Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
fom
Posts:
1,037
Registered:
12/4/12
|
|
Re: Cantor's absurdity, once again, why not?
Posted:
Mar 17, 2013 2:05 AM
|
|
On 3/16/2013 5:06 AM, WM wrote:
> On 16 Mrz., 00:09, fom <fomJ...@nyms.net> wrote:
>> On 3/15/2013 2:12 AM, WM wrote:
>>
>>> On 14 Mrz., 23:36, fom <fomJ...@nyms.net> wrote:
>>>> On 3/14/2013 5:15 PM, WM wrote:
>>
>>>>> distinguishable, that means definable by finite words
>>
>>>> How does a definition "distinguish"?
>>
>>> A definition is a name.
>>
>> Ok. But, then I would have to ask
>> what you mean by name.
>
> A name is a finite sequence of letters that two or more persons have
> agreed upon to be used for a given object. This object may be material
> or immaterial.
I had simply been a little
surprised in the other response
and gave a slightly short-tempered
remark.
So I should be asking how two
individuals come to agreement
as to the meaning of names.
The following summarizes various
discussions in the literature concerning
agreement with regard to identifying
reference in language.
The idea of an agreement coincides
with what we have mentioned
before. Namely, that language
meaning does derive from pragmatic
considerations and that the
"ideal language theory" that is
predominant in metamathematical
ought to be more informed by
pragmatics.
With regard to "learning" scenarios,
there are two of which I am aware.
Mostly, people think of how
children acquire langauge. For
the most part, that would not
apply here except in a strange
way that I will make clear
now.
Certainly, many have discussed the
issue of language acquisition, but
I am taking from the presentation
from Strawson "Individuals".
What seems to be relevant is
Strawson's observation that
children begin by treating all
nouns as mass terms. A mass term
is distinguished from a singular
term in the sentences,
'I drink water'
'I pet the cat'
As a child is learning, one would
be more likely to hear the statments,
'I drink water'
'I pet cat'
I mention this only because of a
strange translator's footnote
in Lesniewski,
"As the Polish language does
not contain counterparts of
'a' and 'the', the translator
has had to add the appropriate
article whenever English has
required it."
I cannot speak to what the
Polish language has as counterparts
to definite and indefinite
references, but I can imagine that
the difference in the languages
could explain how Lesniewski
had been so astute to reject
the claims of Russell's paradox
at such an early date.
The second learning scenario
is that given by Quine in
"Word and Object". The idea is
that an anthropological linguist
is visiting an indigenous
population of people and attempting
to formulate the first translation
of their language.
This is what has been referred
to on wikipedia as the Quinean
double standard.
Now, the general pragmatic notion
of agreement between speakers is
given by Grice. I have no
original sources for Grice, but
in the literature I do have there
are three principles by Levinson
that seem to be accepted by others.
They are what would be called
Neo-Gricean inferential princples.
Q-principle:
Speaker's maxim-
Do not provide a statement that
is informationally weaker than
your knowledge of the world
allows, unless providing a
stronger statement would
contravene the I-principle.
Recipient's corollary-
Take it that the speaker made
the strongest statement
consistent with what he knows,
and therefore that:
i)
if the stated expression is
informationally weaker than
some another comparable
statement, infer that the
speaker knows the stronger
statement to be false
ii)
if the stated expression
fails to entail another
comparable statement that
a stronger statement would
entail,
I-principle:
Speaker's maxim-
Produce the minimal linguistic
information sufficient to
achieve your communicational
ends (bearing the Q-principle
in mind)
Recipient's corollary-
Amplify the informational
content of the speaker's
utterance, by finding the
most specific interpretation,
up to what is judged to be
the speaker's intention
unless the speaker has
used a marked expression.
M-principle:
Speaker's maxim-
Indicate an abnormal,
non-stereotypical situation
by using marked expressions
in contrast to what one would
use to describe normal
stereotypical expresssions.
Recipient's corollary-
What is said in an abnormal
way indicates an abnormal
situation.
Clearly these rules of implicature
are not directly relevant to the
issue of naming. They are presented
here as background for a discussion
of Searle's account of reference
in terms of language acts. Unlike
simple description theories, Searle
takes into account the language acts
of a speaker and the recognition of
speaker intentions by a hearer.
There are some preliminary conditions
to Searle's positions given by
Boersema:
1)
The axiom of existence: There must
exist one and only one object to
which the speaker's utterance may
apply.
2)
The axiom of identification: The
hearer must be given sufficient
means to identify the object from
the speaker's utterance of the
expression.
3)
A necessary condition for the
successful performance of a definite
reference in the utterance of the
expression is that either the
expression must be an identifying
description or the speaker must
be able to produce an identifying
description on demand.
Given these conditions, Boersema
presents Searle's account as
follows:
Given that speaker S utters an expression
R in the presence of hearer H in a context
C, then in the literal utterance of
expression R, speaker S successively and
non-defectively performs the speech act
of singular identifying reference if and
only if the following 7 conditions
obtain,
1)
Normal input and output conditions
obtain (speaker S and hearer H
understand one another and participate
in the language act felicitously)
2)
The utterance of expression R occurs
as part of the utterance of some sentence
or similar unit of discourse T
3)
The utterance or discourse T is the
purported performance of an illocutionary
act
4)
There exists some object X such that
either expression R contains an identifying
description of object X or speaker S is
able to supplement expression R with an
identifying description of object X
5)
Speaker S intends that the utterance of
expression R wil pick out or identify
object X to hearer H
6)
Speaker S intends that the utterance of
expression R will identify object X to
hearer H by means of H's recognition of
S's intention to identify object X and
speaker S intends this recognition to be
achieved by means of H's knowledge of the
rules governing expression R and his
awareness of context C
7)
The semantical rules governing
expression R are such that it is correctly
uttered in discourse T and in context C
As I pointed out in the other post,
your views presuppose authorial intention
(or, in Searle's construction, speaker's
intention).
Standard mathematics attempts to avoid
this complexity by asserting an
extensional foundation.
It is a simple matter to use the word
"agreement". It is far more difficult
to explain it as "obvious" if others
are aware that this has been and is
currently being investigated.
You have yet to explain yourself
adequately.
|
|
|
|
