Semantika ja analüütiline filosoofia
Code: ITV9070 "A sign is anything that can be used to tell a lie." --Umberto Eco “I’m writing a book on magic,” I explain, and I’m asked, “Real magic?” By real magic people mean miracles, thaumaturgical acts, and supernatural powers. “No,” I answer: “Conjuring tricks, not real magic.” Real magic, in other words, refers to the magic that is not real, while the magic that is real, that can actually be done, is not real magic. --Lee Siegel |
Sisukord
NB!
The 18. December exam consultation will take place on teams only, not in the lecture room. Here is the meeting link.
The agency questionnaire is now up! Please take some time and answer!
Exam times and places are as follows:
- 6. jaanuar: kell 12 ja kell 15, ruumis NRG-131, Energeetikamaja
- 13. jaanuar: kell 13 ja kell 15:30, ruumis U06A-229, Õppehoone 6a
- 21. jaanuar: kell 11 ja kell 14, ruumis U02-102, Õppehoone 2
During each exam day you may choose yourself which of the two time slots to use. The exams will take place together with the exams for "IT sissejuhatus" (this one has quite a lot of students).
Recordings
Several recordings are available, but we do not plan to record all the lectures/seminars.
- A recording of the first lecture (4. sept) is available here (in Estonian).
- The teams recording of the second lecture/seminar. The telco link is inside the course teams group
- The teams recording at 25. Sept is available
Time, place, credits
Time: Every Wednesday 11:40 - 13:55
Normally we will have student presentations during the lecture time, along with planning following presentations and brief intros by the lecturer. We will follow the schedule
Location:
- Mostly: IT College building room ICO-219
- Sometimes: telco over teams (these will be announced a week earlier)
Credits: 6
The lectures will be in English, unless everybody understands Estonian, in which case they will be in Estonian.
The presentations in practice sessions can be given in English or Estonian, as you prefer.
The contents of practice sessions are presentations by students and their discussion. For all students, presence in the practice sessions is important and is accounted for in the final grade.
We will probably succeed with saving the videos of lectures: will check out during the first weeks.
The course will finish with a written exam. The materials below marked with a red E will be critical for studying for the exam, while the materials marked with blue L are also used but less important. Materials without such marks will not be used for the exam questions.
In order to be allowed to take the exam,
- each Ph.D student should give at least four presentations.
- each master student should give at least two presentations. In case it turns out we will have enough time, an additional third short presentation might be asked for as a bonus.
Presentations are not graded, but when they are determined not to be satfisfactory, they should be re-done.
The lecture times will be used for both
- Short intros to thematic blocks by Tanel
- Student presentations
NB! Presence at student presentations will be registered: failing to participate at many presentations will have a negative effect on the final grade.
Initial course plan, materials and topics
We consider several topics, starting from general ones and moving to more specific.
The main goal of the lectures is to make it easier to understand the concepts and ideas in the topics, in order to better understand the reading materials.
Intro, semiotics, philosophy
- Source for the first round of presentations: Tähendus, tõde, meetod.. Separate original articles can be found by googling.
Main materials:
- Semiotics for beginners. first half is obligatory. E
- Quine: Two Dogmas of Empiricism. E
- what is analytic philosophy.
- analytic/synthetic. E
- logical positivism.
- Problem of universals nominalism/realism. L
- functionalism. E
- phenomenology.
- Propp.
Useful to read/listen:
- philosophy bites podcasts. Start with this strongly recommended episode.
- Sam Harris with David Chalmers
- L Philosophy of Metzinger: background reading Self models and look, for example: Metzinger video
- Tractatus andTractatus: structured full text. L. Wittgenstein. Read a bit, along with a commentary
- Philosophical investigations: read the first 100.A A small summary of early vs late Wittgenstein
About the alphabet:
- http://en.wikipedia.org/wiki/Egyptian_hieroglyphs
- http://en.wikipedia.org/wiki/Written_Chinese
- comparison ja wiki and unicode
- http://en.wikipedia.org/wiki/Phoenician_alphabet
- http://en.wikipedia.org/wiki/Egyptian_uniliteral_signs
- http://en.wikipedia.org/wiki/Cumae_alphabet
Notes on structuralism, deconstruction and friends:
- structuralism L, dekonstruktivism, dekonstrueerimise kiirõpetus, Derrida section, hermeneutics
- insheeption
- sympathetic magic: wiki, Frazer
Notes on Propp:
Notes on the Vienna circle and logical positivism:
- Main ideas: "First, experience is the only source of knowledge; second, logical analysis performed with the help of symbolic logic is the preferred method for solving philosophical problems."
