# Logical intuition

**intuitionintuitive evaluationsmathematical intuitionrational intuition**

Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how and savviness often associated with the ability to perceive logical or mathematical truth — and the ability to solve mathematical challenges efficiently.wikipedia

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### Intuition

**intuitiveintuitivelyIntuition (knowledge)**

Henri Poincaré distinguished logical intuition from other forms of intuition.

This definition is commonly referred to as rational intuition.

### Truth

**trueTruth theorytheory of truth**

The passage goes on to assign two roles to logical intuition: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments.

Gödel agreed that the ability to perceive the truth of a mathematical or logical proposition is a matter of intuition, an ability he admitted could be ultimately beyond the scope of a formal theory of logic or mathematics and perhaps best considered in the realm of human comprehension and communication, but commented:

### Intuitionism

**intuitionistintuitionisticintuitionistic mathematics**

In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that construction by intuition.

### Theorem

**theoremspropositionconverse**

Humans apply logical intuition in proving mathematical theorems, validating logical arguments, developing algorithms and heuristics, and in related contexts where mathematical challenges are involved.

### Genetic programming

**automatic evolution of computer programmesgenetic optimisationgenetic program evolver**

The ability may not be realizable in a computer program by means other than genetic programming or evolutionary programming.

### Evolutionary programming

**evolutionary**

The ability may not be realizable in a computer program by means other than genetic programming or evolutionary programming.

### Plato

**Plato's dialoguesDialogues of PlatoPlatonic dialogues**

Plato and Aristotle considered intuition a means for perceiving ideas, significant enough that for Aristotle, intuition comprised the only means of knowing principles that are not subject to argument.

### Aristotle

**AristotelianAristotelesAristote**

Plato and Aristotle considered intuition a means for perceiving ideas, significant enough that for Aristotle, intuition comprised the only means of knowing principles that are not subject to argument.

### A priori and a posteriori

**a prioria posterioriA priori'' and ''a posteriori**

Plato and Aristotle considered intuition a means for perceiving ideas, significant enough that for Aristotle, intuition comprised the only means of knowing principles that are not subject to argument.

### Henri Poincaré

**PoincaréJules Henri PoincaréH. Poincaré**

Henri Poincaré distinguished logical intuition from other forms of intuition.

### The Value of Science

In his book The Value of Science, he points out that:

### Axiom

**axiomspostulateaxiomatic**

The passage goes on to assign two roles to logical intuition: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments.

### Logic

**logicianlogicallogics**

The passage goes on to assign two roles to logical intuition: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments.

### Bertrand Russell

**RussellRussell, BertrandBertrand Russel**

Bertrand Russell, though critical of intuitive mysticism, pointed out that the degree to which a truth is self-evident according to logical intuition can vary, from one situation to another, and stated that some self-evident truths are practically infallible:

### Mysticism

**mysticmysticalmystics**

Bertrand Russell, though critical of intuitive mysticism, pointed out that the degree to which a truth is self-evident according to logical intuition can vary, from one situation to another, and stated that some self-evident truths are practically infallible:

### Self-evidence

**self-evidentself-evidentlyevident**

Bertrand Russell, though critical of intuitive mysticism, pointed out that the degree to which a truth is self-evident according to logical intuition can vary, from one situation to another, and stated that some self-evident truths are practically infallible:

### Infallibility

**infallibleimmaculateinfallibly**

### Kurt Gödel

**GödelGödel, KurtGodel, Kurt**

Kurt Gödel demonstrated based on his incompleteness theorems that intuition-based propositional calculus cannot be finitely valued.

### Gödel's incompleteness theorems

**Gödel's incompleteness theoremincompleteness theoremincompleteness theorems**

Kurt Gödel demonstrated based on his incompleteness theorems that intuition-based propositional calculus cannot be finitely valued.

### Propositional calculus

**propositional logicpropositionalsentential logic**

Kurt Gödel demonstrated based on his incompleteness theorems that intuition-based propositional calculus cannot be finitely valued.

### Many-valued logic

**multi-valued logicmultivalued logicpolyvalent**

### Philosophical realism

**realismrealistmetaphysical realism**

Gödel also likened logical intuition to sense perception, and considered the mathematical constructs that humans perceive to have an independent existence of their own.

### Finite set

**finitefinitelyfinite sets**

Under this line of reasoning, the human mind's ability to sense such abstract constructs may not be finitely implementable.

### Artificial intelligence

**AIA.I.artificially intelligent**

Dissent regarding the implications of logical intuition in the fields of artificial intelligence and cognitive computing may similarly hinge on definitions.

### Cognitive computing

**cognitivecognitive computing systemsCognitive reasoning**

Dissent regarding the implications of logical intuition in the fields of artificial intelligence and cognitive computing may similarly hinge on definitions.