Logic was studied in several ancient civilizations, including Greece, India, and China. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Hindus, Buddhists and Jains.
The concept of logical form is central to logic. The validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.
Woodin's Ω-conjecture asserts that if there is a proper class of Woodin cardinals (for technical reasons, most results in the theory are most easily stated under this assumption), then Ω-logic satisfies an analogue of the completeness theorem. From this conjecture, it can be shown that, if there is any single axiom which is comprehensive over (in Ω-logic), it must imply that the continuum is not . Woodin also isolated a specific axiom, a variation of Martin's maximum, which states that any Ω-consistent (over ) sentence is true; this axiom implies that the continuum is .
Logic, the study of the principles and criteria of valid inference and demonstration
Mathematical logic, a branch of mathematics that grew out of symbolic logic
Philosophical logic, the application of formal logic to philosophical problems
Mathematical logic, a branch of mathematics that grew out of symbolic logic
Philosophical logic, the application of formal logic to philosophical problems
Logic may also refer to:
Entertainment
"A Logic Named Joe", a science fiction short story by Murray Leinster (using his given name, Will F. Jenkins) first published in the March 1946 issue of Astounding Science Fiction
Lamont "LOGiC" Coleman, a musician who collaborated on rapper Jim Jones' fifth studio album, Capo (album) (2011) on E1 Music
Try to Solve Crazy Logic Task with Omega Nuggets from Gegagedigedagedago #gedagedago #omeganugget
published: 24 Jun 2024
Try to Solve Amazing Logic Task with Omega Nugget by Gedagedago #gedagedago #omeganugget #logic
published: 18 Jun 2024
Try to Solve Crazy Logic Task with Omega Nuggets by Gedagedago #gedagedago #omeganugget #funny
published: 14 Jun 2024
Try to Solve this Funny Logic Task with Omega Nuggets in Carrot Style 🥕 #gegana #gegagedigedagedago
published: 24 Jun 2024
Coolest Logic Task with Omega Nuggets by Gedagedago #gedagedago #funny #omeganugget #funny #logic
published: 09 Sep 2024
Space Traveler Omega - Logic circuits
The track was created using the Beat Machine app on android (Synthwave pack). Images generated by Midjourney 6 alpha, based on the artist Wayne Barlowe.
published: 24 Jan 2024
A Reassessment of Gödel’s Doctrine: The Necessity of Infinity (Patrick Ryan, Chapman University)
The Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics takes place at Chapman University as its main host, and is co-organized together with researchers from UC Riverside, CSU San Bernardino, and Pitzer College. It also occasionally integrates the Chapman University D.Sc. program in Math, Philosophy and Physics as its Graduate Colloquium.
The seminars are held in hybrid format on the Chapman University campus in the Keck Center, home of Schmid College of Science and Technology, or on Zoom. On November 1, 2024, Patrick Ryan presented his talk, "A Reassessment of Gödel’s Doctrine: The Necessity of Infinity".
ABSTRACT:
In his landmark 1931 paper, Gödel demonstrated the existence of finitary statements that required infinitary resources to prove them....
published: 04 Nov 2024
Try to Solve Amazing Logic Task with Omega Nugget & Minions 🤯 #gegagedigedagedago #despicableme
The track was created using the Beat Machine app on android (Synthwave pack). Images generated by Midjourney 6 alpha, based on the artist Wayne Barlowe.
The track was created using the Beat Machine app on android (Synthwave pack). Images generated by Midjourney 6 alpha, based on the artist Wayne Barlowe.
The track was created using the Beat Machine app on android (Synthwave pack). Images generated by Midjourney 6 alpha, based on the artist Wayne Barlowe.
The Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics takes place at Chapman University as its main host, and is co-org...
The Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics takes place at Chapman University as its main host, and is co-organized together with researchers from UC Riverside, CSU San Bernardino, and Pitzer College. It also occasionally integrates the Chapman University D.Sc. program in Math, Philosophy and Physics as its Graduate Colloquium.
The seminars are held in hybrid format on the Chapman University campus in the Keck Center, home of Schmid College of Science and Technology, or on Zoom. On November 1, 2024, Patrick Ryan presented his talk, "A Reassessment of Gödel’s Doctrine: The Necessity of Infinity".