- taust: analüütiline/sünteetiline, apriori/aposteriori
- classical positivism as the background: more here
- a small lecture about the Vienna cicle
- Vienna circle: good short overview ja a longish paper from the Stanfordi encyclopedia of philosohy and Vienna circle manifesto
- Logical positivism: good overview
- wiki logical positivism
Evolution of brain, intelligence and society
Sociobiology, evolutionary psychology and memetics.
Main material:
- Evolution: intro lecture.
- Sociobiology in wikipedia. E.
- Evolutionary psychology in wikipedia. E. You may also want to read more details in primer ja conceptual grounds
- Memetics in wikipedia. E
- Universal grammar L theory of Chomsky
Recommended overviews:
- wiki on the theories of origin of language
- overview of Chomsky theories of language evolution
- wiki on horizontal gene transfer
Recommended books:
- The Selfish Gene
- Guns, Germs and Steel
- Sapiens: A Brief History of Humankind
- Homo Deus: A Brief History of Tomorrow
Important papers:
- BRAIN EVOLUTION AND NEUROLINGUISTIC PRECONDITIONS L
- pdf version and textual: CO-EVOLUTION OF NEOCORTEX SIZE, GROUP SIZE AND LANGUAGE IN HUMANS L
- Precis of Origins of the Modern Mind: Three Stages in the Evolution of Culture and Cognition L
- DNA seen through the eyes of a coder
- Epigenetics vt ka seda artiklit
Additional notes and recommendations, not obligatory:
- natural language and natural selection
- Language as an Adaptation to the Cognitive Niche
- Faculty of Language: What Is It, Who Has It, and How Did It Evolve?
- Agner Fog: cultural selection
- Buss lab publications
- Changizi publications: vt allpool peatükk ARTICLES AND BOOKS ntx Economically organized hierarchies in WordNet and the Oxford English Dictionary, citybrain, colorface, xray vision
- the brain from 25000 feet
- John Eccles: Evolution of consciousness
Brain science
For exam:
- https://en.wikipedia.org/wiki/Cognitive_neuroscience L
- https://en.wikibooks.org/wiki/Cognitive_Psychology_and_Cognitive_Neuroscience/Memory L
- https://en.wikipedia.org/wiki/Computational_theory_of_mind E
Good general overviews:
- background reading for further reading or listening about brain
- https://grey.colorado.edu/CompCogNeuro/index.php/CCNBook/Main
- https://en.wikibooks.org/wiki/Cognitive_Psychology_and_Cognitive_Neuroscience
- Neurons are Now More Complex than We Thought
Important podcasts:
- Brain Inspired: a podcast where neuroscience and AI converge. A somewhat newer and somewhat technical podcast. Also based on interviews, but with currently active top researchers about their current work.
- Brain science (see also the episodes page) : an old podcast series, still going strong. Basically interviews with important people in the field, many of them classics. Not very technical (mostly); recommended podcasts in BS, youtube lectures and background for these
- Some of the Lex Fridman podcast episodes are relevant, like Jeff Hawkins, Karl Friston, David Eagleman
General notes:
- https://en.wikipedia.org/wiki/Cognitive_neuroscience
- https://en.wikipedia.org/wiki/Computational_theory_of_mind
- https://en.wikipedia.org/wiki/Global_Workspace_Theory
- https://en.wikipedia.org/wiki/Grandmother_cell
Read also:
Infinity, logic and philosophy of mathematics
The first topic is intro to the philosophy of mathematics, mainly the questions of infinity and unsolvability.
Materials to read:
- English intro: infinity, limits of computation and undecidability E
- in parallel, the same themes supporting text, written by the lecturer as an afterword to the book about Gödel's incompleteness theorems. You may try to use Google translate or some such for the English version: however, it is not a an obligagtory material.
- numbers, infinity and metaphors (in Estonian, very short, metaphorical)
- Ordinals: read from 6.2 Classifying the ordinals
- Russell paradox from wikipedia
Videos have heads down:
- Intro lecture: 6. oct 2022, in Estonian.
- Seminar lecture: 6. oct 2022, in Estonian.
More about infinity and computability:
- Salvestus teamsis, 13. oktoober, in Estonian.
