Syntax and semantics

The syntax-semantics distinction

An analogy: the distinction between syntax and semantics is like the distinction between a train of wagons and what's in the wagons.

Grammar

How are we to think of the syntax of a language?

In traditional 'grammar' there were different categories of words, and rules which said how these might be combined if a properly grammatical sentence was to be arrived at.

Uninterpreted symbols

What is there in language that corresponds to the empty wagon?

'Uninterpreted symbol': a language element which has not got any meaning.

A simple formal language:-

Symbols:

‡

µ

¥

Rules:

To form a properly grammatical sentence in this language:

  1. There must be a ‡
  2. There must be either µ or ¥ before the ‡
  3. There must be either µ or ¥ after the ‡

This permits just two grammatical sentences:µ ‡ ¥ and ¥ ‡ µ

Logical calculi

Now think of adding a third feature, besides symbols and rules for sequencing them: derivation rules

Think of a rule which says: if you have got sequence A then add sequence B.

Eg if you've got µ ‡ ¥ then add ¥ ‡ µ

A calculus: a set of uninterpreted symbols with rules which say which further sequences you can have, given what you've already got. It's a calculus.

And a system of this kind - uninterpreted symbols, rules that legitimize certain sequences if certain others are already legitimized - gets intriguing if the rules you set up copy the rules that appear to be used in real argument, or real sums. Then you have got a formalisation of argument - logic - or a normalization of calculation - mathematics.

In a logical calculus there are simply:

1. Rules for determining what counts as an expression in the system

2. What sequences of expressions count as well-formed (well-formed formulae or wffs).

3. Which sequences of expressions count as proofs.

 

TWO SENSES OF SYMBOL

1. A something that stands for something.

2. A mark that belongs to a set marks, and a set of rules, such that the rules determine how the marks may be combined.

'Grammar' in natural languages

Chomsky: if you are to get a machine to speak like we do, you will have to get it to speak grammatically. And the way to do this is to program into it the syntactical categories, and the rules governing how they may legitimately be sequenced.

Semantics

If we can understand how the brain might manipulate uninterpreted symbols according to rules, how are we to understand how those symbols might stop being uninterpreted and carry meaning?

An approach through causality.

Here is a starting idea: a 'symbol', if we are thinking of a mechanical brain, is something electronic, a pattern of electrical activity in a set of neurons. Suppose it was always stimulated by a particular type of thing in the environment. Wouldn't that give it meaning? If a particular pattern of electrical activity in the brain was always triggered by your seeing a badger, wouldn't that confer the meaning 'badger' on the pattern?

 

END

Revised 19:01:03

 
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