary qualities, it can both "occur" and "not occur" in any material fact possible for the object. It follows that the object of pure logical possibilities is indeed "simple".
Obviously, the object of logical possibilities itself is neither observable nor thinkable, just as logical possibilities themselves. Now I want to show that it will remain the same in the case of its actual occurrence in facts. Here again we must note that no actual quality of an observed or imagined object is necessary for it.
One can object that, observing, for example, a tree, we observe an object with its necessary qualities. Such an objection implies empirical, not logical connections; logically not a single thinkable quality of any object is necessary. Any fact (for example, a tree's having roots, foliage, etc.) may "not be the case", any proposition about qualities (or relations) can be negated. This means that not only at the level of unthinkable possibilities, but also at the level of actual facts the object does not have any necessary qualities; for it there is "nothing what it's like". But "nothing what it's like" of an object can be observed due to the same logical form: "A speck in a visual field <...> must have a colour <...> A tone must have a pitch, the object of the sense of touch a hardness, etc. (TLP 2.0131)". Everyone can see this from their own experience. There is, of course, logical necessity in the "must haves" listed, but this necessity is devoid of concreteness, and only a concrete quality can be observed. Since no specific quality is logically necessary for an object, any specific quality is extrinsic to it. That is why the object remains simple in the facts that are the case: not a single observable quality or relation is its own, the object itself is "nothing what it's like" (colorless, ethereal, unextended, timeless, etc.).
Lewis Carroll spoke of similar things in his book The Logic Game: "People have asked the question 'Can a Thing exist without any Attributes belonging to it?' It is a very puzzling question, and I'm not going to try to answer it: let us turn up our noses, and treat it with contemptuous silence, as if it really wasn't worth
1 The "form of dependence" and the "form of independence" are the two sides of an object's logical possibility to occur in facts; both forms characterize precisely the possibility, and not reality. Both forms, therefore, are related to the internal and not external (material, realized) qualities of the object.
noticing" [20. P. 2]. Thanks to Wittgenstein, we can now stop turning up our noses and provide to the "puzzling question" a perfectly accurate (albeit "meaningless") answer: in the material world, any object will inevitably have some attributes (the material world consists of facts), but none of these attributes will be necessary for the object; any object can have any attributes possible for it.
Carroll's next question is even closer to our topic: "But, if they put it the other way, and ask 'Can an Attribute exist without any Thing for it to belong to?', we may say at once 'No: no more than a Baby could go a railway-journey with no one to take care of it!' You never saw 'beautiful' floating about in the air, or littered about on the floor, without any Thing to BE beautiful, now did you?" [20. P. 2]. Of course, Wittgenstein in the Tractatus offers more convincing arguments, where the object turns out to the thing that provides certainty to the world (TLP 2.021, 20211, 2.0212) and acts as a condition for the proposition's truth value, making every proposition "articulate" (TLP 3.141, 3.251). In addition, Wittgenstein shows that the object of any quality or relation is "simple": only concerning a simple object can any thinkable qualities or relations be affirmed or denied. Carroll's answer is also quite convincing: a property cannot "float" without its object. If there are any properties and relations, then there must be objects of these properties and relations.
Of course, it does not follow from what has been said that a simple object is hidden in things as an invisible "spirit" of these things. On the contrary, a simple object turns out to be indifferent to all the properties that form things known to us. There is nothing in the simple object that would induce it to realize these and not other of its possibilities to occur in facts. Apparently, there is no point in discussing how it exists and whether it exists at all. The parts of the Tractatus dealing with the existing object should obviously be understood as metaphors. Wittgenstein was interested not in the ontological, but exclusively in the logical status of simple objects. All that can be said is that logic organizes language in this way, "the language which I understand" (TLP 5.62). For the same reason, one should not try to "count" objects, i.e., asking the question "how many simple objects are there in a compound called a tree?". Obviously, simple objects do not pile up in a logical structure like bricks at a construction site: rather, one should speak of an object as an inevitable effect of the way a fact or a proposition is formed in logic1. It is clear that there is only one such way: the occurrence of an object in a fact, and this way necessarily implies an object (thing) of any qualities and relations - approximately in the same way as addition implies added terms. After all, we do not ask how many added terms (concepts, not numbers) exist in the world. Of course, one and the same effect can manifest itself many times over (in each case when an object occurs in a fact), and in this sense we can speak of an "expanding set" of objects, by analogy with how the set of added terms expands with each new operation of addition. The same analogy explains the reference to objects in the plural in the Tractatus (and in this paper).
