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11101924 No.11101924 [Reply] [Original]

>The book on Seth Theory uses Logic.
>The book on Logic uses Seth Theory.
I feel sick.
Is there an exposition on the subject without such loops?

>> No.11101993

Paste the two books together into a single book.

>> No.11102004
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11102004

Come Home, White Man.

>> No.11102019

>>11102004
Brainlet, category theory is utterly broken and still relies on set theory in the end.

Do what the cool kids have been doing, i.e. Type Theory.

http://www.cs.ru.nl/~herman/onderwijs/provingwithCA/paper-lncs.pdf

>> No.11102091

>>11101924
>>The book on Logic uses Seth Theory.
No it doesn't.
It uses model theory, which relies on an informal theory of classes.

>> No.11102115

>>11102091
It uses the axioms of set theory so it does use set theory.
There's the empty set.
There's intersection, unions, etc...
There's functions, natural numbers, etc...
The fuck are you on.

>> No.11102246

>>11102115
>It uses the axioms of set theory
So?

>> No.11102253

>>11101924
no matter what you do, you need naive set theory and naive logic to define axiomatic set theory, mathematical logic or any other foundation. there's no other way.

>> No.11102461

>>11101924
Who is this Seth and what is his theory?

>> No.11102491

>>11101924
>Seth Theory

>> No.11102496
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11102496

>>11102491
Seth, the third son of adam and eve. Don´t you kids know anything?

>> No.11102505

>>11101924
HOLY ESL

>> No.11102534

>>11102004
Irrelevant.

>> No.11102544
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11102544

>>11101924
>>11102115
>>11102253

No it doesn't. Set theory, like group theory, are just common examples for the kind of theories logic enables you to write down.
There is a notion of collection in logic, namely the universe of discourse, but it's not a "set". You don't speak of membership (or intersections, etc.) there.
Logic stands on its own and just requires the capacity of rewriting

https://en.m.wikipedia.org/wiki/Abstract_rewriting_system

>>11102019
No, you can write down category theory as a first order theory and define subobjects via what amounts to characteristic functions in pullbacks. This is just commuting diagrams