My primary research interests fall into three broad areas of inquiry: history of philosophy, philosophy of logic, and metaphysics. Within these disciplines, the specific focus of my research is the history of the principle of non-contradiction (PNC) in Western philosophical thought and the emergence of non-classical conceptions of logic in Europe at the beginning of the twentieth century. Additional interests include philosophy of art as well as Buddhist and Taoist philosophy. Supervisors: Graham Priest and Greg Restall Phone: 4155680479 Address: ImpactHub Honolulu 1050 Queen Street, Suite 100 Honolulu, HI 96814
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter X, Łukasiewicz distinguishes two proofs in Aristotle’s elenctic
demonstration by refut... more In Chapter X, Łukasiewicz distinguishes two proofs in Aristotle’s elenctic demonstration by refutation. Fhe first and simpler proof relies on the Principle of Double Negation (PDN), the second and more complicated one is based on the Aristotelian concepts of essence and substance. Both proofs are based on the consequences that follow from the acceptance of a definition and, more specifically, the consequences that follow from the determination of the meaning of a term based on its definition.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter IX, Łukasiewicz points out that Aristotle appears to contradict himself when he assert... more In Chapter IX, Łukasiewicz points out that Aristotle appears to contradict himself when he asserts that the PC, as a first principle, cannot be proven directly but then nevertheless proceeds to present a series of arguments that aim to offer explicit proofs the PC. To resolve the issue, Łukasiewicz sets out to determine whether Aristotle’s account presents (or intends to present) a direct demonstration or proof of the principle, which would mean that Aristotle does contradict himself, or whether Aristotle’s account presents a collection of reasons or considerations that support the PC in some other fashion. The focus of Łukasiewicz’ discussion in this chapter is on the formal structure of Aristotle’s demonstration by refutation and subsequent arguments that Aristotle presents in favor of the PC.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter VIII, Łukasiewicz argues that the Principle of Identity (PI) is not an ultimate princi... more In Chapter VIII, Łukasiewicz argues that the Principle of Identity (PI) is not an ultimate principle either. The definition of a true statement, on the other hand, presents the most convincing candidate for an ultimate principle because it is possible to prove the PI based on a (suitable) definition of truth. However, the definition of a true statement, Łukasiewicz claims, does constitute an ultimate principle.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter VII, Łukasiewicz argues that the principle of identity (PI) presents a compelling alte... more In Chapter VII, Łukasiewicz argues that the principle of identity (PI) presents a compelling alternative for a simpler and more basic first principle than the principle of contradiction (PC). It is introduced as the initial axiom in the propositional logic that Łukasiewicz presents in the Appendix and, furthermore, it provides the foundation for a challenge to Aristotle’s claim that the PC cannot be derived from another, simpler principle.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter VI of his work on the Principle of Contradiction in Aristotle, Łukasiewicz returns to ... more In Chapter VI of his work on the Principle of Contradiction in Aristotle, Łukasiewicz returns to issues surrounding the ontological and logical principle of contradiction (PC). The focus of his investigation is the examination of the reasons and arguments that would compel an acceptance of the PC in its onto- logical (object-theoretical) formulation and, more specifically, its acceptance as a first principle.
In Aristotle’s conception of scientific knowledge, first princi- ples constitute the foundation of a hierarchical structure. They are universal statements that furnish the starting points of chains of inferences that generate the content of a science. The broadest and most general of all sciences is the science that investigates being qua being.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
The failure of an argument to establish its conclusion is not sufficient
to show that the conclus... more The failure of an argument to establish its conclusion is not sufficient to show that the conclusion is false. It only shows that the conclusion is not a logical consequence of the premises of the argument. Recognizing this, Łukasiewicz examines the possibility that a different set of premises may be sufficient to establish Aristotle’s psychological formulation of the PC. It would be sufficient to establish the psychological PC by showing that beliefs in contradictory statement are exclusive of each other, rather than attempting to demonstrate that they are contrary to each other, which is the crucial claim in Aristotle’s argument.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
Łukasiewicz presents two critical objections to Aristotle’s account.