Helpful read: cardinality wikipedias. Read more about Gödel's incompleteness theorem from SEP: a part of a larger incompleteness-article.
A longer story about the philosophy of mathematics from SEP.
Nonclassical logics, related to the philosophy of mathematics:
- In Estonian: mitteklassikalised loogikad. Siin on pealeloetud jutuga variant: E downloadi ja vaata normaalses täisekraan-vaatamisreziimis, siis kuuled slaidide juures minu juttu.
- A good technical read from SEP about intuitionist logic.
- Estonian material and videos about modal logics: modaalsed loogikad L ja vaata eelmise aasta teamsi salvestust samast loengust
- Good half-hour presentations about axioms of modal logic and kripke semantics / possible worlds. A more philosophical take available in the series (playlist) from the same author, but long. Additionally useful presentation . SEP has good articles om modal logic and related philosophy, both highly technical.
More on nonclassical logics:
- modal logic in wikipeda
- philosophy around modal logic from SEP
- philosophy around intuitionistic logic from SEP L
Thinking and AI
Classic ideas about the main questions of AI philosophy (close to the questions about functionalism):
First, a somewhat old interview with a classic:
- Steven Pinker from the lex fridman ai podcast.
Read the wiki pages of main issues:
- http://en.wikipedia.org/wiki/Philosophy_of_artificial_intelligence L
- Functionalism E
- SEP artikkel AI-st: read partially, could be partially boring
Technical stuff from Graziano about neuroscience related to consciousness:
Detailed arguments and counterarguments for the
Some good core stuff
- For starters Rodney Brooks's small AI series part 1, part 2 , part 3 , part 4 and predictions scorecard 2020, scorecard 2024
- Importantly, two interesting essays by Rodney Brooks from 2023 What Will Transformers Transform? L and Three Things That LLMs Have Made Us Rethink L
- Listen to Stuart Russell on AI dangers
Living classics from the lex fridman podcast:
- https://lexfridman.com/david-ferrucci/
- https://lexfridman.com/gary-marcus/
- https://lexfridman.com/david-silver/
- https://lexfridman.com/tomaso-poggio/
- https://lexfridman.com/richard-dawkins/
- https://lexfridman.com/noam-chomsky/
- https://lexfridman.com/nick-bostrom/
- https://lexfridman.com/jeff-hawkins/
- https://lexfridman.com/judea-pearl/
Semantics of natural language
We will look into both
- Vector semantics
- Semantics based on world model
Details will be added when the block starts
Dialog, pragmatics, uncertain knowledge
The first subject is dialogue pragmatics. Several related branches (have a brief look, but no need to read deeply unless you become interested):
- Speech acts L sentences doing something, not just conveying information
- Implicature L with Grice's maxims as a central theme
- Relevance theory further development of Grice's maxims
To start, certainly look/listen these short lectures:
- pragmatics and speech acts 11 minutes intro to the whole subject
- Grice's Maxims, Implicature, Presupposition: especially nice 12 minute more detailed lecture about Grice maxims
- Deceiving with words in case you did not listen before, do it now!
In case you just want to read original Grice:
- Logic and conversation: Grice himself about the maxims
- further examples, analyzed quite deeply
Have a look at
- Relevance theory, ie further development: 32 pages by main folks working on the subject
- Jurafsky & Martin chapter 26 Dialogue Systems and Chatbots the practical pre-LLM systems from their extremely good NLP book
Additionally, nice to listen and :
- NLP podcasti episode 89 about pre-LLM dialog systems
- Implicature Calculation, Pragmatics or Syntax, or both: more detailed analysis of implicature
- implicature with experiments
- very detailed with some focus on automatization
- dialogue pragmatics from SEP
- implicature from SEP
The next theme is uncertain information and probabilities: how to understand, write down and make conjectures.
Read this intro: Numeric uncertainty (L as explained next):
- Certainly up the the section "Different ways to encode confidences in logic", also looking at the wikipages pointed to
- Briefly look into the following sections, but do not focus or spend much time on these. The Numeric uncertainty intro was originally made for this course.
Then read the first parts and have brief looks at the SEP articles:
Here are some of our papers on our system, about confidence and reasoning with exceptions.
Recommended podcasts
- The Gradient: a good AI podcast, relatively deep, several philosophical themes / episodes
- Brain Inspired: real neuroscience with focus on AI related themes.
