Priest, Tanaka, and Weber have revised their SEP-entry on paraconsistent logic, https://plato.stanford.edu/entries/logic-paraconsistent/
#sep #paraconsistent #explosive #logic #philosophy #logiikka #filosofia #matematiikka #mathematics #paradoxes #beliefs #dialetheism #consistency #inconsistency
Think of x.
Now, think of [the thought of x].
Now think of [the thought of [the thought of [x]]].
Repeat.
You now have an unlimited iterator r.
Let T be the totality of all iterations of r. Obviously, T has no last member; so there can be no thought of T - as that would be such a last member, by definition (Transcendence).
Yet, you just thought of T. (Closure)
For more on the Inclosure Schema see Graham Priest, Limits of Thought, 2002 (2nd edition).
Moral #dialetheism
This is nice. It's not mathematics as such, but the idea of "true contradictions" is on a solid foundation there.
Can a sentence be both true and false in the same sense? - Dialetheism
It might seem nonsensical until one sees the liar's #paradox:
This sentence is false.
Using classical #logic, this sentence seems to be both true and false. Due to the explosion rule, that implies every sentence. This is absurd, but philosophers don't agree on what has gone wrong here.
#Dialetheism is the #philosophy that accepts that it is both true and false and modifies logic to exclude the principle of explosion
Ihmettä odottaville tiedoksi, että SEP-entry niistä on uusittu, https://plato.stanford.edu/entries/miracles/
Tieteenfilosofit taas kokenevat velvollisuudekseen tarkistaa, onko teorioiden yhteismitattomuutta ahtaan puoleisessa Kuhn-Feyerabend-kontekstissa käsittelevään entryyn tullut olennaista uutta, https://plato.stanford.edu/entries/incommensurability/
Meitä ajattelussamme vakavasti kyllä-ja-ei-syndroomaan törmänneitä loogikoita puolestaan tieto dialetismi-entryn päivityksestä ilahduttanee - vai oliko se turhauttanee? https://plato.stanford.edu/entries/dialetheism/ 🤔
#sep #miracles #ihmeet #revision #incommensurable #measure #ontology #philosophyOfScience #logic #truth #dialetheism
@appassionato @bookstodon A good compliment to this book is to think about the #philosophy of #dialetheism. Its response to the paradoxes of self-reference is to simply accept the contradictions they imply as true. For example, the following sentence:
This sentence is false.
is both true and false according to dialetheism
Laitoin ylle IEP-linkin näkyviin jälestäpäin, koska sen kautta pääsee ehkä helpommin sisään parakonsistentin logiikan lupauksiin (esim. luku 4).
Ite tietysti ajauduin noiden kautta maistelemaan Dialetismia eli näkemystä, että voi olla tosia väitteitä, joiden negaatio on myös samalla tosi,
https://plato.stanford.edu/entries/dialetheism/
Aina välillä käy kuin hyvää sarjakuvaa lukiessa, että ei malta olla kääntämättä sivua. 🙂
@andrejbauer (I am assuming classical logic, but nothing really changes if we switch to intuitionistic logic, just replace Boolean algebras with Heyting algebras.)
This is a bit like saying "I am assuming euclidean geometry but nothing really changes if we switch to spherical." Because there are more than 2 kinds of geometry, and intuitionistic logic is not the only other choice here. Is RH "neither true nor false" or perhaps RH is "both true and false"? You need a dialetheic logic, a #paraconsistent logic. And in that case, these are both valid truth values, and RH would be formally undecidable. But more than that, asking for it to have no truth value at all is different from just not being true and also not being false. It might be similar to Graham Priest's "ineffable" logical value. #logic #dialetheism #twothingscanbetrue
Lupposofi
Distractions
CubeRootOfTrue
J Lou
Lupposofi