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Intuitionistic Logic | Attic Philosophy
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. It's an exciting areas of logic to learn, and important for philosophers, mathematicians and computer scientists. In this tutorial video, we'll introduce the basics of intuitionistic logic, and set the stage for more in-depth tutorials.
00:00 - Intro
01:19 - Classical logic
02:08 - Excluded Middle
02:36 - Non-classical logic
02:59 - Intuitionistic logic
03:40 - Double negation elimination
04:07 - Indirect proof
05:33 - Constructive reasoning
06:54 - Mathematical proofs
07:17 - Disjunction
08:37 - Excluded middle again
09:18 - Information
12:20 - Anti-Realism
12:51 - Verificationism
13:15 - Use theory of meaning
13:50 - Wrap up
More videos on intuitionist...
published: 20 Feb 2021
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Meaning in Intuitionistic Logic | Attic Philosophy
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. In this video, we start to look at what it means, by presenting the Kripke (relational model) semantics.
00:00 - Intro
01:14 - History
02:13 - States of Information
04:42 - Conjunction and Disjunction
05:25 - Implication
07:47 - Negation
09:13 - Avoiding Excluded Middle
10:13 - Validity
10:31 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: h...
published: 06 Mar 2021
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Intuituionism I: Brouwer's CONSTRUCTIVISM ⟨06,05⟩—optional
Intuitionism makes a radical departure from classical logic and mathematics. Instead of treating logic and math as means of discovering mind-independent truths, Intuitionism emphasises proof as a means of creating mental constructions. Thus, for intuitionism, logic and math are explorations of mind, not of some external, mind-independent realm of Platonist ideas. This has significant implications for the way we think about logic.
Here, I set out the intellectual background: Schopenhauer's claim about the relationship between mathematics and time, and his idealism—briefly, the view that we only directly know our mental representation of the world, not the world independent of the mind per se. These views had a profound influence on the mathematician LEJ Brouwer who—apart from inventing mo...
published: 03 Jun 2021
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Minimal Logic vs. Intuitionistic Logic vs. Classical Logic Part 1
published: 14 Apr 2020
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Intuitionistic Logic and Constructive Proof | Attic Philosophy
A central idea in Intuitionistic logic is that proofs should be constructive. In this video, we look at what that means, why it might be important, and how it gives intuitionistic logic its special character.
00:00 - Intro
00:57 - What is a constructive proof?
02:06 - Non-Constructive Example
04:54 - How to avoid non-constructive proofs
05:43 - Law of Excluded Middle
06:29 - Non-Constructive natural Deduction Proofs
07:55 - Should we accept non-constructive proofs?
10:36 - Mathematical entities
11:25 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: http...
published: 24 Feb 2021
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The Philosophy behind Intuitionistic Logic | Attic Philosophy
Why does intuitionistic logic reject classical principles like the Law of Excluded middle, Double Negation Elimination, and Indirect Proof? What's the philosophical motivation behind those moves? In this video, we discuss the philosophy behind Intuitionistic Logic.
00:00 - Intro
00:52 - Anti-Realism
03:17 - Verificationism
06:01 - Use Theory of Meaning
08:14 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/...
published: 27 Feb 2021
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Foundations 5: Intuitionistic Logic and Type Theory
In this series we develop an understanding of the modern foundations of pure mathematics, starting from first principles. We start with intuitive ideas about set theory, and introduce notions from category theory, logic and type theory, until we are in a position to understand dependent type theory, and in particular, homotopy type theory, which promises to replace set theory as the foundation of modern mathematics. We also take an interest in computer science, and how to write computer programming languages to formalize mathematics.
In this video we introduce a type theoretic description of Heying algebras/ intuitionistic logic. We prove a few important results about intuitionistic logic, and then informally introduce some more ideas from type theory.
published: 11 Jan 2021
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Natural Deduction for Intuitionistic Logic | Attic Philosophy
Natural deduction is a natural fit for intuitionistic logic. Simply by dropping one proof rule, we can go from classical to intuitionistic logic. In this video, we see how to use natural deduction for intuitionistic logic, and what happens when we can't use rules like Indirect Proof or Double-Negation Elimination.