The first charges that Arist... more Łukasiewicz presents two critical objections to Aristotle’s account. The first charges that Aristotle sorts the strength of opposition between beliefs by appealing to different degrees of truth contained in the beliefs. However, in Łukasiewicz’ view, the distinction between truth and falsity is applicable only to statements and, further, the distinction is exclusive and exhaustive. Every statement has exactly one of two truth-values; either a statement is true or it is false, and nothing else. Beliefs, on the other hand, are not the type of object that can be sorted in terms of truth or falsity and even less so in terms of degrees of truth or falsity. Thus, Łukasiewicz points out, if there is no range or hierarchy of degrees of truth in beliefs, then there are no corresponding degrees of opposition between beliefs. Without a range in degrees of opposition, Aristotle’s argument collapses.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter III, Łukasiewicz turns his attention to the psychological formulation of the principle... more In Chapter III, Łukasiewicz turns his attention to the psychological formulation of the principle, which he discusses over the span of three chapters. He presents an analysis and elucidation of Aristotle’s account of the psychological version of the principle. Łukasiewicz argues that Aristotle considers the psychological PC as a consequence of the logical and ontological principles and that Aristotle presents an argument which aims to show that this is so.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
Prompted by the question whether the three formulations of the Principle of Contradiction (PC) --... more Prompted by the question whether the three formulations of the Principle of Contradiction (PC) -- ontological, logical, and psychological -- articulate three distinct principles or whether they are different formulations of one and the same principle, Łukasiewicz first investigates “in what cases two statements, composed of different words, express the same thought” (II, 90). He distinguishes between statements that have the same meaning and statements that are logically equivalent. Then, based on his account of propositional equivalence, he offers a proof of the equivalence of the ontological and logical formulations of the PC that relies on a realist conception of truth.
The Principle of Contradiction in Aristotle. A Critial Analysis, 2021
Chapter 1 of Jan Łukasiewicz (2021) The Principle of Contradiction in Aristotle. Translated with ... more Chapter 1 of Jan Łukasiewicz (2021) The Principle of Contradiction in Aristotle. Translated with commentary by Holger R. Heine.
Three Formulations of the Principle of Contradiction distinguishes and examines different formulations of the principle that are offered by Aristotle in the Metaphysics
The Principle of Contradiction in Aristotle: A Critical Study, 2021
ToC, Introduction, and Chapter 1 of Jan Łukasiewicz' pioneering investigation into the Principle... more ToC, Introduction, and Chapter 1 of Jan Łukasiewicz' pioneering investigation into the Principle of Contradiction in Aristotle. Translated by Holger R. Heine
The Principle of Contradiction in Aristotle: A Critical Study, 2021
Jan Łukasiewicz’ work on Aristotle and the principle of non-contradiction, originally published i... more Jan Łukasiewicz’ work on Aristotle and the principle of non-contradiction, originally published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle.
Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it.
This introduction to examines the historical and philosophical background of Łukasiewicz’ work, its relation to Hegel 's metaphysical logic which gave rise to the debate about Die logische Frage (the question of logic), and Łukasiewicz’ attempt to develop a first Non-Aristotelian logic, a logic that does not require or endorse Aristotle's principle of non-contradiction.
generation/mutation - from crowdsourced to ai-sourced new media art, 2020
Based on the idea of crowdsourcing creative work online, years before the term
“crowdsourcing” w... more Based on the idea of crowdsourcing creative work online, years before the term
“crowdsourcing” was coined, the collaborative online project generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Chapter 1, Crowds, examines the evolution of the first version of the project and its dependence on digital networks, image editing software, and foundational technologies like web browsers and email clients.
The Principle of Contradiction in Aristotle: A Critical Study, 2021
For more than two thousand years, Aristotle’s Principle of Non-Contradiction was almost universal... more For more than two thousand years, Aristotle’s Principle of Non-Contradiction was almost universally accepted as the most certain and best known of all logical and metaphysical principles in Western philosophical thought. Hegel was the first modern philosopher to challenge its validity, but it was not until the emergence of modern analytic philosophy in the late nineteenth and early twentieth century that the truth of the principle became the object of critical analysis and debate.