- Philosophy bites: real philosophers conveying ideas rather clearly in ca 15 minutes
- Robinsons podcast: Really good stuff with famous philosophers and related thinkers. One example: Donald Hoffman.
- Making sense by Sam Harris sometimes does deep interviews with philosophers, like the following highly recommended Andy Clark episode (predictive brain, embodied cognition, and the extended mind) full version. If that does not work for some reason, check out the shorter version here.
- Highly popular Lex Fridman podcast has sometimes deep interviews with AI and comp sci peaople. Specifically about AI I'd recommend some widely different views from Francois Chollet, Yann LeCun, Gary Marcus, Demis Hassabis, Ilya Sutskever, Ben Goertzel.
- The Mindscape podcast of an important physicist has often quite philosophically interesting or cognitive science and AI interviews. Some recommendations: Blaise Agüera y Arcas, David Krakauer, Christoph Adami, Peter Godfrey-Smith, Yejin Choi, Hugo Mercier, Andrew Pontzen.
Random extra stuff
- A good Slate article about the background of the OpenAI soap opera.
- A famous killerbot warning video.
Presentation schedule
- 11. sept:
- Georg: Nick Boström Are we living in simulation. Vt taustaks Nick Boström (wiki) ja taust/analüüs wikis. Googelda juurde veel analüüse/arvamusi/vastuväiteid.
- Hannaliina: Quine: empirismi kaks dogmat. Linke: siin, siin. Vt ka taust/analüüs wikis.
- Eleriin: Confirmation bias, start with this article and search for more. Vaata lisaks wikist.
- 18. sept:
- Andres (tõstsin üle 11. septembrilt): Putnam: tähendus ja osutus. Meaning and reference. Lisaks tasub vaadata ülevaadet. Vaata ka Social_constructionism wikis ja ntx siin ja taustaks kindlasti Functionalism (SEP), Functionalism (wiki): Googelda artiklile juurde seletusi/analüüse.
- Danyil: neurons are more complicated than we thought.
- Viktoria: Strawson: tähendus ja tõde (meaning and truth). One fulltext here. Look at SEP about Strawson. There is a Robinson's podcast video episode about the Strawson approach (at ca 1:21) and another podcast episode about the context of Strawson/Austin debate on theme.
- Liisi: Intuitsionistlik loogika: näited teoreemidest, mis kehtivad klassikaliselt, kuid mitte intuitsionistlikult. Näiteid tõestustest, millel lihtne klassikaline, kuid keeruline intuitsionistlik tõestus (standardnäide: ruutjuur kahest on irratsionaalne, vt näiteks siit ja googelda juurde). Vaata intuitsionisliku loogika kohta wikist ja SEPist. NB! Intuitsionistlik loogika on oluline teema matemaatika filosoofias: Tanel teeb sellele hilisemates loengutes eraldi sissejuhatuse.
- 25. sept
- Raul (moved here from 18. sept): Dummett: Truth. One fulltext here. You may also want to read comments like this and background like this
- Kauri: Ramsey subjektiivne tõenäosusteooria. Full text of his paper. Important background: interpretations of probability, esp "The Subjective Interpretation" and specifically about Ramsey's views.
- Jonatan: antroopsusprintsiip. See the take by SEP. A good listen by a theoretical physicist is here. You may want to have a look at the book by Nick Boström, the classic full paper by Brandon Carter, and the full book by Barrow and Tipler. Related tidbit: there is a very early paper about the anthropic principle in microcosmos by Tanel, closely related to Boltzmann brain.
- 2 okt
- Epp: Tarski: semantiline tõekontseptsioon. About Tarski. The original paper and the SEP explanations/details/background
- 9 okt
- Mihkel: pragmatism. Start with the SEP article and search for more.
- Anzelika: infinity: Ordinaalid ja kardinaalid. Maybe start with a good exposition at in this discussion. Continue with cardinals and ordinals in wiki, check out Russell's paradox, read about transfinite ordinals
- Otto: main points of Chomsky's theories of language. This is so widely discussed that it is easy to google. You may want to listen to some podcasts with Chomsky himself: for example, this and this. Certainly read about criticism. You may want to listen to this episode with a critical analysis of Chomsky.
- Enrico: Paul Grice: "meaning" and overview of other important parts of Grice claims and theory. This is also so widely discussed that it is easy to google. Start with SEP. Some nice intros to implicatures: here and this wikipage. Grice himself about this stuff. More detailed stuff. Check also the relevance theory. Certainly look through a very nice video about flouting/violating the maxims in relation to irony, sarcasm and jokes.
