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The Linguistic Limitations of Sets

 
 
saw038
 
Reply Fri 16 Sep, 2016 11:25 pm
If I say there exists an inside (i);

I am also saying there exists and outside (o).

I could then come up with a third category - a boarder one:

The set that contains o and i.

The definition of inside is: "the inner side of a thing."
So, let us presume that the broader category including i and o is called t (things).

But, we have produced a useless statement - a trap!

Because, the definition of a thing is "an object that one need not, cannot, or does not wish to give a specific name to."

The problem is we just gave this overarching class a name: thing; which is nonspecific..
But, I wanted to be specific with my naming, I wanted the name to only include inside and outside.

I wanted the entire set to only be comprised of (i,o).

But, what I am neglecting, is the fact the () carries some significance to it.

I don't have to define it as a 'thing' because the moment I put () around i,o...it becomes a singular entity.
What I am highlighting is a predicated relationship:

An outside is defined as "the external side of something," while an inside is: "the inner side of a thing."
The common factor being a 'thing'.

My point being is this:

The definition of inside is predicated by an outside and and vice versa;

Furthermore, they also share the existence of a 'thing'.

But, this 'thing' must be nonspecific, but my use runs contrary to its definition;

I want the set to only include inside and outside.

So,

these become my questions:

what would be the above (overarching) class of a inside/outside?

Even if the overarching set could be categorized by a word, would it not be a tautology?

If anything ever takes upon the existence of all, can 'all' not only be defined by the parts that make up all?
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Fil Albuquerque
 
  2  
Reply Sat 17 Sep, 2016 07:48 am
@saw038,
Belong or not belong is enough of a solution for your so called "linguistic" problem.
saw038
 
  1  
Reply Sat 17 Sep, 2016 10:00 am
@Fil Albuquerque,
But what would be the higher category that belong and non-belonging would fall under?
fresco
 
  2  
Reply Sat 17 Sep, 2016 12:23 pm
@saw038,
The key issues are definitions of 'existence' and 'thing'. Your focus on 'inside' and 'outside' is a subsidiary issue explored in part by Lakoff et al with respect to the 'non-representational' view of language.
saw038
 
  1  
Reply Sat 17 Sep, 2016 01:03 pm
@fresco,
I realize my example my not have been the best, and you are completely right it is subsidiary. I think the points you make are closer to what I was really trying to get at. Could you elaborate more on what you know about the idea of a 'non-representational' view of language?
fresco
 
  1  
Reply Sat 17 Sep, 2016 03:49 pm
@saw038,
Simplisically, following Wittgenstein's principle that 'meaning is usage', words are not to be taken as representational of 'things in themselves' but are 'nodes of significance' within communicative behavior whose utility is evaluated by successful goal attainment. Meanings cannot be divorced from the contexts in which they are used and they in turn are agents in the construction of those transient states we call 'reality'. Lakoff goes further than this by arguing that all language is embedded in bodily behaviors such as 'entering', 'leaving', falling etc...hence the human concepts of 'inside', 'outside' etc. Thus 'words' are 'metaphors' for our bodily relationsips with what we call 'the world'.
As far as 'set theory' is concerned and its foundation for classical logic, this is related to the human behavior we call 'measurement' the first level of which
is 'the nominal' or 'naming'. The disadvantage of this is that 'things' are then deemed to have 'independent properties' which cement their set membership, when in fact set membership can be contextually dynamic as far as behavior is concerned. Non binary logics such as 'fuzzy logic' have been subsequently developed as a result.
You will find, by the way, by reading my posting history that I take the view 'existence' is always relative, and never absolute. What 'exists' is often 'agreed' by most humans because of their common physiology and needs, but where needs differ arguments about 'absolute existence' are futile.












saw038
 
  1  
Reply Sat 17 Sep, 2016 05:38 pm
@fresco,
That is a lot to chew on. Very interesting stuff and well stated. I'll have to read some of your posts on existence because that topic really has everything to do with how we perceive reality and I believe it to be foundation from which other areas of philosophy originate.

Thanks for the comments. They were exactly the sort of feedback I was looking for!
fresco
 
  2  
Reply Sun 18 Sep, 2016 01:25 am
@saw038,
NB This summary of Wittgenstein's point is well written.
https://philosophyforchange.wordpress.com/2014/03/11/meaning-is-use-wittgenstein-on-the-limits-of-language/
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Fil Albuquerque
 
  2  
Reply Sun 18 Sep, 2016 03:34 am
@saw038,
The limits of a set are classically defined by those menbers who satisfy menbership requisites.. A set of all sets its by definition unknoable once it doesn't properly establish what does not belong. While one could argue that excludes those things which are not in a set one could counter argue there there is no thing which is not fitable for a set in one way or another.
If there is somethig that perhaps the set of all sets excludes its irrationality...that said, there is a distinction to be made between perceived irrationalitty, data complexity, and perceptive noise, and actual irrationality which may well not be a feature of Reality. What does it mean to define Rationality without counterpoint ? Well that that which is in the ratio is its own thing it doesn't require any justification. Logic does not require menbership of itself. Logos cannot be questioned without appealing to its very own ontological roots. In sum, Truth its its own !
Fil Albuquerque
 
  2  
Reply Sun 18 Sep, 2016 03:50 am
While Fresco makes the categorical mistake of questioning language foundations in expressing anything other then reality I've tried to say something similar in relation to the limits of a Set and Logic without getting Logic on trial through logic itself. It is not coherent. As for embodied cognition what to say ? Information always reports data about behaviour of things not about ghosts and shadows...its a mistake to appeal to ghosts and shadows to speak about the obvious, that is, data reports behaviour of things which have contextual functionality.
0 Replies
 
saw038
 
  1  
Reply Sun 18 Sep, 2016 09:58 am
@Fil Albuquerque,
Let me provide a better example of what I am trying to talk about:

If we want to define consciousness, you have to use consciousness to do so.

Therefore, whatever definition you come up for the notion of consciousness contains the application of consciousness itself.

Put another way, within your definition of consciousness is the very identity and a truer identity of consciousness than any of your words. In essence your definition becomes a tautology to some extent and it's unavoidable.

fresco
 
  2  
Reply Sun 18 Sep, 2016 11:56 pm
@saw038,
This problem of 'tautology' was recognized by Maturana's concept of languaging as a behavior, rather than a 'conscious process'. His criterion for accepting such an alternative approach was described by him as 'a matter of emotion'.
This article by Von Glasersfeld is a bit easier to read than Maturana himself.
http://www.univie.ac.at/constructivism/EvG/papers/125.2.pdf
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