This is one way among many to deploy the population-genetic principle of HWP. In contrast, clustering analysis e. Edwards can be readily performed even with the small amount of among-continent genetic variance in Homo sapiens. Winther , — That is, for a cluster to eventually be robust in the modeling runs, it should meet HWP expectations. Clustering analysis has sometimes been interpreted as a justification for a realist stance towards biological race see discussions in Hochman ; Kaplan and Winther , ; Winther and Kaplan ; Winther ; Edge and Rosenberg forthcoming; Spencer forthcoming.

This example of the mathematical modeling of human genomic diversity teaches that basic and simple formal components can be used in different ways to develop and apply theory, both inside and outside of science. These ontological ruptures can be identified despite the fact that both research projects assess population structure by examining departures from HWP i. This exploration of how the three views on the structure of scientific theory address population genetics, and in particular HWP, invites a certain meta-pluralism.

That is, the Syntactic View carefully breaks down fundamental concepts and principles in genetics and population genetics, articulating definitions and relations among terms. The Semantic View insightfully decomposes and interweaves the complex mathematical edifice of population genetics.

The Pragmatic View sheds light on modeling choices and on distinct interpretations and applications of the same theory or model, both within and without science. The three perspectives are hardly mutually exclusive. The structure of scientific theories is a rich topic. Theorizing and modeling are core activities across the sciences, whether old e.

Furthermore, theory remains essential to developing multipurpose tools such as statistical models and procedures e. Given the strength and relevance of theory and theorizing to the natural sciences, and even to the social sciences e. This piece has focused on a comparison of three major perspectives: Syntactic View, Semantic View, and Pragmatic View. In order to handle these complex debates effectively, we have sidestepped certain key philosophical questions, including questions about scientific realism; scientific explanation and prediction; theoretical and ontological reductionism; knowledge-production and epistemic inference; the distinction between science and technology; and the relationship between science and society.

Each of these topics bears further philosophical investigation in light of the three perspectives here explored. Table 2. The Syntactic, Semantic, and Pragmatic views are often taken to be mutually exclusive and, thus, to be in competition with one another. They indeed make distinct claims about the anatomy of scientific theories.

But one can also imagine them to be complementary, focusing on different aspects and questions of the structure of scientific theories and the process of scientific theorizing. For instance, in exploring nonformal and implicit components of theory, the Pragmatic View accepts that scientific theories often include mathematical parts, but tends to be less interested in these components. Moreover, there is overlap in questions—e. How are these three views ultimately related? A standard philosophical move is to generalize and abstract, understanding a situation from a higher level.

Chakravartty Finally, the Pragmatic View, which did not exist as a perspective until relatively recently, imagines theory as pluralistic and can thus ground a holistic philosophical investigation. It envisions a meta-pluralism in which reconstructive axiomatization and mathematical modeling remain important, though not necessary for all theories. By design, the ecumenical meta-pluralism sanctioned by the Pragmatic View does not completely offset identity and combat strategies. Even so, the complementarity strategy might be worth developing further.

## Measurement in Science

Compared to identity and combat meta-perspectives, it provides broader—or at least different—insights into the structure of scientific theories. More generally, exploring the relations among these views is itself a rich topic for future philosophical work. Introduction 1. The Syntactic View 2. The Semantic View 3.

The Pragmatic View 4. Population Genetics 6. Introduction In philosophy, three families of perspectives on scientific theory are operative: the Syntactic View , the Semantic View , and the Pragmatic View. Savage distills these philosophical perspectives thus: The syntactic view that a theory is an axiomatized collection of sentences has been challenged by the semantic view that a theory is a collection of nonlinguistic models, and both are challenged by the view that a theory is an amorphous entity consisting perhaps of sentences and models, but just as importantly of exemplars, problems, standards, skills, practices and tendencies.

In a classic exposition, the logical positivist Carnap writes: If in an investigation explicit reference is made to the speaker, or, to put it in more general terms, to the user of a language, then we assign it to the field of pragmatics. Whether in this case reference to designata is made or not makes no difference for this classification.

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If we abstract from the user of the language and analyze only the expressions and their designata, we are in the field of semantics. And if, finally, we abstract from the designata also and analyze only the relations between the expressions, we are in logical syntax. The whole science of language, consisting of the three parts mentioned, is called semiotic. Examples of such queries are: What would be the most convenient metamathematical axiomatization of evolutionary processes e.

In which formal language s would and could such axiomatizations be articulated e. Which formal and methodological tools would permit a smooth flow from the metamathematical axiomatization to the mathematical theory of population genetics? Very generally, this exploration involves the following questions: What is the form and content of the directly presented class of mathematical models of evolutionary theory e. How could and should we organize the cluster of mathematical models sensu Levins of population genetics?

Which additional models e. What are the relations among theoretical mathematical models, data models, and experimental models? How does theory explain and shape data? How do the data constrain and confirm theory?

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The following questions about the structure of population genetic theory might be here addressed: What role did R. How did the development of computers and computational practices, statistical techniques, and the molecularization of genetics, shape theory and theorizing in population genetics, especially from the s to today?

The Syntactic View According to the Syntactic View, which emerged mainly out of work of the Vienna Circle and Logical Empiricism see Coffa ; Friedman ; Creath ; Uebel , philosophy most generally practiced is, and should be, the study of the logic of natural science, or Wissenschaftslogik Carnap , ; Hempel The Semantic View An overarching theme of the Semantic View is that analyzing theory structure requires employing mathematical tools rather than predicate logic.

First-Order Predicate Logic Objection. This places heavy explanatory and representational responsibility on relatively inflexible and limited languages. Theory Individuation Objection. Since theories are individuated by their linguistic formulations, every change in high-level syntactic formulations will bring forth a distinct theory. Unintended Models Objection.

## Philosophy of Science in the Twentieth Century : Donald Gillies :

There is no clear way of distinguishing between intended and unintended models for syntactically characterized theories e. Confused Correspondence Rules Objection. Correspondence rules are a confused medley of direct meaning relationships between terms and world, means of inter-theoretic reduction, causal relationship claims, and manners of theoretical concept testing. Trivially True yet Non-Useful Objection. Presenting scientific theory in a limited axiomatic system, while clearly syntactically correct, is neither useful nor honest, since scientific theories are mathematical structures.

Practice and History Ignored Objection. Syntactic approaches do not pay sufficient attention to the actual practice and history of scientific theorizing and experimenting. Consider the axioms of a projective plane: For any two points, exactly one line lies on both. For any two lines, exactly one point lies on both. There exists a set of four points such that no line has more than two of them. A figure of a geometric model that makes this theory true is: Figure 1.

Figure 2. Figure 3. Yes No Yes, although the distinction is hard to make. Bibliography Apostel, L. Awodey, S. Bailer-Jones, D. Machamer and M. Silberstein eds. Barbujani, G. Ghirotto, and F.

### Understanding Philosophy of Science

Minch, and L. Bartha, P. Zalta ed. Beatty, J. Bergstrom, C. Dugatkin, , Evolution , New York: Norton. Bird, A. Boumans, M. Morgan and M. Morrison eds.