However, the Tractatus also contains statements that seem to indicate there is a difference in the logical form of objects, and hence in objects themselves: "If I know an object, then I also know all the possibilities of its occurrence in atomic facts" (TLP 2.0123). Should we not, after all, in this case, recognize the diversity of
1 An object's occurrence in a fact is isomorphic to a name's occurrence in a proposition.
objects in the logical structure? Most likely not, for this aphorism only emphasizes the already stated (earlier in the Tractatus) the presence of all the possibilities for an object to occur in a fact, and their presence all at once. "To know all objects" means to know all these possibilities. The diversity of these possibilities is determined by the difference in "logical spaces" (color, length, density, etc.), while the object itself relates to its logical form (i.e., to all logical possibilities to occur in a fact) as simple. Therefore, it does not make sense to look for differences in objects themselves.
Now I propose the following definition of a simple object. A simple object is an unobservable and unthinkable object of any thinkable quality or relation. This object is simple, since any thinkable (concrete) quality or relation is not logically necessary for it and is not its own quality.
6. The object in coordination with observable things and events
Now it is time to harmonize the logical structure with ordinary language and the familiar picture of the world. For example, imagine a specific apple and try to identify its logical form. As an object "in a visual field", the apple must have a color; as a "spatial object", it must have some form; as an "object of the sense of touch", some density, etc. Let this apple be red and round (we will not specify its other qualities).
Now, pointing at this apple, let us ask ourselves: what is it? What exactly is red, round, etc.? Apparently, this, of course, is an apple. The relative stability of the apple's qualities makes it possible to reliably distinguish it from other objects (although sometimes there is a risk of confusing an apple with similar objects, for example, with a quince). When we describe this apple, we proceed from the fact that we already know what an apple is in general, and in relation to this apple we only specify its specific qualities (for example, this apple is red, although apples can also be yellow or green).
But what exactly do we mean by the apple itself? Whose qualities do we specify? What is the apple itself, as a "thing" known to us?
If you look closely, it turns out that by using the name "apple" we are able to indicate only the properties and relations that characterize the apple as "this" object. And nothing else is given to us. When being observed, the object of these properties and relations does not manifest itself in any way, and only the logical structure does not allow us to doubt that this object exists. And this is so not only by virtue of the proof that Wittgenstein provides in his Tractatus. We are really unable to imagine glossy, white or heavy, without always imagining an object having these properties. It is the object that makes any material image "articulate" (TLP 3.251) allowing us to affirm or deny any thinkable qualities (or relations): the object is red, but may not be red, the object grows on a branch, but may not grow on a branch, and the same for all other qualities that characterize an apple. It is clear that if all the qualities of the apple are negated, nothing will remain of the apple, but until the very last negation, the object will appear in the proposition, and it will obviously be simple. Of course, this object will not be given either in observation or thought, but it will conscientiously perform its function so long as we affirm or negate any of its qualities or relations. Its qualities and relations and not those of the apple. We only thought that we were discussing the apple's qualities and not those of this mysterious object. Our ability to negate any
thinkable quality refers us precisely to a simple object that has no name in natural language. Only the names for compound things exist in our language, and we have no choice but to use them to designate objects with qualities and relations.
7. Object in coordination with natural language names
And yet, where does the word "apple" come from? The Tractatus, as usual, does not contain a direct answer to such questions, but it contains a suggestive remark (see TLP 3.342). It says that this word, like any other, is an "arbitrary" naming of a distinct complex of atomic facts, i.e., a complex of certain properties and relations. Since any fact may or may not be the case, any complex could not exist, but some complexes are stable, and therefore we are accustomed to think of them as "things" and come up with meaningful names for them (see TLP 5.471). Obviously, all physical "things" (apples, cats, trees, tables), as well as their names in natural language, are complexes, and complexes themselves are formed due to the multitude of arbitrary occurrences of objects in specific configurations (facts). Each specific configuration contains "zero", unthinkable, uncolored, unextended, immaterial "points" - simple objects. Each configuration is a realization of simplest logical possibilities for a simple object in the "physical world". The whole world consists of such simple situations. Stable complexes of some situations figure in the world as "things" named in the language.
8. Atomic facts as images of simple propositions
It is clear that in natural observation we do not encounter either simple objects or individual "acts" of their realization. In practice, we deal only with complexes, with "things" in their established qualities and relations with other things. And yet, logically, every thing is reduced exhaustively to atomic facts, and every description of a thing is reduced to simple propositions as their images.
