-
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid (Official Video)
Download/Stream "EVERYBODY" here: http://smarturl.it/LogicEverybody?iqid=yt
Director - Andy Hines
Executive producer- Luga Podesta & Brandon Bonfiglio
Producer- Andrew Lerios & Alex Randall
Director of photography- Jeff Bierman
Production Designer - Hannah Beachler
Edited by Joe Calardo
Casting - German Legarreta
Assistant production supervisor - Kai Lusk
Assistant Director - Giovanni Cotto-Ortiz
Sound- Joe Bartone & Eric Ballew
Gaffer- Theodore Rysz
Grip- Matthew Lim
Stylist- Antionette Messam
Color by Sean Coleman
Additional footage by- Justin Fleischer, Mike Holland, Josh Rimmey & Zach Williams
Production Assistant Alec Schweitzer
Written & Directed by Andy Hines
Music video by Logic performing 1-800-273-8255. (C) 2017 Def Jam Recordings, a division of UMG Recordings, Inc.
http...
published: 17 Aug 2017
-
Logic - Homicide ft. Eminem (Official Video)
#Homicide
"Homicide" available on all streaming services now: https://logic.lnk.to/Homicide
Music video by Logic performing Homicide. © 2019 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/gXjTAg
published: 28 Jun 2019
-
Logic - 1-800-273-8255 ft. Alessia Cara & Khalid (Official Audio)
Listen to the official audio of 1-800-273-8255 by Logic ft Alessia Cara & Khalid.
Buy Everybody Deluxe Edition which includes the Everybody Documentary!
http://bit.ly/Logic-Everybody-Album
SUBSCRIBE to the official Visionary Music Group channel for more original material from Logic & Jon Bellion including music video premieres, behind the scenes & more: http://bit.ly/Subscribe-to-VMG
Follow Visionary Music Group:
https://twitter.com/TeamVisionary
https://fb.com/VisionaryMusicGroup
http://instagram.com/teamvisionary
published: 12 May 2017
-
Joyner Lucas ft. Logic - ISIS (ADHD)
Available on Spotify and iTunes: https://orcd.co/adhd
Merch (shop now): https://bit.ly/2LphKWy
Tully App: https://tullyapp.com
Create, Manage & Distribute Music using Tully. The #1 tool for Independent Artists offering monthly opportunities.
Tully opportunity drops include: features, cash giveaways, a touring opportunity and more! Tully App is a blueprint for the entrepreneur artist to successfully operate in today's music industry. You can Create, Manage, Distribute music in one app.
#tullyapp #joynerlucas #adhd #evolution
published: 23 May 2019
-
Logic - 5AM (Prod. C-Sick)
Subscribe to SwagyTracks for more music daily !
http://bit.ly/SubscribeSwagy
.........
• Logic -
https://twitter.com/Logic301
http://www.facebook.com/mindoflogic
http://mindoflogic.com/
Download this track •
http://piff.me/e9615f2
Picture credit •
https://www.flickr.com/photos/117317408@N03/12616735133/in/photostream/
If you are the owner of this picture and want it removed,contact me and I will delete the video as soon as possible,no drama!
.........
Follow SwagyTracks on
Facebook • http://www.facebook.com/SwagyTracks
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SoundCloud • https://soundcloud.com/SwagyTracks
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Tumblr • http://swagytracks.tumblr.com
.........
You can find this picture here •
http://bit.ly/133Gdoq
.........
There is no cop...
published: 23 Jun 2013
-
Truth Table Tutorial - Discrete Mathematics Logic
Here is a quick tutorial on two different truth tables.
If there's anyone wondering about the "IF/THEN" statements (the one way arrows), please read below:
Think about the statement "If you get an A on your exam, then I will give you $100". This statement will only be False if I break my promise to you.
Therefore:
- If it's TRUE (you got an A), and it's TRUE (I gave you $100), then it's TRUE (I kept my promise).
- If it's TRUE (you got an A), and it's FALSE (I didn't give you $100), then it's FALSE (I broke my promise).
