Natural and artificial languages

Belette makes a breathtaking comment here that deserves comment. 

I know about the difference between a pointer and the thing pointed to. I'm a software engineer. Its all a lot clearer in an artificial language; one day philosophers will realise that.

This is breathtaking both in its ignorance and (for that reason) in its arrogance.  For the entire history of Anglo-American philosophy since Frege in the 1880s and Russell in the 1900s onwards is about using the insights acquired from the development of the predicate calculus - mainly by Russell and Whitehead in Principia Mathematica - to address ancient philosophical problems.

Russell says "I remain convinced that obstinate addiction to ordinary language in our private thoughts is one of the main obstacles to progress in philosophy"*.    Russell's early work explored the idea that the misleading subject-predicate form of traditional Aristotelian logic was responsible for the pernicious defects of monism.  His theory of descriptions is intended to show that by using a formal language to analyse a problematic sentence like 'the king of France is bald', we can resolve an apparently intractable philosophical problem.  Following that, almost the entire program of Anglo-American analytic philosophy (AAA) is to address philosophical problems by analysing ambigous, vague statements expressed in ordinary language into precise, crisp, verifiable statements in some formal or artificial language. Obviously the distinction between 'pointer and thing pointed to', which is essential to Tarski's theory of truth, has a significant place in this program.

So what is it that philosophers are not realising? 

*Quoted in R.M. Sainsbury, "The Perfect Language", Russell, Routledge 1979, p.140

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.

It goes the other way about

Here is a blog that I don't follow enough. Cambridge logician Peter Smith reflects on some profound issues on the philosophy of logic and language while drinking wine in Tuscany (how much do they pay him?). In this post he makes two points close to my heart.

1) Formal languages don't magically do what ordinary language can't do: they just do ordinary things like use singular terms and quantify in tidier ways.

2) We can't first pick out a class of genuine objects and then locate the genuine singular terms as those that refer to them: it goes the other way about.

Yes. The second point in particular makes a point that divides the philosophers of language from the metaphysicians - a shame Vallicella is in his self-imposed temporary exile. Metaphysically-inclined types will want to look for and investigate 'objects' first. Analytic types will investigate the language by which we talk about objects.

But this still leaves us with the problem of empty names. Signifying follows understanding, as the medievals said: significare sequitur intelligere. And it seems we can understand empty names, so why don't they signify? My understanding of 'Noah' is just the same whether or not 'Noah' refers to an existing person, or not. And 'Noah' seems a 'genuine singular term' in Smith's sense. But there may be no corresponding object.

We could resolve the difficulty by dropping or modifying (1). Perhaps empty names are not those items of ordinary language that we can 'tidy up' using the formal apparatus of constants and quantifiers. But that goes against the spirit of it. Formal language doesn't magically do what ordinary language can't. It is, literally 'formal'. It captures the 'form', literally the figure, that is characteristic of certain propositions and arguments.

There is a difficulty with this that I don't altogether see how to resolve.