Jan Łukasiewicz’ work on Aristotle and the principle of contradiction, first published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle. Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it. Łukasiewicz’ goal, however, is far more ambitious than a critical analysis of the principle. He wants to develop a revolutionary new logic, a non-Aristotelian logic, a formally constructed logic that does not include or endorse the principle of contradiction in its Aristotelian conception! As such, his work on Aristotle and the principle of contradiction marks the first step in his search for a new logic that does not entail the consequence of an all-encompassing logical determinism, a search that saw its first success some ten years later with his development of a three-valued propositional calculus in 1920.
Łukasiewicz’ approach to the issues surrounding the Aristotelian conception of the principle of contradiction and its modern descendants is both historical and analytical—it is a sustained and methodical effort to think critically and historically about logic and the foundations of logical inference. The arguments and results that Łukasiewicz develops in his metalogical analysis touch on many topics that are still part of a lively and often inconclusive debate that continues to this day.
generation/mutation - from crowdsourced to ai-sourced new media art, 2020
The new media artwork, generation/mutation, spans more than twenty years of online art. Launched ... more The new media artwork, generation/mutation, spans more than twenty years of online art. Launched in the early days of the Internet, before Google or Facebook or iPhones, generation/mutation explores the new possibilities of collaborative art production and distribution afforded by the evolution of digital technologies.
Based on the idea of crowdsourcing creative work online, years before the term “crowdsourcing” was coined, generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Over time, generation/mutation evolved from an online exhibition showing crowdsourced contributions created by human artists to the inclusion of machine-made contributions found on Google Street View, to completely ai-generated contributions, generated by neural style transfer (NST) algorithms.
As a creative exploration, generation/mutation is a deeply philosophical work. Not in the traditional form of a book or academic journal paper, but in the form of a collaborative and creative meditation on the nature of artistic practices at the onset of the twenty-first century, an articulation of new methods of artistic collaboration in an age of global digital networks.
Conze’s monograph on The Principle of Contradiction is his most important philosophical work and ... more Conze’s monograph on The Principle of Contradiction is his most important philosophical work and the foundation for his later publications as a Buddhist scholar and translator.
The openly Marxist work was published under considerable risk to both printer and author alike in December 1932 in Hamburg, Germany. Only months later, in May 1933, almost all of the five hundred copies of the first edition were destroyed during the Nazi book burning campaign. It is only now, more than eighty years later, that Conze’s key philosophical work is made available to a broad audience in this English translation by Holger Heine.
In the work, Conze sets out to develop a detailed account of the historical and material conditions that support the emergence, production, and transmission of theoretical knowledge—as exemplified by the principle of contradiction—and, furthermore, to show that under different social and historical conditions the allegedly necessary truth and indubitable content of the principle would dissolve and be replaced by a radically different understanding of the principle of contradiction—a dialectic understanding of the principle that would compel a rejection of the Aristotelian dogma.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter X, Łukasiewicz distinguishes two proofs in Aristotle’s elenctic
demonstration by refut... more In Chapter X, Łukasiewicz distinguishes two proofs in Aristotle’s elenctic demonstration by refutation. Fhe first and simpler proof relies on the Principle of Double Negation (PDN), the second and more complicated one is based on the Aristotelian concepts of essence and substance. Both proofs are based on the consequences that follow from the acceptance of a definition and, more specifically, the consequences that follow from the determination of the meaning of a term based on its definition.