[FOM] Logic moving from philosophy to mathematics

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Thu Feb 3 06:44:49 EST 2005

> It seems to me that "logic" as a subject moved from being the interest 
> of some philosophers -- in the early 19th century, and maybe later -- 
> to the interest of some mathematicians, by the early 20th century, and 
> maybe earlier. Philosophers still study logic, of course, but they now 
> study mathematical logic. Everyone that I've talked to about this 
> agrees that this has happened, but I have not been able to find a 
> secondary source analyzing this important shift.

"Logic" was understood much more broadly in the old days. J.S. Mill's Logic 
dealt e.g. with the philosophy of science, the philosophy of language etc. 
Russell, Wittgenstein etc. too took it widely: for them logic meant 
something like philosophical conceptual analysis. Also, for Frege and 
Russell, for example, formal logic was made for use - it was a universal 
medium. They did not study its metalogical properties (arguably such 
questions were not even possible for them). 

I think that a major change happened with Hilbert's program. Hilbert and 
his followers started to study formal systems mathematically from the 
metalogical perspective. It seems that this is what we nowadays usually 
mean by "logic". So I submit that it is the use of the word "logic" that 
has changed. 



Panu Raatikainen
Helsinki Collegium for Advanced Studies
P.O. Box 4
FIN-00014 University of Helsinki
Tel:  +358-(0)9-191 23437
Mobile:  +358-(0)40-840 0789
Fax:  +358-(0)9-191 24509
Email: panu.raatikainen at helsinki.fi

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