It envisions a meta-pluralism in which reconstructive axiomatization and mathematical modeling remain important, though not necessary for all theories. In short, for the Semantic View the structure of a scientific theory is its class of mathematical models. According to some advocates of this view, the family of models can itself be axiomatized, with those very models (or buy xanax without prescrition other models) serving as axiom truth-makers. Because both of the underlined sentences are true, (9) and (10) are a pair of sentences which differ only with respect to substitution of expressions (namely, the underlined sentences) with the same reference.

Suppose that you and I believe the exact same thing—both of us believe the world to be just the same way. Intuitively, it seems not; it seems incoherent to say that we both believe the world to be the same way, but that I get things right and you get them wrong. (Though see the discussion of relativism in §2.3.2 below for a dissenting view.) So it seems that if two sentences express the same proposition, they must have the same truth value. （2）Models of Theory."Representation Theorems," permit us "to discover if an interesting subset of models for the theory may be found such that any model for the theory is isomorphic to some member of this subset" (Suppes 1957, 263).

In other words, the Fano plane has beenembeddedin a Euclidean plane. Below we return to the concepts of embedding and isomorphism, but this example shall suffice for now to indicate how a geometric model can provide a semantics for the axioms of a theory. First, a "dialectical opposition" between "logic and experience," "form and content," "constitutive principles and empirical laws," and "‘from above’… [and] ‘from below’" pervades the work of the syntacticists (Friedman 1999, 34, 63). Whether syntacticists believe that a synthesis or unification of this general opposition between the theoretical (i.e., logic, form) and the observational (i.e., experience, content) is desirable remains a topic of ongoing discussion.

There are complex mappings between models of experiment thus specified, and (i) models of theory, (ii) theories of measurement, and (iii) models of data. That is, if the entire universe consisted solely of these seven points and seven lines, the projective plane theory would be true. Because Euclidean geometry includes parallel lines, the Fano plane is not a model of Euclidean geometry. Even so, by drawing the plane, we have shown it to beisomorphicto parts of the Euclidean plane.

(4) Function.Characterizations of the nature and dynamics of theory structure should pay attention to the user as well as to purposes and values (e.g., Apostel 1960; Minsky 1965; Morrison 2007; Winther 2012a). Idealized theory structure might be too weak to ground the predictive and explanatory work syntacticists and semanticists expect of it (e.g., Cartwright 1983, 1999a, b; Morgan and Morrison 1999; Suárez and Cartwright 2008). To complete the visualization above, an epimorphism is a surjective homomorphism, and an endomorphism is a mapping from a structure to itself, although it need not be a symmetrical—i.e., invertible—mapping, which would be an automorph. Drawing the theoretical/observational distinction in terms of language is inappropriate, as observability pertains to entities rather than to concepts. Under this analysis, "the correct tool for philosophy of science is mathematics, not metamathematics"—this is Suppes’ slogan, per van Fraassen (1989, 221; 1980, 65).

What examples like (12) are often taken to show is that the reference of an expression must be relativized, not just to a context of utterance, but also to acircumstance of evaluation—roughly, the possible state of the world relevant to the determination of the truth or falsity of the sentence. In the case of many simple sentences, context and circumstance coincide; details aside, they both just are the state of the world at the time of the utterance, with a designated speaker and place. Phrases like "In 100 years" shift the circumstance of evaluation—they change the state of the world relevant to the evaluation of the truth or falsity of the sentence—but don’t change the context of utterance. That’s why when I utter (12), "I" refers to me—despite the fact that I won’t exist to utter it in 100 years time. Can two sentences express the same proposition, but differ in truth-value? It seems not, as can be illustrated again by the role of propositions as the objects of belief.

Correspondence rules attach to the content of observational sentences. Observational sentences were analyzed as (i)protocol sentencesorProtokollsätze(e.g., Schlick 1934; Carnap 1987 [1932], 1937, cf. 1963; Neurath 1983 [1932]), and as (ii)experimental laws(e.g., Campbell 1920; Nagel 1961; Carnap 1966; cf. Duhem 1954 [1906]). Although constrained byCalc, the grammar of these sentences is determined primarily by the order of nature, as it were. In general, syntacticists do not consider methods of data acquisition, experiment, and measurement to be philosophically interesting.

Obviously, this difference in truth-value is traceable to some difference between the expressions ‘Barack Obama’ and ‘John McCain.’ What about these expressions explains the difference in truth-value between these sentences? It is very plausible that it is the fact that ‘Barack Obama’ stands for the man who is in fact the 44th president of the United States, whereas ‘John McCain’ stands for a man who is not. This indicates that the reference of a proper name—its contribution to the determination of truth conditions of sentences in which it occurs—is the object for which that name stands. Criteria of experimental design motivate choices for how to set up and analyze experiments.

There is no clear way of distinguishing between intended and unintended models for syntactically characterized theories (e.g., the Löwenheim-Skolem theorem, Bays 2014). I offer you that kernel of myself that I have saved somehow -the central heart that deals not in words, traffics not with dreams and is untouched by time, by joy, by adversities.我给你我设法保全的我自己的核心——不营字造句，不和梦想交易，不被时间、欢乐和逆境触动的核心。 The functional view not only sees language as a __ system but also a __ for doing things. _ theory emphasizes interaction and engagement with the target language in a social context. It is important to note at the outset that the Pragmatic View takes its name from the linguistic trichotomy discussed above, in the Introduction.

In§§2.1.1–4the theoretical framework common to classical semantic theories is explained; in§§2.1.5–7the differences between three main versions of classical semantic theories are explained. In§2.2there is a discussion of the alternatives to classical semantic theories. In§2.3few general concluding questions are discussed; these are questions semantic theorists face which are largely, though not completely, orthogonal to one’s view about the form which a semantic theory ought to take.