Concept
Abstract algebraic logic
Overview
In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systems
arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Nevertheless, in each decade since 1850 more has been done to advance the subject than in the whole period from Aristotle to Leibniz. People have discovered how to make reasoning symbolic, as it is in Algebra, so that deductions are effected by mathematical rules. They have discovered many rules besides the syllogism, and a new branch of logic, called the Logic of Relatives,[11] has been invented to deal with topics…
Bertrand Russell, Mysticism and Logic and Other Essays
Close in meaning to Abstract algebraic logic; the term itself is not named.
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 Abstract algebraic logic is.
Instead of mercury put a mere letter which is the name of some undetermined thing: we get-- The specific heat of _x_ is 0·033. This is not a proposition; it has been called by Russell a propositional function. It is the logical analogy of an algebraic expression. Let us write ƒ(_x_) for any propositional function. We could also generalise still further, and say, The specific heat of _x_ is _y_.
Alfred North Whitehead, The organisation of thought, educational and scientific
States what Abstract algebraic logic is.
Philosophers who discussed Abstract algebraic logic
Related ideas
- First-order logic
- Intuitionistic logic
- Propositional logic
- Group (mathematics)
- Mathematical logic
- Model theory
- Set theory
- Modal logic
- George Boole
- Boolean algebra (structure)
- Formal system
- Deduction theorem
- Boolean algebra
- Alfred Tarski
- Charles Sanders Peirce
- Signature (logic)
- Algebraic logic
- Jerzy Łoś
- Relation algebra
- Modal algebra
Place in the tradition
Part of Non-classical logic.