Underdetermination

In this essay, I describe, using examples, what I call intrinsic and non-intrinsic underdetermination. I distinguish between underdetermination as it is commonly used in philosophy of science, with underdetermination in a broader sense, which encompasses issues in the philosophy of language, philosophy of art, and philosophy of perception. Understood in this broader sense, I show how the notion of underdetermination serves to illuminate philosophical debates and philosophical intuitions.

Underdetermination is the phenomenon by which there are at least two different or alternative theories that fit the same data set. This is exemplified by the classic example in mathematics, where we are able to draw two very different lines that intersect on all the data points in a graph. For ease of discussion, we will stick to only two competing theories. In theory, there can be any number of possible theories fitting the same data set.

The notion of underdetermination is well discussed in the philosophy of science. Specifically, the notion of underdetermination has been couched and countlessly discussed in the context of the Duhem-Quine thesis, according to which that it is impossible to test a scientific hypothesis in isolation, because an empirical test of the hypothesis requires one or more background assumptions. Given a scientific hypothesis H, H cannot be confirmed as true or false independently of background assumptions and context. For H is true or false only within the context of a theory. As such, the evidence E is said to confirm H whenever E verifies the predictions of H, given certain background assumptions. In this essay, I will not be discussing this definition of underdetermination.

My starting point for discussion begins with considering that, in the literature on underdetermination as related to scientific theories, underdetermination occurs wherever there are empirically equivalent theories. A famous example is Newton’s cosmology, where the same empirical predictions are made whether or not it is assumed that the universe is at rest, or that the universe is moving at a constant velocity in a particular direction. Since the empirical predictions are the same, we cannot decide between the theories based on empirical evidence.

Roughly, underdetermination of scientific theories occurs whenever the evidence or data that is used to support the theory T1 can also support the theory T2. If evidence appears that supports one theory rather than another, it does not entail that the theory is the true one. Instead, the other theory may be supported as true by modification of its background assumptions. The consequence of underdetermination in science is that it becomes difficult to tell if there are true scientific claims and theories, and scientific realism is threatened.

There has not been, however, in the literature concerning underdetermination, a view that broadly connects the notion of underdetermination to philosophical problems in many central areas of philosophy, such as the philosophy of art, the philosophy of perception, the philosophy of knowledge, and the philosophy of language. Yet, if this could be done, we would see the notion of underdetermination as central to philosophical study and to philosophical knowledge, something that has not been the case before.

Philosophical underdetermination

One might ask, why are core philosophical problems, problems? And a description of what is encountered when facing these philosophical problems is that of underdetermination of theory by data. Theories are said to be underdetermined when there are plausible multiple theories that fit the facts. Is the categorisation of our experience to be concluded as being a dreaming state, or a reality? Both theories seem equally valid, and as such, it is underdetermined as to whether or not all experience is a dream or reality. Once we grasp this fact, we manage all at once to pin down the very problem that haunts us and the cause of the existential philosophical anxiety that accompanies the problem.

Taking theory in a broad sense to encompass perspective and interpretation, our theories about the world are underdetermined by the facts that we collect about the things in the world, or else by statements which are underspecified or ambiguous. The object, for example, a box of Brillo soap, gives no clue as to whether it is an everyday object or a masterpiece illustration on a sculpture and hence a work of art. The ambiguous statement, “I am going to the bank”, for instance, fails to specify whether or not I am going to the river bank, or to the money bank.

The drawing of connections between the notion of underdetermination and the various philosophical problems makes the notion of underdetermination not simply an explanatory notion with respect to scientific theories, but a philosophical notion that bridges philosophical fields of inquiry. Hence, philosophical underdetermination. The leading idea is that underdetermination is not simply a cognitive or intellectual phenomenon, but is one that is phenomenological or that can be experienced. The experience of underdetermination is either existential in character or situated as part of a truth-seeking enterprise.

Philosophical underdetermination is not the same as the philosophy of underdetermination, or the underdetermination of philosophical theories. The philosophy of underdetermination would, in an analytic philosophical approach, aim towards the explication and analysis of the concept of underdetermination. The underdetermination of philosophical theories, is merely one example, and as such, a subset of philosophical underdetermination.

Non-intrinsic underdetermination

In the case of knowledge, underdetermination applies to theories, concepts, statements, ideas, and so on. In typical cases of underdetermination, we do not know which of the theories is true, unless we have further background information and context information. Call this non-intrinsic underdetermination. Once we have more information, we will be able to assess which of the theories better fits the context and background and is in this sense, the true theory. On this view, the less abstract a theory, concept, statement or idea is, the less underdetermined it will be. The process of making a theory, concept, statement or idea less abstract seems to describe the truth-seeking enterprise of research.

I will describe three examples of non-intrinsic underdetermination.

The first example is found in the philosophy of language. What is the meaning of “bank”? Does it refer to a river bank, or does it refer to a bank that supports the monetary savings of its patrons? Similarly, what is the meaning of ‘chair’? Does it refer to a piece of furniture, or a position in the hierarchy of an organisation? As a word by itself, understanding of the word is underdetermined. It alerts us to Frege’s contention that it is only within the context of a sentence that an individual word has meaning.

