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Gödel Machines: Towards a Technical Justification of Consciousness [chapter]

Jürgen Schmidhuber
2005 Lecture Notes in Computer Science  
Here we point out that the recently formulated Gödel machines may provide just such a technical justification.  ...  The growing literature on consciousness does not provide a formal demonstration of the usefulness of consciousness.  ...  Our fully self-referential Gödel machine [43, 45] may be viewed as providing just such a technical justification.  ... 
doi:10.1007/978-3-540-32274-0_1 fatcat:twyyq4cqmzeednza23ilvqu2tm

Why Gödel didn't have church's thesis

Martin Davis
1982 Information and Control  
Every algorithm can be programmed on a one-tape Turing machine.  ...  Although none of those theorems were very hard, what was interesting was that Post quite clearly and consciously took the propositional calculus as a combinatorial calculus as an object of study.  ... 
doi:10.1016/s0019-9958(82)91226-8 fatcat:qajogh5tdnhjhgbz2mdvj6k5dy

Naïve Thoughts on the Paradox of Gödel

Philip Davis
2001 Humanistic Mathematics Network Journal  
"GIT a part of a 'golden braid' of math , art and music that penetrates the very nature of human consciousness.  ...  The modes of its discoveries, developments, justifications, and interpretations cannot be formalized in a few paragraphsif at all.  ... 
doi:10.5642/hmnj.200101.24.07 fatcat:ft4etr4sgjcv7itraeuxtzgooa

Richard Tieszen, After Gödel. Platonism and Rationalism in Mathematics and Logic

Paola Cantu
2014 Journal for the History of Analytical Philosophy  
account the correlations to Gödel's technical results, including the incompleteness theorems and the remarks on Turing's machines.  ...  This is the reason for the choice of the title "After Gödel", which is very appropriate, because the author follows Gödel up to a certain point that seems defensible.  ... 
doi:10.15173/jhap.v2i8.972 fatcat:avvmpsnllzftrjpe3ygxux5dgm

Can a machine think (anything new)? Automation beyond simulation

M. Beatrice Fazi
2018 AI & Society: The Journal of Human-Centred Systems and Machine Intelligence  
The point that I would like to consider here, however, is that machine learning is also a black box in another, more technical, sense.  ...  However, the machine does not have any understanding or consciousness of the faculty of speaking Chinese: it is only processing symbols. Syntax, in other words, does not account for semantics.  ... 
doi:10.1007/s00146-018-0821-0 fatcat:hkckw4g4yrelvk5bqm4zy4vgja

The Ghost in the Financial Machine

Arjun Appadurai
2011 Public culture  
My starting point is Jacques Derrida's (1994) famous argument about the "impossibility" of the gift, which annuls itself by its implicit expectation (a negative performative) of a return.  ...  I focus here on the idea of the "return" as one entry into a new approach to contemporary financial devices.  ...  But the availability of such extra-technical information is a truism.  ... 
doi:10.1215/08992363-1336399 fatcat:wfx3x3ncavchvhz3xunqbl54iy

The Ghost in the Quantum Turing Machine [article]

Scott Aaronson
2013 arXiv   pre-print
I focus relatively narrowly on a notion that I call "Knightian freedom": a certain kind of in-principle physical unpredictability that goes beyond probabilistic unpredictability.  ...  I investigate how far one can go toward solving those problems, and along the way, encounter (among other things) the No-Cloning Theorem, the measurement problem, decoherence, chaos, the arrow of time,  ...  It goes without saying that none of the people mentioned necessarily endorse anything I say here (indeed, some of them definitely don't!).  ... 
arXiv:1306.0159v2 fatcat:bhn6y7jtfnex3jr46gh3twkl4i

Do the laws of physics forbid the operation of time machines?

