The Tractatus and the Problem of Universals
The Tractatus and the Problem of Universals


The question we wish to raise here is the following: what are the objects of the Tractatus ? This problem is old, and received a wide variety of solutions. But, there is no consensus about it. The problem car reformulated as “What is the composition of an elementary proposition?”. Does it contain only particulars or particulars and universal or only universal? Unfortunately, Wittgenstein said that this question cannot be answered a priori or by logical investigation. He thought that we could discover the composition of elementary propositions by the philosophy of psychology which he seems to conceive as an a posteriori investigation. As long as we do logic, we cannot answer the question “How many are there in the world?” because it is a matter of fact. Thus, the problem of universal does not seem to be a problem for armchair philosophers, contrary to logic. So, it seems that there is nothing to say about it. Nevertheless, we should distinguish two questions. 1) Is there some universal? 2) What universals exist? Do answers to these questions depend on an a posteriori investigation? An a posteriori realist as D.Armstrong argue for the existence of universals and against nominalisms on a priori grounds, even if he thinks that the second of our question can only be answered on the basis of total science. So our enterprise may not be hopeless. Our aim here will be to consider two simple arguments in favour of a realist interpretation of the Tractatus.

Table of contents

    A) The problem of objects

    What we called the problem of objects covers different questions. We can distinguish the metaphysical problem and the epistemological one. The metaphysical one is concerned with 1) the existence of universals and particulars and 2) with the nature of those things. The epistemological one is “Have we some sort of knowledge of objects?” and, if yes, “What kind of knowledge?”. Here we will be interested with the problem of the existence of universals.

    The problem of objects received numerous answers. Without details, we can give an idea of the different points of view. The important point is that there is no consensus about the community. The difficulty with that problem is that there is no textual evidence to support one of the possible solutions. We can briefly expose some of the existing solutions. From our two principal questions about the objects, we can classify the authors. 1) The Epistemological question: How can we know the objects? 2) The Ontological question: What is their ontological status?

    Those who think that we can answer to the two questions.

    Jaakko and Meril Hintikka (1989) argued that the tractatian’s objects are russellian’s disguised objects1 except the logical one. So objects can be known by acquaintance and ontologically they are particulars and universals.

    Those who answers the ontological question and deny we can answer the epistemological one.

    Peter Hacker (1972) affirmed that the objects are universals and we cannot say that they are objects of acquaintance.

    Elizabeth Anscombe and Irving Copi, think that the objects are particulars Note and we cannot say that they are objects of acquaintance.

    Those who think we can answer neither the ontological nor the epistemological question.

    David Pears (1988), Anthony Kenny (1973) think that we cannot answer these questions because Wittgenstein does not know. They consider this as a lack.

    Sebastian Gandon (2003) asserts that Wittgenstein does not know but that is not a lack. He believes the necessity to answer the questions is a delusion2.

    B) First argument

    Our first argument is ground on the distinction between a proposition and a name. We will not explain in details what exactly Wittgenstein’s conception of these two things is. We need not to do that. Nevertheless, we should say that by name we mean real name, that is a complete symbol and not a description or a logical fiction. A proposition is distinguished from a name by being in a relation of denotation with the world, whereas a name means. What is the difference? When some sign which can denote something do not actually refer to a fact it does not loose its sense. Consider the following example: Jones says that “Brandy is a nice cat”. In that case, even if Brandy is not nice, the proposition Jones pronounced is perfectly intelligible or has a sense. But Wittgenstein thinks that a name is not mere noises if and only if a name has a meaning, or is related to an object in reality. It is some kind of rigid designator. It is difficult to illustrate this conception with some example for nobody, even Wittgenstein, has found real name. In fact, the only plausible candidate I can see is “this”. A real name may refer to an object directly experienced. If this is true, this means that Wittgenstein endorses a russellian epistemology as Jaako and Meril Hintikka affirmed it. But we do not want to discuss the very controversial point here. The point here is that Wittgenstein needs to make this distinction in order to differentiate the symbolic behaviour of a proposition from the one of a constituent. A proposition is bipolar, which means that a proposition necessarily can be true or false otherwise it is just nonsense. In other words, there is an internal relation between a proposition and its truth-conditions. And a name needs to be related to an object in order to safe the sense of a proposition.

    Another crucial distinction between a real name and a proposition is that a name is a simple symbol which means a simple object, whereas a proposition is a complex symbol which denotes a complex of objects (state of affairs or facts).

    Now, suppose that Wittgenstein’s ontology is nominalist, that is only concrete particulars exist. We said that a proposition is necessarily a complex otherwise the essential feature of propositions could not be bipolarity. So, at least, a proposition has two constituents. That is, according to the nominalist interpretation, a proposition is necessarily composed of two concrete particulars. But this is very doubtful. How could there be two concrete particulars in “This is red” or “Jones is nice” or “this painting is beautiful”. It seems very counterintuitive. And suppose that a proposition is composed of only one constituent. In that case, we cannot say that for the simplest proposition, there is a difference between a proposition and a name. But the distinction between a proposition and a name is a crucial one in the tractarian’s system. In fact, When Wittgenstein criticized Frege and Russell, he precisely insisted on this point.

    C) Second argument

    Our second argument focuses on the notion of concrete particulars and the notion of property. Each object, Wittgenstein says, has internal and external properties. There is no doubt that Wittgenstein thought that there are concrete particulars or individuals. Why?

