Wednesday, September 07, 2011

Two senses of ‘formal’

There are two interesting posts by Catarina here and here about the problem of ‘system imprisonment’. This is what happens, she says, when the process of formalising arguments or observations leads to the replacement of real issues by system-generated ones, which are really issues emerging from the formalism being used, and not the underlying or real issue. She says her favorite example here is the issue of 'free variables' in de re modal sentences, which then became seen as a real, deep metaphysical issue.

This is close to some concerns I have aired here over the past year, and I will take this up again in subsequent posts. To begin with, it should be noted that there are at least two senses of the term ‘formalise’.

Formalisation in the strict sense means representing sentences or arguments in any language (usually a natural language like English or, in the case of the medievals, Latin) with schematic letters in place of expressions, in order to display the logical form of the sentence or argument. Thus “every B is C, every A is B, therefore every A is B” represents the form of the ‘Barbara’ syllogism. Every instance of that argument form, i.e. every instance obtained by replacing ‘A’, ‘B’, ‘C’ etc., with common nouns like ‘man’, ‘animal’ and so on, is valid – the premisses cannot be true and the conclusion false. In this sense Aristotle, who seems to have been the first to use such schematic representations, was the originator of formal logic

In another sense, formalisation means the translation of ordinary language sentences into a formal language, usually a calculus with a syntax and vocabulary that does not resemble natural language much at all. Thus, we translate ‘every man is an animal’ into the formal language as (for example) ‘Ax [ man(x) -> animal(x) ]’.

I believe that Catarina means ‘formalisation’ in the second sense. Without formalisation in the first sense, i.e. representing different arguments as having a common ‘valid’ form, it is not clear we could do logic at all. But with formalisation in the second sense, i.e. using a non-natural ‘formal’ language into which metaphysical statements or arguments are translated, we run the risk of being trapped inside that language in the way that Catarina is worried about.

More later.