The second example is found in the philosophy of art. What is the difference between an object of art and an everyday object? This question has been famously posed by the philosopher Arthur Danto, in the light of contemporary and conceptual Western art. What differentiates a can of Campbell’s soup from its similar-looking counterpart in a museum? Another more general and related question would be, what makes something a work of art? There is usually agreement that something is a work of art, but what causes this agreement? Is there something objective in the arrangement of the artwork that causes some kind of aesthetic experience in each of us? Or is it entirely a subjective interpretation, hence that only some people will evaluate and understand something as a work of art?

One reply would be to say that there is nothing in the materials itself that makes something a piece of art. Rather, the spectator gives an interpretation to the materials, conceiving of something as a work of art. Using the notion of underdetermination, on the other hand, it becomes apparent that our understanding of the object as itself is neither everyday object or art sculpture until we gain further information about the object. Is it placed in a museum? Has it been constructed out of plain materials with the intention of the artist to making a sculpture? Or was it manufactured in a factory with the purpose of providing soup?

The third example is found in the philosophy of perception. How do we know whether a certain perception is a normal perception or a hallucination? In Shakespeare’s Macbeth, Macbeth saw a dagger before him, and was struggling to know whether it was hallucination or actual perception. The common response to this problem is to assert either that there is no genuine subjective difference between hallucinations and actual perceptions, or else to argue that there is an epistemological and possibly metaphysical difference between the two (disjunctivism about perception). Yet this seems to neglect Wittgenstein’s insight that we can never get out of ourselves to look and to judge the world, independently of our experiences.

A different response to the problem here might be to say, the placement of the perception of the dagger in Macbeth’s mind was underdetermined. Suppose he had the additional knowledge that the dagger was hanging in mid-air, and knowledge of the fact that daggers do not fly. Then he would be able to tell that the perception of the dagger was indeed a hallucination and not an actual perception.

All three examples of non-intrinsic determination are said to be context-sensitive in that the determination or understanding of what the objects are depend on the context. Just as we can know what makes the sentence ‘I am hungry’ true only if we are aware of the context, we can know whether or not the object, say, the perception is hallucination or actual perception, in the light of the context.

Underdetermination is a consequence of failure to define criteria or conditions for a particular fact. The question of what makes something a work of art occurs because it is underdetermined as to whether an object is an everyday object or an object of art. But what causes this underdetermination? It may be argued that underdetermination is the consequence of the lack of criteria or specified conditions for the fact that something is a work of art. Just as a mathematical function of the form f(x) = ax + b remains vague insofar as its parameters are left undefined, or just as the everyday statement that “I met a man” remains general insofar as it does not specify who the man is, failure to, as a preliminary, define a work of art is what results in the phenomenon of underdetermination.

This is not to say that underdetermination means the same thing as vagueness. Vagueness is a property of concepts, and it is used to describe concepts that are somehow fuzzy around the edges. For example, “…is bald” is a vague concept as we cannot draw the line between someone’s being not bald and someone’s being bald. There can be underdetermination without vagueness, for instance, in the case where Wittgenstein says, “Whereof one cannot speak of, thereof one must be silent”, it is underdetermined if he refers to the idea that there are limits to language, or if he refers to the idea that the Tractatus is itself nonsense and must be thrown away. The statement is not itself vague, though the various interpretations of the statement are underdetermined.

A second cause of non-intrinsic underdetermination is ambiguity. If I say to you that “The chicken is ready to eat”, I could mean either that there is a chicken and that chicken is hungry, or I could mean that the chicken has been prepared as a dish and is ready for us to eat. Because of the multiple meanings of the statement, your understanding of my statement is said to be underdetermined.

Intrinsic underdetermination

By contrast, intrinsic underdetermination is when we cannot know which of the theories is true, even if we have further background information and context information. If two theories are intrinsically underdetermined, it leads to the type of phenomenon reflected in the problem of Buridan’s ass, according to which an ass placed equidistant between two bales of hay starves to death because it has no reason to choose one bale over the other. If two theories are intrinsically underdetermined, the experience of underdetermination becomes existential in character, as there is no way to go forward towards determining which of the theories is true. In other words, philosophical underdetermination is the result of intrinsic underdetermination.

I will describe three examples of intrinsic underdetermination.

The first example can easily be seen in optical illusions such as the Necker cube, where a cube can be seen as jutting out in two different ways. Which perspective is the right one? The mind arbitrarily flips from one perspective to the other.

The second example is the underdetermination of philosophical theories. There can be two philosophical paradigms, one in the philosophy of language and one in the philosophy of mathematics, for example. Yet both can tackle and interpret Wittgenstein’s Tractatus Logico-Philosophicus within the context of their own paradigms. Can we decide which one is the true interpretation?

Intrinsic underdetermination is also borne out in general sceptical theories such as Descartes’ sceptical assertion that we can never tell whether or not present experience is a dream or reality. In the sceptical framework, since we cannot distinguish between experiences of dreams and experiences of reality, and if knowledge is acquired through sense experience, then we could be living in a dream, with no real knowledge of objects. As such, it is underdetermined as to whether or not our everyday experience is dream or reality.