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پژوهشکدهٔ ریاضیات


Mathematical Logic Weekly Seminar سمینار هفتگی منطق ریاضی




TITLE  
Talking About the Sentences that Talk About Themselves!


SPEAKER  
Saeed Salehi  
University of Tabriz & IPM  
 


TIME  
Thursday, June 20, 2019,   14:00 - 16:00


VENUE   Lecture Hall 1, Niavaran Bldg.



SUMMARY

 

Talking about oneself is natural in natural languages. But it can be ambiguous or can cause difficulties in formal languages. For example, the following sentence Ax Ey (x=2y ˅ x=2y+1) says that every number is either odd or even. But how can a sentence talk about itself? Gödel had the opinion that if the biconditional φ ↔ Ψ(#φ) holds, where #φ is the Godel code of φ, then φ says about itself that it has the Ψ property. In this talk, we will discuss on this interpretation and will give some mathematical arguments for some philosophical discussions on the truth or falsity of Gödelean sentences of arithmetical theories. By definition, a sentence γ is a Gödelean sentence of theory T when the biconditional γ ↔ ¬ PrT(#γ) is provable in T where PrT(x) is the provability predicate of T.

 




تهران، ضلع‌ جنوبی ميدان شهيد باهنر (نياوران)، پژوهشگاه دانش‌های بنيادی، پژوهشکده رياضيات
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Niavaran Bldg., Niavaran Square, Tehran
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