[FOM] The Open Logic Project

[Richard Zach]

It's been a few year since the first announcement, and you may have been following the progress of the Open Logic Project. If not, here are some updates:

Coverage has grown significantly and now also includes:

  *   Introduction to mathematical proof and induction for novices
  *   Four different proof systems for propositional and first-order logic (axiomatic proofs, tableaux, natural deduction, and sequent calculus)
  *   Second-order logic
  *   Models of arithmetic
  *   Lambda calculus (including equivalence of lambda computable and recursive functions)
  *   Intuitionistic propositional logic
  *   Normal modal logics
  *   Conditional logics (counterfactuals)
  *   Infinity and construction of number systems in naive set theory
  *   Development of set theory in ZFC (ordinal and cardinal arithmetic)
  *   Short biographies of 11 logicians

Thanks to some grant funding I was able to obtain high-quality photos and and commission illustrated portraits of several dozen logicians (at https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_OpenLogicProject_photos&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=99PfY1iwyoOOjEs0it2h4u_GsaHjRTwXzZf97J4yk6M&e=  and https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_OpenLogicProject_portraits&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=_Qrq-Gh_l-yfij_Wd-1GWSeLwSezKsSrH6sgryFgtLU&e= ).

This is all freely available in LaTeX source code and one 900+-page PDF, at https://urldefense.proofpoint.com/v2/url?u=https-3A__openlogicproject.org_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=A0jeH79LuHD0BH9tdpb0CZ_Bjv3Vuqp-ANdH0hfJAgk&e= .

As the content is very modular, it is relatively easy to select, reorder, and mix and match the content. There are now also four self-contained textbooks (of more manageable size) based on the material in the project:

Sets, Logic, Computation covers basic set theory; syntax, semantics, and proof theory of first-order logic (natural deduction and sequent calculus); completeness, compactness, and Löwenheim-Skolem theorems; Turing machines and the halting problem; undecidability of first-order logic.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_phil379_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=l2FFb1vzQUmXLc4Sueq54q2arrzADQxYM1lNLKszXSs&e= 

Incompleteness and Computability covers basic recursive function theory, arithmetization of syntax (for proof predicates for axiomatic deduction, natural deduction, and sequent calculus), representability in Q, first and second incompleteness theorems, models of arithmetic, second-order logic, lambda calculus.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_phil479_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=UkVWXqumfAc2JsVdrD8VYHkOP_CMfXWN5_7JI1Ma24g&e= 

Boxes and Diamonds covers syntax, semantics, and proof theory of normal modal logics (axiomatic deductions and prefixed tableaux), intuitionistic propositional logic, and counterfactuals.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_boxes-2Dand-2Ddiamonds_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=L3OJUaC7p3olP4-cF0khOAEgK0NRv3ZOmH--sHrZuYQ&e= 

Set Theory covers development of elementary mathematics in naive set theory, the cumulative hierarchy, ordinal and cardinal arithmetic, and the axiom of choice.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_set-2Dtheory_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=U8KcgMBwcGgjEjvwQf-h5qzX0Js-JL5zkgE_Ypykhhs&e= 

(Most of the set theory material is brand new, adapted from Tim Button's Open Set Theory book).

On 2015-10-25 8:36 a.m., Richard Zach wrote:

You may have hear of it already, but I thought I'd announce the Open
Logic Project to the FOM list specifically.

We're working on an open-source, customizable, free logic textbook. The
project website is here:

https://urldefense.proofpoint.com/v2/url?u=http-3A__openlogicproject.org_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=dAtnWWU5ZMg1XwYKhXi7ZohRlk3SibScBS0YfhPv2lg&e= 

The target audience is advanced undergraduate students without a
background in mathematics, in particular, we're trying to provide course
texts for courses in mathematical logic as taught in philosophy
departments. Right now we have material on naive set theory, first order
logic and completeness, recursion theory, incompleteness, and some model
theory. We're now working on expanding the chapter on Turing machines,
and are planning to also cover set theory and modal logic in the near
future.

Contributions in the form of reports of errors, additional exercises,
and additional expository material (your lecture notes, perhaps) are
more than welcome.


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