Formal Calculus

2004 ◽  
pp. 21-48
Author(s):  
James Lepowsky ◽  
Haisheng Li
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 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.

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