[FOM] expressive power of natural languages

ARF (Richard L. Epstein) rle at AdvancedReasoningForum.org
Wed Nov 30 18:57:15 EST 2011

Ordinary language is not first-order, nor is it second-order.  Fragments of it can be formalized in
first-order logic and in second-order logic, but only with very strong metaphysical assumptions.
Those assumptions are more suspect than any evidence we may have that the use of the language
commits us to belief in classes.  In my *Predicate Logic* I discuss formalizations of ordinary
language in predicate logic and show how the use of second-order quantification appears to be
necessary for many of them.  But it should be noted that this is against a background of metaphysics
of predicate logic, and in any case it is not a demonstration that there cannot be formalizations of
those examples in first-order logic, only that there cannot be such formalizations that respect the
metaphysics of predicate logic.  In my *The Internal Structure of Predicates and Names with an
Analysis of Reasoning about Process* (a draft of which is available at
www.AdvancedReasoningForum.org) I give strong evidence that English and other European languages are
not universal, for they cannot express simple claims about the world as process.

Richard L. "Arf" Epstein

"americanmcgeesfr at gmx.net" wrote:

> Hello FOMers,
> I was wondering if there is any (at least semi-)conclusive view about
> the expressive power of a natural language like english resulting in a
> statement like "whatever it is, it is a language of at least 2nd order".
> Of course, I know of Tarski´s comment suspecting natural languages to
> be somehow (semantically) universal. But what I´m interested in is a
> hint pointing me in a direction what to look for, i.e. is the fact that
> one quantifies over classes in a natural language enough to label it
> higher order? Can there be anything wrong to take it to be at least a
> many-sorted first-order language?
> Thanks
> Alex Nowak
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