- If it's FALSE (you didn't get an A), and it's TRUE (I gave you $100), then it's TRUE (I didn't break my promise, I was just feeling sorry for you and felt like being generous).
- If it's FALSE (you didn't get an A), and it's FALSE (I didn't give you $100), then it's TRU...
published: 26 Mar 2014
-
Logic, Marshmello - Everyday
Get 'Everyday': https://Logic.lnk.to/Everyday
Listen to the full "Bobby Tarantino 2" Album here: http://bit.ly/2p8DTtU
Music video by Logic, Marshmello performing Everyday. © 2018 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/ty6WPn
published: 17 Apr 2018
-
Logic - Self Medication [feat. Seth MacFarlane, Redman & Statik Selektah] (Official Audio)
Ultra 85 out now: logic.lnk.to/Ultra85
My independent debut album 'College Park' out now
https://Logic.lnk.to/CollegeParkID
Follow Logic:
Instagram: http://www.Instagram.com/logic
Twitter: https://twitter.com/Logic301
TikTok: https://www.tiktok.com/@logic?lang=en
Logic Merch: http://LogicMerch.com
Featuring samples from the Windy City recording “If By Chance” Licensed courtesy of Demon Music Group.
#SelfMedication #Logic #Collegepark #HipHop
published: 24 Feb 2023
-
Mosaic blocks:terahex ep.2 #logic #iq
Mosaic blocks:terahex ep.2 #logic #iq #toys #games #block #fypシ゚viral #chillmusic #puzzle #maths
published: 02 Dec 2024
-
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid (Lyric Video)
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid [Lyric Video]
You're Beautiful
Watch till the end
published: 25 Jan 2019
7:00
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid (Official Video)
Download/Stream "EVERYBODY" here: http://smarturl.it/LogicEverybody?iqid=yt
Director - Andy Hines
Executive producer- Luga Podesta & Brandon Bonfiglio
Producer...
Download/Stream "EVERYBODY" here: http://smarturl.it/LogicEverybody?iqid=yt
Director - Andy Hines
Executive producer- Luga Podesta & Brandon Bonfiglio
Producer- Andrew Lerios & Alex Randall
Director of photography- Jeff Bierman
Production Designer - Hannah Beachler
Edited by Joe Calardo
Casting - German Legarreta
Assistant production supervisor - Kai Lusk
Assistant Director - Giovanni Cotto-Ortiz
Sound- Joe Bartone & Eric Ballew
Gaffer- Theodore Rysz
Grip- Matthew Lim
Stylist- Antionette Messam
Color by Sean Coleman
Additional footage by- Justin Fleischer, Mike Holland, Josh Rimmey & Zach Williams
Production Assistant Alec Schweitzer
Written & Directed by Andy Hines
Music video by Logic performing 1-800-273-8255. (C) 2017 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/geBjT1
https://wn.com/Logic_1_800_273_8255_Ft._Alessia_Cara,_Khalid_(Official_Video)
Download/Stream "EVERYBODY" here: http://smarturl.it/LogicEverybody?iqid=yt
Director - Andy Hines
Executive producer- Luga Podesta & Brandon Bonfiglio
Producer- Andrew Lerios & Alex Randall
Director of photography- Jeff Bierman
Production Designer - Hannah Beachler
Edited by Joe Calardo
Casting - German Legarreta
Assistant production supervisor - Kai Lusk
Assistant Director - Giovanni Cotto-Ortiz
Sound- Joe Bartone & Eric Ballew
Gaffer- Theodore Rysz
Grip- Matthew Lim
Stylist- Antionette Messam
Color by Sean Coleman
Additional footage by- Justin Fleischer, Mike Holland, Josh Rimmey & Zach Williams
Production Assistant Alec Schweitzer
Written & Directed by Andy Hines
Music video by Logic performing 1-800-273-8255. (C) 2017 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/geBjT1
- published: 17 Aug 2017
- views: 450614404
7:13
Logic - Homicide ft. Eminem (Official Video)
#Homicide
"Homicide" available on all streaming services now: https://logic.lnk.to/Homicide
Music video by Logic performing Homicide. © 2019 Def Jam Recordings...