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter IX, Łukasiewicz points out that Aristotle appears to contradict himself when he assert... more In Chapter IX, Łukasiewicz points out that Aristotle appears to contradict himself when he asserts that the PC, as a first principle, cannot be proven directly but then nevertheless proceeds to present a series of arguments that aim to offer explicit proofs the PC. To resolve the issue, Łukasiewicz sets out to determine whether Aristotle’s account presents (or intends to present) a direct demonstration or proof of the principle, which would mean that Aristotle does contradict himself, or whether Aristotle’s account presents a collection of reasons or considerations that support the PC in some other fashion. The focus of Łukasiewicz’ discussion in this chapter is on the formal structure of Aristotle’s demonstration by refutation and subsequent arguments that Aristotle presents in favor of the PC.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter VIII, Łukasiewicz argues that the Principle of Identity (PI) is not an ultimate princi... more In Chapter VIII, Łukasiewicz argues that the Principle of Identity (PI) is not an ultimate principle either. The definition of a true statement, on the other hand, presents the most convincing candidate for an ultimate principle because it is possible to prove the PI based on a (suitable) definition of truth. However, the definition of a true statement, Łukasiewicz claims, does constitute an ultimate principle.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter VII, Łukasiewicz argues that the principle of identity (PI) presents a compelling alte... more In Chapter VII, Łukasiewicz argues that the principle of identity (PI) presents a compelling alternative for a simpler and more basic first principle than the principle of contradiction (PC). It is introduced as the initial axiom in the propositional logic that Łukasiewicz presents in the Appendix and, furthermore, it provides the foundation for a challenge to Aristotle’s claim that the PC cannot be derived from another, simpler principle.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter VI of his work on the Principle of Contradiction in Aristotle, Łukasiewicz returns to ... more In Chapter VI of his work on the Principle of Contradiction in Aristotle, Łukasiewicz returns to issues surrounding the ontological and logical principle of contradiction (PC). The focus of his investigation is the examination of the reasons and arguments that would compel an acceptance of the PC in its onto- logical (object-theoretical) formulation and, more specifically, its acceptance as a first principle.
In Aristotle’s conception of scientific knowledge, first princi- ples constitute the foundation of a hierarchical structure. They are universal statements that furnish the starting points of chains of inferences that generate the content of a science. The broadest and most general of all sciences is the science that investigates being qua being.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
The failure of an argument to establish its conclusion is not sufficient
to show that the conclus... more The failure of an argument to establish its conclusion is not sufficient to show that the conclusion is false. It only shows that the conclusion is not a logical consequence of the premises of the argument. Recognizing this, Łukasiewicz examines the possibility that a different set of premises may be sufficient to establish Aristotle’s psychological formulation of the PC. It would be sufficient to establish the psychological PC by showing that beliefs in contradictory statement are exclusive of each other, rather than attempting to demonstrate that they are contrary to each other, which is the crucial claim in Aristotle’s argument.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
Łukasiewicz presents two critical objections to Aristotle’s account.
The first charges that Arist... more Łukasiewicz presents two critical objections to Aristotle’s account. The first charges that Aristotle sorts the strength of opposition between beliefs by appealing to different degrees of truth contained in the beliefs. However, in Łukasiewicz’ view, the distinction between truth and falsity is applicable only to statements and, further, the distinction is exclusive and exhaustive. Every statement has exactly one of two truth-values; either a statement is true or it is false, and nothing else. Beliefs, on the other hand, are not the type of object that can be sorted in terms of truth or falsity and even less so in terms of degrees of truth or falsity. Thus, Łukasiewicz points out, if there is no range or hierarchy of degrees of truth in beliefs, then there are no corresponding degrees of opposition between beliefs. Without a range in degrees of opposition, Aristotle’s argument collapses.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
In Chapter III, Łukasiewicz turns his attention to the psychological formulation of the principle... more In Chapter III, Łukasiewicz turns his attention to the psychological formulation of the principle, which he discusses over the span of three chapters. He presents an analysis and elucidation of Aristotle’s account of the psychological version of the principle. Łukasiewicz argues that Aristotle considers the psychological PC as a consequence of the logical and ontological principles and that Aristotle presents an argument which aims to show that this is so.