00:00 - Intro
01:07 - Recap of Rules
01:54 - Double Negation Elimination
03:51 - Excluded Middle
08:50 - Non-Contradiction
10:16 - Explosion
11:19 - Negation
14:15 - Paraconsistent Intuitionistic Logic
15:05 - Disjunction Property
17:42 - Indirect proof
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
M...
published: 03 Mar 2021
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Intuitionistic Logic (with Dimitri Shatkov)
My friend Dima wanted to know more about inituitionistic logic and I was happy to oblige... We cover Krippe models, Grothendieck models, and chat a bit about Type Theory and DIY philosophy.
published: 13 Jul 2020
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Intuitionistic Logic
Well hello, I'm happy you decided to learn something today. if you'd like to see more content like this or even help us produce more content within one of our subjects, please visit or contact us at our website. everything here is from a project I've been working on since I was 11 years old, so I hope you enjoy. I'll be adding more content every day.
Our Website:
https://multifariousroots.com/all-forms-of-knowledge/
published: 06 Jul 2024
14:33
Intuitionistic Logic | Attic Philosophy
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. It's an exciting areas o...
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. It's an exciting areas of logic to learn, and important for philosophers, mathematicians and computer scientists. In this tutorial video, we'll introduce the basics of intuitionistic logic, and set the stage for more in-depth tutorials.
00:00 - Intro
01:19 - Classical logic
02:08 - Excluded Middle
02:36 - Non-classical logic
02:59 - Intuitionistic logic
03:40 - Double negation elimination
04:07 - Indirect proof
05:33 - Constructive reasoning
06:54 - Mathematical proofs
07:17 - Disjunction
08:37 - Excluded middle again
09:18 - Information
12:20 - Anti-Realism
12:51 - Verificationism
13:15 - Use theory of meaning
13:50 - Wrap up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #meaning
https://wn.com/Intuitionistic_Logic_|_Attic_Philosophy
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. It's an exciting areas of logic to learn, and important for philosophers, mathematicians and computer scientists. In this tutorial video, we'll introduce the basics of intuitionistic logic, and set the stage for more in-depth tutorials.
00:00 - Intro
01:19 - Classical logic
02:08 - Excluded Middle
02:36 - Non-classical logic
02:59 - Intuitionistic logic
03:40 - Double negation elimination
04:07 - Indirect proof
05:33 - Constructive reasoning
06:54 - Mathematical proofs
07:17 - Disjunction
08:37 - Excluded middle again
09:18 - Information
12:20 - Anti-Realism
12:51 - Verificationism
13:15 - Use theory of meaning
13:50 - Wrap up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #meaning
- published: 20 Feb 2021
- views: 11579
11:49
Meaning in Intuitionistic Logic | Attic Philosophy
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. In this video, we start ...
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. In this video, we start to look at what it means, by presenting the Kripke (relational model) semantics.
00:00 - Intro
01:14 - History
02:13 - States of Information
04:42 - Conjunction and Disjunction
05:25 - Implication
07:47 - Negation
09:13 - Avoiding Excluded Middle
10:13 - Validity
10:31 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #semantics
https://wn.com/Meaning_In_Intuitionistic_Logic_|_Attic_Philosophy
Intuitionistic logic rejects one of the central building blocks of classical logic: that we can always say 'true or false', A-or-not-A. In this video, we start to look at what it means, by presenting the Kripke (relational model) semantics.
00:00 - Intro
01:14 - History
02:13 - States of Information
04:42 - Conjunction and Disjunction
05:25 - Implication
07:47 - Negation
09:13 - Avoiding Excluded Middle
10:13 - Validity
10:31 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #semantics
- published: 06 Mar 2021
- views: 1926
3:34
Intuituionism I: Brouwer's CONSTRUCTIVISM ⟨06,05⟩—optional
Intuitionism makes a radical departure from classical logic and mathematics. Instead of treating logic and math as means of discovering mind-independent truths,...
Intuitionism makes a radical departure from classical logic and mathematics. Instead of treating logic and math as means of discovering mind-independent truths, Intuitionism emphasises proof as a means of creating mental constructions. Thus, for intuitionism, logic and math are explorations of mind, not of some external, mind-independent realm of Platonist ideas. This has significant implications for the way we think about logic.
