[om-list] On the Analytical Semantics of Natural Languages

[Mark Butler]

I have lately discovered that although analytical linguistics is a big 
deal these days, no one seems to do pure research into analytical 
semantics.  The existing research in semantics (what is or should be the 
study of the correspondence between language and reality) is largely 
pre-analytical.

One might say with some justice that even the philosophers are more 
grounded in reality than the linguists.  Given the reputation of 
philosophers, I find this mildly amusing.  The linguists might say that 
they study language in a content neutral fashion - legitimately 
separated from epistemology the same way mathematics is from science.  
But linguistics as a whole seems to have a concerted bias against both 
science and epistemology, largely because they spend too much time 
associating with loopy philosophers (Nietzche, Foucault, ...) and not 
enough with sound ones (Frege, Wittgenstein, ...), let alone with many 
natural scientists.

 Now of course, Peircean semiotics is an improvement, but it is largely 
pre-analytical. And of course generative grammars and syntax are highly 
analytical, but as far as I can tell the analytical study of absolute 
(as opposed to relative) meaning is confined to the field of analytical 
philosophy. 

What we have in essence in analytical structuralism (Chomsky, et seq) is 
a mathematical model of syntax.  But it is a superficial model, because 
generative grammars in natural language does not have the amazing 
properties that generative grammars have in mathematics.   In the 
pristine world of mathematics, a generative grammar can be used to  
generate all the provable theorems of an axiomatic system - provided you 
have a computer fast enough or can wait an infinite amount of time for 
the result.

But in natural language, a generative grammar, the glory of analytical 
structuralism, just enumerates the sentences that are grammatical, i.e. 
it can be used in principle to distinguish English from gibberish.  
However, it tells you nothing about the truth of a statement, not even 
about its very logical consistency. 

Take the logical contradiction, "A is not A". An English generative 
grammar will correctly tell you that that statement is grammatical, but 
cannot be used to tell you that it is a contradiction.  Logic, the field 
that tells you why this sentence is meaningless, doesn't seem to be much 
of a focus of linguistics (if pursued at all), perhaps because it the 
traditional domain of the departments of philosophy and mathematics.

For a sentence to be meaningful, it must generally be grammatical. For 
anything larger than a single sentence to be meaningful, it must be 
logically self-consistent.  And of course for a sentence to be true, it 
must correspond to the real world.

What we have in lingustics is a good theory of syntax and grammar, in 
philosophy and math we have basic theories of multi-valued logic 
(bipolar logic is a near disaster in natural language), but no one seems 
to work on analytical semantics - the mathematical representation of the 
correspondence between symbol and reality, save for a few rogue AI types.

As a field of study, analytical semantics doesn't seem to exist at all.  
As far as I can tell, a proper theory of linguistic meaning, must be 
based on the following, in order of importance to meaning:

1. A full blown "fuzzy" logic compatible with the target language
2. An analytical model of grammatical operators (and/or/not) in terms of 
a multi-valued "fuzzy" logic
3. An analytical verb tense model
4. A generative grammar of the target language
5. A probalistic or statistical model of knowledge
6. An analytical tranformation procedure based on (1-5) to generate a 
full analytical model of any text.
7. A basic analytical model of natural science
8. An analytical model of the relevant facts
9. An analytical model of the relevant beliefs and belief systems of 
both the author/speaker, and the target audience

The reason why analytical semantics of natural language does not exist 
as a body of knowledge appears to be that no one does seems to do pure 
(rather than applied) research into steps (2), (6), (8) except the rogue 
AI types I mentioned.  No one does research into (9)  yet, as far as I 
can tell.  (1) appears to be well accomplished, I am sure some research 
has been done on (2) and (3). (4) is well in hand, the groundwork for 
(5) is well laid, (7) has been done by AI people before.

Comments anyone?

 - Mark Butler




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