The Principle of Contradiction in Aristotle. A Critical Study, 2021
Prompted by the question whether the three formulations of the Principle of Contradiction (PC) --... more Prompted by the question whether the three formulations of the Principle of Contradiction (PC) -- ontological, logical, and psychological -- articulate three distinct principles or whether they are different formulations of one and the same principle, Łukasiewicz first investigates “in what cases two statements, composed of different words, express the same thought” (II, 90). He distinguishes between statements that have the same meaning and statements that are logically equivalent. Then, based on his account of propositional equivalence, he offers a proof of the equivalence of the ontological and logical formulations of the PC that relies on a realist conception of truth.
The Principle of Contradiction in Aristotle. A Critial Analysis, 2021
Chapter 1 of Jan Łukasiewicz (2021) The Principle of Contradiction in Aristotle. Translated with ... more Chapter 1 of Jan Łukasiewicz (2021) The Principle of Contradiction in Aristotle. Translated with commentary by Holger R. Heine.
Three Formulations of the Principle of Contradiction distinguishes and examines different formulations of the principle that are offered by Aristotle in the Metaphysics
The Principle of Contradiction in Aristotle: A Critical Study, 2021
ToC, Introduction, and Chapter 1 of Jan Łukasiewicz' pioneering investigation into the Principle... more ToC, Introduction, and Chapter 1 of Jan Łukasiewicz' pioneering investigation into the Principle of Contradiction in Aristotle. Translated by Holger R. Heine
The Principle of Contradiction in Aristotle: A Critical Study, 2021
Jan Łukasiewicz’ work on Aristotle and the principle of non-contradiction, originally published i... more Jan Łukasiewicz’ work on Aristotle and the principle of non-contradiction, originally published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle.
Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it.
This introduction to examines the historical and philosophical background of Łukasiewicz’ work, its relation to Hegel 's metaphysical logic which gave rise to the debate about Die logische Frage (the question of logic), and Łukasiewicz’ attempt to develop a first Non-Aristotelian logic, a logic that does not require or endorse Aristotle's principle of non-contradiction.
generation/mutation - from crowdsourced to ai-sourced new media art, 2020
Based on the idea of crowdsourcing creative work online, years before the term
“crowdsourcing” w... more Based on the idea of crowdsourcing creative work online, years before the term
“crowdsourcing” was coined, the collaborative online project generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Chapter 1, Crowds, examines the evolution of the first version of the project and its dependence on digital networks, image editing software, and foundational technologies like web browsers and email clients.
The Principle of Contradiction in Aristotle: A Critical Study, 2021
For more than two thousand years, Aristotle’s Principle of Non-Contradiction was almost universal... more For more than two thousand years, Aristotle’s Principle of Non-Contradiction was almost universally accepted as the most certain and best known of all logical and metaphysical principles in Western philosophical thought. Hegel was the first modern philosopher to challenge its validity, but it was not until the emergence of modern analytic philosophy in the late nineteenth and early twentieth century that the truth of the principle became the object of critical analysis and debate.
Jan Łukasiewicz’ work on Aristotle and the principle of contradiction, first published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle. Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it. Łukasiewicz’ goal, however, is far more ambitious than a critical analysis of the principle. He wants to develop a revolutionary new logic, a non-Aristotelian logic, a formally constructed logic that does not include or endorse the principle of contradiction in its Aristotelian conception! As such, his work on Aristotle and the principle of contradiction marks the first step in his search for a new logic that does not entail the consequence of an all-encompassing logical determinism, a search that saw its first success some ten years later with his development of a three-valued propositional calculus in 1920.
Łukasiewicz’ approach to the issues surrounding the Aristotelian conception of the principle of contradiction and its modern descendants is both historical and analytical—it is a sustained and methodical effort to think critically and historically about logic and the foundations of logical inference. The arguments and results that Łukasiewicz develops in his metalogical analysis touch on many topics that are still part of a lively and often inconclusive debate that continues to this day.
generation/mutation - from crowdsourced to ai-sourced new media art, 2020
The new media artwork, generation/mutation, spans more than twenty years of online art. Launched ... more The new media artwork, generation/mutation, spans more than twenty years of online art. Launched in the early days of the Internet, before Google or Facebook or iPhones, generation/mutation explores the new possibilities of collaborative art production and distribution afforded by the evolution of digital technologies.