#Homicide
"Homicide" available on all streaming services now: https://logic.lnk.to/Homicide
Music video by Logic performing Homicide. © 2019 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/gXjTAg
https://wn.com/Logic_Homicide_Ft._Eminem_(Official_Video)
#Homicide
"Homicide" available on all streaming services now: https://logic.lnk.to/Homicide
Music video by Logic performing Homicide. © 2019 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/gXjTAg
- published: 28 Jun 2019
- views: 103584430
4:11
Logic - 1-800-273-8255 ft. Alessia Cara & Khalid (Official Audio)
Listen to the official audio of 1-800-273-8255 by Logic ft Alessia Cara & Khalid.
Buy Everybody Deluxe Edition which includes the Everybody Documentary!
http:/...
Listen to the official audio of 1-800-273-8255 by Logic ft Alessia Cara & Khalid.
Buy Everybody Deluxe Edition which includes the Everybody Documentary!
http://bit.ly/Logic-Everybody-Album
SUBSCRIBE to the official Visionary Music Group channel for more original material from Logic & Jon Bellion including music video premieres, behind the scenes & more: http://bit.ly/Subscribe-to-VMG
Follow Visionary Music Group:
https://twitter.com/TeamVisionary
https://fb.com/VisionaryMusicGroup
http://instagram.com/teamvisionary
https://wn.com/Logic_1_800_273_8255_Ft._Alessia_Cara_Khalid_(Official_Audio)
Listen to the official audio of 1-800-273-8255 by Logic ft Alessia Cara & Khalid.
Buy Everybody Deluxe Edition which includes the Everybody Documentary!
http://bit.ly/Logic-Everybody-Album
SUBSCRIBE to the official Visionary Music Group channel for more original material from Logic & Jon Bellion including music video premieres, behind the scenes & more: http://bit.ly/Subscribe-to-VMG
Follow Visionary Music Group:
https://twitter.com/TeamVisionary
https://fb.com/VisionaryMusicGroup
http://instagram.com/teamvisionary
- published: 12 May 2017
- views: 180640884
4:05
Joyner Lucas ft. Logic - ISIS (ADHD)
Available on Spotify and iTunes: https://orcd.co/adhd
Merch (shop now): https://bit.ly/2LphKWy
Tully App: https://tullyapp.com
Create, Manage & Distribute Mu...
Available on Spotify and iTunes: https://orcd.co/adhd
Merch (shop now): https://bit.ly/2LphKWy
Tully App: https://tullyapp.com
Create, Manage & Distribute Music using Tully. The #1 tool for Independent Artists offering monthly opportunities.
Tully opportunity drops include: features, cash giveaways, a touring opportunity and more! Tully App is a blueprint for the entrepreneur artist to successfully operate in today's music industry. You can Create, Manage, Distribute music in one app.
#tullyapp #joynerlucas #adhd #evolution
https://wn.com/Joyner_Lucas_Ft._Logic_Isis_(Adhd)
Available on Spotify and iTunes: https://orcd.co/adhd
Merch (shop now): https://bit.ly/2LphKWy
Tully App: https://tullyapp.com
Create, Manage & Distribute Music using Tully. The #1 tool for Independent Artists offering monthly opportunities.
Tully opportunity drops include: features, cash giveaways, a touring opportunity and more! Tully App is a blueprint for the entrepreneur artist to successfully operate in today's music industry. You can Create, Manage, Distribute music in one app.
#tullyapp #joynerlucas #adhd #evolution
- published: 23 May 2019
- views: 80593684
3:42
Logic - 5AM (Prod. C-Sick)
Subscribe to SwagyTracks for more music daily !
http://bit.ly/SubscribeSwagy
.........
• Logic -
https://twitter.com/Logic301
http://www.facebook.com/mindofl...
Subscribe to SwagyTracks for more music daily !
http://bit.ly/SubscribeSwagy
.........
• Logic -
https://twitter.com/Logic301
http://www.facebook.com/mindoflogic
http://mindoflogic.com/
Download this track •
http://piff.me/e9615f2
Picture credit •
https://www.flickr.com/photos/117317408@N03/12616735133/in/photostream/
If you are the owner of this picture and want it removed,contact me and I will delete the video as soon as possible,no drama!
