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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Temporality and Consciousness: possible rolesfor logic
Notes for the NY Phenomenology Reading Group
Andrés Villaveces / Universidad Nacional de Colombia - Bogotá
August 2020
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Stops
Phenomenology, reality, invariance
Time Consciousness - Transcendental Logic
THK: Beginning TL?
Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Where from? (Ettinger and Zalamea)
In 2018 we started a long (slow) project with Mark Ettinger (herepresent!), vaguely connected to shared preoccupations withI Phenomenology,I Logic,I Time Perception,I Temporality (and the role of the Self),I Other kinds of connections between Mathematics and the
previous (category theory, etc.)
In early 2019 I was invited to Fernando Zalamea’s 60th BirthdayFestschrift. My lecture dealt with some of these connections. Somewinter weeks spent in Italy ended up being providential for thisproject.Zalamea has written provocative works on the philosophy ofmathematics and the role of logic and categories.Here is part of the blend.
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Where from? (Ettinger and Zalamea)
In 2018 we started a long (slow) project with Mark Ettinger (herepresent!), vaguely connected to shared preoccupations withI Phenomenology,I Logic,I Time Perception,I Temporality (and the role of the Self),I Other kinds of connections between Mathematics and the
previous (category theory, etc.)In early 2019 I was invited to Fernando Zalamea’s 60th BirthdayFestschrift. My lecture dealt with some of these connections. Somewinter weeks spent in Italy ended up being providential for thisproject.Zalamea has written provocative works on the philosophy ofmathematics and the role of logic and categories.Here is part of the blend.
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Plan
Phenomenology, reality, invariance
Time Consciousness - Transcendental Logic
THK: Beginning TL?
Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Phenomenology:
“the study of everything that remains invariant under a change ofmode of reality”. . .simulation / dream / . . .
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Phenomenology:
“the study of everything that remains invariant under a change ofmode of reality”. . .simulation / dream / . . .
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Fenomenología:
“the study of everything that remains invariant under a change ofmode of reality”. . .simulation / dream / . . .
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Blue
the experience of perception of “being blue” and in particular itsanchoring in spatiality is invariant under a change of reality mode
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Dependence/Fundierung
Dependence of “blue” on spatiality
Blue 7→ SpatialityLife 7→ C+O
Consciousness 7→ Synapses
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Dependence/Fundierung
Dependence of “blue” on spatiality
Blue 7→ SpatialityLife 7→ C+O
Consciousness 7→ Synapses
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Blue
Blue ↔ Spatiality
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Blue
Blue ↔ Spatiality
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
More variations around Fundierung
. . . eyes moving, neuronalactivations occurring as we read,the parsing of words letter byletter, the understanding of eachindividual word, etc. clearly arenot sufficient to “determineunequivocally someone isreading”
Wittgenstein / Rota
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
The big question
Husserl. . . as Gian-Carlo Rota put it:
What kind of logic govern the Fundierung relation?
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
The big question
Husserl. . . as Gian-Carlo Rota put it:
What kind of logic govern the Fundierung relation?
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Propositional Logic. . .millennia ago
(Images by John F. Sowa in his comment of Peirce’s MS 514)Kossak/Siedlecka project for Mapping Traces
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Not taking the world for granted
not taking for granted, as something obvious the “world” wascrucial to unveil, millennia ago, the structural character ofpropositional sentences
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Where? |=?
I Model Theory?I Homotopic Type Theory?I Topos Theory?
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Plan
Phenomenology, reality, invariance
Time Consciousness - Transcendental Logic
THK: Beginning TL?
Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Protención / Intencionalidad
From those two elements (retention and protention), Husserl buildsa whole web of time decomposition into a continuum ofanticipations and interpolations, protentions and intentionalities,extremely refined and irreductible to a merely analytical description.
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
The role of logic
Anchoring in a common way all possibleexperiences of knowledge of the world.
Husserl basically constructs two levels of logic:
formal logic and transcendental logic.
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
The role of logic
Anchoring in a common way all possibleexperiences of knowledge of the world.
Husserl basically constructs two levels of logic:
formal logic and transcendental logic.
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
The three levels, Sokolowski
Consistency Logic, Truth Logic and finallyTranscendence Logic: Under the risk of an extremereduction, there are some kind of strong Peirceanechoes in this a posteriori analysis of Husserl’slogic.
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Plan
Phenomenology, reality, invariance
Time Consciousness - Transcendental Logic
THK: Beginning TL?
Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Zalamea’s model (rthk: Riemann, topoi, sheaves,
Kripke)
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Zalamea’s model (rthk: Riemann, topoi, sheaves,
Kripke)
I “Base” level K (Kripke): beginning of “temporality” (still at avery primitive level compared to Husserl, but already morecomplex than in Tarskian semantics),
I “Intermediate” level sH (sHeaves): coherence and glueing -beginning of synthetic substratum in Husserl (intentionality),
I “Upper” level T (Topoi): the emergence of topos logic - maybethe point where transcendental logic may start (stage I).
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
K
Initial temporal level - Kripke models - variable structures - firstflexibilization - temporality
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
sH
Intermediate sheaf level: coherence and (continuous) glueing - theplace of the obstructions - spatiality I
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
T
Upper level (“topos”): places “similar to set-theoretic universes” butwith the flexibility of the two lower levels - spatiality II
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
r
Zalamea proposes a way of “glueing” the three levels, inspired byramification points on Riemann surfaces (whence “R”)
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Two answers that have had some impact
Husserl: manifold - multiplicity Tarski: M |= ϕ. . .
|=
Sokolowski proposes to identify “model” in Tarski’s sense and theHusserl notion of “manifold”.Gödel’s completeness theorem filters in an effective way the notionof model and makes it “manifold”. However. . .
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Limitations of earlier proposals:
I Tarskian models cannot incorporate time perception in the extremely refinedsense proposed by Husserl.
I Most logical systems lack compactness; when it is present, there are sheaf-like(global/local) properties. . .
I Theories of symbiosis (between higher order logic and set theory) and ofInternal Categoricity seem to be crucial for any attempt at building Husserl’stranscendental logic. Transitions. . .
I Grothendieck (topoi + motives + formalism freeness) seems to be thelandmark of future logic(s). In addition to sensitivity to local/global aspects,they also seem to be sensitive to measuring failure of smoothness(cohomology)
I back and forth between Grothendieck and Shelah (contemporary modeltheory as a “ultrageometry”)
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Plan
Phenomenology, reality, invariance
Time Consciousness - Transcendental Logic
THK: Beginning TL?
Conclusion
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
Pessimistic conclusion . . .
I The richness of Husserl’s questions (in Rota’s version) on alogic for Fundierung and transcendental logic has not yet beenattained by the mathematizations of logic.
I There is (as of now) a mathematical version of transcendentlogic.
I Rota’s question has not quite been answered.
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Phenomenology, reality, invariance Time Consciousness - Transcendental Logic THK: Beginning TL? Conclusion
. . .ma non troppo!
On the other hand the richness of mathematical constructionsconnected mainly with Grothendieck and Shelah and their twoparallel schools (especially when they will get entangled) has so farnot been matched by philosophers’ study of mathematics and logic.Zalamea’s (r)THK model is a beginning.