As a logical postulate it is not very radical ; it is possible within a finitary framework to develop that part of mathematics that is used or has potential applications in natural science , such as mathematical analysis ( cfXXX Mycielski 1981 ) .
analysis without actual infinityquot
J Mycielski
This Principle of Finitism is also assumed by Johnson-Laird ( 1983 ) , Jackendoff ( 1983 ) , Kamp ( 1981 ) , and implicitly or explicitly by almost all researchers in computational linguistics . As a logical postulate it is not very radical ; it is possible within a finitary framework to develop that part of mathematics that is used or has potential applications in natural science , such as mathematical analysis ( cfXXX Mycielski 1981 ) . On the other hand , a possible obstacle to our strategy of using only finite objects is the fact that the deductive closure of any set of formulas is not finite in standard logic , while , clearly , we will have to deduce new facts from formal representations of text and background knowledge .
As a logical postulate it is not very radical ; it is possible within a finitary framework to develop that part of mathematics that is used or has potential applications in natural science , such as mathematical analysis ( cfXXX @@CITATION ) .