- 16 okt
- Viktor: Frame problem. Good stuff to read, maybe in that order SEP, Dennett, Blocks world example, Morgenstern. Beware that none of the various "solutions" are not really satisfactory: they should be considered as possible approaches, not solutions.
- Lulof: Kant's theory of judgement.
- Enrico: statistical machine translation, incl major waves/paradigms of machine translation.
- 23 okt
- Lulof: Wittgenstein's Tractatus Logico-Philosophicus vs Philosophical Investigations. Also: background and influences (like, for PI pragmatism via Ramsey). Tanel has done a very brief intro to the topic, so we can continue from there. I.e recall Tractatus, but do not spend much time there, assuming we have already looked into this. Spend more time on PI and especially the comparison between the Tractatus phase (early Wittgenstein) and PI phase (late Wittgenstein). This is a popular topic, easy to google.
- Enrico: Kripke semantics of modal logics. Also, check out the relevant materials from the section "Infinity, logic and philosophy of mathematics" above.
- Georg: Dennett: kvaalide kvainimine (quining qualia). Full text here. About the views of Dennett by himself (search for e.g. "Welcome to Strong Illusionism") and others. Some discussion on reddit. Wikipedia about qualia.
- Hannaliina: How do bacteria and simple organisms communicate. Start with this TED talk and search for more. For example, a SciAm article, this (alternatively here) is an in-depth paper, this handles bacteria working through insects.
- 30 okt
- Lulof: About the paper "Computational irreducibility and compatibilism: towards a formalization". Free will issues connected to computation.
- Eleriin: Frege (first part of the presentation): Frege tähendusest ja osutusest. Read an overview/background from wikipedia and Frege's own paper On Sense and Reference. There is a youtube video about the paper. See SEP on Frege, Frege's logic and wikipedia about Begriffsschrift (the book inventing predicate calculus).
- Andres: solipsism. Certainly consider several types of solipsism, starting from wiki. See also methodological solipsism and methodological individualism in contrast to externalism of Putnam etc
- 6. November, biology/evolution focused themes:
- Eleriin: Frege: second part of the presentation (no biology here)
- Andres: Karl Friston and the free energy principle . A usefulpodcast episode and the homepage.
- Viktoria: Antonio Damasio and the origin of important stuff in homeostasis. Interview and a ted talk. See also https://en.wikipedia.org/wiki/Somatic_marker_hypothesis
- Liisi: Donald D. Hoffman and the user interface (MUI) theory of mind. Easy to google, highly popular.
- 13. November, agency & extras:
- Tanel will present the draft of agency questionnaire and we will discuss and improve it interactively.
- Danyil, moved from 30 Oct: Main points from Clark in the Andy Clark episode (predictive brain, embodied cognition, and the extended mind) full version from the Making sense podcast by Sam Harris. If the full version link does not work for some reason, check out the shorter version here and ask Tanel for help. You may also want to google papers by Andy Clark and/or select for reading some papers from the scholar site or his own site.
- Otto, moved from 6 Nov: Randy Gallistel on memory interview 1 and maybe also interview 2. Some additional background: here
- If we have time, Tanel will speak about various current AI philosophy themes and about the neurosymbolic reasoning research area.
- 20. November, continuing evolution
- Raul: Mike Frank: Early Language and Cognition. Interview and perhaps a longer paper 1 and paper 2
- Kauri: Evolution of morals. alusta siit ja otsi ise edasi. Vaata ka wiki põhiartiklit ja lähedalt seotud altruismi teemat. Important background is sociobiology and evolutionary psychology.
- Jonatan: Anil Seth on consciousness. A useful podcast episode and a homepage.
- Epp: Symbolic_interactionism https://en.wikipedia.org/wiki/
- 27. November: complex systems and weird/radical worldviews
- Mihkel: David Krakauer about complex systems. See https://davidckrakauer.com/ and listen to https://www.preposterousuniverse.com/podcast/2023/07/10/242-david-krakauer-on-complexity-agency-and-information/
- Anzelika: panpsychism and Philip Goff. A useful podcast episode. Also, have a quick intro look into the “hard problem of consciousness” of Chalmers.
- Otto: Max Tegmark and the mathematical multiverse. A useful podcast episode.
