#Deontic & Epistemic & Perf:
Aun, ya
Curry, propositional logic
List of paradoxes by type
https://www.princeton.edu/~hhalvors/teaching/phi340_f2005/handouts/deontic.pdf https://www.princeton.edu/~hhalvors/teaching/phi340_f2005/
Good Samaritan Paradox
https://iep.utm.edu/contrary-to-duty-paradox/ https://www.jimpryor.net/teaching/courses/akrasia/2015/ https://www.jimpryor.net/teaching/courses/akrasia/2015/deontic.html https://en.m.wikipedia.org/wiki/Deontic_logic https://en.m.wikipedia.org/wiki/Akrasia https://aristotle.rutgers.edu/joomlatools-files/docman-files/Help_for_the_Good_Samaritan.pdf https://www.google.com/search?q=gettier+problem&oq=gettier+&gs_lcrp=EgZjaHJvbWUqDQgAEAAYkQIYgAQYigUyDQgAEAAYkQIYgAQYigUyBggBEEUYOTINCAIQLhivARjHARiABDIHCAMQABiABDIHCAQQABiABDIHCAUQABiABDIHCAYQABiABDIHCAcQABiABDINCAgQLhivARjHARiABDIHCAkQABiABDIHCAoQABiABDIHCAsQABiABDIHCAwQABiABDIHCA0QABiABDINCA4QLhivARjHARiABNIBCDM3NDVqMGo3qAIUsAIB8QWCXJC2sm0JZA&client=tablet-android-samsung-rvo1&sourceid=chrome-mobile&ie=UTF-8 https://en.m.wikipedia.org/wiki/Gettier_problem
https://en.m.wikipedia.org/wiki/Absolute_infinite
Yablo https://iep.utm.edu/yablo-pa/
Berry: Answer: Let me propose a candidate: “Kolmogorov complexity is not computable.” from https://mathoverflow.net/questions/454105/are-there-any-undecidability-results-that-are-not-known-to-have-a-diagonal-argum
https://math.andrej.com/2007/04/08/on-a-proof-of-cantor's-theorem/ - shortest desc of Lawvere fp thm.
https://terrytao.wordpress.com/2009/11/05/the-no-self-defeating-object-argument/ https://terrytao.wordpress.com/2010/10/18/the-no-self-defeating-object-argument-revisited/ https://www.nearly42.org/cstheory/halting_to_kolmogorov/ https://mathoverflow.net/questions/454105/are-there-any-undecidability-results-that-are-not-known-to-have-a-diagonal-argum
Prerequisits:
Classes vs Sets
In my humble opinion, a Set is something that can exists, at least potentially; exists possibly, in a possible world; assumption of it’s existence doesn’t lead to a logical contradiction. A Class - is something that exists in name only, something that necessarily doesn’t exist, something that involves a logical contradiction and thus doesn’t occur in any possible world [excepting fictional/illogical ones]. Obviously, we can come up with a name and ascribe some qualities to the name - this doesn’t mean that there is anything behind that name. Think “ghosts” for example. Or, temperatures below 0K. These examples are physical rather than logical, but they may convey the meaning.
Popper (3), Wilde #
Re: possible worlds, modal logic, necessary [] vs possible <> cf. ….
Diagonalization
Casual/informal/verbal, Logic (first-order logic or modal logic), ST: Set Theory language, Comp: Theory of Computation language
Russel’s paradox & Diagonalization.
- Casual: Barber paradox: https://en.m.wikipedia.org/wiki/Barber_paradox
- Logic: Bp wiki
- Comp: https://math.stackexchange.com/questions/2150898/why-cant-russells-paradox-be-solved-with-references-to-sets-instead-of-contain, https://www.linkedin.com/pulse/20141122040705-3300752-a-progrmmer-s-take-on-russell-s-paradox cf.refs to Dijkstra there!
- ST: Tao
Set of all sets (also, z u {z})
Omniscience
Alternatively: Cantor’s Diagonal Argument.
https://www.codecademy.com/resources/docs/markdown/tables
Generalization: Lawvere fp th - see below. What is CCC, fixed point. Andrej Bauer, too.
Burali-Forti paradox Grelling - Adj, THP, Turing with Oracle, Turing degree, Goedel, Tarski (Liar), Loeb, Richard etc.
Adj: https://en.m.wikipedia.org/wiki/Grelling%E2%80%93Nelson_paradox
Richard: https://en.m.wikipedia.org/wiki/Richard%27s_paradox
John Buridan on Self-Reference: Chapter Eight of Buridan’s ‘Sophismata’, with a Translation, an Introduction, and a Philosophical Commentary https://annas-archive.org/md5/3665e907a985fe37473e250702b4e606
II
Berry paradox https://en.m.wikipedia.org/wiki/Berry_paradox Casual: Beckenbach Logic: cf wiki Comp: answer to Tao: https://mathoverflow.net/questions/454105/are-there-any-undecidability-results-that-are-not-known-to-have-a-diagonal-argum
Kolmogorov complexity https://www.nearly42.org/cstheory/halting_to_kolmogorov/ Chaitin #
III
Free Will:
Unexpected hanging Crocodile https://en.m.wikipedia.org/wiki/Newcomb%27s_paradox
“While it is not possible for the halting problem for a given computing language to be computable in that language, it is certainly possible that it is computable in a strictly stronger language. When that is the case, one can then invoke Newcomb’s paradox to argue that the weaker language does not have unlimited “free will” in some sense” Tao
Modal logic, Future contingents, Master Argument.
IV