LoginRegistration
For instance: The List of VAK
About consortium subscription Contacts
(812) 4095364 Non-commercial partnership
St. Petersburg
university
consortium

Articles

The Scientific Opinion №7-8 (Psycho-pedagogical and philosophy of science), 2018

QUANTIFIERS AS AN ADJOINT SITUATION

I. E. Yegorychev
Price: 50 руб.
 DOI: https://doi.org/10.25807/PBH.22224378.2018.10.11.18
The  author  based  his  work  on  the  conviction  that  the  adjoint  situation  is  one  of 
the  fundamentals  in  the  category  theory.  The  surprisingly  deep  insight  of  the 
prominent  mathematician  William  Lawvere  that  all  logical  operations  should  arise 
as  adjunction  to  some  basic  functors  between  categories  convinced  the  mathematic 
community that categorial analysis of logic might be fruitful and correct. In this article, 
this analysis is applied to existential and universal logical quantifiers.
Key  words:  category  theory,  categorial  analysis  of  logic,  adjoint  situation,  logic 
quantifiers, context.
References
 
1. Awodey S. Category theory. N.Y. Oxford, 2010.
2. Carnap R. Logical Syntax of Language. London, Routledge, 2000.
3. Goldblatt R. Topoi. The categorial analysis of logic. N.Y. Dover Publications Inc. 2006.
4. Johnstone P. The Sketches of The Elephant. Vol.2, Part D. Toposes as theories. Clarendon Press, Oxford, 2002.
5. Lawvere F. W. Adjointness in Foundations, Dialectica, 23: 281–295.
6. Lawvere F. W. Tools for the advancement of objective logic: closed categories and toposes. 56 р.
7. Lawvere F. W. & Rosebrugh R. 2003, Sets for Mathematics, Cambridge: Cambridge University Press.
8. Lawvere F. W. & Schanuel S. 1997, Conceptual Mathematics: A First Introduction to Categories, Cambridge: Cambridge University Press.
9. Leinster T. Basic Category Theory. UK, Cambridge University Press, 1994
10. Mac Lane, Saunders. Categories for the Working Mathematician. N. Y., Springer, 1978.
11. Marquis J.-P. & Reyes G. 2012, “The History of Categorical Logic: 1963–1977”, Handbook of the History of Logic, Vol. 6, D. Gabbay & J. Woods, eds., Amsterdam: Elsevier, 689–800.
Price: 50 рублей
To order