- Andres: Wolfram's theory of the world, using hypergraphs. A useful podcast and ted talk and some earlier writings
- 4. December: more complexity, then probabilities, motivation, causation and friends
- Viktor: Assembly Theory. See also a Nature paper. Recommended: especially, a good discussion with Sara Walker, and another with Lee Cronin.
- Enrico: Kahneman & Tversky: briefly about Prospect theory and more on System 1 and System 2 thinking
- Lulof: Judea Pearl on causality. A useful podcast episode and another and yet another and homepage.
- Otto: David Deutsch and the probabilistic (or rather, not) nature of scientific theories. A useful podcast. Also the homepage. Here is one complicated paper on constructor theory, as a potential additional deep source.
- 11. December: reserve.
- Probably some presentations planned for earlier will be moved here, for various reasons
- Tanel will speak about several themes
- The agency questionnaire: current state / results / etc
- 18. December: exam stuff
- Q&A about the exam
- We will quickly go over main exam materials, possible questions etc
Initial ideas for the agency experiment
Draft questionnaire for agency
Initial ideas:
Agency / Intelligence / consciousness / sentience
Agency measure: social question?? Let us make a questionnaire and ask students!
facets/dimensions
- more intelligent has more agency
- more money, then more agency
- more free, more agency
- physically strong
- ability is not the same as will (avoid free will issue)
- more facets??
comparisons for objects like
- rocks/waterfall/earth/virus/bacteria/worm/dog/human/computer/clock/phone ... / country
- small rock / meteorite / flying rock
- different software kinds?
- short term / long term
- rock / sculpture
- effect of environment on people
What to do:
- google about agency discussions
- questionnaire suggestions
Important: sensible comparison items for different facets; also how to ask?
Agency questionnaire draft development
Some themes for selection
Ideas for the first rounds from this book (search originals from the web):
- Putnam: tähendus ja osutus. (Meaning and reference)
- Quine: empirismi kaks dogmat. (Two dogmas of empiricism)
- Dummett: Truth.
- Tarski: semantiline tõekontseptsioon.
- Strawson: tähendus ja tõde
- Ramsey subjektiivne tõenäosusteooria.
Further:
- Analytic / synthetic vs apriori / aposteriori (Kant etc)
- Frege: Frege tähendusest ja osutusest.
- Dennett: kvaalide kvainimine (quining qualia).
- Paul Grice: "meaning" and overview of other important parts of Grice claims and theory.
- Nick Boström "are we living in simulation". http://www.simulation-argument.com/ and http://www.nickbostrom.com/
- Evolution of morals. alusta siit ja otsi ise edasi.
- Chomsky keeleteooria põhipunktid
- Mirror Neurons mh alustuseks brain science podcast 35 Mirror Neurons ja podcast 39 (Discusses the role of mirror neurons in imitation and language) pluss googelda veidi juurde.
- Frame problem in AI. Start with http://en.wikipedia.org/wiki/Frame_problem and continue to find additional materials and examples.
- How do bacteria and simple organisms communicate. Start with this TED lecture.
- infinity: cardinals and ordinals.
- Overview of pragmatism as a philosophical school: main ideas, development etc.
- example of a proof which is classically easy but intuitionistically hard: irrationality around square root of two.
- Anthropic principle and the Boltzmann brain.
- modal logics S4 ja S5 and possible worlds (Kripke semantics).
- neurons.
- Research and give an overview of the state of the art in machine translation: top systems, their capacity and the main principles of how they work.
- Statistical principles in machine translation a la Google
- Confirmation bias, start with this article
- How do bacteria and simple organisms communicate. Start with this TED lecture
- Evolution of morals. alusta siit
- How do bacteria and simple organisms communicate. Start with this TED lecture
- Frame problem in AI. Start with http://en.wikipedia.org/wiki/Frame_problem and continue to find additional materials and examples.
- Intuitsionistlik loogika: näited teoreemidest, mis kehtivad klassikaliselt, kuid mitte intuitsionistlikult. Näiteid tõestustest, millel lihtne klassikaline, kuid keeruline intuitsionistlik tõestus.
- Ordinaalid ja kardinaalid.
- Neuroimaging, auditory hallucinations, and the bicameral mind.pdf start here and download pdf
- Neurons are more complex than we thought, see here and here for starters.
- Could a Neuroscientist Understand a Microprocessor?
- The Hyperbolic Geometry of DMT Experiences and see this for some background.
- Perception Without Representation
- Brain Computation Is Organized via Power-of-Two-Based Permutation Logic