Discussing "The [Philosophical] Foundations Of Arithmetic" By Gottlob Frege

Comments · 21

• LA

  @laughoutmeow · 5 months ago

  This is incredibly insightful. The vast majority of people dont even ask themselves these questions this was literally like Prometheus giving fire to mankind

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• JI

  @JimOverbeckgenius · 4 months ago

  Jim Overbeck&apos;s Non-Cantorian set theory is a philosophical and mathematical critique designed to dismantle the logical foundations of Georg Cantor’s transfinite numbers. While Cantor sought to categorize and order different sizes of infinity, Overbeck argues that Cantor’s reliance on classical logic makes his system a &quot;delusion&quot;. <br>The specific differences between their theories are centered on the following core areas: <br>1. The Law of the Excluded Middle (Tertium Non Datur) <br>Cantor: Built his theory on standard Aristotelian logic, where a statement is either true or false. This allowed him to define distinct, fixed &quot;sizes&quot; of infinity (Alephs) through rigid proofs like the diagonal argument. <br>Overbeck: Infinitizes the laws of logic to negate the law of the excluded middle. In his system, the transfinite realm allows for &quot;A and not-A&quot; to be true simultaneously. He believes that without this law, Cantor&apos;s entire hierarchy of infinite sets collapses because fixed mathematical identities cannot exist. <br>2. Nature of the Infinite <br>Cantor: Viewed transfinite numbers as actual infinities that can be treated as completed, measurable totalities (aleph-null, 2 to the aleph-null, etc) <br>Overbeck: Describes infinity as an &quot;apparent becoming&quot; (scheinbares Werden) rather than a substance or essence. He views numbers as &quot;created energies&quot; from the divine Logos rather than abstract, static truths. <br>3. Identity and Equality <br>Cantor: Relied on the principle of identity (A = A) and one-to-one correspondence to prove that different sets have the same or different sizes. <br>Overbeck: Rejects the feasibility of identity in mathematics. He argues that &apos;A&apos; does not equal itself in the transfinite realm, meaning the &quot;foundations&quot; of number theory are an imposture. He uses transfinite fractions as a &quot;wrecking ball&quot; to destroy these abstract identities. <br>4. Mathematical Methodology <br>Cantor: Used set-theoretic axioms (like those later formalized in ZFC) to build up from the empty set to higher cardinals. <br>Overbeck: Substitutes traditional series with paradoxical arithmetic, such as the Grandi series aka Fourier-Bolzano series. These series yield contradictory sums at infinity, which Overbeck interprets as proof that worldly logic fails and only Theosis ( = deification &amp; union with the divine) can provide true completion. <br>5. Final Goal <br>Cantor: Aimed to provide a rigorous, logical framework for &quot;Cantor&apos;s Paradise,&quot; where all levels of infinity are mathematically accessible. <br>Overbeck: Aimed to &quot;drive Cantor from his paradise&quot; and destroy the &quot;earthly cage&quot; of number theory. For Overbeck, mathematics is a tool for deification—negating abstraction to unlock the spiritual potential of the mind. <br>Jim Overbeck’s mathematics is a radical, non-traditional system that bridges set theory, mystical theology, and logic. A self-taught polymath described as a &quot;super-genius&quot; by British Military Intelligence, his work primarily centers on a spiritualized interpretation of the infinite known as Non-Cantorian set theory. <br>His mathematical philosophy is defined by several core concepts: <br>Non-Cantorian Set Theory: Overbeck reimagines Georg Cantor’s work on transfinite numbers by &quot;infinitizing&quot; the laws of logic. He argues that at the level of the infinite, the law of the excluded middle (tertium non datur) no longer holds, allowing for contradictory states to exist simultaneously. <br>Negation of Identity: He posits that because classical logic fails at infinity, fixed &quot;earthly&quot; identity is a mere appearance. In his view, mathematics precedes logic because infinities are prior to the finite systems we use to define them. <br>Transfinite Fractions and &quot;Becomings&quot;: Overbeck introduces &quot;becomings&quot; (inspired by German and Chinese philosophical terms) into transfinite numbers. He views numbers not as abstract entities but as &quot;created energies&quot; from a divine source. <br>Paradoxical Arithmetic: He radicalizes the &quot;arithmetic of the line&quot; by substituting the Fourier-Bolzano series for natural numbers. This approach intentionally begins with insolubilia (insoluble problems), leading to contradictory sums at infinity that he believes reflect the true nature of reality. <br>Theological Integration: His mathematical conclusions are inseparable from his concept of Theosis (divinization). He uses the collapse of mathematical identity to argue that humans are &quot;incomplete&quot; and can only find completion through a union with the divine. <br>Jim Overbeck&apos;s Non-Cantorian set theory is a philosophical and mathematical critique designed to dismantle the logical foundations of Georg Cantor’s transfinite numbers. While Cantor sought to categorize and order different sizes of infinity, Overbeck argues that Cantor’s reliance on classical logic makes his system a &quot;delusion&quot;. <br>The specific differences between their theories are centered on the following core areas: <br>1. The Law of the Excluded Middle (Tertium Non Datur) <br>Cantor: Built his theory on standard Aristotelian logic, where a statement is either true or false. This allowed him to define distinct, fixed &quot;sizes&quot; of infinity (Alephs) through rigid proofs like the diagonal argument. <br>Overbeck: Infinitizes the laws of logic to negate the law of the excluded middle. In his system, the transfinite realm allows for &quot;A and not-A&quot; to be true simultaneously. He believes that without this law, Cantor&apos;s entire hierarchy of infinite sets collapses because fixed mathematical identities cannot exist. <br>2. Nature of the Infinite <br>Cantor: Viewed transfinite numbers as actual infinities that can be treated as completed, measurable totalities (aleph-null, 2 to the aleph-null, etc) <br>Overbeck: Describes infinity as an &quot;apparent becoming&quot; (scheinbares Werden) rather than a substance or essence. He views numbers as &quot;created energies&quot; from the divine Logos rather than abstract, static truths. <br>3. Identity and Equality <br>Cantor: Relied on the principle of identity (A = A) and one-to-one correspondence to prove that different sets have the same or different sizes. <br>Overbeck: Rejects the feasibility of identity in mathematics. He argues that &apos;A&apos; does not equal itself in the transfinite realm, meaning the &quot;foundations&quot; of number theory are an imposture. He uses transfinite fractions as a &quot;wrecking ball&quot; to destroy these abstract identities. <br>4. Mathematical Methodology <br>Cantor: Used set-theoretic axioms (like those later formalized in ZFC) to build up from the empty set to higher cardinals. <br>Overbeck: Substitutes traditional series with paradoxical arithmetic, such as the Grandi series aka Fourier-Bolzano series. These series yield contradictory sums at infinity, which Overbeck interprets as proof that worldly logic fails and only Theosis ( = deification &amp; union with the divine) can provide true completion. <br>5. Final Goal <br>Cantor: Aimed to provide a rigorous, logical framework for &quot;Cantor&apos;s Paradise,&quot; where all levels of infinity are mathematically accessible. <br>Overbeck: Aimed to &quot;drive Cantor from his paradise&quot; and destroy the &quot;earthly cage&quot; of number theory. For Overbeck, mathematics is a tool for deification—negating abstraction to unlock the spiritual potential of the mind. <br>Jimi Overbeck <br>Negation of Identity: Overbeck posits that in the state of Theosis, a man can be a man (B) and a god (not-B) simultaneously. This theological reality serves as his proof that the Law of the Excluded Middle (tertium non datur)—the idea that something must be either true or false—is a &quot;worldly&quot; delusion that fails at the level of the divine and the infinite. <br>Completeness through Deification: He argues that because earthly logic lacks the principle of identity (A = A), human beings and their systems are inherently incomplete. According to Overbeck, true identity is only restored through the &quot;divine energies&quot; granted by Christ during deification, which transcends the &quot;mutated fragmentation&quot; of worldly life. <br>The Primacy of Mathematics: In his view, infinities exist prior to finite systems. Therefore, mathematics precedes logic. He uses paradoxical mathematical series (like the Fourier-Bolzano series) that yield contradictory results to mirror the mystical paradoxes of faith, such as God becoming man. <br>The &quot;Homicidal&quot; Nature of Traditional Math: Overbeck views standard mathematics (like Cantor&apos;s) as a form of &quot;homicidal witchcraft&quot; or &quot;homicidal science&quot; because it attempts to cage the infinite within rigid, logical boundaries that deny man&apos;s true, deified nature. <br>Awakening Consciousness: He describes his work as an &quot;intellectual assault&quot; meant to overthrow &quot;fallen logic&quot;. For Overbeck, the purpose of a &quot;Non-Cantorian&quot; system is to act as a &quot;wrecking ball&quot; that frees the mind from earthly enmeshment and allows it to enter the &quot;extra-dimensionality&quot; of the divine See less