ABSTRACT:
In his landmark 1931 paper, Gödel demonstrated the existence of finitary statements that required infinitary resources to prove them. This led him to postulate what Solomon Feferman called Gödel’s Doctrine, namely, that “the unlimited transfinite iteration of the powerset operation is necessary to account for finitary mathematics.” This claim garnered further support over the course of the 20th century because of the production of various other “finitary independence” results. Nonetheless, proof theoretic work by Feferman and others showed that these finitary results could be proved using relatively weak systems, e.g., predicatively justifiable systems, thereby challenging Gödel’s Doctrine. In this talk, I would like to argue that, though the technical results of Feferman and others are unimpeachable, their philosophical significance is overstated. That is, even if Gödel’s Doctrine is dubious when we understand "necessary" to mean "proof theoretically necessary," it can be vindicated when we think of other senses in which strong infinitary resources might be necessary for mathematics. This is done by investigating a fascinating collection of finitary statements that possess multiple proofs employing both infinitary and finitary resources. I consider how an analysis of such results can inform debates in the philosophy of mathematics, especially discussions of purity, content, and explanation. In particular, if a finitary theorem τ has a perfectly cogent, finitary proof, why then provide an infinitary proof of τ , a proof involving principles of an ostensibly different sort? What is gained? Do such infinitary proofs play an explanatory role? Is there then a sense in which infinity is necessary? I conclude by indicating some promising directions for future research.
The Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics takes place at Chapman University as its main host, and is co-organized together with researchers from UC Riverside, CSU San Bernardino, and Pitzer College. It also occasionally integrates the Chapman University D.Sc. program in Math, Philosophy and Physics as its Graduate Colloquium.
The seminars are held in hybrid format on the Chapman University campus in the Keck Center, home of Schmid College of Science and Technology, or on Zoom. On November 1, 2024, Patrick Ryan presented his talk, "A Reassessment of Gödel’s Doctrine: The Necessity of Infinity".
ABSTRACT:
In his landmark 1931 paper, Gödel demonstrated the existence of finitary statements that required infinitary resources to prove them. This led him to postulate what Solomon Feferman called Gödel’s Doctrine, namely, that “the unlimited transfinite iteration of the powerset operation is necessary to account for finitary mathematics.” This claim garnered further support over the course of the 20th century because of the production of various other “finitary independence” results. Nonetheless, proof theoretic work by Feferman and others showed that these finitary results could be proved using relatively weak systems, e.g., predicatively justifiable systems, thereby challenging Gödel’s Doctrine. In this talk, I would like to argue that, though the technical results of Feferman and others are unimpeachable, their philosophical significance is overstated. That is, even if Gödel’s Doctrine is dubious when we understand "necessary" to mean "proof theoretically necessary," it can be vindicated when we think of other senses in which strong infinitary resources might be necessary for mathematics. This is done by investigating a fascinating collection of finitary statements that possess multiple proofs employing both infinitary and finitary resources. I consider how an analysis of such results can inform debates in the philosophy of mathematics, especially discussions of purity, content, and explanation. In particular, if a finitary theorem τ has a perfectly cogent, finitary proof, why then provide an infinitary proof of τ , a proof involving principles of an ostensibly different sort? What is gained? Do such infinitary proofs play an explanatory role? Is there then a sense in which infinity is necessary? I conclude by indicating some promising directions for future research.
The track was created using the Beat Machine app on android (Synthwave pack). Images generated by Midjourney 6 alpha, based on the artist Wayne Barlowe.
The Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics takes place at Chapman University as its main host, and is co-organized together with researchers from UC Riverside, CSU San Bernardino, and Pitzer College. It also occasionally integrates the Chapman University D.Sc. program in Math, Philosophy and Physics as its Graduate Colloquium.
The seminars are held in hybrid format on the Chapman University campus in the Keck Center, home of Schmid College of Science and Technology, or on Zoom. On November 1, 2024, Patrick Ryan presented his talk, "A Reassessment of Gödel’s Doctrine: The Necessity of Infinity".
