Brent wrote: *1. Presumably those true things would not be 'real'. Only provable things would be true of reality.* ** *2. Does arithmetic have 'finite information content'? Is the axiom of succession just one or is it a schema of infinitely many axioms?* ** Appreciable, even in layman's logic.
In '#1' - I question "provable" since in my agnosticism an 'evidence' is partial only, leaving open lots of (so far?) unknown/able aspects to be covered. In the infinity(?) of the "world" also the contrary of an evidence may be 'true'. #2 is a technically precise formulation of what I tried to express in my post to Bruno. IFF!!! "anything" (i.e. everything) can be expressed by numerals, the information included into arithmetic * IS* infinite, however as it seems: in our (restricted) view of "the world" (Nature?) there seem to be NO numbers to begin with. In our human 'translation' we see 1,2, or 145, or a million "OF SOMETHING" - no the (integer?) numerals. Axioms? in my vocabulary: imagined things, necessary for certain theories we cannot substantiate otherwise. In another logic than human, in another figment of a "physical world" different axioms would serve science. 2+2=4? not necessarily in the (fictitious) "octimality" of the '[Zarathustran' aliens in the Cohen-Stewart books (still product of human minds). -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
