Plato’s Allegory of the Cave

Plato’s Allegory of the Cave – Alex Gendler


If You Don’t Know You Are Held Captive, Does It Matter?
June 10, 2015
Marcelo Gleiser

the classic movie The Matrix. As a counterpoint, they also read Plato’s “Allegory of the Cave” from Book VII of his dialogue The Republic. Both can be seen as explorations of the value of knowledge and freedom.

If you were a chained slave or a human in a cocoon, would you like to know? Is “ignorance is bliss” a viable life?


Consciousness is a mathematical pattern
Max Tegmark at TEDxCambridge 2014



Kierkegaaard’s View of Socrates

Kierkegaaard’s View of Socrates
Why did Kierkegaaard believe that Socates gave rise to so many  competing philosophical schools?

– With no positive doctrine, interpretations were limitless

Søren Kierkegaard – Subjectivity, Irony and the Crisis of Modernity
University of Copenhagen
Jon Stewart, PhD, Dr theol & phil

Emergence (process)

[philosophy, systems theory, science, and art] a process whereby larger entities, patterns, and regularities arise through interactions among smaller or simpler entities that themselves do not exhibit such properties

“emergence” would have clarified–even made redundant–the discussion:

Emergence and Complexity
Stanford. May 21, 2010
Robert Sapolsky
cellular automaton

butterfly effects

gradients of information
gradients of attraction and repulsion
gradients provide a lot of the optimization in the systems
neighbor-to-neighbor interactions
generalists work better in these systems than specialists
bottom-up systems
attractors and chaos


Emergence Into The Adjacent Possible
January 2, 2010

Sorites Paradox

Sorites Paradox
Dec 6, 2011

The sorites paradox is the name given to a class of paradoxical arguments, also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved.
For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap.
We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion.

This phenomenon at the heart of the paradox is now recognised as the phenomenon of vagueness. Though initially identified with the indeterminacy surrounding limits of application of a predicate along some dimension, vagueness can be seen to be a feature of syntactic categories other than predicates.
Names, adjectives, adverbs and so on are all susceptible to paradoxical sorites reasoning in a derivative sense.


concept used by:
Logic: Language and Information 1
The University of Melbourne

Thinking Thoughts No One Has Thunk

Thinking Thoughts No One Has Thunk
by Robert Krulwich
July 06, 2011

a young Canadian filmmaker in Alberta, Nick Saik, gave his sister Laura a hula hoop. On it, he’d clamped a light-weight, wide-angle camera. All he did was ask her to hula.

This is the first time I’ve ever seen hooping from the hoop’s point of view.
Instead of a ring twirling around a girl, in this version the ring seems stock still. It’s the girl who does all the twirling. It’s so wonderfully weird.

As somebody wrote on YouTube: “that girl isn’t good at Hula Hooping, the Hula Hoop is good at Girling.”

This talent for topsy-turvying, for knowing that how you view the world is just one way among many, that there are always other ways, and sometimes those other ways may overthrow everything you believe — this is a rare and brave thing to do.

‘Bioshock Infinite’: A First-Person Shooter, A Tragic Play

‘Bioshock Infinite’: A First-Person Shooter, A Tragic Play
April 01, 2013

BioShock Infinite creator Ken Levine

Back in 2007, in the first installment of BioShock, Levine created a world based on Ayn Rand‘s individualist philosophy and let it play out. This time, Levine has turned a game into an Aristotelian tragedy and used the model of great tragic heroes.

“Whether it’s Hamlet or Oedipus, there’s a notion of greatness to them,” Levine says, “and a notion of what would’ve / could’ve [been]. And what’s so painful about them is how wrong they went and how right they could have gone.”


Gödel’s incompleteness theorems

Gödel’s incompleteness theorems’s_incompleteness_theorems

The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.

For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system.

The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.

Relation to the liar paradox
The liar paradox is the sentence “This sentence is false.” An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true). A Gödel sentence G for a theory T makes a similar assertion to the liar sentence, but with truth replaced by provability: G says “G is not provable in the theory T.”

Extensions of Gödel’s original result
… it is common to state the effectiveness and expressiveness conditions as hypotheses for the incompleteness theorem, so that it is not limited to any particular formal theory. The terminology used to state these conditions was not yet developed in 1931 when Gödel published his results.

the epistemological relevance of the second incompleteness theorem

Examples of undecidable statements
There are two distinct senses of the word “undecidable” in mathematics and computer science. The first of these is …

Limitations of Gödel’s theorems
The conclusions of Gödel’s theorems are only proven for the formal theories that satisfy the necessary hypotheses.
Not all axiom systems satisfy these hypotheses, …

Gödel’s theorems only apply to effectively generated (that is, recursively enumerable) theories.
If all true statements about natural numbers are taken as axioms for a theory, then this theory is a consistent, complete extension of Peano arithmetic (called true arithmetic) for which none of Gödel’s theorems apply in a meaningful way, because this theory is not recursively enumerable.

Minds and machines
Authors including J. R. Lucas have debated what, if anything, Gödel’s incompleteness theorems imply about human intelligence. Much of the debate centers on whether the human mind is equivalent to a Turing machine, or by the Church–Turing thesis, any finite machine at all. If it is, and if the machine is consistent, then Gödel’s incompleteness theorems would apply to it.