[FOM] First- Vs Second-Order Logic: Origins of the Distinction?

Walt Read walt.read at gmail.com
Sat May 21 00:31:48 EDT 2016

I don't have ready access to the book just now but as I recall Badesa
sees a key stage in separating out first-order in L\"{o}wenheim's work
around 1915 related to L\"{o}wenheim-Skolem.


On Thu, May 19, 2016 at 7:59 PM, Alasdair Urquhart
<urquhart at cs.toronto.edu> wrote:
> Greg Moore's article "The Emergence of First-Order Logic" is a good place to
> start.  It's in "History and Philosophy of Modern Mathematics" edited
> by Aspray and Kitcher.
> Moore emphasizes (and I agree with him) that the appearance of Gödel's
> incompleteness theorem was a key event in separating first- and second-order
> logic.
> On Thu, 19 May 2016, Richard Heck wrote:
>> Does anyone have a good reference for historical work on the emergence of
>> the distiction between first- and second-order logic? I'm
>> particularly interested in how first-order logic came to be seen as
>> "really logic". Quine was of course famously hostile to
>> second-order 'logic', but I am guessing that there were earlier
>> antecedents, probably emerging from work in mathematical logic
>> itself.
>> If anyone is able to sketch that story, I'd love to hear it.
>> Thanks,
>> Richard Heck
>> PS What I myself know about this concerns only the emergence of Frege's
>> awareness of the distinction. That part of the story gets
>> told in my paper "Formal Arithmetic Before Grundgesetze", section 3, which
>> can be found on my website.
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