/r/neologicism

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Neo-logicism is a theory about the nature of logic and mathematics. The fundamental claim of logicism is that all mathematical truths can be expressed in terms of logical truths.

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Neo-logicism is a theory about the nature of logic and mathematics. The fundamental claim of logicism is that all mathematical truths can be expressed in terms of logical truths.

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/r/neologicism

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2

Am I missing something? Hasn't Godel stopped this dead in its tracks already?

If I've misunderstood the incompleteness theorems, please let me know, I still have like 6 quarantine based weeks until I do the full proof ;)

Isn't it the point of the incompleteness theorems that if an arithmetic has an isomorphism with FOL, then it is incomplete? Doesn't this more or less cause dramatic issues for the logicist? Any interesting readings based on this?

3 Comments
2020/03/27
03:14 UTC
4

Tarski "What are logical notions?"

I found English version of this interesting article trying to capture (in a rather normative fasion) the notion of logical object/property. Starting with lovely extrapolation of Erlangen program Tarski conducts a witty and rather easy to grasp reconstruction of notions used in Principia:
https://www.researchgate.net/publication/243776379_What_Are_Logical_Notions

I already mentioned it on r/logic twice in the context of two "is mathematics logic/is logic mathematics" debates, because it ends up with pleasant relativity; starting from pure set theory a'la ZF one gets mathematical notions/constructions not logical (because membership relation itself isn't), while starting from typed theory with urlements (PM but it should be ok with NFU too) they are logical.

Perhaps you'd find that amusing.

2 Comments
2020/03/20
17:34 UTC
2

Crisis in the Foundation of Mathematics [PBS Infinite Series]

1 Comment
2020/03/17
18:39 UTC
2

Russell's Paradox - A Ripple in the Foundations of Mathematics [YouTube]

0 Comments
2020/03/17
18:32 UTC
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