    In asking whether there is individuals or concrete particulars, we do not mean “Are concrete particulars reducible to universals?”. If there are only universals, no concrete particulars can be subject of a proposition. So the only propositions which exist are proposition as “Blueness is a colour” or “Triangularity is a shape” in which no concrete particular is referred to. Moreover, we should note that if it is true, Wittgenstein’s conception of universals is Platonist because these universal exist independently of any concrete instance. In an Aristotelian conception, the existence of universal is dependent upon the existence of their instances. If there are only platonic universals, the only propositions we could make are necessary: “Triangularity is necessarily a shape”, “Blueness is necessarily a colour”, etc. Platonic universals could be constituents in contingent propositions such as “I thought to Blueness this morning”. But such propositions suppose the existence of concrete particulars (me, this morning, etc.) But it is evident that Wittgenstein’s conception of propositions is not compatible with this. Every proposition with a sense is contingent. Necessary propositions are logical and empty of sense, or metaphysical and without sense. For that reason, we believe that Wittgenstein’s conception of language and the world implies the existence of concrete particulars. One could reply that in a bundle theory of particulars, the only things that exist are universals. A proposition is for example “Blueness is co-present with Squareness”. And this is a purely contingent proposition for Blueness could be co-present with Roundness. But in that analysis, you said that concrete particulars are reducible to co-instantiated universals.

    There are three conceptions of concrete particulars: 1) the bundle theory, 2) the substratum theory, and 3) the substance theory. What do they say? According to the Substratum theory, “a concrete particular is a whole made up of the various properties we associate with the particular together with an underlying subject or substratum that has an identity independent of the properties with which it found – a bare particular.3” According to the Bundle theory “There are no underlying substrata; ordinary particulars are constituted exclusively by the properties associated with them, there are “bundles” or “clusters” of those properties.”4 These two theory share the common assumption that a concrete familiar particular (like a chair) is not a basic entity but is a whole made up of more basic constituents. There is a third theory: the substance theory. This theory takes the concrete particulars to be ontologically basic entities. There are not reducible to properties or to a bare substratum. Another point suggests a crucial difference between these three theories: the question of identity. The bundle theory is an essentialist one. This means that each property is essential. If a bundle looses one of its properties, it becomes another thing. The substratum theory is anti-essentialist because the very identity of the particular is assumed by the bare substratum, so each property is contingent. The identity of the particular does not depend upon its properties. In a substance theory, a particular has essential and inessential properties. Essential properties are generally thought as Kinds (Universal). A Kind term show what is the particular. For example, if you ask “What is Boby?”, the answer is “Boby is a man.”. But there are other properties which permit us to answer the question “How is it?”. For example: “Boby is beautiful”. The substance theory is generally understood as a realist one, which commits us to the existence of universal. Kinds are typically universals. The other theories are compatible with a trope-theory. And typically, an austere nominalist thinks that we cannot investigate the ontological structure of concrete particulars5. We do not want to discuss the merits or difficulties of each theory here. Now, come back to Wittgenstein. We just saw that the substance theory distinguish the following questions: 1) What is it?; 2) How is it?. Wittgenstein clearly distinguish these one too. For example take the remark 3.221. And in his ontology, he insists on the fact that objects have internal and external properties. The internals properties are such that it is unthinkable that the object do not possess them. And external properties can be possessed or not by the objects. The last thing is a matter of fact. In fact, Wittgenstein seems to avoid problems met by the Bradley and Russell in their account of relations. According to Bradley, each property of a particular is inherent to it or internally related to it. Each property is essential to the particular. According to Russell, there is no internal relation. Then, each property is externally related to a particular. That the particular possesses a property is always a matter of fact. There is no essential property. Bradley and Russell seem to be committed respectively to a bundle theory and a Substratum theory. So he seems to hold a substance theory of concrete particulars (Except for the subject of thoughts for which he seems to maintain a substratum theory.)

    So we have presented two arguments in support of a realist interpretation of the Tractatus. Obviously, many things should be said to reply objections or to clear up our discussion. But we lack place. So, the discussion, I hope, will serve to answer questions and perplexities.


    1. ARMSTRONG David, Nominalism and realism, Universal and scientific realism, volume 1 and 2, Cambridge University Press, Melbourne, 1978.
    2. AUNE Brian, Metaphysics The Elements, University of Minnesota Press, Minneapolis, London, 1985.
    3. HINTIKKA, Jaako and Méril, Investigating Wittgenstein, 1989, New York, Blackwell.
    4. LOUX Michael J, Metaphysics a contemporary introduction, Third edition, Routledge, New York, 2006.
    5. LOWE Jonhatan E, The possibility of metaphysics, Oxford University Press, New York, 1998.
    6. Mc DONALD Cynthia, The variety of Things, foundations of contemporary metaphysics, Routledge, Victoria, 2005
    7. Van INWAGEN Peter and ZIMMERMAN Dean (edition), The Oxford Handbook of Metaphysics, Oxford University Press, New York, 2003.
    8. WITTGENSTEIN Ludwig, Tractatus logico philosophicus, 1961, English Translation by Pears David and Mc Guinness Brian, London, Routledge.
    Russell’s thought during the two first decades of the twentieth century changed a lot. The expression “russellian’s objects” refers to his posthumous book written in 1913 Theory of knowledge.
    The supporters of the New Wittgenstein did not give any direct interpretation of the problem. However, we can consider, even if he probably disagrees with this, that Sebastian Gandon’s book is a speech for the defence of the Diamond-Conant’s point of view.
    Loux, 2006, 84.
    Loux 2006, p 106-7 and Chapter 2.
    Eric Lemaire. Date: XML TEI markup by WAB (Rune J. Falch, Heinz W. Krüger, Alois Pichler, Deirdre C.P. Smith) 2011-13. Last change 18.12.2013.
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