scholarly journals A Formal Calculus for Informal Equality with Binding

2007 ◽  
pp. 162-176 ◽  
Author(s):  
Murdoch J. Gabbay ◽  
Aad Mathijssen
Keyword(s):  
Formal Calculus

Euler operators and conservation laws of the BBM equation

1979 ◽  
Vol 85 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Calculus Of Variations ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Formal Calculus ◽  
Euler Operators ◽  
Bbm Equation

AbstractThe BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

A component for the formal calculus

1993 ◽  
pp. 210-223
Author(s):  
Michel Gauthier
Keyword(s):  
Formal Calculus

A Neo-Formalist Approach to Mathematical Truth

1998 ◽  
pp. 41-47
Author(s):  
Alan Weir
Keyword(s):  
Ontological Commitment ◽  
Abstract Objects ◽  
Mathematical Truth ◽  
Truth Conditions ◽  
The Status ◽  
Formal Calculus

I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results seem to pose for the tight link assumed between truth and proof.

Political Science and the Uses of Functional Analysis

1968 ◽  
Vol 62 (2) ◽  
pp. 425-439 ◽  
Author(s):  
A. James Gregor
Keyword(s):  
Social Sciences ◽  
Political Science ◽  
Alternative Interpretation ◽  
Cognitive Effort ◽  
Formal Calculus ◽  
Specialized Language ◽  
System 2 ◽  
Empirical Tests ◽  
Reliable Knowledge ◽  
Partial Formalization

Political science, as an empirical enterprise, shares with the other behavioral or social sciences at least one characteristic feature: partial formalization. For a science to most reliably discharge its two principal functions, explanation and prediction, statements embodying acquired knowledge must be systematically organized in subsumptive or deductive relations. Minimally, a set of such systematically related propositions, which include among them some lawlike generalizations, and which can be assigned specific truth value via empirical tests, is spoken of as a theory. A theory, in a substantially formalized system, includes as constituents (1) an uninterpreted or formal calculus which provides for syntactical invariance in the system, (2) a set of semantic rules of interpretation which assign some determinate empirical meanings to the formal calculus thereby relating it to an evidential or empirical base, and (3) a model for the uninterpreted calculus, in terms of more or less familiar conceptual or visualizable materials, which illustrates the relationships between variables in structural form, an alternative interpretation of the same calculus of which the theory itself is an interpretation.The virtues of standard formalization need hardly be specified. For our purposes here it is sufficient to indicate that formalization seeks to satisfy the minimal requirements of any serious knowledge enterprise: to provide for syntactical and semantic invariance without which reliable knowledge is simply not conceivable. The language shift, exemplified in any cognitive effort, from ordinary to specialized language style is the consequence of attempting to reduce the vagueness, ambiguity and tense obscurity that afflicts common speech.

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