John Earman, Christopher Smeenk, Christian Wüthrich
2008 Synthese  
Despite the effort put into these no-go theorems, there is no widely accepted definition of a time machine.  ...  along the way towards quantum gravity.  ...  Special thanks are due to the participants of a symposium held in honor of Arthur Fine (where an earlier version of this paper debuted) for stimulating discussion and questions.  ... 
doi:10.1007/s11229-008-9338-2 fatcat:n4pdhebuz5h2fabtjpgj2mboje

Turing's Error-revised

2016 International Journal of Philosophy Study  
Since there is no mathematical justification to such selection, it is possible to say that relevance and related concepts are beyond the power of expression of mathematics and computation.  ...  Therefore, we critically studied the foundations of used theory languages. By looking critically some of the main arguments of machine thinking, one can find unifying factors.  ...  ACKNOWLEDGEMENTS This research is partially funded by the Industrial Design Department of Eindhoven University of Technology and Design United (Netherlands).  ... 
doi:10.14355/ijps.2016.04.004 fatcat:7krl6obqlbaebalpaienmvpt6a

"Gödel's Modernism: On Set-Theoretic Incompleteness," Revisited [chapter]

Mark van Atten, Juliette Kennedy
2009 Logicism, Intuitionism, and Formalism  
Study, for facilitating our research, and overall for ensuring such a pleasant stay in the archive; also, we are much obliged to the Institute for Advanced Study which kindly granted permission to quote  ...  We are grateful to the staff of the Department of Rare Books and Special Collections at the Firestone Library of Princeton University, and to Marcia Tucker of the Library of the Institute for Advanced  ...  As we saw above, Gödel also had a (much more conclusive) justification of inaccessibles from an analysis of the concept of set.  ... 
doi:10.1007/978-1-4020-8926-8_15 fatcat:fjosoetpufh7vikbk2fq2zkaku

Betting your life on an algorithm

Daniel C. Dennett
1990 Behavioral and Brain Sciences  
mechanisms of theory justification.  ...  consciousness, albeit a difficult .one to pin down, and any small progress toward understanding some part of this concept will lead ultimately to progress toward understanding the rest of it.  ...  Penrose would lose in the game, "Show me an example of nonalgorithmic thinking and I will implement it on the computer," with an AI system builder worth his LISP machine.  ... 
doi:10.1017/s0140525x00080742 fatcat:oksxbigvojgmfnrkc73qgp3qmq

Physics of brain-mind interaction

John C. Eccles
1990 Behavioral and Brain Sciences  
Penrose has produced an accessible, Information-packed compilation over a wide-ranging selection of difficult topics. One  ...  mechanisms of theory justification.  ...  consciousness, albeit a difficult .one to pin down, and any small progress toward understanding some part of this concept will lead ultimately to progress toward understanding the rest of it.  ... 
doi:10.1017/s0140525x00080778 fatcat:hsnvygzhgnckdk3wqswlr3b63y

A refutation of Penrose's Gödelian case against artificial intelligence

Selmer Bringsjord, Hong Xiao
2000 Journal of experimental and theoretical artificial intelligence (Print)  
The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light.  ...  Having, as it is generally agreed, failed to destroy the computational conception of mind with the Gödelian attack he articulated in his The Emperor's New Mind, Penrose has returned, armed with a more  ...  In order to grasp our exegesis, think back to the machines M 1 , M 2 , and M 3 in the justification given above for (T 1 ).  ... 
doi:10.1080/09528130050111455 fatcat:cm5wmkjpznh5rjmjn7iz2uwv44

Not Finitude but Countability: Implications of Imagination Positing Countability in Time

Fionn Murtagh
2011 Kritike: An Online Journal of Philosophy  
At the heart of our discussion is a technical argument arising from Cantor's diagonal method.  ...  We discuss Kant, Heidegger and Gödel in this light. We draw out implications for "machine imagination," and we propose a new basis for understanding human creativity and imagination.  ...  Dehaene, "A few steps towards a science of mental life," in Mind, Brain, and Education, 1 (2007) 28-47 and V.  ... 
doi:10.25138/5.1.a.6 fatcat:wka7x6xhybdsjhd4e3zhysz7re

"That Which Surpasses All Understanding": The Limitations of Human Thought

Mark J. Nielsen
2009 Dialogue : A Journal of Mormon Thought  
All things are full of labour; man cannot utter it: the eye is not satisfied with seeing nor the ear filled with hearing.—Ecclesiastes 1:4-8  ...  The wind goeth toward the south, and turneth about unto the north; it whirleth about continually, and the wind returneth again according to his circuits.  ...  Godel can prove us wrong by constructing a true statement in arithmetic that our machine will never prove.  ... 
doi:10.5406/dialjmormthou.42.3.0001 fatcat:h57s2zywrnfbnj5idajzy43lia
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