logicism
Học thuậtThân thiện
Definition
Noun: 1. (Philosophy) The philosophical theory that all of mathematics can be derived from, or reduced to, the principles of formal logic. It asserts that mathematical concepts and truths are ultimately logical concepts and truths.
Usage
- logicism is used as a singular, uncountable noun.
- It is a technical term primarily used in the contexts of philosophy of mathematics, logic, and the history of philosophy.
- It refers to a specific school of thought or program, most famously associated with philosophers like Gottlob Frege and Bertrand Russell.
Examples
- As a subject of discussion:
- Frege was a major proponent of logicism.
- The lecture explored the successes and failures of the logicism program.
- Describing its tenets:
- Logicism attempts to ground mathematics in pure logic.
- A core claim of logicism is that arithmetic is analytic.
Advanced Usage
- Historical Context: Logicism was a dominant program in the early 20th century. Its development was significantly impacted by Russell's paradox, which revealed a contradiction in Frege's logical system.
- Critique: The term is often used when discussing critiques, such as those from intuitionists or after Gödel's incompleteness theorems, which are seen by many as limiting the ambitions of logicism.
Variants and Related Words
- Logicist (noun): A person who advocates or supports logicism.
- Bertrand Russell was a noted logicist.
- Logicist (adjective): Of or relating to logicism.
- He presented a logicist interpretation of number theory.
Synonyms
- There are no perfect synonyms, as it is a precise technical term. It can be described as:
- The logical foundation of mathematics
- The reduction of mathematics to logic
Different Meanings
This word has only one specific, technical meaning within philosophy. It does not have common everyday definitions.
Noun
- (philosophy) the philosophical theory that all of mathematics can be derived from formal logic