Date: Jul 15, 2013 9:59 PM
Subject: Re: Ordinals describable by a finite string of symbols
On 7/12/2013 9:51 AM, apoorv wrote:
> On Wednesday, July 10, 2013 7:22:46 PM UTC+5:30, Aatu Koskensilta wrote:
>> dull..@sprynet.com writes:
>>> Sigh. Taking 'describable' to mean 'describable (definable?) by any
>>> String of symbols' makes no sense! Symbols don't mean anything - it's
>>> impossible to use a string of symbols to describe anything.
>> As you say, we must assign some meaning to a string of symbols for it
>> to describe anything.
> How is this meaning assigned? By another string of symbols?
Well, I had hoped someone else would have answered this.
At the very minimum, you need to get a notion of
truthmakers and truthbearers. This first link will
discuss "truth and language",
You will find that it immediately discusses truth
Do not spend too much time on this. Just know that
this is the basic jargon involved.
This link specifically discusses truthmakers,
These queries will bring up other links,
Tarski presents his views as a variation on correspondence
theories. Others interpret his views as a deflationary
theory. But, this does not get to the real matter of your
question. You should pursue the various mentions of
Tarski in these links simply because of his influence on
the foundations of mathematics.
Few mathematicians have really considered what they are
saying when they point to Russell's work. Being a prolific
philosopher, Russell's ideas are well documented. And, it
is my personal view that Russell's rejection of Frege's
theories is significant. So, one should at least look at
elements associated with Russell since they are available
Russellian description theory influenced the construction
of "Principia Mathematica". It is true that Russell spoke
of "logical proper names". Since you have shown some concern
with "definability", I would think you would reject this part
of his ideas outright. Under that presumption, note that
Russell held a viewpoint called "knowledge by acquaintance".
Here are links relating to Russell's views:
At a more metaphysical level, Russell proclaimed himself
as a neutral monist. I think you will just adore what is
"meaningful" behind his logical reductions,
I am not saying that these are "mathematical" answers.
But, I have yet to find any "mathematical" answers that
do not rely on *given* objects which I simply cannot
accept as "given". So, I prefer the idea of a logical
foundation in which every symbol that is not a logical
constant is defined (or definable in principle).
Anyway, I hope you find the links informative (don't go
crazy trying to piece them together). I also hope that
someone else can give a better answer to your question
than I have attempted.