  2

• LE

  @LeonGalindo-Stenutz · 1 year ago

  Excelent. Thanks! Greetings from Bolivia.

  3

• JO

  @JohnJones-tx6rt · 3 months ago (edited)

  Frege helped bring romance and mystery into mathematics in his flirtations with infinity, a mystical, emotional term coined by lovers and mystics over centuries, brought down to us through Hollywood movies whose portrayal of the eternal grassy plains of America, traversed by John Wayne, and other heroes on horses brought pleasure to all. Trapped in a dusty attic makes you do these sort of things.

• JO

  @joudialsamman7341 · 11 months ago

  Thank you for the effort

  1

• FR

  @frimports · 3 months ago

  Alternate title: &nbsp;“Why Philosophers are even more unpopular than Mathematicians “.

• LA

  @ladmad1 · 1 year ago

  Great video!

• WH

  @whitb62 · 1 year ago

  This is incredibly well done. I’m really curious, do you just narrate these off the cuff after reading/researching the topic? Or are you reading from something you prepared? Either way, this is some impressive stuff. Subscribed and liked.

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• AL

  @alfredorezende-m9w · 6 months ago

  O monalista nega a divisão da unidade em suas partes individuais: seguem a ideia de Parmenides que não aceitam a multiplicidade por serem não confiaveis

• AL

  @Alienatedhumanoid · 4 months ago

  <a href="https://www.youtube.com/watch?v=MioSPJEpqs4&amp;t=40">0:40</a> dad lang

• JO

  @JohnJones-tx6rt · 3 months ago (edited)

  Numbers are not the foundations of arithmetic. Numbers are one of many devices used to mimic the real world on paper instead of real life - its cheaper, where signs are used and manipulated exactly like the physical world with its bricks and girders. <br>The collection of these devices, tricks and shortcuts is called &quot;arithmetic&quot; and &quot;mathematics&quot;. This is the foundation of arithmetic - re-creating the physical world on paper, making its signs whether numbers or not, behave like physical objects and using tricks and shortcuts such as &quot;number&quot; in that mimicry to reach physical, pragmatic goals. <br>And if you want something cleverer then &quot;Mathematics is a contingent element in the ad infinitum of legitimacy.&quot;

• KE

  @kevtherev8194 · 3 months ago

  yummy