#Russell’s Paradox

[wouldyourfavepaychildsupport]

Would the set of all sets that do not contain themselves pay child support?

[leonvisionchronicles]

The Leadership Paradox: Finding Meaning in a World of Perspectives

By David Dantes Introduction: A World of Contradictions Leadership is often perceived as a straightforward path—a set of principles that, if followed, guarantee success. Yet, reality paints a different picture. Leadership is not a linear journey but a paradoxical experience, filled with contradictions and unexpected turns. Like light passing through a prism, the truth of any situation depends…

[dandelionjack]

so in case anyone’s wondering how Mr Miles is doing. the pattern continues. he must be exhausted

[earl-grey-teacake]

oooo logan’s magical paradox sounds interesting

The synopsis is provided in this ask. I can, however, offer a snippet.

*************

“George!” Alex moved in between George and the child who was a crumpled heap on the ground. A deadly silence settled between all of them until a whimper began to grow louder and louder.

*hic* *hic* “WAHHHHHHH!” Blood was dripping from his nose and a dark purple bruise was forming on his forehead. The cute, chubby face turned a violent red as streams of tears fell down the child’s face.

“Logan?” Alex bent down tentatively, an arm outstretched but not close enough to reach.

The little boy looked up and gave a timid smile, the blood from his nose was smeared all over his face. “It is Logan, right?”

Logan didn’t respond, only giving a shaky nod.

“Hey, how about you come here and let me clean your face? Come on.” Alex opened his arms and Logan came rushing in, smushing his blood, tears, and snot covered face all over Alex’s jacket.

The other two stared in shock as Alex soothed the crying child.

“Call James” he mouthed to Elias.

“I’ll call the others. They might know how to help.” George said, looking quite shell-shocked at the fact he attacked a child.

Logan cried softly as Alex carried him to the couch and tried to clean up the bloody mess on Logan’s face. Elias applied a healing spell to stop the blood and soothe the deep purple bruise on Logan’s forehead. George sat on the far end of the L-shaped couch, wanting to be close but clearly worried about his recent actions.

“There, that should do it.” The spell transformed the bruise into a light pink color.

“Hahhh!” Logan giggled as the sparkles of light disappeared.

“Did it tickle?” Alex grinned.

Logan nodded. “Smells minty. Like the blue jar.”

“Blue jar? Oh you mean the vaporub!”

Before Logan could respond, a knock cut through the conversation. Logan’s eyes widen with fear before he grabbed at Alex’s hoodie and hid his face in it, his body trembling.

George jumped up to open the door, revealing James, Lewis, Max, and Oscar. Oscar looked as if he ran the length of the hotel to get here judging by the sweat on his brow and the heaviness of his breathing. Before George could invite them in, Oscar shoved his way through.

“Where’s Logan?” Oscar panicked, his eyes darting everywhere in the room before settling on the trembling child in Alex’s arms. He knew those blonde locks anywhere.

“Logan?” Oscar stepped towards him to get a better look.

“GO AWAY!” Piercing eyes stared into Oscar’s soul. He knew those eyes. He dreamt of those eyes. But never once in his life did he think those eyes would state at him with such fear and hatred.

*****************

Please Enjoy❤️

[eightdoctor]

i haven’t seen anyone actually talk about it on here yet but if you want some actually good sutekh content that doesn’t portray the god of death as some continuity-obsessed fan who just wants to know the identity of ur mum lol then pleaseeee listen to the audio drama series the true history of faction paradox. he’s actually a fleshed out & competently written antagonist in those

[novelties-and-notions]

FLOSTRE: Enough of this tittle-tattle! Can we just talk about logic for a bit?

SOCRATES [Peers at audience]: Do you think that will go down better? If you ask me, you should bring on the dancing girls while you're ahead.

FLOSTRE: I'm not asking you. All I want to know is what do you know about logical matters?

SOCRATES: All I know is that I know nothing.

FLOSTRE: You never actually said that until just now, did you?

SOCRATES: I don't know. All I know is that I know nothing.

FLOSTRE: Is that a paradox?

SOCRATES: Only if it's true. How about this one: I only know one thing?

FLOSTRE: And what's that?

SOCRATES: That I only know one thing.

FLOSTRE [and audience]: And what's that?

SOCRATES: That I only know one thing.

A MATHEMATICIAN IN THE AUDIENCE: Apply a fixed-point function!

FLOSTRE: I'm sorry mon ami. I left my fixed-point function in my other suit. It was one of those Y-shaped chrome-plated ones designed by Haskell Curry, with the attachment for taking stones out of horses hoofs. But hélas, I do not have it with me. Now where were we?

