Date: Jul 15, 2013 9:59 PM Author: fom 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?

> -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/knowledge-acquaindescrip/

http://plato.stanford.edu/entries/propositions-singular/

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/neutral-monism/

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.