logic

Étienne de Condillac and the Importance of Language in Logical Reasoning

Étienne de Condillac and the Importance of Language in Logical Reasoning

On September 30, 1714, French philosopher and epistemologist Étienne Bonnot de Condillac was born. A leading advocate in France of the ideas of John Locke de Condillac further emphasized the importance of language in logical reasoning, stressing the need for a scientifically designed language and for mathematical calculation as its basis.[4] “The art of reasoning is nothing more than a language well arranged.” – Étienne de Condillac, as quoted in [5]  Étienne de Condillac…
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Giuseppe Peano and the Axiomatization of Mathematics

Giuseppe Peano and the Axiomatization of Mathematics

On August 27, 1858, Italian mathematician and philosopher Giuseppe Peano was born. He is the author of over 200 books and papers, and is considered the founder of mathematical logic and set theory. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and completeness of number…
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Immanuel Kant – Philosopher of the Enlightenment

Immanuel Kant – Philosopher of the Enlightenment

On February 12, 1804, the great German philosopher Immanuel Kant passed away. He is widely considered to be a central figure of modern philosophy. He argued that human concepts and categories structure our view of the world and its laws, and that reason is the source of morality. His thought continues to hold a major influence in contemporary thought, especially in fields such as metaphysics, epistemology, ethics, political philosophy, and aesthetics. The problem…
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Alfred Tarski and the Undefinability of Truth

Alfred Tarski and the Undefinability of Truth

On January 14, 1902, Polish-American mathematician and logician Alfred Tarski was born. A prolific author he is best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy. For my Semantic Web Technologies lecture series I always introduce my students to model-theoretic semantics as means to enable a formal representation of meaning for languages. I…
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George Boole – The Founder of Modern Logics

George Boole – The Founder of Modern Logics

On December 8, 1864, British mathematician and logician George Boole passed away. He is best known as the inventor of the prototype of what is now called Boolean logic, which became the basis of the modern digital computer. Thus, Boole also is regarded as one of the founders of the field of computer science. “It appeared to me that, although Logic might be viewed with reference to the idea of quantity, it…
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Augustus de Morgan and Formal Logic

Augustus de Morgan and Formal Logic

On June 27, 1806, British mathematician and logician Augustus De Morgan was born. He formulated De Morgan‘s laws and introduced the term mathematical induction, a method of mathematical proof typically used to establish a given statement for all natural numbers. As a computer scientist, I am of course familiar with De Morgan‘s laws, which are fundamental for Boolean logic. De Morgan‘s laws are merely transformation rules for two of the basic operators…
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The time you enjoy wasting is not wasted time – Bertrand Russell, Logician and Pacifist

The time you enjoy wasting is not wasted time – Bertrand Russell, Logician and Pacifist

On July 11, 1906, mathematician and philosopher Bertrand Russell was suspended from Trinity College, Cambridge due to his engagement in pacifist activities. The remarkable Bertrand Russell, a philosopher, logician, mathematician, historian, and social critic was best known for the famous ‘Principia Mathematica‘, which he published along with Alfred North Whitehead between 1910 and 1913. “Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of…
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Lewis Carroll – Mathematician and Creator of the Wonderland

Lewis Carroll – Mathematician and Creator of the Wonderland

On January 27, 1832, British mathematician, photographer, and children’s book author Charles Lutwidge Dodgson, better known under his pen name Lewis Carroll, creator of the stories about ‘Alice in Wonderland‘, was born. With his ability for pun, logic and fantasy he managed to captivate a wide audience. His works, known as nonsense literature, have remained popular to this day and have influenced not only children’s literature, but also writers such as James Joyce, surrealists…
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Paul Bernays and the Unified Theory of Mathematics

Paul Bernays and the Unified Theory of Mathematics

On October 17, 1888, Swiss mathematician and logician Paul Isaac Bernays was born. Bernays made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator of David Hilbert.[6] Bernays is known for his attempts to develop a unified theory of mathematics. “Enlightened humanity has sought in rational definiteness its liberating refuge from the dominating influence of the merely authoritative. At the present time,…
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Johann Heinrich Lambert – A Swiss Polymath

Johann Heinrich Lambert – A Swiss Polymath

On August 26, 1728, Swiss polymath Johann Heinrich Lambert was born. Lambert provided the first rigorous proof that pi is irrational (i.e. it cannot be expressed as the quotient of two integers). He also was the first to introduce hyperbolic functions into trigonometry as well as the first mathematician to address the general properties of map projections. He also made significant contributions to physics, philosophy, and logic. “We would wish to discover the…
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