SOCRATES: That I only… Oh, forget it. When do the dancing girls come on?

FLOSTRE: Later. There is much to discuss before then.

SOCRATES: I was afraid of that.

FLOSTRE: Talking of paradoxes, did you know that there's a village where the barber shaves every man who doesn't shave himself?

SOCRATES: I've been there. It's no paradox.

FLOSTRE: Comment ça?

SOCRATES: Because the barber is a woman. [B-boom on the bass drum.]

FLOSTRE: That's the Theory of Types for you, folks.

[omegaphilosophia]

The Philosophy of Set Theory

The philosophy of set theory explores the foundational aspects of set theory, a branch of mathematical logic that deals with the concept of a "set," which is essentially a collection of distinct objects, considered as an object in its own right. Set theory forms the basis for much of modern mathematics and has significant implications for logic, philosophy, and the foundations of mathematics.

Key Concepts in the Philosophy of Set Theory:

Definition of Set Theory:

Basic Concepts: Set theory studies sets, which are collections of objects, called elements or members. These objects can be anything—numbers, symbols, other sets, etc. A set is usually denoted by curly brackets, such as {a, b, c}, where "a," "b," and "c" are elements of the set.

Types of Sets: Sets can be finite, with a limited number of elements, or infinite. They can also be empty (the empty set, denoted by ∅), or they can contain other sets as elements (e.g., {{a}, {b, c}}).

Philosophical Foundations:

Naive vs. Axiomatic Set Theory:

Naive Set Theory: In its original form, set theory was developed naively, where sets were treated intuitively without strict formalization. However, this led to paradoxes, such as Russell's paradox, where the set of all sets that do not contain themselves both must and must not contain itself.

Axiomatic Set Theory: In response to these paradoxes, mathematicians developed axiomatic set theory, notably the Zermelo-Fraenkel set theory (ZF) and Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC). These formal systems use a set of axioms to avoid paradoxes and provide a rigorous foundation for set theory.

Set Theory and the Foundations of Mathematics:

Role in Mathematics: Set theory serves as the foundational framework for nearly all of modern mathematics. Concepts like numbers, functions, and spaces are all defined in terms of sets, making set theory the language in which most of mathematics is expressed.

Mathematical Platonism: The philosophy of set theory often intersects with debates in mathematical Platonism, which posits that mathematical objects, including sets, exist independently of human thought. Set theory, from this perspective, uncovers truths about a realm of abstract entities.

Philosophical Issues and Paradoxes:

Russell's Paradox: This paradox highlights the problems of naive set theory by considering the set of all sets that do not contain themselves. If such a set exists, it both must and must not contain itself, leading to a contradiction. This paradox motivated the development of axiomatic systems.

Continuum Hypothesis: One of the most famous problems in set theory is the Continuum Hypothesis, which concerns the possible sizes of infinite sets, particularly whether there is a set size between that of the integers and the real numbers. The hypothesis is independent of the ZFC axioms, meaning it can neither be proven nor disproven within this system.

Axioms of Set Theory:

Zermelo-Fraenkel Axioms (ZF): These axioms form the basis of modern set theory, providing a formal foundation that avoids the paradoxes of naive set theory. The axioms include principles like the Axiom of Extensionality (two sets are equal if they have the same elements) and the Axiom of Regularity (no set is a member of itself).

Axiom of Choice (AC): This controversial axiom asserts that for any set of non-empty sets, there exists a function (a choice function) that selects exactly one element from each set. While widely accepted, it has led to some counterintuitive results, like the Banach-Tarski Paradox, which shows that a sphere can be divided and reassembled into two identical spheres.

Infinity in Set Theory:

Finite vs. Infinite Sets: Set theory formally distinguishes between finite and infinite sets. The concept of infinity in set theory is rich and multifaceted, involving various sizes or "cardinalities" of infinite sets.

Cantor’s Theorem: Georg Cantor, the founder of set theory, demonstrated that not all infinities are equal. For example, the set of real numbers (the continuum) has a greater cardinality than the set of natural numbers, even though both are infinite.

Philosophical Debates:

Set-Theoretic Pluralism: Some philosophers advocate for pluralism in set theory, where multiple, possibly conflicting, set theories are considered valid. This contrasts with the traditional view that there is a single, correct set theory.

Constructivism vs. Platonism: In the philosophy of mathematics, constructivists argue that mathematical objects, including sets, only exist insofar as they can be explicitly constructed, while Platonists hold that sets exist independently of our knowledge or constructions.

Applications Beyond Mathematics:

Set Theory in Logic: Set theory is foundational not only to mathematics but also to formal logic, where it provides a framework for understanding and manipulating logical structures.

