The Logical Structure of Mathematical Physics

Sneed, Joseph D.; Good, Ron

doi:10.1119/1.1986599

Cited by 178 publications

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“…Sneed (1979) discovered a serious problem inherent in the standard view but not arising in the Ramsey view. This problem concerns the mutual dependency of the extension of the axioms Φ T C and the extension of the theoretical terms.…”

Section: The Ramsey Viewmentioning

confidence: 99%

A modal view of the semantics of theoretical sentences

Andreas

2009

Synthese

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Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these terms are introduced through the axioms of a theory.

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Section: The Ramsey Viewmentioning

confidence: 99%

A modal view of the semantics of theoretical sentences

Andreas

2009

Synthese

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“…Here I refer to the work of Sneed (1971), S t e p d i e r (1973,1976,1979), Moulines (1975Moulines ( , 1976, Moulines and Sneed (1979), and Baker (1978), together with a number of other articles or books by these authors. The literature is now large and it will not be possible to survey it in detail, but there are some important points raised by the structuralist viewpoint represented by Sneed, Stegmuer, and their colleagues, and consequently it is appropriate to comment on it here.…”

Section: B Qmentioning

confidence: 99%

Axiomatic Methods in Science

Suppes

1992

Nature, Cognition and System II

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Philosophical analysis of axiomatic methods goes back at least to Aristotle. In the large literature of many centuries a great variety of issues have been raised by those holding viewpoints that range from that of Proclus to that of Hilbert. Here I try to consider in detail only a highly selected set of ideas, but they are ones I judge important.The first section gives a brief overview of the formalization of theories within frrst-order logic. The second section develops the axiomatic characterization of scientific theories as set-theoretical predicates. This approach to the foundations of theories is then related to the older history of the axiomatic method in the following section. Theories with Standard FormalizationA theory with standard formalization is one that is formalized within first-order predicate logic with identity. The usual logical apparatus of first-order logic is assumed, mainly variables ranging over the same set of elements and logical constants, in particular, the sentential connectives and the universal and existential quantifiers, as well as the identity symbol. Three kinds of nonlogical constants occuf, the predicates or relation symbols, the operation symbols and the individual constants.The expressions of the theory, i.e., finte sequences of symbols of the language of the theory, are divided into terms and formulas. Recursive defrntions of each are ordinarily given, and in a moment we shall consider several simple examples. The simplest terms are variables or individual constants.New terms are built up by combining simpler terms with operation symbols in the appropriate fashion. Atomic formulas consist of a single predicate and the appropriate number of terms. Molecular formulas, i.e., compound formulas, are built from atomic formulas by means of sentential connectives and quantifiers. A general characterization of how all this is done is quite familiar from any discussion of such matters in books on logic. We shall not enter into details here. The intuitive ídea can probably be best conveyed by considering some simple examples. In considering these examples, we shall not say much of an explicit nature about first-order logic itself, but assume some familiarity with it. In a theory with standard formalization we must first begin with a recursive definition of terms and formulas based on the primitive nonlogical constants of the theory. Secondly, we must say what formulas of the theory are taken as axioms.' (Appropriate logical rules of inference and logical axioms are assumed as available without finther discussian.) 205M. E. Carvallo (ed.), Nature, Cognition and System II. 205-232.

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“…is Sneed 1971), the construction of a new paradigm is attempted. As the concept of paradigm, even its more precise formulation in the non-statement view of theories, has been introduced by the philosophy of science only by way of reconstruction, the cowstructive use suggested here entails considerable problems -problems, however, that will not be discussed in this context because both approaches in question -Schmidt's and mine -are confronted with them.…”

Section: The Problemmentioning

confidence: 99%

“…Consequently, Schmidt (1980) seeks to develop the theory of an ESL in the sense of a Sneed-matrix in direct connection with Sneed (1971). Theories as understood by Sneed are structures of the set-theoretical specification T = (K,I), i.e.…”

Section: The Problemmentioning

confidence: 99%

The function of interpretation in an empirical science of literature

Groeben¹

1983

Poetics

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The Logical Structure of Mathematical Physics

Cited by 178 publications

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A modal view of the semantics of theoretical sentences

A modal view of the semantics of theoretical sentences

Axiomatic Methods in Science

The function of interpretation in an empirical science of literature

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