Logicism

Logicism is an attitude towards mathematics according to which it is an extension of logic and therefore all mathematical concepts and theories are reducible to logic. If this program were feasible, it could support logical positivism in particular, and reductionism in general. Bertrand Russell and Alfred North Whitehead defended this approach, created by mathematician Gottlob Frege.

Logicism played a key role in the development of analytical philosophy in the twentieth century.

Frege, Russell and Whitehead

Louis Couturat, Bertrand Russell and Alfred North Whitehead supported this theory created by Gottlob Frege. Gottlob Frege abandoned the project after Russell discovered a paradox brought to light by a contradiction in naive set theory. Russell and Whitehead continued the project in their book Principia Mathematica.

Neo-logicism

Although arithmetic was reduced by Cantor to set theory, set theory itself could never be derived from pure logic. However, Gödel’s incompleteness theorem, discovered in 1931, showed that any system rich enough to formalize arithmetic would contain truths which could not be demonstrated within this system. This put an end to the initial program of logicism.

Although the ambition of this reductionist project thus had to be revised downwards, the major part of modern mathematics continues today to be thought by many mathematicians and logicians as being reducible to a logic which would be based on axioms of Zermelo-Fraenkel theory, which does not present, for the moment, any known contradictions. There is thus a neo-logicism, which is based in particular on the so-called “Hume principle”, and defended in particular by Crispin Wright and Bob Hale.

The singularities as ontological limits of the general relativity
The singularities as ontological limits of the general relativity

Author: Nicolae Sfetcu ESSAYS Collection The singularities from the general relativity resulting by solving Einstein’s equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If … Read More

not rated $0.00$2.19 Select options
Evolution and Ethics of Eugenics
Evolution and Ethics of Eugenics

As eugenics is defined, it is very difficult to make a clear distinction between science (medicine, genetic engineering) and eugenics as a included field. And to set a line over which genetic engineering should not go further, according to moral, … Read More

not rated $0.00 Select options
Isaac Newton vs. Robert Hooke on the law of universal gravitation
Isaac Newton vs. Robert Hooke on the law of universal gravitation

One of the most disputed controversy over the priority of scientific discoveries is that of the law of universal gravitation, between Isaac Newton and Robert Hooke. Hooke accused Newton of plagiarism, of taking over his ideas expressed in previous works. … Read More

not rated $0.00 Select options

Leave a Reply

Your email address will not be published. Required fields are marked *