Based on the idea of crowdsourcing creative work online, years before the term “crowdsourcing” was coined, generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Over time, generation/mutation evolved from an online exhibition showing crowdsourced contributions created by human artists to the inclusion of machine-made contributions found on Google Street View, to completely ai-generated contributions, generated by neural style transfer (NST) algorithms.
As a creative exploration, generation/mutation is a deeply philosophical work. Not in the traditional form of a book or academic journal paper, but in the form of a collaborative and creative meditation on the nature of artistic practices at the onset of the twenty-first century, an articulation of new methods of artistic collaboration in an age of global digital networks.
Conze’s monograph on The Principle of Contradiction is his most important philosophical work and ... more Conze’s monograph on The Principle of Contradiction is his most important philosophical work and the foundation for his later publications as a Buddhist scholar and translator.
The openly Marxist work was published under considerable risk to both printer and author alike in December 1932 in Hamburg, Germany. Only months later, in May 1933, almost all of the five hundred copies of the first edition were destroyed during the Nazi book burning campaign. It is only now, more than eighty years later, that Conze’s key philosophical work is made available to a broad audience in this English translation by Holger Heine.
In the work, Conze sets out to develop a detailed account of the historical and material conditions that support the emergence, production, and transmission of theoretical knowledge—as exemplified by the principle of contradiction—and, furthermore, to show that under different social and historical conditions the allegedly necessary truth and indubitable content of the principle would dissolve and be replaced by a radically different understanding of the principle of contradiction—a dialectic understanding of the principle that would compel a rejection of the Aristotelian dogma.
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Papers by Holger Heine
demonstration by refutation. Fhe first and simpler proof relies on the Principle of Double Negation (PDN), the second and more complicated one is based on the Aristotelian concepts of essence and substance. Both proofs are based on the consequences that follow from the acceptance of a definition and, more specifically, the consequences that follow from the determination of the meaning of a term based on its definition.
In Aristotle’s conception of scientific knowledge, first princi- ples constitute the foundation of a hierarchical structure. They are universal statements that furnish the starting points of chains of inferences that generate the content of a science. The broadest and most general of all sciences is the science that investigates being qua being.
to show that the conclusion is false. It only shows that the conclusion is not a logical consequence of the premises of the argument. Recognizing this, Łukasiewicz examines the possibility that a different set of premises may be sufficient to establish Aristotle’s psychological formulation of the PC. It would be sufficient to establish the psychological PC by showing that beliefs in contradictory statement are exclusive of each other, rather than attempting to demonstrate that they are contrary to each other, which is the crucial claim in Aristotle’s argument.
The first charges that Aristotle sorts the strength of opposition
between beliefs by appealing to different degrees of truth
contained in the beliefs. However, in Łukasiewicz’ view, the distinction
between truth and falsity is applicable only to statements
and, further, the distinction is exclusive and exhaustive. Every
statement has exactly one of two truth-values; either a statement is
true or it is false, and nothing else. Beliefs, on the other hand, are
not the type of object that can be sorted in terms of truth or falsity
and even less so in terms of degrees of truth or falsity. Thus,
Łukasiewicz points out, if there is no range or hierarchy of degrees
of truth in beliefs, then there are no corresponding degrees of opposition
between beliefs. Without a range in degrees of opposition,
Aristotle’s argument collapses.
two statements, composed of different words, express the same
thought” (II, 90). He distinguishes between statements that have
the same meaning and statements that are logically equivalent.
Then, based on his account of propositional equivalence, he offers
a proof of the equivalence of the ontological and logical formulations
of the PC that relies on a realist conception of truth.
Three Formulations of the Principle of Contradiction distinguishes and examines different formulations of the principle that are offered by Aristotle in the Metaphysics
Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it.