.........
Follow SwagyTracks on
Facebook • http://www.facebook.com/SwagyTracks
Twitter • https://twitter.com/SwagyTracks
SoundCloud • https://soundcloud.com/SwagyTracks
Instagram • http://instagram.com/swagytracks
Tumblr • http://swagytracks.tumblr.com
.........
You can find this picture here •
http://bit.ly/133Gdoq
.........
There is no copyright infringement intended for the song or picture. If you have an issue with me posting this song or picture please contact me through one of my social networks or YouTube private messaging system. Once I have received your message and determined you are the proper owner of this content I will have it removed, no drama at all. This channel is strictly for promotion towards the artists of the music. I try to help promote their music and their social networks.
https://wn.com/Logic_5Am_(Prod._C_Sick)
Subscribe to SwagyTracks for more music daily !
http://bit.ly/SubscribeSwagy
.........
• Logic -
https://twitter.com/Logic301
http://www.facebook.com/mindoflogic
http://mindoflogic.com/
Download this track •
http://piff.me/e9615f2
Picture credit •
https://www.flickr.com/photos/117317408@N03/12616735133/in/photostream/
If you are the owner of this picture and want it removed,contact me and I will delete the video as soon as possible,no drama!
.........
Follow SwagyTracks on
Facebook • http://www.facebook.com/SwagyTracks
Twitter • https://twitter.com/SwagyTracks
SoundCloud • https://soundcloud.com/SwagyTracks
Instagram • http://instagram.com/swagytracks
Tumblr • http://swagytracks.tumblr.com
.........
You can find this picture here •
http://bit.ly/133Gdoq
.........
There is no copyright infringement intended for the song or picture. If you have an issue with me posting this song or picture please contact me through one of my social networks or YouTube private messaging system. Once I have received your message and determined you are the proper owner of this content I will have it removed, no drama at all. This channel is strictly for promotion towards the artists of the music. I try to help promote their music and their social networks.
- published: 23 Jun 2013
- views: 81220157
7:51
Truth Table Tutorial - Discrete Mathematics Logic
Here is a quick tutorial on two different truth tables.
If there's anyone wondering about the "IF/THEN" statements (the one way arrows), please read below:
Thi...
Here is a quick tutorial on two different truth tables.
If there's anyone wondering about the "IF/THEN" statements (the one way arrows), please read below:
Think about the statement "If you get an A on your exam, then I will give you $100". This statement will only be False if I break my promise to you.
Therefore:
- If it's TRUE (you got an A), and it's TRUE (I gave you $100), then it's TRUE (I kept my promise).
- If it's TRUE (you got an A), and it's FALSE (I didn't give you $100), then it's FALSE (I broke my promise).
- If it's FALSE (you didn't get an A), and it's TRUE (I gave you $100), then it's TRUE (I didn't break my promise, I was just feeling sorry for you and felt like being generous).
- If it's FALSE (you didn't get an A), and it's FALSE (I didn't give you $100), then it's TRUE (I kept my promise, you didn't earn the $100 from me)!
https://wn.com/Truth_Table_Tutorial_Discrete_Mathematics_Logic
Here is a quick tutorial on two different truth tables.
If there's anyone wondering about the "IF/THEN" statements (the one way arrows), please read below:
Think about the statement "If you get an A on your exam, then I will give you $100". This statement will only be False if I break my promise to you.
Therefore:
- If it's TRUE (you got an A), and it's TRUE (I gave you $100), then it's TRUE (I kept my promise).
- If it's TRUE (you got an A), and it's FALSE (I didn't give you $100), then it's FALSE (I broke my promise).
- If it's FALSE (you didn't get an A), and it's TRUE (I gave you $100), then it's TRUE (I didn't break my promise, I was just feeling sorry for you and felt like being generous).
- If it's FALSE (you didn't get an A), and it's FALSE (I didn't give you $100), then it's TRUE (I kept my promise, you didn't earn the $100 from me)!
