fom
Posts:
1,969
Registered:
12/4/12


Re: Ordinals describable by a finite string of symbols
Posted:
Jul 15, 2013 9:59 PM


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? > Apoorv >
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",
http://plato.stanford.edu/entries/truth/#TruLan
You will find that it immediately discusses truth bearers.
Do not spend too much time on this. Just know that this is the basic jargon involved.
This link specifically discusses truthmakers,
http://plato.stanford.edu/entries/truthmakers/
These queries will bring up other links,
http://plato.stanford.edu/search/searcher.py?query=truthmakers
http://plato.stanford.edu/search/searcher.py?query=truth+bearers
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 and "judgeable".
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:
http://plato.stanford.edu/entries/knowledgeacquaindescrip/
http://plato.stanford.edu/entries/propositionssingular/
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,
http://plato.stanford.edu/entries/neutralmonism/
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.

