If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Forum Home

Introduction

Terms of Use

RSS feed | RSS help

Introduction

Terms of Use

*Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.*

RSS feed | RSS help

RECENT POSTS IN THIS TOPIC

**Emile**: *on* 12/21/07 at 20:35pm UTC, wrote I give my understanding of the place of Topos theory in mathematics : ...

FQXi FORUM

November 22, 2019

I give my understanding of the place of Topos theory in mathematics :

Traditional mathematics are based on both the langage of set theory and classical logic . This means that any mathematical object is then described as a set with elements which becomes more and more complex as its level of abstraction increases.

Topos theory is issued from the langage of categories. More precisely Topos realise a kind of minimal interpretation of set theory in the langage of categories. This new view on sets gives a lot of freedom on the properties of the universe of sets on which the mathematician intends to works. For exemple it is claimed possible to consider sets without having to deal with the notion of elements of this set.

It seems that it is easier to cope with mathematical abstraction in category theory than in classical set theory. This is, may be, one part of the explanation for the vast amount of conceptual creation in mathematics brought by the German/Ukrainian/French mathematician Alexander Grothendieck.

It would be interesting to know from C. Isham if these considerations are important or not for the use of Topos theory he envisages in Physics

report post as inappropriate

Traditional mathematics are based on both the langage of set theory and classical logic . This means that any mathematical object is then described as a set with elements which becomes more and more complex as its level of abstraction increases.

Topos theory is issued from the langage of categories. More precisely Topos realise a kind of minimal interpretation of set theory in the langage of categories. This new view on sets gives a lot of freedom on the properties of the universe of sets on which the mathematician intends to works. For exemple it is claimed possible to consider sets without having to deal with the notion of elements of this set.

It seems that it is easier to cope with mathematical abstraction in category theory than in classical set theory. This is, may be, one part of the explanation for the vast amount of conceptual creation in mathematics brought by the German/Ukrainian/French mathematician Alexander Grothendieck.

It would be interesting to know from C. Isham if these considerations are important or not for the use of Topos theory he envisages in Physics

report post as inappropriate

Login or create account to post reply or comment.