Philosophy of Language: In philosophy of language, set theory underlies the formal semantics of natural languages, helping to model meaning and reference in precise terms.

The philosophy of set theory is a rich field that explores the foundational principles underlying modern mathematics and logic. It engages with deep philosophical questions about the nature of mathematical objects, the concept of infinity, and the limits of formal systems. Through its rigorous structure, set theory not only provides the bedrock for much of mathematics but also offers insights into the nature of abstraction, existence, and truth in the mathematical realm.

[quads-and-monsters]

Proving that straight sex is dangerous: The Chris Cwej method.

Chris Cwej has gay sex: Gets blown in the back of a cab in the 80s, trace elements of his 30th century super semen are used to cure AIDS.

Chris Cwej has straight sex: Cries during and after sex, proceeds to end the world and die of radiation poisoning before regenerating into a redditor.

Still think straight sex is a joke???

[hezigler]

Watch "The Liar Paradox - an explanation of the paradox from 400 BCE" on YouTube

Russell's Paradox

[wholieta]

what do you mean you needed a way to explain the doctor meeting himself. TIME TRAVEL

[russell-crowe]

putting my chin in my hands and thinking about “(...) but that is the same of both protagonists and villain, heroes and bad boys, or bad girls. but I haven’t been asked to play a bad girl lately“ and “I’d like to play passionate women, but no one will let me“ and “I'm not a hard man, I like poetry and wear make-up for a living” and “rock 'n' roll is a lot better with a saliva filled asshole, I've always found" and “I shall come off this stage and I shall jam my stiletto in the crack of your ass” and deciding i want to study russell crowe like a bug

[wouldyourfavepaychildsupport]

Would the set of all sets that don't contain themselves and don't pay child support, pay child support?

[dandelionjack]

a planet called Homeworld razed to the ground huh?. its inhabitants — stuck-up upper-class racially prejudiced elites? the faction keeps haunting the edges of the narrative, i wouldn’t go as far as to say the actual narrative, but. somewhere out there beyond the page there’s a paradox peeking through . like boom with its imaginary enemy. i suppose this is inevitable — fp is a metatextual shadow of whatever “doctor who” tries to be at any given moment, and, like any inverted doppelganger, evil twin, malformed caricature, it pops up in the unlikeliest untoward places to spook the hell out of the doctor and us

[birdsonpowerlines]

In this episode we're back to talking about Doctor Who. We finally had a chance to watch the 2024 Christmas special, and had a lot of fun watching it so that is the topic of this podcast. We really loved the play on the "timey wimey!" What did you think about this year's Christmas special? How does it compare to others that you've seen? If you want to hear more of our Doctor Who-related podcasts, be sure to explore our episode playlist - there are quite a few podcasts focused on The Doctor.

If you haven't listened to our podcasts before, we use a voice messenger app to share our thoughts with each other to discuss a variety of topics as we go about our day.

Who are we at the Birds on Power Lines Podcast? We are a mom and young adult child team having the time of our lives talking about things we love and care about!

Links for the artist, Curtis Epperson, who we talk about at the end of the podcast: https://www.curtiseppersonart.com/ https://www.popgalleryorlando.com/collections/curtis-epperson https://www.popgalleryorlando.com/collections/curtis-epperson/products/tardis-by-curtis-epperson

Find the full set of podcasts on YouTube here: https://www.youtube.com/playlist?list=PLWyQ8KHWi2wBg3ZXuABXeaHAdrcJ2da67

We are also on (look for Birds on Power Lines Podcast): Apple Podcasts Spotify Facebook Podbean

Art: All watercolor art by me: Evelyn Voura for Birds on Power Lines @BirdsOnPowerLines

Music: Music by my child for Birds on Power Lines @BirdsOnPowerLines

Bird sounds from: Macaulay Library at the Cornell Lab of Ornithology https://www.youtube.com/watch?v=hrgGTvzuA1I

[dandanjean]

Le paradoxe de Russell

Cette vidéo explore deux des énigmes les plus célèbres de la logique : le Paradoxe de Russell et le Paradoxe du Barbier. Découvrez comment ces énigmes défient notre compréhension de la logique et de la vérité, remettant en question des notions fondamentales. Rejoignez-nous pour une discussion captivante et approfondie qui vous invite à repenser les limites de la pensée logique Cours 2 : Le…

[epicscizor]

Fandom needs to learn Zermelo-Frenkel set theory smh

The "D&D is actually a queer game and I will never touch an actual queer game" takes feel indistinguishable from "everything I like is punk; I also don't like punk music or fashion." Does that make sense