ABSTRACT:
In his landmark 1931 paper, Gödel demonstrated the existence of finitary statements that required infinitary resources to prove them. This led him to postulate what Solomon Feferman called Gödel’s Doctrine, namely, that “the unlimited transfinite iteration of the powerset operation is necessary to account for finitary mathematics.” This claim garnered further support over the course of the 20th century because of the production of various other “finitary independence” results. Nonetheless, proof theoretic work by Feferman and others showed that these finitary results could be proved using relatively weak systems, e.g., predicatively justifiable systems, thereby challenging Gödel’s Doctrine. In this talk, I would like to argue that, though the technical results of Feferman and others are unimpeachable, their philosophical significance is overstated. That is, even if Gödel’s Doctrine is dubious when we understand "necessary" to mean "proof theoretically necessary," it can be vindicated when we think of other senses in which strong infinitary resources might be necessary for mathematics. This is done by investigating a fascinating collection of finitary statements that possess multiple proofs employing both infinitary and finitary resources. I consider how an analysis of such results can inform debates in the philosophy of mathematics, especially discussions of purity, content, and explanation. In particular, if a finitary theorem τ has a perfectly cogent, finitary proof, why then provide an infinitary proof of τ , a proof involving principles of an ostensibly different sort? What is gained? Do such infinitary proofs play an explanatory role? Is there then a sense in which infinity is necessary? I conclude by indicating some promising directions for future research.
Logic was studied in several ancient civilizations, including Greece, India, and China. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Hindus, Buddhists and Jains.
The concept of logical form is central to logic. The validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.
[Intro:] (Allllllright) In the sky it's a bird, it's a plane, nah who dat? Everybody want me to save them, I can't do that Gotta little shine and they wonder where the lewd at The life of an artist I had to pursue that [Verse 1:] Superman all the time yea, true dat That's why I laugh when they ask, "Man where the suit at?" I love my family love my friends But when it comes down to money see it all depends Cause now I got new family, I got new friends That I never even seen before, where does it end? See I got loved ones and I got enemies But at the end of the day I don't know the identities So they love the entities And people befronted me for the fame Breaking in the game Life will never be the same... It'll never be the same And they all like [Hook:] You are... My... Superhero (superhero) I said (I said) You are... My... Superhero (superhero) [Verse 2:] I was gone for a minute, came back in a flash Spit crack up a dude's rock like dash Any dame know I got game, go ask This is my true identity- No mask Most wish to get it and rub on a flask I wish to get it and rub on her ass Hip-Hop what I'm talking bout, you ain't on And a metaphor means I am hands on Out for the green with a buzz like Hornet I ain't rip the game yet, I just torn it See the good guy gets the dame And if a shawty got a donk like Lois Lane I turn into the paraphilias from X-Men You ain't get it? I'm all about the brain Step to the mic he a beast Hungry in the game still looking for a feast All about my dough on a rise like yeast And I'm a keep going till a motha fucka deceased See I stood on the side humbly, like Alfred But now it's time to jump in the bat outfit And I could give a damn if you doubt it Cause when I hit the stage they shout it Uh, Yea they shout it (What'd they shout?) They shout [Hook:] You are... My... Superhero (superhero) I said (I said) You are... My... Superhero (superhero) [Verse 3:] No the flow never awkward man Stepped in the booth the like, I'll be Damned Kid opened his mouth and shocked me man And I get the honeys wetter than Aqua-Man See that's that sex appeal I guess that'll add another meal to the deal But right now I'm just trying to get a meal In the bat cave sharpen in the skill With an Iron-Man mindset, they can never steal Villain on the mic though, yea I had to kill it I wrote this rhyme in braille just for you to feel it Let the flow pour for a minute but I gotta seal it [Outro:] Hopefully now (hopefully now) Y'all know me Gotta grip on the game Like it was fresh, about to sewn it [Hook:] You are... My... Superhero (superhero) I said (I said) You are... My...
Brainteasers have been proven to increase your brain age and your lateral-thinking skills – why not give this tricky puzzle a go to see if you can figure out the correct answer? ... .
Rex Reed’s scalpel was particularly sharp in 2024, slicing through 43 films with the kind of ruthless precision only he can wield ... Rex Reed’s 2024 MovieReviewRoundup ... Reed dismisses American Star as “a thriller with no thrills” and even less logic ... .
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the logic of life across sales, given several informational, physical, and chemical boundaries that seem to be inescapable ... machine based on the logic of cellular life and reproduction.
Ever found yourself avoiding a black cat, nervously knocking on wood, or tossing salt over your shoulder after a spill? Congratulations. you’re human. Superstitions, those quirky, ....