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Inquiry Into Inquiry • Discussion 6
• https://inquiryintoinquiry.com/2023/04/30/inquiry-into-inquiry-discussion-6/
Re: Nicole Rust
• https://mathstodon.xyz/@NicoleCRust@neuromatch.social/110197230713039748
❝Computations or Processes —
How do you think about the building blocks of the brain?❞
I keep coming back to this thread about levels, along with others on the related issue of paradigms, as those have long been major questions for me. I am trying to clarify my current understanding for a blog post. It will start out a bit like this —
A certain amount of “level” language is natural in the sciences but “level” metaphors come with hidden assumptions about higher and lower places in hierarchies which don't always fit the case at hand. In complex cases what look at first like parallel strata may in time be better comprehended as intersecting domains or mutually recursive and entangled orders of being. When that happens we can guard against misleading imagery by speaking of domains or realms instead of levels.
To be continued …
#Peirce #Logic #LogicalGraphs #DifferentialLogic #CactusLanguage
#Inquiry #InquiryDrivenSystem #InquiryIntoInquiry #NeuralNetwork
#Semiotics #RelationTheory #SignRelation #TriadicRelation #Model
#ObjectiveReality #MathematicalStructure #SymbolicRepresentation
Inquiry Into Inquiry • Discussion 7
• http://inquiryintoinquiry.com/2023/08/17/inquiry-into-inquiry-discussion-7/
Dan Everett has prompted a number of discussions on Facebook recently which touch on core issues in Peirce's thought — but threads ravel on and fray so quickly in that medium one rarely gets a chance to fill out the warp. Not exactly at random, here's a loose thread I think may be worth the candle.
Re: Facebook • Daniel Everett
• https://www.facebook.com/permalink.php?story_fbid=pfbid0be89MXhhCm8rxahRn4PXif6HHSCmkdiUFfMZ3qS1mNqSzRzUWfqej5a8cyz8TcyJl&id=100093271525294
My Comment —
Compositionality started out as a well-defined concept, arising from the composition of mathematical functions, abstracted to the composition of arrows and functors in category theory, and generalized to the composition of binary, two-place, or dyadic relations. In terms of linguistic complexity it's associated with properly context-free languages. That all keeps compositionality on the dyadic side of the border in Peirce's universe. More lately the term has been volatilized to encompass almost any sort of information fusion, which is all well and good so long as folks make it clear what they are talking about, for which use the term “information fusion” would probably be sufficiently vague.
#Peirce #Logic #Inquiry #Inference #Information #InformationFusion #Semiotics
#CategoryTheory #Compositionality #RelationTheory #TriadicRelationIrreducibility
Inquiry Into Inquiry • Discussion 8
• http://inquiryintoinquiry.com/2023/08/18/inquiry-into-inquiry-discussion-8/
Re: Milo Gardner
• https://www.academia.edu/community/Lbxjg5?c=yqXVog
MG:
❝Peirce sensed that bivalent syntax was superceded by trivalent syntax, but never resolved that nagging question.❞
My Comment —
The main thing is not a question of syntax but a question of the mathematical models we use to cope with object realities and real objectives (“pragmata”). Signs, syntax, and systems of representation can make a big difference in how well they represent the object domain and how well they serve the purpose at hand but they remain accessory to those objects and purposes.
#Peirce #Logic #Inquiry #Inference #Information #InformationFusion #Semiotics
#CategoryTheory #Compositionality #RelationTheory #TriadicRelationIrreducibility
Inquiry Into Inquiry • Discussion 9
• http://inquiryintoinquiry.com/2023/08/19/inquiry-into-inquiry-discussion-9/
Re: Milo Gardner
• https://www.academia.edu/community/VBqzR5?c=Q4jJVy
MG: ❝Do you agree that Peirce was limited to bivalent logic?❞
Taking classical logic as a basis for reasoning is no more limiting than taking Dedekind cuts as a basis for constructing the real number line. For Peirce's relational approach to logic as semiotics the number of dimensions in a relation is more important than the number of values in each dimension. That is where 3 makes a difference over 2.
#Peirce #Logic #Inquiry #Inference #Information #InformationFusion #Semiotics
#CategoryTheory #Compositionality #RelationTheory #TriadicRelationIrreducibility