User:W J Eckerslyke

Me
I am currently looking at some of the parts of Wiki concerned with set theories and other matters related to the “foundations” of mathematics. But I am not a mathematician (as defined in WikiPedia) and am therefore on very shaky ground making any comment at all. Perhaps I should remain silent. On the other hand, not being a mathematician, I have no commitment to vending any specific orthodox views, and hence I am perhaps well placed to examine foundations.

An ignoramus should keep his mouth shut; but an innocent who see the emperor naked should speak up. Hope I find the right balance!

Wikipedia
WikiPedia, being an encyclopaedia, does not publish “original research” but only material already published elsewhere. A good policy: if you cannot cite a source, keep quiet. But the downside is that something which is clearly untrue is acceptable, if sourced, and no objection can be posted unless one knows a counter-source, and that something which is clearly true cannot be posted unless somebody has said it elsewhere. Bizarre but necessary. Fortunately, there are discussion pages where the rules seem not to be applied too stringently!

Cardinality of the continuum
Some comments made. Several very useful responses received. Discussion temporarily retreated to these personal pages.

Richard's paradox
The resolutions presented seem at best rather limp, and generally applicable only to Richard's unnecessarily vulnerable formulation of it. So I used it as the justification for Richard's Principle (See my Discussion page), which I posted as a new Wikipedia entry. But this is likely to be deleted unless I can find a source for it!

Skolem's paradox
I don't fully understand why “mathematicians no longer consider Skolem's result paradoxical”. The resolutions offered seem unconvincing. But I think I'll have to study a bit more before I can make useful comments.

ZFC
At first sight ZFC seems (as presented in WikiPedia) to be riddled with problems. See list of points on my Discussion page, which I posted to ZFC Discussion. Talks continue! And as a result I have formulated a definition of Vacuous sets (see my Discussion page), which I shall have to try to find a use for.

Naif Set Theory
Is a consistent set theory possible? I think so. Watch this space!