Concept
Formal system
Overview
any well-defined system of abstract thought based on the model of mathematics
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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An abstractive hierarchy is called ‘finite’ if it stops at a finite grade of complexity. It is called ‘infinite’ if it includes members belonging respectively to all degrees of complexity. It is to be noted that the base of an abstractive hierarchy may contain any number of members, finite or infinite. Further, the infinity of the number of the members of the base has nothing to do with the question as to whether…
Alfred North Whitehead, Science and the modern world
States what Formal system is.
The nature of abstract mathematics (the general division of which will be examined in the following chapter) is clearly and exactly determined. It is composed of what is called the _Calculus_,[2] taking this word in its greatest extent, which reaches from the most simple numerical operations to the most sublime combinations of transcendental analysis. The _Calculus_ has the solution of all questions relating to…
Auguste Comte, The philosophy of mathematics
States what Formal system is.
Meanwhile every mathematical proposition remains always a universal truth, which is valid for innumerable particular cases; and a graduated process from the simple to the complicated propositions which are to be deduced from them, is also essential to mathematics; therefore, in every respect mathematics is a science. The completeness of a science as such, that is, in respect of form, consists in there being as much…
Arthur Schopenhauer, The World as Will and Idea
States what Formal system is.
Philosophers who discussed Formal system
Related ideas
- Formal language
- First-order logic
- Interpretation (logic)
- Formalism (philosophy of mathematics)
- Kurt Gödel
- Foundations of mathematics
- Formal grammar
- Mathematics
- Axiomatic system
- Mathematical induction
- Augustus De Morgan
- Mathematical logic
- Model theory
- Gongsun Long
- Linguistics
- Domain of discourse
- Symbol (formal)
- Peano axioms
- Rule of inference
- Soundness
- Theory
- Theorem
- Completeness (logic)
- Logical consequence
Opposing perspectives
Place in the tradition
Part of Analytic philosophy.