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

[Stewart Shapiro]

Yes, this article, and other work by Moore, was of great help to me in
writing *Foundations without foundatilonalism* (OUP, 1991).  My book has a
chapter summarizing the historical situation.


On Fri, May 20, 2016 at 8:13 PM, Moshe Vardi <vardi at cs.rice.edu> wrote:

>
> See "The Emergence of First-Order Logic" by G.H. Moore.
>
>
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.476.7046&rep=rep1&type=pdf
>
> Moshe
>
>
> There's some discussion in Badesa's _The Birth of Model Theory_.
>>
>>
>> On Thu, May 19, 2016 at 10:23 AM, Richard Heck <richard_heck at brown.edu>
>> 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.
>>>
>>>
>>> --
>>> -----------------------
>>> Richard G Heck Jr
>>> Professor of Philosophy
>>> Brown University
>>>
>>> Website:   http://rgheck.frege.org/
>>> Blog:      http://rgheck.blogspot.com/
>>> Amazon:    http://amazon.com/author/richardgheckjr
>>> Google+:   https://plus.google.com/108873188908195388170
>>>
>>> Check out my books "Reading Frege's Grundgesetze"
>>>   http://tinyurl.com/ReadingFregesGrundgesetze
>>> and "Frege's Theorem":
>>>   http://tinyurl.com/FregesTheorem
>>> or my Amazon author page:
>>>   amazon.com/author/richardgheckjr
>>>
>>>
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> --
>
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