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The mathematical logic of life
Origins of Life, 1984Protein synthesis can be likened to a particular coded information storage, transmission and execution system. Noise, error or mutations are the essential phenomena to which a living organism is subjected. Genetic coding aims at preserving the integrity of a structure under aggression from the surroundings.
G. Cullmann, J. M. Labouygues
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2022
The precise definition of “logic” is quite broad and literally, hundreds of logics have been studied by philosophers, mathematicians, and computer scientists. When most people say "logic", they mean either propositional logic or predicate logic. The propositional logic is the classical one, in which there are two possible truth values (i.e., true and ...
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The precise definition of “logic” is quite broad and literally, hundreds of logics have been studied by philosophers, mathematicians, and computer scientists. When most people say "logic", they mean either propositional logic or predicate logic. The propositional logic is the classical one, in which there are two possible truth values (i.e., true and ...
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Philosophy, 1928
It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that
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It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that
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2018
It is Frege, not Boole, who is the father of modern logic. What exactly is modern about modern logic? Why did Frege develop it? The answers given here are these. Modern logic is both comprehensive and fully formal. The comprehensiveness in question is the sufficiency for the purposes of mathematics.
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It is Frege, not Boole, who is the father of modern logic. What exactly is modern about modern logic? Why did Frege develop it? The answers given here are these. Modern logic is both comprehensive and fully formal. The comprehensiveness in question is the sufficiency for the purposes of mathematics.
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1995
There are two possible strategies for investigating questions on logic and mathematics. First, one can adopt the pattern recommended by the phenomenologists, which consists in looking for the actual essences of logic and mathematics in order to relate both fields.
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There are two possible strategies for investigating questions on logic and mathematics. First, one can adopt the pattern recommended by the phenomenologists, which consists in looking for the actual essences of logic and mathematics in order to relate both fields.
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Kolmogorov and mathematical logic
Journal of Symbolic Logic, 1992There are human beings whose intellectual power exceeds that of ordinary men. In my life, in my personal experience, there were three such men, and one of them was Andrei Nikolaevich Kolmogorov. I was lucky enough to be his immediate pupil. He invited me to be his pupil at the third year of my being student at the Moscow University.
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1990
For over one hundred years, the links between logic and mathematics have been so close that it is difficult to think of the one without the other. All the persons chiefly responsible for the development of symbolic logic were both mathematicians and logicians.
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For over one hundred years, the links between logic and mathematics have been so close that it is difficult to think of the one without the other. All the persons chiefly responsible for the development of symbolic logic were both mathematicians and logicians.
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The Mathematical Intelligencer, 1993
The author explains a semantic tree based natural deduction style formalization of set theory which is nominalistic in nature, makes interesting use of the distinction of use and mention for (names of) objects, avoids standard set-theoretic paradoxes, but also the common naive form of Cantor's diagonal argument for the uncountability of the reals, and ...
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The author explains a semantic tree based natural deduction style formalization of set theory which is nominalistic in nature, makes interesting use of the distinction of use and mention for (names of) objects, avoids standard set-theoretic paradoxes, but also the common naive form of Cantor's diagonal argument for the uncountability of the reals, and ...
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Philosophy of Mathematics and Logic [PDF]
, 2015 In the present work I attempt to describe Evandro Agazzi’s research on philosophy of logic and mathematics. In particular, after a general introduction to his works, I focus my analysis on the philosophical implications of Godel’s Incompleteness Theorems. This is because they have always remained a constant point of interest in Agazzi’s research.
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From Logic to Mathematical Logic
2011Although methods of logic and were obviously present in many cultures, which all used some intricate systems of reasoning, it is commonly accepted that explicit analysis of the principles of reasoning were developed independently in China, India, and Greece. The later being the most influential to the systems of logic in the West.
Radomir Stankovic, Jaakko Astola
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