- published: 26 Mar 2014
- views: 2172926
10:02
Logic, Marshmello - Everyday
Get 'Everyday': https://Logic.lnk.to/Everyday
Listen to the full "Bobby Tarantino 2" Album here: http://bit.ly/2p8DTtU
Music video by Logic, Marshmello perfor...
Get 'Everyday': https://Logic.lnk.to/Everyday
Listen to the full "Bobby Tarantino 2" Album here: http://bit.ly/2p8DTtU
Music video by Logic, Marshmello performing Everyday. © 2018 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/ty6WPn
https://wn.com/Logic,_Marshmello_Everyday
Get 'Everyday': https://Logic.lnk.to/Everyday
Listen to the full "Bobby Tarantino 2" Album here: http://bit.ly/2p8DTtU
Music video by Logic, Marshmello performing Everyday. © 2018 Def Jam Recordings, a division of UMG Recordings, Inc.
http://vevo.ly/ty6WPn
- published: 17 Apr 2018
- views: 62430350
5:16
Logic - Self Medication [feat. Seth MacFarlane, Redman & Statik Selektah] (Official Audio)
Ultra 85 out now: logic.lnk.to/Ultra85
My independent debut album 'College Park' out now
https://Logic.lnk.to/CollegeParkID
Follow Logic:
Instagram: http://ww...
Ultra 85 out now: logic.lnk.to/Ultra85
My independent debut album 'College Park' out now
https://Logic.lnk.to/CollegeParkID
Follow Logic:
Instagram: http://www.Instagram.com/logic
Twitter: https://twitter.com/Logic301
TikTok: https://www.tiktok.com/@logic?lang=en
Logic Merch: http://LogicMerch.com
Featuring samples from the Windy City recording “If By Chance” Licensed courtesy of Demon Music Group.
#SelfMedication #Logic #Collegepark #HipHop
https://wn.com/Logic_Self_Medication_Feat._Seth_Macfarlane,_Redman_Statik_Selektah_(Official_Audio)
Ultra 85 out now: logic.lnk.to/Ultra85
My independent debut album 'College Park' out now
https://Logic.lnk.to/CollegeParkID
Follow Logic:
Instagram: http://www.Instagram.com/logic
Twitter: https://twitter.com/Logic301
TikTok: https://www.tiktok.com/@logic?lang=en
Logic Merch: http://LogicMerch.com
Featuring samples from the Windy City recording “If By Chance” Licensed courtesy of Demon Music Group.
#SelfMedication #Logic #Collegepark #HipHop
- published: 24 Feb 2023
- views: 4352623
0:23
Mosaic blocks:terahex ep.2 #logic #iq
Mosaic blocks:terahex ep.2 #logic #iq #toys #games #block #fypシ゚viral #chillmusic #puzzle #maths
Mosaic blocks:terahex ep.2 #logic #iq #toys #games #block #fypシ゚viral #chillmusic #puzzle #maths
https://wn.com/Mosaic_Blocks_Terahex_Ep.2_Logic_Iq
Mosaic blocks:terahex ep.2 #logic #iq #toys #games #block #fypシ゚viral #chillmusic #puzzle #maths
- published: 02 Dec 2024
- views: 546
4:39
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid (Lyric Video)
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid [Lyric Video]
You're Beautiful
Watch till the end
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid [Lyric Video]
You're Beautiful
Watch till the end
https://wn.com/Logic_1_800_273_8255_Ft._Alessia_Cara,_Khalid_(Lyric_Video)
Logic - 1-800-273-8255 ft. Alessia Cara, Khalid [Lyric Video]
You're Beautiful
Watch till the end
- published: 25 Jan 2019
- views: 25040226
-
Minecraft Logic('ω') (もういいよ) #minecraft #shorts
published: 04 Nov 2024
-
Minecraft Logic('ω') (もういいよ) #minecraft #shorts
published: 04 Nov 2024
-
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
published: 24 Jun 2024
2:39
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.
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.
https://wn.com/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
- views: 261
1:55:46
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-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.
https://wn.com/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. 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.
- published: 04 Nov 2024
- views: 100