Topic for #67: Carnap on Logic and Science

On 11/15/12 we recorded a discussion of Rudolph Carnap's The Logical Structure of the World (1928), often referred to as "the Aufbau," because it sounds cool, and the German title is Der Logische Aufbau der Welt. Listen to the episode. To get a good sense of Carnap's project, we read pages 1-136, plus the subsequent chapter summaries: pages 166-171, 240-243, 298-300. The project requires some background explanation:

As long-time listeners may recall, Carnap was a leading figure in the Vienna Circle, known as the logical positivists, though in Carnap's case, a more accurate and charitable description would be logical empiricists. In our early Wittgenstein episodes, we discussed how the logical positivists denied that metaphysical claims were meaningful, that, ultimately following Hume, all knowledge has to refer to some experiences, some basic impressions.

In the Tractatus, Wittgenstein sketched a view by which a complicated scientific theory is like a square mesh laid out over a black and white surface, i.e. a field of potential atomic facts which either are actualized (white) or aren't (black). The mesh allows us to characterize the surface by giving the color of the squares it reveals. Now, a mesh with triangular or hexagonal openings would also work to describe the surface, meaning that there are multiple scientific theories that can characterize the data, and which we prefer will be a matter of simplicity and accuracy.

While Wittgenstein was maddeningly vague about what these "atomic facts" would be like and how exactly one might build up to higher levels of description from them, Carnap in the Aufbau uses the same insight (and the same consequent hostility to the unverifiable claims of metaphysics that have hampered the progress of philosophy by presenting insolvable dilemmas) to spell out a much more detailed system. Carnap's goal is to show how all of the things that philosophy and science can legitimately talk about can be logically reduced to one domain of objects. Instead of atomic facts, he refers to "elementary experiences." The funny thing about atomic facts for Wittgenstein was that while they are the basic units from which everything is built, they are also in a sense compound: an atomic fact expresses some property of some individual. But Wittgenstein insisted that it's not the individual or the property that was basic; these things would be meaningless considered apart from each other, i.e. you can't have a "bare particular" with no properties, but of course you can imagine such a particular having different properties, e.g. green instead of blue. Carnap reproduces this picture in his elementary experiences. They are, strictly speaking, unanalyzable basics of our experience. You can't reduce them to individual "sense data" like "green." At the same time, we can compare these unanalyzable experiences and, by comparing them, perform what Carnap calls "quasi-analysis" on them, and so come up with a class of green experiences by grouping a bunch of them together.

The key here is the difference between a property like green and a relation between experience X and experience Y and experience Z. Properties, by definition, attribute something to an individual, but if a basic experience is unanalyzable, then you can't really attribute a property to it; that would be analyzing the experience into properties and substances. A relation, on the other hand, is (according to Carnap) extrinsic; you can form a class without attributing any properties to the individuals. Such a class, then, allows us to create a new type of "quasi-object," i.e. green, which is not a part of the basic ontology, the basic domain of objects, and in fact any sentence about the color green can be decomposed (at least theoretically) into sentences about this class of experiences.

So there you go: using a basic relation (remembered similarity) and a basic element (elementary experiences), and the logical apparatus of set theory, we can set up classes of increasing levels of abstraction to talk about (in approximately this order) our own mental states, space and time, the physical objects studied by science, other people's mental states, and cultural objects like art, economics, and ethics. The program is reductionist, in that ultimately the statements about more complicated things could be decomposed into very very long strings referring only to the basic elements, but it doesn't result in trying to get rid of this more complex talk, and in fact aims to clear up some philosophical problems by emphasizing that quasi-objects at different levels of abstraction belong to different "object spheres." Science can thus be as multi-faceted as it needs to be to talk about history, ethics, sociology, economics, etc., but ultimately, ontologically unified.

It should be noted that construction theory, as Carnap calls his project, is supposed to be neutral as to whether we actually create these quasi-objects ourselves (a la Kant) or just discover them as natural phenomena. Also, he's not trying to give a psychological account of how we actually put together the objects of our experience, nor a series of metaphysical reductions. He's trying to give a logical schematic. So, for instance, to know other people's psychological states, we rely on their behavior (and could potentially use brain scans). Whether someone else's pain is metaphysically identical to his pain-behavior or pain-brain-state is irrelevant for Carnap (it's not even a sensible question); we only need to establish the correlation to say how we could construct our understanding of someone else being in pain based on seeing their behavior and/or brain. So all statements about their pain can be recast as statements about these objective things without a change in truth value.

This example illustrates one of the primary characteristics of Carnap's reductions: they are extensional, which means he's only concerned with the identity of classes (or coextensiveness, to use the technical term: it means they have the same members). If other's-pain-state statements can be translated to be other's-behavior/brain statements (which in turn can be translated into more basic statements, all the way back to statements about elementary experiences), then that means that these statements are all ultimately about the same things. But of course there are differences in our epistemic access to these different spheres, and I surely can't, for instance, be sure if someone is faking his pain in a particular instance just by looking at him. By looking only at extensions (i.e. what the statement is actually talking about, instead of how it's being talked about, which would be intensions) in determining what's reducible to what, he's trying to keep science focused on the objective.

To make this clearer, I encourage listeners to go back to our Frege episode. Carnap studied under Frege, who came up with the distinction between the reference for a phrase and its sense: "Clark Kent" and "Superman" have the same referent (extension), i.e. they're objectively about the same thing, whereas they have different senses (intensions), because people know this one referent according to epistemically different designations. Carnap's picture is all about expunging subjectivism from science, and it involves, then, coming up with a definition for each complex concept (quasi-object) in terms of a set of necessary and sufficient conditions (where these "conditions" are simpler terms in his hierarchy of object spheres) for falling under that concept. This means he can express these relationships between quasi-objects from lower and higher spheres in terms of class membership: your pain as a concept is a class of (potential) behaviors and/or brain states that exhibit similarity in a manner comparable to how the class (quasi-object) "green" was formed from the relation between a group of experiences.

Sounds crazy? Well, it is, but it's a fun exercise: the book is surprisingly readable, and an approachable introduction to set theory and mathematical logic to boot! As one hint to its relevance, we chose to read this because it's the foundational text motivating the latest book by David Chalmers, who will be our guest for ep. 68, and who is profoundly not a behaviorist, or reductionist about pains, or any of that archaic-sounding part of Carnap's project.

Get the book to read along with us.


  1. Billie Pritchett says

    Great essay, Mark! This is such a clear, concise but thorough explanation of Carnap’s project. I can’t wait for the episode!


Leave a Reply

Your email address will not be published. Required fields are marked *