7 Sept 2007
For Ermeine on request .
“Physics from Fisher information” by B.R.Frieden ISBN 052163167X
http://andreswhy.blogspot.com : see in general , or search for “mining the Oort” ,
Topos is simply a new name for non-Aristotelian logical systems .
Gauss saw it , but did not publish , deeming it too controversial . (He hated controversy.)
Russell and Whitehead proved that A and not-A is less than the Universum .
Godel’s work was a consequence of this .
What does it mean?
If you say that something exists (say A) , it means it must be defineable in some way , separate . In other words , the person talking about A plays a role , he defines it . Even using a symbol like A makes it separate .
But there is then always something left over . The indefinables . In other words , A and not-A is not the Universum .
This has been rigorously proved . It is obvious from the above .
True is defined as existing . Existence is defined as defineable . Something that is not defineable then is true and not-true . The essence of quantum systems .
If you have read and understood what I wrote before , you know more about these systems than the Topos authors .
Unless a Wright-proof (ie an undeniable physical gadget ) results , these theories become froth on the gales of history .
Topos is a typical publish or perish phenomenon . Dress up old , known things in a new guise . Some quotes from the Topos paper :
“Intuistionic logic” : what does not fit , gets swept under the carpet . They should get a fuzzy logic Roomba .
“Heyting algebra” : fuzzy logic , as used by your fridge or microwave , but a neat term .
“Sets” is used in the argument : sets? Sets are a number of similar identifiable items , these being identified and counted by the hypothetical observer . This directly contradicts the basic assumption of Topos .
Notice how classical set theory warps if you add the hidden assumption of somebody doing the defining and counting .
Topos is not a very good attempt . Frieden did better .