Of course, this reduction is not a natural language practice: "simple images", like simple objects, are not distinguishable either in observation or in thought. And yet, simple images of "realized" logical possibilities can, conditionally, be singled out from the complex that accompanies their existence.
For example, the image of a "cat on a rug" can, conditionally, be considered simple if we consider that this is an image of only one atomic fact, only one realized logical possibility, consisting in a spatial configuration of primordially simple and nameless objects lacking any definition. But this simple image merges in our imagination with many other images accompanying it. This is how complex "things" familiar to us emerge: a cat and a rug. The material image corresponding to the elementary proposition appears for us in unity with other material images (observed and remembered). This unity comes from the relative stability of some compounds so-named. This stability prompts us to imply additional images that are not directly generated by this simple proposition. A compound image covers an indefinite set of observable and recalled qualities of a cat and a rug: it is difficult to determine which qualities we include in the complex and which we do not. Many qualities of compound things that we know may not be taken into account (for example, we may not think the cat has a skeleton), but it is quite obvious that the image of each simple proposition is combined with a number of other, implied images. That image includes something more than, for example, only the spatial arrangement of objects.
A complex, compound image seems to us to be simple. We are not aware that the additional qualities of this cat and this rug (shape, color, density) are determined by other realized atomic facts. These latter are other images that are described by other propositions which are implied propositions.
For logic, it is completely indifferent what kind of compound things we are talking about: a proposition can report the configuration of a given cat and a given rug (in their specific physical qualities), the configuration of a rug, floor and ceiling in this room, or, say, the configuration of the cat's brain and its circulatory system, etc. In all cases, the names denote some stable compounds in a proposition, but each simple proposition reports only one realized possibility (all the rest configurations are only implied).
Simple (i.e., those not containing logical conjunctions) natural language propositions "stuff' the names we are used to with all the "off-screen" configurations. By concentrating on one specific quality, propositions "pull together" all the implied qualities into one whole, "into a unit" [21. P. 71].
This is how the illusion arises that named compounds of atomic facts (as physical realizations of incorporeal objects) have integrity. The illusion leads to the erroneous belief that a simple proposition can be understood from itself
This illusion is called a "universal" in philosophy. The same illusion prompts us to see things around us, not facts, but now it should become clear that logically (i.e., by absolute necessity) things are nothing but relatively stable compounds of elementary facts that are contingent by their logical nature.
9. Can a hare be different?
The stability of linguistically named complexes is due to observation or invention. If we so desire, we ourselves can create stable complexes, invent unicorns, dragons, centaurs, etc. We can also literally produce various complexes (furniture, clothes, technical devices, etc.).
In logic itself, there is nothing that makes complexes exist necessarily:
5.634. Everything we see could also be otherwise.
Everything we can describe at all could also be otherwise. There is no order of things a priori.
So, everything thinkable, observable, expressible in a language can be different. Every quality of a material (including imaginary) thing, insofar as it is conceivable, turns out to be accidental and contingent.
In connection with the last statement, it is worth thinking again about the so-called "essential" qualities of things: is it possible, for example, to think of a cubic and blue hare? Would a hare remain a hare?
It is clear that an object's simplicity already excludes all the necessary qualities of things, and yet this question can be confusing.
In order to understand this, it is necessary to clarify once again exactly how complex "things" ("objects") are conceived.
From the logical point of view, each concrete object is a contingent complex of atomic facts arbitrarily named by some name. The complex called "hare" was formed in the same way as any other complex: in one atomic fact, a simple object occurred in the space of color (as having such and such a color), in another it occurred in the space of density, and so on. Since we repeatedly encountered
complexes similar to each other, the name "hare" was fixed in the language and received its status of a "common" name.
Since contingent complex "things" do not have any necessary qualities, at any moment they can be of any form: become round, cubic, hard, soft, blue, red, etc.
Nevertheless, hares, like all other objects designated in the language, cannot be anything at all if these names have already been used (albeit arbitrarily) to refer to quite definite complexes of atomic facts. It is clear that if a certain complex is already conceived in a definite form, it cannot simultaneously be conceived differently, in a different form. Instead of such complexes, there can of course appear other complexes, but if we already mean this complex, then it cannot be meant as another complex.
