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CONLANG  December 2012, Week 5

CONLANG December 2012, Week 5

Subject:

Re: If

From:

"Jacob O." <[log in to unmask]>

Reply-To:

Constructed Languages List <[log in to unmask]>

Date:

Mon, 31 Dec 2012 12:39:56 -0500

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (59 lines)

On Sat, 29 Dec 2012 14:11:47 -0500, Alex Fink <[log in to unmask]> wrote:

>On Fri, 28 Dec 2012 22:42:43 -0500, Jacob O. <[log in to unmask]> wrote:


>UNLWS being a language with full expressive capability, I'm sure there will eventually arise other ways to talk about these notions.  (Leave the absurd "there's only one way to do it" to Python!)  But, formally speaking, we have (at present) given these worldy predicates forms which are quite unlike the usual glyphs-and-binding-points one, with an eye towards them being the most grammaticalised and thus most basic options.

Most language-users don't mean to make reference to a plurality of worlds in day to day speech about contingency. More often, they wish to express a plurality of conceivables (mental possibility). One of the problems with David Lewis' Counterpart Theory is that you're forced to strip actuality of its meaning--for David Lewis, actuality is an indexical rather than a modality.

The point I was trying to make about Descartes is that modality is never only a content. If D. doubts certainty, what has he done? He has applied the modality of possibility to that of which he is certain, or, in other words, to necessity. If some parts of modality are irretrievably mixed into the content--as Lewis does by turning actuality into an indexical--you make impossible a good deal of conversational nuance. 

Meaningful use of contingency implies at least two options, i.e. implies possibility: "If A then B" means nothing if "A" is not possible. Similarly, if "A" is necessary, then "If A then B" might as well be "A and B", or even simply "B", since "Not A" was never possible in the first place. In everyday use the possibility (plurality of options) is in the language-user's mind, as it is uncertainty (possibility/plurality of options in thought) about "A" that makes the expression of "If A then B" a useful one. Of course, out of "A" and "Not A", one might be vastly more likely, but the fact that both are *mentally possible* is what makes the statement one worth uttering.
 
When someone expresses mental uncertainty, it's nothing to write home about. When, on the other hand, a physicist expresses uncertainty between options, they might meaningfully mean any one of the following options:
a) there are possible worlds and we can't know which one we live in until we make an observation;
b) the [actual] world is simultaneously in multiple states until an act of observation;
c) there is no [possibility of] knowledge until an act of observation is made.


>>Somewhat in line with this, have you considered ways of bracketing out one or more of the Language-Thought-Reality trio? Bracketing reality, for instance, to talk only about the interaction between thought and language, or bracketing language (by treating it as transparent). A non-linear system might be able to more precisely/succinctly express these distinctions by making explicit discursive restrictions. More concretely, Descartes would want to put discussions of reality off-limits because part of his project is _doubting certainty_, which seems downright bizarre unless you can express the modalities of different levels.
>
>This trio is new to us.  Google seems to suggest it's due to Whorf: is there something we should read for it?

I don't think anything in particular needs to be read, because at its heart my point doesn't require a lot of theoretical understanding. I'm simply arguing that modality needs to be separable from content, and that only by doing this can your language succeed in being 'fully expressive'. Otherwise it fails to allow some modal configurations that are, even if you don't believe they're correct, at least not provably wrong.

Modal disagreements occur all the time because of the difficulty of answering the following question: "How do we know the modality of any statement?".

Some types of empiricists, for instance, will claim that "2*2=4" is possible or probable, but will also admit the possibility that they have made a mistake somewhere--or indeed, that in the past when they calculated the product they were correct, but that if the experiment were conducted on Alpha Centauri, or 12 billion years in the future, or whatever, the results might vary.

>I'm inclined to the idea, which I picked up mostly from Less Wrong, that one should be careful about introducing reality onto the stage with these other two at all -- none of us have any sort of privileged access to reality, after all, just our percepts and our mental models, and a cognitive algorithm which operates as if that _was_ direct access to reality.  And it's objects within those mental model that are the natural referents of language.  
>

In a way, that's exactly my point: you've already gone and bracketed out reality and the modality of actuality.

I agree that bringing all three onto the stage at once leads to confusion; there's really only room for two. The question then becomes, "Which two?" and I answer that it depends on what the language-user wants to express.

An eliminative materialist like Pat Churchland might wish to speak about reality, but to do away with talk about most things mental. By disallowing discussions about reality (as distinct from thought and language), you make anyone who believes the statements of eliminative materialism sound absurd--and that one might disagree with those statements does not imply that one would want discussions of/about it to be rendered nonsense.

Since Pat Churchland doesn't believe in mental phenomena, she would be forced to assert seemingly bizarre and possibly even contradictory things, all the while mangling the semantics of your language by e.g. using words you use to refer to mental phenomena to make reference to things that must be separated from the mental before consideration.


>>>So though many loglangs love their logical conjunctions, so far we
>>>don't have any. :-P (OTOH, UNLWS doesn't _set out_ to be a loglang,
>>>but primarily rather a 2D written language.)
>>
>>Makes me wonder whether there is a clear way of setting up truth-tables for non-linear logics. (It sounds like a nightmare.)
>
>Well, step one, what's a non-linear logic?!

A non-linear logic would be a formal version of UNLWS (or some comparable system). I don't know how feasible a proof would be of the non-equivalence between such a Fully Two Dimensional Formal Language (FTDFL) and predicate logic, so I'm not going to attempt one. I'll sketch out instead the criteria that define the equivalence or non-equivalence of the two.

Each FTDFL statement p* translates into a set of linear statements P in a predicate logic by cycling through traverse orders, start-, and end-points. If p* has a translation in a predicate logic that preserves all of the information in p*, then that statement will be p', or the linear translation of p*.
I suspect that P might not always be finite, but that it will always be countable, and I'm operating under that assumption.

1. For all p*, there is at least one member of P that can reconstitute p*.
    There need not be a decision procedure for choosing p' out of the members of P. If p' exists for all p*, then FTDFL is equivalent to predicate logic.
2. For all p*, all members of P have the same truth conditions, or subsets of the same set of truth conditions.
    If this is the case, p* might be reconstituted from P as a whole--although if p* is equivalent to some logical composition (over linear operators) of the members of P, the logical composition should itself be a member of P and should be equivalent to p', or itself be p'. If irreducibly non-linear operators are required to compose p* out of the members of P, then FDTFL is not equivalent to predicate logic.

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October 2002, Week 1
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