Here, I set out the intellectual background: Schopenhauer's claim about the relationship between mathematics and time, and his idealism—briefly, the view that we only directly know our mental representation of the world, not the world independent of the mind per se. These views had a profound influence on the mathematician LEJ Brouwer who—apart from inventing modern topology—established Intuitionism. Brouwer thinks mathematics is grounded in our perception of the flow of time, which comes in two irreducible forms: the continuous (i.e. the smooth flow of time itself) and the discrete (i.e. the distinguishable objects and events we encouter in time).
https://wn.com/Intuituionism_I_Brouwer's_Constructivism_⟨06,05⟩—Optional
Intuitionism makes a radical departure from classical logic and mathematics. Instead of treating logic and math as means of discovering mind-independent truths, Intuitionism emphasises proof as a means of creating mental constructions. Thus, for intuitionism, logic and math are explorations of mind, not of some external, mind-independent realm of Platonist ideas. This has significant implications for the way we think about logic.
Here, I set out the intellectual background: Schopenhauer's claim about the relationship between mathematics and time, and his idealism—briefly, the view that we only directly know our mental representation of the world, not the world independent of the mind per se. These views had a profound influence on the mathematician LEJ Brouwer who—apart from inventing modern topology—established Intuitionism. Brouwer thinks mathematics is grounded in our perception of the flow of time, which comes in two irreducible forms: the continuous (i.e. the smooth flow of time itself) and the discrete (i.e. the distinguishable objects and events we encouter in time).
- published: 03 Jun 2021
- views: 3318
12:05
Intuitionistic Logic and Constructive Proof | Attic Philosophy
A central idea in Intuitionistic logic is that proofs should be constructive. In this video, we look at what that means, why it might be important, and how it g...
A central idea in Intuitionistic logic is that proofs should be constructive. In this video, we look at what that means, why it might be important, and how it gives intuitionistic logic its special character.
00:00 - Intro
00:57 - What is a constructive proof?
02:06 - Non-Constructive Example
04:54 - How to avoid non-constructive proofs
05:43 - Law of Excluded Middle
06:29 - Non-Constructive natural Deduction Proofs
07:55 - Should we accept non-constructive proofs?
10:36 - Mathematical entities
11:25 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #proof
https://wn.com/Intuitionistic_Logic_And_Constructive_Proof_|_Attic_Philosophy
A central idea in Intuitionistic logic is that proofs should be constructive. In this video, we look at what that means, why it might be important, and how it gives intuitionistic logic its special character.
00:00 - Intro
00:57 - What is a constructive proof?
02:06 - Non-Constructive Example
04:54 - How to avoid non-constructive proofs
05:43 - Law of Excluded Middle
06:29 - Non-Constructive natural Deduction Proofs
07:55 - Should we accept non-constructive proofs?
10:36 - Mathematical entities
11:25 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #proof
- published: 24 Feb 2021
- views: 6451
9:00
The Philosophy behind Intuitionistic Logic | Attic Philosophy
Why does intuitionistic logic reject classical principles like the Law of Excluded middle, Double Negation Elimination, and Indirect Proof? What's the philosoph...
Why does intuitionistic logic reject classical principles like the Law of Excluded middle, Double Negation Elimination, and Indirect Proof? What's the philosophical motivation behind those moves? In this video, we discuss the philosophy behind Intuitionistic Logic.
00:00 - Intro
00:52 - Anti-Realism
03:17 - Verificationism
06:01 - Use Theory of Meaning
08:14 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #meaning
https://wn.com/The_Philosophy_Behind_Intuitionistic_Logic_|_Attic_Philosophy
Why does intuitionistic logic reject classical principles like the Law of Excluded middle, Double Negation Elimination, and Indirect Proof? What's the philosophical motivation behind those moves? In this video, we discuss the philosophy behind Intuitionistic Logic.
00:00 - Intro
00:52 - Anti-Realism
03:17 - Verificationism
06:01 - Use Theory of Meaning
08:14 - Wrap-up
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #meaning
- published: 27 Feb 2021
- views: 2651
55:03
Foundations 5: Intuitionistic Logic and Type Theory
In this series we develop an understanding of the modern foundations of pure mathematics, starting from first principles. We start with intuitive ideas about ...
In this series we develop an understanding of the modern foundations of pure mathematics, starting from first principles. We start with intuitive ideas about set theory, and introduce notions from category theory, logic and type theory, until we are in a position to understand dependent type theory, and in particular, homotopy type theory, which promises to replace set theory as the foundation of modern mathematics. We also take an interest in computer science, and how to write computer programming languages to formalize mathematics.
