This response is based on the summary by Joel Steinmetz of an article by John Haldane:

http://guweb2.gonzaga.edu/faculty/calhoun/socratic/Steinmetz-Problem_of_Intentionality.pdf

It is not based on the not the original article by Haldane, so my remarks here must be regarded as provisional and informal. Still, I would like to address a few points.

Haldane’s argument, as presented here, is somewhat confusing because of the terminology employed. The key terms are “extension,” “intension (with an ‘s’),” and “intentionality.” It is easy to get confused with such similar-sounding terms. The “extension” of a predicate is the set of objects picked out by that predicate. Thus “cat” picks out the set of all felines. The “intension” is the principle or criterion whereby those objects to which the predicate applies are picked out. In other words, the intension specifies the conditions that must be met for the predicate to be correctly applied to the object. For instance, we identify the items picked out by the term “weekday” as {x | x is a day of the week and x is neither Saturday nor Sunday}.

When a term refers to a single object, like the White House, the extension of the term will be the object itself. The intension will be any concept that picks out that object, such as “the residence at 1600 Pennsylvania Avenue, Washington, D.C.,” or “The official residence of the sitting President of the United States.” “Intentionality,” on the other hand, refers to the “aboutness” property of conscious states. Thoughts are about objects, whether those objects exist or not. Thus, I can think about a golden mountain just as easily as Pike’s Peak. Philosophers therefore say that conscious states like believing, wishing, hoping, etc. have “intentional” objects, i.e. objects that might exist or not.

A sentence establishes an extensional context when any co-extensive term may be substituted for another without changing the truth value of the sentence. Thus, “Barack Obama resides at 1600 Pennsylvania Avenue” is true and “Barack Obama lives at the official residence of U.S. Presidents” is also true because the extension of “1600 Pennsylvania Avenue” and “official residence of U.S. Presidents” have the same extension, namely, the White House.

A sentence establishes an intensional context when you cannot necessarily substitute once concept for another—where both concepts pick out the same object—without changing the truth value of the sentence. For instance, “Sam believes that the successor of George W. Bush lives in the White House” may be true whereas “Sam believes that the 44^th President of the U.S. lives in the White House” may not be true because Sam knows that Barack Obama is the successor of George W. Bush but does not know that he is the 44^th President. Sam does not know that the concept “successor of George W. Bush” and the concept “44^th President of the U.S.” pick out the same individual, Barack Obama.

OK, so what is the relationship between extension, intension (with an ‘s’) and intentionality (with a ‘t’)? I think it is this: Any language that meaningfully describes an intrinsically intentional state, one where a mental state is directed towards an intentional object, will necessarily be expressed by sentences that establish an intensional context. Those sentences will describe the intentional state in terms of beliefs, meanings, and concepts, not in terms of the objects picked out by those concepts (which might not exist), and, in particular not in terms of physical objects or physical properties. Thus, to describe my intentional state of thinking about the Eifel Tower, the account will not be in terms of the Eifel Tower itself but how it appears or seems to me.

Haldane’s argument then seems to be that, in principle, physical descriptions must all be expressible in extension-language, i.e. in terms of the objects picked out, their relations, and properties. There can be no irreducibly intensional contexts in physical science. Physical science must describe in terms of what is, not in terms of concepts or meanings or presentational aspects. Of course, science does frequently employ concept-language, for instance every time it gives a definition, e.g. according to my Dictionary of Science (Brockhampton Press, 1997), Deuterium is defined as: “naturally occurring heavy isotope of hydrogen, mass number 2, (one proton and one neutron)…” This sentence states the criterion whereby something counts as deuterium, and employs concepts such as “mass number,” and “isotope.” Therefore the definition of “deuterium” employs intensional language.

However, I think that Haldane’ point is that any physical account, description, or definition must be, in principle, a third-person description in terms of physical objects, their properties, relations, interactions, etc. and not in terms of first-person accounts of how things appear, seem, feel, etc. Further, he asserts that there are intrinsically intentional states, states that can only be expressed in terms of their presentational aspects (how they appear, seem, feel, etc.) and not in terms of the properties of physical objects, such as neurotransmitters, synapses, etc. The upshot, as he sees it, is that there are some real states, namely intentional states, that cannot be adequately described—fully and without residue—in physical terms. Therefore, physicalism, as a comprehensive metaphysical theory, a theory about the ultimate terms of ontology, cannot be correct. There will be some real states, viz. intentional states, that, in principle, cannot be described in third-person, extensional, physical terms.

I agree with Haldane and Searle that there are intrinsically intentional states and that intrinsically intentional states cannot be reduced to purely third-person, extensional, object-language terms. However, for several reasons, I am not convinced by his argument.

First, note that explanatory physical models do not have to use only physical terms. Most obviously, explanatory physical models use the language of mathematics, and mathematical language refers to nothing physical and derives none of its meaning from anything physical. Indeed, the universal applicability of mathematics is due to the fact that its terms and meanings are abstracted from any particular context or reference. Consider E = mc². It refers to physical terms such as energy, light, and mass, but the equation also employs mathematical concepts such as equality and multiplication. Mathematical equality and multiplication are not found in the physical world, nor does their meaning depend on physical states. Therefore, Haldane’s apparent assumption that physical accounts can employ only physical terms seems quite wrong.

Perhaps Haldane would say that he means only to insist that there can be no irreducible references to meanings, conceptual contents, or presentational aspects in physical theory. Maybe he is right that physical theory currently does not countenance such intentional terms, at least not irreducibly, in physical accounts. Yet Haldane seems to be invoking an essentialist and ahistorical criterion about the kind of language that physical science “must” use. From a more historical perspective, the kind of language that physical science employs evolves over time. For Aristotle, talk about natural place and final causes was fine. Newton banished natural place and final causes. Newton also banished talk about the causes of gravitational attraction with his famous “Hypotheses non fingo” dismissal. Einstein brought back a physical account of gravitation in terms of the warping of space-time by massive bodies.

As Kuhn pointed out long ago, the language acceptable to scientific communities is something that changes over time. The language changes as needed to accommodate our best current understanding of the world. The most relevant question to ask, then, is not whether current scientific language can describe intentional states. Suppose it cannot. So what? The question to ask is whether intentional states are something that can be accomplished by physical systems. That is, can a physical thing, for instance, think about a cat? Is “thinking about” something that a physical thing can do? If it turns out that it is, then scientific language will—because it must—adjust to that reality. Science will have to begin using intentional language as well as physical object language if it turns out that some physical objects can have intentional states. If Haldane wants to rule this out, he cannot appeal to language. He has to appeal to the physical world and show that, no matter how a physical thing is organized, it cannot, say, think about a cat. It is not clear at all how Haldane could even begin to show that no physical system can have intentional states. At bottom, there is no basis for saying what the physical world can do than by observing what it does do.

In conclusion, I would like to propose that physicalism not be understood, as Haldane apparently considers it, as the effort to describe everything exclusively in terms of extensional states. Rather, I would characterize physicalism as the thesis that all phenomena have physical causes, in other words, that physical models can, in principle, explain all occurrences. Physical models explain in terms of physical entities, forces, relations, interactions, etc. However, the language that physical models employ will have to encompass not only what explains but what is explained. If what is explained is something not expressible in extensional, physical-object language, then the relevant physical model will have to incorporate the language needed to capture that actual cause-and-effect relationship. Scientific language cannot determine the world. It must be determined by the world, and if the world is such that physical things can have intentional states, then to explain this fact science will have to develop the language necessary to do so.