On Thursday May 14th Tristan wrote :

I'd take grammars as modelling systems. Grammars for mathematical languages as well as grammars for natural languages model the use of a certain vocabulary following a given syntax. Grammars for natural language or for mathematical languages can of course be expressed with natural language, but also with stricter and less ambiguous languages. With many precautions, it may be possible with natural language to define precisely a strict grammar for a strict language.

The *causal structure* is not directly sketched by the grammar, but rather by a conceptual system (like an ontology) AND a semantic system (which can be driven by lexicon and by syntactic relations). Over the semantic system comes the interpretative system (a truth value machine). For evaluable expressions, the interpretation (the value) of mathematical expressions or natural language propositions is given by an *interpretation function* applied on the source expression.

Tristan – I agree that a grammar for a natural language (taken as a semi-formal system and described syntactically) is only concerned with the "well-formedness" of sentences, and that a sentence such as

i. "Socrates died because the Japanese bombed Pearl Harbor"

is grammatically correct, whatever its status as the expression of some particular causal relation.

However, I'm more concerned with the "temporal implications" underlying *tense* –and these are usually considered to be questions of syntax rather than of either ontology or semantics. This covers evidently non-standard constructions such as *I will had seen him*, but might also concern sentence-level structures. For example, is the unacceptability of

ii. "Socrates died because the Japanese will have bombed Pearl Harbor"

a matter of grammar (syntactical structure) or a matter of 'interpretation' (ontology, semantics…)?

The structure of (ii) implies that a PAST event S occurred because a FUTURE event B will occur at or before a certain point P (which is also in the future); which is – at least – conceptually unacceptable, regardless of the actual relations obtaining between the particular events mentioned.

However, I'd also agree that the atomic sentences which make up (ii) are individually well-formed; the question concerns the FORM of implications allowed by, for example, a causal conjunction such as "because".

"Natural language may be ambiguous, but remains a modelling system. With enough linguistic precautions, you can agree with someone on the non-ambiguity of your model."

This, I think, requires one or two philosophical remarks. "Natural language" as a whole cannot be clearly delimited, as it would seem to include whatever metalanguage one might establish in order to describe it; given a certain understanding of "natural language", it also includes mathematical and formal languages (which are thus considered as "special cases" of natural language). On this understanding, the grammar of a given natural language (let's take English as the obvious example) is a model of the syntactical rules governing whether a certain structure or expression is "well-formed" or not. However, we should be wary of REDUCING a grammar to the syntax of the language. A grammar should tell us why sequences such as

*iii. will the a by and she the happy in be was under

are ill-formed on the sentence level, but also why the verb phrase in

*iv. he will walked a mile

is ill-formed. I think (*iv) is of interest here when we consider the kind of "correction" it might encounter – that is, suggesting that it be re-written either as "he walked a mile", "he will walk a mile", or "he will have walked a mile". In each case, the "grammatical" correction falls under a "notional" category (past simple, future simple, future perfect simple).

Now, while the notions "past", "present", and "future" are – as concepts – more a matter of the semantic dimension of English, the terms "present simple", "future simple", etc. would seem to 'name' *structures*. Can we detach the "notional content" of such structures from the kind of "grammatical" description we would give of them?

Returning to (*iv) above. If we explain that "we will walked" is unacceptable because "will" takes a bare infinitive, we have ALREADY made an assumption about the sense of (*iv) – that it expresses some event which a putative speaker places in the future. If we offer the reformulation "he will have walked a mile", we are presupposing that the putative speaker is stating that by some point in the future an event of walking a mile will be in the past. And if we reject the "will" entirely, we are assuming that it expresses an event which the speaker places in the past.

Any "correction" made to the syntax of (*iv) is based on a notional assumption; this implies that any explanation of why (*iv) is ill-formed requires that we state the alternatives AND the contexts in which each alternative would be "correct". It would be very difficult to imagine a purely mechanical process by which such syntactical errors could be rectified without reference to the wider context of the ill-formed item, which implies that the well-formedness of certain items depends in part on their notional rather than purely syntactical context. This is borne out at sentence level by a sentence such as

*v. He will see me before he went home

where the atomic sentences are well-formed but where the conjunction doesn't permit a sequence of future and past tenses. On the 'purely' syntactical level, (*v) is well-formed, yet it is grammatically incorrect.

There would seem to be a "temporal structure" to a natural language, such as English, which operates on the grammatical level (dictating which sequences of symbols are acceptable). On the purely syntactical level, analysis of sentences such as (*iv) and – perhaps – (*v) will only show that they are not well-formed; it will not suggest which of several alternatives IS well-formed; the "correct" temporal sequence depends not on syntactic elements but on either the extension or the intension of the terms used.

Personally, I'd contend that (*v) is SYNTACTICALLY well-formed but not GRAMMATICALLY well-formed; this would seem to suggest that a "grammar" makes certain notional assumptions that are absent from any "purely syntactical" description of a given language. In this respect, "grammar" has more the sense given to it by the Second Wittgenstein (St Ludwig, like Henry IV, came in parts**).

As to the "ambiguity" of the modelling system: hmm. Let me think.

[**I said "parts", Missus, not "quarts". St Ludwig was not an elephant.]

Tristan - it's good to see you back!

I've developed the ideas a bit, working more on the "comparison of models"; I've decided that the purely synactical angle risks being a bit of a red herring, though our syntax *should* suggest something about the way we regiment experience in this or that language - or rather, the way this or that language regiments "possible experience".

In many ways, it's a question of taking Quine to the limits...