This introduction to examines the historical and philosophical background of Łukasiewicz’ work, its relation to Hegel 's metaphysical logic which gave rise to the debate about Die logische Frage (the question of logic), and Łukasiewicz’ attempt to develop a first Non-Aristotelian logic, a logic that does not require or endorse Aristotle's principle of non-contradiction.
“crowdsourcing” was coined, the collaborative online project generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Chapter 1, Crowds, examines the evolution of the first version of the project and its dependence on digital networks, image editing software, and foundational technologies like web browsers and email clients.
Books by Holger Heine
Jan Łukasiewicz’ work on Aristotle and the principle of contradiction, first published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle. Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it. Łukasiewicz’ goal, however, is far more ambitious than a critical analysis of the principle. He wants to develop a revolutionary new logic, a non-Aristotelian logic, a formally constructed logic that does not include or endorse the principle of contradiction in its Aristotelian conception! As such, his work on Aristotle and the principle of contradiction marks the first step in his search for a new logic that does not entail the consequence of an all-encompassing logical determinism, a search that saw its first success some ten years later with his development of a three-valued propositional calculus in 1920.
Łukasiewicz’ approach to the issues surrounding the Aristotelian conception of the principle of contradiction and its modern descendants is both historical and analytical—it is a sustained and methodical effort to think critically and historically about logic and the foundations of logical inference. The arguments and results that Łukasiewicz develops in his metalogical analysis touch on many topics that are still part of a lively and often inconclusive debate that continues to this day.
Based on the idea of crowdsourcing creative work online, years before the term “crowdsourcing” was coined, generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Over time, generation/mutation evolved from an online exhibition showing crowdsourced contributions created by human artists to the inclusion of machine-made contributions found on Google Street View, to completely ai-generated contributions, generated by neural style transfer (NST) algorithms.
As a creative exploration, generation/mutation is a deeply philosophical work. Not in the traditional form of a book or academic journal paper, but in the form of a collaborative and creative meditation on the nature of artistic practices at the onset of the twenty-first century, an articulation of new methods of artistic collaboration in an age of global digital networks.
The openly Marxist work was published under considerable risk to both printer and author alike in December 1932 in Hamburg, Germany. Only months later, in May 1933, almost all of the five hundred copies of the first edition were destroyed during the Nazi book burning campaign. It is only now, more than eighty years later, that Conze’s key philosophical work is made available to a broad audience in this English translation by Holger Heine.
In the work, Conze sets out to develop a detailed account of the historical and material conditions that support the emergence, production, and transmission of theoretical knowledge—as exemplified by the principle of contradiction—and, furthermore, to show that under different social and historical conditions the allegedly necessary truth and indubitable content of the principle would dissolve and be replaced by a radically different understanding of the principle of contradiction—a dialectic understanding of the principle that would compel a rejection of the Aristotelian dogma.
demonstration by refutation. Fhe first and simpler proof relies on the Principle of Double Negation (PDN), the second and more complicated one is based on the Aristotelian concepts of essence and substance. Both proofs are based on the consequences that follow from the acceptance of a definition and, more specifically, the consequences that follow from the determination of the meaning of a term based on its definition.
In Aristotle’s conception of scientific knowledge, first princi- ples constitute the foundation of a hierarchical structure. They are universal statements that furnish the starting points of chains of inferences that generate the content of a science. The broadest and most general of all sciences is the science that investigates being qua being.
to show that the conclusion is false. It only shows that the conclusion is not a logical consequence of the premises of the argument. Recognizing this, Łukasiewicz examines the possibility that a different set of premises may be sufficient to establish Aristotle’s psychological formulation of the PC. It would be sufficient to establish the psychological PC by showing that beliefs in contradictory statement are exclusive of each other, rather than attempting to demonstrate that they are contrary to each other, which is the crucial claim in Aristotle’s argument.