In this video we introduce a type theoretic description of Heying algebras/ intuitionistic logic. We prove a few important results about intuitionistic logic, and then informally introduce some more ideas from type theory.
https://wn.com/Foundations_5_Intuitionistic_Logic_And_Type_Theory
In this series we develop an understanding of the modern foundations of pure mathematics, starting from first principles. We start with intuitive ideas about set theory, and introduce notions from category theory, logic and type theory, until we are in a position to understand dependent type theory, and in particular, homotopy type theory, which promises to replace set theory as the foundation of modern mathematics. We also take an interest in computer science, and how to write computer programming languages to formalize mathematics.
In this video we introduce a type theoretic description of Heying algebras/ intuitionistic logic. We prove a few important results about intuitionistic logic, and then informally introduce some more ideas from type theory.
- published: 11 Jan 2021
- views: 5319
19:02
Natural Deduction for Intuitionistic Logic | Attic Philosophy
Natural deduction is a natural fit for intuitionistic logic. Simply by dropping one proof rule, we can go from classical to intuitionistic logic. In this video,...
Natural deduction is a natural fit for intuitionistic logic. Simply by dropping one proof rule, we can go from classical to intuitionistic logic. In this video, we see how to use natural deduction for intuitionistic logic, and what happens when we can't use rules like Indirect Proof or Double-Negation Elimination.
00:00 - Intro
01:07 - Recap of Rules
01:54 - Double Negation Elimination
03:51 - Excluded Middle
08:50 - Non-Contradiction
10:16 - Explosion
11:19 - Negation
14:15 - Paraconsistent Intuitionistic Logic
15:05 - Disjunction Property
17:42 - Indirect proof
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #meaning
https://wn.com/Natural_Deduction_For_Intuitionistic_Logic_|_Attic_Philosophy
Natural deduction is a natural fit for intuitionistic logic. Simply by dropping one proof rule, we can go from classical to intuitionistic logic. In this video, we see how to use natural deduction for intuitionistic logic, and what happens when we can't use rules like Indirect Proof or Double-Negation Elimination.
00:00 - Intro
01:07 - Recap of Rules
01:54 - Double Negation Elimination
03:51 - Excluded Middle
08:50 - Non-Contradiction
10:16 - Explosion
11:19 - Negation
14:15 - Paraconsistent Intuitionistic Logic
15:05 - Disjunction Property
17:42 - Indirect proof
More videos on intuitionistic logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: http://markjago.net
My book What Truth Is: http://bit.ly/JagoTruth
Most of my publications are available freely here: https://philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Instagram: https://www.instagram.com/AtticPhilosophy
Twitter: https://twitter.com/PhilosophyAttic
#logic #philosophy #meaning
- published: 03 Mar 2021
- views: 4380
1:27:50
Intuitionistic Logic (with Dimitri Shatkov)
My friend Dima wanted to know more about inituitionistic logic and I was happy to oblige... We cover Krippe models, Grothendieck models, and chat a bit about Ty...
My friend Dima wanted to know more about inituitionistic logic and I was happy to oblige... We cover Krippe models, Grothendieck models, and chat a bit about Type Theory and DIY philosophy.
https://wn.com/Intuitionistic_Logic_(With_Dimitri_Shatkov)
My friend Dima wanted to know more about inituitionistic logic and I was happy to oblige... We cover Krippe models, Grothendieck models, and chat a bit about Type Theory and DIY philosophy.
- published: 13 Jul 2020
- views: 2623
2:47
Intuitionistic Logic
Well hello, I'm happy you decided to learn something today. if you'd like to see more content like this or even help us produce more content within one of our s...
Well hello, I'm happy you decided to learn something today. if you'd like to see more content like this or even help us produce more content within one of our subjects, please visit or contact us at our website. everything here is from a project I've been working on since I was 11 years old, so I hope you enjoy. I'll be adding more content every day.
Our Website:
https://multifariousroots.com/all-forms-of-knowledge/
https://wn.com/Intuitionistic_Logic
Well hello, I'm happy you decided to learn something today. if you'd like to see more content like this or even help us produce more content within one of our subjects, please visit or contact us at our website. everything here is from a project I've been working on since I was 11 years old, so I hope you enjoy. I'll be adding more content every day.
Our Website:
https://multifariousroots.com/all-forms-of-knowledge/
- published: 06 Jul 2024
- views: 4