[FOM] Natural and Formal Languages and Reasoning

henriknordmark@mac.com henriknordmark at mac.com
Thu Nov 25 10:25:57 EST 2004

On Nov 23, 2004, at 11:06 PM, Arnon Avron wrote:

> reasoning comes before languages, and that *all* languages (whether 
> "natural" or "formal") just model reasoning

I am not really convinced that there really is such a thing as 
non-linguistic reasoning.
(Nor am I absolutely convinced that all reasoning is linguistic 

> there are plenty of geometrical ways of reasoning that can easily be 
> visualized and understood, but are extremely difficult to be 
> translated into any natural language.

I agree that reasoning can be greatly enhanced by visualizing certain 
things geometrically. For example, reasoning about Euclidean geometry 
is much easier with geometric intuitions guiding the process, than 
trying to reason things out solely in a purely linguistic or formal 
fashion like Hilbert did. And this seems to suggest that there really 
is some sort of non-linguistic reasoning going on.

However, it is also possible that visualizing things geometrically 
simply provides good intuitions, but doesn't really provide *reasoning* 
per se. And that if you really want to reason about something you are 
forced to introduce language in some form or another.

It seems to boil down to what do we exactly mean by *reasoning*.

> I have always taken for granted the complete opposite: that both 
> natural languages and formal languages are used to model valid 
> reasoning and arguments, and that formal languages are designed 
> precisely because natural languages fail to do it adequately

If reasoning really is ontologically prior to language then I would 
agree with the statement above.

However, since I consider it possible and more plausible that 
language/reasoning come together as package that cannot be separated, I 
would be more inclined to say that...

Formal languages and natural languages are means by which we are able 
to reason. And formal languages were designed by people like Frege 
because natural languages were not adequate for their purposes.

Henrik Nordmark
Institute for Logic, Language and Computation
Universiteit van Amsterdam

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