April 14, 2010
I have not yet read all of Nic Weaver’s comment on the liar paradox however the beginning is interesting enough to mention it here.

Edit: If I understand him correctly, then he claims that the law of excluded middle is not applicable for what he calls ‘heuristic concepts’, which are (and here I interpret freely) concepts with some immanent circularity.

Leave a Comment » | Foundations and Philosophy | Tagged: Mathematics, Negation, Proof, Truth | Permalink

Posted by Uwe Stroinski

August 29, 2009
The LaTex to WordPress converter is installed and tested. I seem to be able to handle it. Meanwhile my guest took up speed and produces material at an enormous rate. Things you can expect within the next few days in no particular order are:

- He explains the nature of scientific laws. (This is cute, pretty standard and understandable. Finally something!)
- He goes into details on defining and describing notions. Apparently there is a third way to introduce notions. He calls these notions ’emergent’. (I am not sure, whether I got that.)
- He comments on an approach (by scientists) to estimate the probability of unconditional existence of things. (What? That is hopefully not publicly funded!)
- He laments on our understanding of ‘truth’. (I guess he criticizes that we still use a notion of truth in mathematics which in essence is several thousands of years old. Modern truth theories provided by philosophers are just ignored. I fail to see his point. What else should we do? Maybe I point him towards Tarski.)
- He presents his view on the ontological status of mathematical objects. (I guess I understand what he is saying here and this sends shivers down my spine.)

Leave a Comment » | Logistics | Tagged: Emergence, Mathematics, Ontology, Scientific Law, Truth | Permalink

Posted by Uwe Stroinski