Theology and the Philosophy of Science: The Syntactic and Semantic Views

The Received View in the [hilosophy of science is the syntactic view.  Accordingly, scientific theory is construed as a set of sentences with the laws of the scientific theory being its axioms. By inputting initial conditions and conjoining these conditions to the laws (axioms) of the theory, one deduces future states of the system as theorems.  This is the theory's predictions. The syntactic conception of scientific theory is clearly in the tradition of Euclid, Aristotle, Newton, Carnap and the Logical Positivists. But as we pointed out in the last post, there are problems with the account. 

One problem is that the syntactic view presupposes the so-called analytic/synthetic distinction, that is, the distinction between what is true by definition versus what is true because of the way that the world is. The distinction is rooted in the work of Immanuel Kant (1724-1804). Kant famously claimed that an analytical statement or proposition is true because the meaning of the predicate is included in the meaning of the subject.  A synthetic statement, on the other hand is ampliative in that the meaning of the predicate is not included in the meaning of the subject.  The first effectively decomposes the meaning of the subject, finding that what makes the subject true also makes the predicate true. The second amplifies the meaning of the subject; it asserts of the subject that something is true that is not included within the very meaning of the subject. 

While this semantic distinction in Kant must be distinguished from the epistemological distinction between what is known "prior to" experience (the a priori) and what is known "after" or on the basis of experience (the a posteriori), we often today simply identify the a priori with analytical judgments and the a posteriori with synthetic judgments.  For instance, "a bachelor is unmarried" is a true analytic statement because one cannot think of married bachelors, but "a bachelor is happy," if it is true, would be a true synthetic statement.  We would know the second on the basis of experience, e.g., surveys, personal observations, controlled experiments, etc. 

W. V. O. Quine famously criticized the analytic-synthetic distinction about seven decades ago, calling it one of the "dogmas" of empiricism.  He claimed that the analytic-synthetic distinction is not a matter of meaning over and against experience, that it is not a matter of the necessary truth of the former over and against the contingent truth of the latter. The distinction is not absolute at all, he avers, but it is merely a matter of degree, of what statements we will give up last.  In our "webs of belief," we hold onto some statements longer than others.  We might say, "water is H20" and "water is odorless," and dutifully subject each statement to our "tribunal of experience."  It is clear that confronted with experience, we would hold onto the truth that water is H20 much longer than water is odorless.  In fact, I can imagine some experience which would compel us to claim that water is not in fact odorless.  Of course, the latter statement could be "saved" from repudiation by declaring that it is not water itself that is not being odorless, but something in the water that is smelling foul.  

Problems with the analytic/synthetic distinction were a profound challenge for the syntactic view of scientific theory because the "bridge rules" of the theory coordinating the theoretical and observational terms were supposed to be a matter of meaning alone.  This theoretical term just means this observational term. In fact, the higher level terms and propositions of the theory could be in principle reduced to phenomenal experience. The classic text of this approach is Carnap's The Logical Construction of the World.  Clearly, if analyticity does not hold by meaning alone, then the very notion of bridge rules is undermined. 

There were, of course, other difficulties with the syntactic approach. It turned out that rigorous axiomatic laws were too cumbersome to be used by actual scientists. Also, because scientific theory was construed in terms of sentences, endless debates in the philosophy of language ensued.  Finally, there were Goedel problems.  As it turns out, no axiom set and system of proof within a theory could prove all of the sentences regarded as true within the theory. The result was the overturning of the syntactic view of scientific theory.  The new approach was called the semantic view of scientific theory.

Emerging in the 1970s and 80s, the semantic view of scientific theory generally identified theories with classes of models or model-types along with hypotheses of how these models relate to nature. A theory thus could thus be cast as a "class of fully articulated mathematical structure-types" using set-theoretical predicates.  (See Demetris Portides, "Scientific Models and the Semantic View of Scientific Theories" in Philosophy of Science, December 2005, pp. 1287-98.)  

Models are thus included in the the theory structure, and are themselves constructed on the basis of data within a context of experimental design and auxiliary theories.  On the semantic view model A is equivalent to Model B if and only if there is a correspondence of the elements and relations of A and B.  (Some advocates claims there must be an isomorphism, some a partial isomorphism and some merely a similarity.) 

Advocates of the semantic view claim that a physical system is represented by a class of model types. Semantic theorists generally hold that data alone does not falsify a theory, but that  data, design and auxiliary theory are important in the construction of data structures. These data structures must be sharply distinguished from the theoretical model, in that the latter is a construction out of the data structure.  But the question arises: What exactly is a data structure? 