The first charges that Aristotle sorts the strength of opposition
between beliefs by appealing to different degrees of truth
contained in the beliefs. However, in Łukasiewicz’ view, the distinction
between truth and falsity is applicable only to statements
and, further, the distinction is exclusive and exhaustive. Every
statement has exactly one of two truth-values; either a statement is
true or it is false, and nothing else. Beliefs, on the other hand, are
not the type of object that can be sorted in terms of truth or falsity
and even less so in terms of degrees of truth or falsity. Thus,
Łukasiewicz points out, if there is no range or hierarchy of degrees
of truth in beliefs, then there are no corresponding degrees of opposition
between beliefs. Without a range in degrees of opposition,
Aristotle’s argument collapses.
two statements, composed of different words, express the same
thought” (II, 90). He distinguishes between statements that have
the same meaning and statements that are logically equivalent.
Then, based on his account of propositional equivalence, he offers
a proof of the equivalence of the ontological and logical formulations
of the PC that relies on a realist conception of truth.
Three Formulations of the Principle of Contradiction distinguishes and examines different formulations of the principle that are offered by Aristotle in the Metaphysics
Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it.
This introduction to examines the historical and philosophical background of Łukasiewicz’ work, its relation to Hegel 's metaphysical logic which gave rise to the debate about Die logische Frage (the question of logic), and Łukasiewicz’ attempt to develop a first Non-Aristotelian logic, a logic that does not require or endorse Aristotle's principle of non-contradiction.
“crowdsourcing” was coined, the collaborative online project generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Chapter 1, Crowds, examines the evolution of the first version of the project and its dependence on digital networks, image editing software, and foundational technologies like web browsers and email clients.
Jan Łukasiewicz’ work on Aristotle and the principle of contradiction, first published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle. Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it. Łukasiewicz’ goal, however, is far more ambitious than a critical analysis of the principle. He wants to develop a revolutionary new logic, a non-Aristotelian logic, a formally constructed logic that does not include or endorse the principle of contradiction in its Aristotelian conception! As such, his work on Aristotle and the principle of contradiction marks the first step in his search for a new logic that does not entail the consequence of an all-encompassing logical determinism, a search that saw its first success some ten years later with his development of a three-valued propositional calculus in 1920.
Łukasiewicz’ approach to the issues surrounding the Aristotelian conception of the principle of contradiction and its modern descendants is both historical and analytical—it is a sustained and methodical effort to think critically and historically about logic and the foundations of logical inference. The arguments and results that Łukasiewicz develops in his metalogical analysis touch on many topics that are still part of a lively and often inconclusive debate that continues to this day.
Based on the idea of crowdsourcing creative work online, years before the term “crowdsourcing” was coined, generation/mutation received contributions from an international group of new media artists. During its first two years, the project’s online exhibition attracted more than 2.5 million visitors and has remained one of the most iconic collaborative new media artworks online.
Over time, generation/mutation evolved from an online exhibition showing crowdsourced contributions created by human artists to the inclusion of machine-made contributions found on Google Street View, to completely ai-generated contributions, generated by neural style transfer (NST) algorithms.
As a creative exploration, generation/mutation is a deeply philosophical work. Not in the traditional form of a book or academic journal paper, but in the form of a collaborative and creative meditation on the nature of artistic practices at the onset of the twenty-first century, an articulation of new methods of artistic collaboration in an age of global digital networks.
The openly Marxist work was published under considerable risk to both printer and author alike in December 1932 in Hamburg, Germany. Only months later, in May 1933, almost all of the five hundred copies of the first edition were destroyed during the Nazi book burning campaign. It is only now, more than eighty years later, that Conze’s key philosophical work is made available to a broad audience in this English translation by Holger Heine.
In the work, Conze sets out to develop a detailed account of the historical and material conditions that support the emergence, production, and transmission of theoretical knowledge—as exemplified by the principle of contradiction—and, furthermore, to show that under different social and historical conditions the allegedly necessary truth and indubitable content of the principle would dissolve and be replaced by a radically different understanding of the principle of contradiction—a dialectic understanding of the principle that would compel a rejection of the Aristotelian dogma.