Of course, we can imagine a winged blue cubic "creature", but why on earth would we call it a hare? The currently existing language conventions do not provide any basis for this (although it cannot be ruled out in the future). Anyway, the question comes down to what qualities or relations we mean when we use the name "hare". If now by "hare" we mean something oblong, white or gray, then a blue cubic being would not be a hare, in exactly the same sense as something oblong is not cubic, and something white or gray is not blue.
In itself, the question whether the hare will be preserved after a radical modification of its material properties simply does not make sense for logic. For logic, there is no hare and never has been. There have been and are only complexes of possible atomic facts. The fact that some complexes are regularly reproduced is of no interest to logic, as well as the fact that we have arbitrarily designated a certain stable, regularly renewed material complex by the name "hare".
Thus, the famous philosophical problem of essence and substance gets incredibly more simple and appears in the form of a question whether it is possible to think of something white as something blue, of a one-meter length as a two-meter length, etc. Of course, this is impossible. Moreover, it is logically impossible, and everything that concerns the "essence" of a hare and all other objects known to us is connected to this impossibility.
In this and subsequent discussion, I am guided by TLP 6.3751 and by Wittgenstein's idea in Some Remarks on Logical Form which limited the Tractatus statement about the compatibility of all elementary propositions: "The mutual exclusion of unanalyzable statements of degree contradicts an opinion which was published by me several years ago and which necessitated that atomic propositions could not exclude one another" [22. P. 168]. Ian Proops also writes about the need to mathematically differentiate qualities: "Wittgenstein concludes that the impossibility of something's having both exactly one and exactly two degrees of brightness emerges as an irreducibly mathematical impossibility" [11].
10. Logically impossible configurations
Since every thing is a complex of logically possible object configurations (atomic facts), any configuration realizes only what is logically possible. Since names (nominal forms) of natural language are tied to certain complexes, and since verbs and adjectives report a certain configuration of specific complexes, some configurations turn out to be logically impossible.
In his Private Notebooks: 1914-1916, Wittgenstein remarks that it is impossible to imagine a clock sitting on a table: "Unthinkable!" [21. P. 70], but not
because the clock cannot assume any position of its own accord: the point, apparently, is that it does not have corresponding "external", physical qualities. There are no "movable joints" that allow the clock to assume a sitting position.
Another example from the Notebooks is that it is impossible to "lean the ball against the wall"namely, this is precisely logically impossible. Due to its round shape, the ball cannot be supported by a vertical plane. It cannot be leaned against a support without which it would fall.
For the same reasons that blue cannot be white, round cannot be cubic, etc., a ball cannot be leaned against a wall, and a clock cannot sit on a table.
Conclusion
I hope I succeeded in showing how the object (or thing) of any qualities and relations can remain simple. For this, it was necessary to independently affirm the inconceivability and unimaginability of logical possibilities: at the level of conceivable, material images, any object always has some qualities that mask its simplicity. However, if we ignore material images, then the object's simplicity becomes obvious: at the level of pure logical possibilities, the object still does not have any actual qualities; none of its possible qualities have taken place yet. Accordingly, the object does not have any qualities "of its own", i.e., logically necessary qualities inherent in the object. Therefore, in the material world, in the facts that have taken place, the object will remain simple because it may not have any of the qualities or relations acquired by it; accordingly, any proposition about any fact admits its negation.
The stability of named complexes in the language prompts us to consider certain qualities as necessary, essential, proper qualities of named things (tables, trees, hares, etc.). However, the Tractatus is not about empirical laws, but about logical requirements; logically speaking, no conceivable quality is necessary, and therefore the object of any conceivable quality is in itself "simple". Of course, such an object cannot be given in observation or representation, and yet there is no need to assume it has a special metaphysical status: it is enough to keep it in mind as a necessary element of our language's logic, since any quality or relation must have its own object.
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Information about the author:
Danko S.V. - Cand. Sci. (Philosophy), docent, independent researcher (Moscow, Russian Federation). E-mail: danko.sofia@gmail.com
The author declares no conflicts of interests.
Сведения об авторе:
Данько С.В. - кандидат философских наук, доцент, независимый исследователь (Москва, Россия). E-mail: danko.sofia@gmail.com
Автор заявляет об отсутствии конфликта интересов.
The article was submitted 10.06.2023; approved after reviewing 12.07.23; accepted for publication 18.08.2023 Статья поступила в редакцию 10.06.2023; одобрена после рецензирования 12.07.23; принята к публикации 18.08.2023