It seems that the models in question can be either more abstract, e.g., mathematical structures, or more concrete, e.g., visual models of molecules. Proponents of the semantic view often claims a superiority over the syntactic conception in that scientific theory now is understood as actually focussing on the actual things that scientists treat within their theories.  Moreover, they claim that the semantic view allows that scientific theories can be clearly seen as not simply related to actual chunks of the world, but rather to mathematical objects as idealizations that are connectable to the world. Such idealizations, they claim, are the true objects of science. Accordingly, abstract mathematical structures come to be understood as that which the theory is about. Thus, semantic theories privilege mathematics -- especially "set-theoretical" entities -- over first-order predicate logic.

Rasmus Groenfeldt Winther's article in the Stanford Encyclopedia of Philosophy distinguishes two general strategies within the semantic view generally.  The state-state approach focuses upon the mathematical models of actual science such that the scientific theory just is a class of mathematical models. Alternatively, the set-model theoretic approach emphasizes that the axioms, theorems and laws of a theory are satisfied, or made true by, certain mathematical structures or models of the theory.  The second approach is often deemed the more fruitful. 

I find Michael McEwan's 2006 article "The Semantic View of Theories: Models and Misconceptions," helpful in understanding what the semantic view is and is not.  McEwan points to the following slogan of the semantic view: A theory is a collection of models (1).  On what he calls the naive semantic view, the "is" here is the "is" of identity. Tarski famously connects models to semantic concepts through the notion of satisfaction.  He uses model-theoretic models in accomplishing this. A model-theoretic model is an interpretation which satisfies a class of statements by specifying a domain of individuals and defining the predicate symbols, relations and functions on this set of individuals.  Accordingly, a theory is a collection of model-theoretic models (2).  

On the model-theoretic model the theory is a set of sentences and the models are interpretations in which the set of sentences turn out to be true. A model-theoretic theory is true for a given model just in case the sentences are true on that model. The class of model-theoretic models make true the model-theoretic theory.  McEwan calls the identification of the model-theoretic theory with the class of its models a naive semantic view.  If, however, the class of models satisfies the sentences of the model-theoretic theory, McEwan no longer dubs this a simple naive semantic view.  He specifies the naive semantic view as having the following conditions (3).

•  It is identified with M, the class of model-theoretic models,
• The models in M are directly defined, 
• The naive-theory is true for model n just in case n is an element in M. 

One problem with the naive theory is that it is difficult to see how any of it touches the world.  As it turns out, no n need represent the world at all! Another problem is that since the theory itself is just the class of models, it is what it is only when each model is true. This means that no model really instances the theory, for the theory would not be that theory if it had other instances!  As McEwan points out, the question of whether the solar system instances Newtonian mechanics is not a non-trivial one, but on the naive theory, it would be true just in case we stipulate that it is so (5).  Simply put, if the naive theory were true, then one could not axiomatize in model-theoretic theory without knowing in advance which interpretations would satisfy the model-theoretic theory.  But we do not always know in advance which interpretations satisfy our theory; there are sometimes unintended models. (Consider the non-trivial question of whether a newly discovered solar system obeys Newtonian laws.) Thus, by modus tollens, naive theory is not true.  McEwan puts the matter bluntly: "There is nothing above and beyond the models themselves to decide whether a theory is applicable to some model or not" (7). 

Fortunately, the semantic view is not identified with the naive theory.  Indeed, the semantic view realizes that the models of M must represent the world in some way.  Clearly, realists and many empiricists would want this to be so. Why not then simply identify n with a physical model?  But how can a physical system be an interpretation of a formal language?  This seems to have the matter backward.  

As it turns out, semantic views are plagued by the representation problem. Consider the claim that one of the models of M (say n) is the faithful representation of the physical world. But on what basis is n the representation? If the theory is the class of models, one of which is the real world, then why identify the theory with the class of models in the first place (8)?

It seems that the semantic view must somehow deal with the representation problem.  However, Bas von Fraasen a theory's models is identified with a class of structures.  He writes: 

The syntactic picture of a theory identifies it with a body of theorems, stated in one particular language chosen for the expression of that theory.  This should be contrasted with the alternative of presenting a theory in the first instance by identifying a class of structures as its models.  In this second, semantic, approach the language used to express the theory is neither basic nor unique; the same class of structures could well be described in radically different ways, each with its own limitations.  The models occupy center stage.  

So what of these model that occupy center stage? What becomes of realism on the semantic view?  If the models are mathematical structures, then are the objects in these models "real enough" for one to claim that one's scientific theory is true of the real world?  Is the wave function a mathematical object and thus real in the sense that a scientific realist wants?  What would distinguish a real physical object from other pretenders?  What about unobservables -- are they real?  What would distinguish an unobservable mathematical object from an on observable "real" one?  The representation problem is clearly a problem for realism. 

While one might claim that the semantic view is the new "received view" in the philosophy of science, there are very strong voices that have emerged which have pointed to the "extra-scientific" or "extra-rational" factors at work in science, factors that seem as almost as deadly to the semantic view as they are to the syntactic view. We shall attend to these in the next post.