# Category:Law of Excluded Middle

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This category contains pages concerning **Law of Excluded Middle**:

The **law of (the) excluded middle** is a valid argument in certain types of logic dealing with disjunction $\lor$ and negation $\neg$.

This includes classical propositional logic and predicate logic, and in particular natural deduction, but for example not intuitionistic propositional logic.

### Proof Rule

- $\phi \lor \neg \phi$ for all statements $\phi$.

### Sequent Form

The Law of Excluded Middle can be symbolised by the sequent:

- $\vdash p \lor \neg p$

## Subcategories

This category has only the following subcategory.

## Pages in category "Law of Excluded Middle"

The following 133 pages are in this category, out of 133 total.

### B

### C

- Cantor's Theorem
- Cantor's Theorem/Proof 1
- Cantor-Bernstein-Schröder Theorem
- Cantor-Bernstein-Schröder Theorem/Proof 6
- Clavius's Law
- Clavius's Law implies Law of Excluded Middle
- Clavius's Law/Formulation 1/Proof 1
- Clavius's Law/Formulation 2
- Clavius's Law/Formulation 2/Proof 1
- Clavius's Law/Formulation 2/Proof 2
- Compact Hausdorff Space with no Isolated Points is Uncountable/Lemma
- Condition for Composite Mapping on Left
- Conditional is Equivalent to Negation of Conjunction with Negative/Formulation 1/Reverse Implication
- Conditional is Equivalent to Negation of Conjunction with Negative/Formulation 2
- Conditional is Equivalent to Negation of Conjunction with Negative/Formulation 2/Proof 1
- Conditional is Equivalent to Negation of Conjunction with Negative/Formulation 2/Reverse Implication
- Conjunction is Equivalent to Negation of Conditional of Negative/Formulation 1/Reverse Implication
- Conjunction with Law of Excluded Middle
- Conjunction with Negative is Equivalent to Negation of Conditional/Formulation 1/Reverse Implication
- Conjunction with Negative is Equivalent to Negation of Conditional/Formulation 2/Reverse Implication
- Conjunction with Tautology/Proof 1
- Contradiction is Negation of Tautology
- Contradiction is Negation of Tautology/Proof 1
- Contradiction is Negation of Tautology/Proof 3

### D

- De Morgan's Laws (Logic)/Conjunction/Formulation 1/Reverse Implication
- De Morgan's Laws (Logic)/Disjunction of Negations/Formulation 1/Reverse Implication
- De Morgan's Laws (Logic)/Disjunction/Formulation 1/Reverse Implication
- De Morgan's Laws (Predicate Logic)/Assertion of Existence
- De Morgan's Laws (Predicate Logic)/Assertion of Universality
- De Morgan's Laws (Predicate Logic)/Denial of Universality/Formulation 1
- Disjunction and Conditional
- Disjunction of Conditional and Converse
- Disjunction of Conditional and Converse/Proof 1
- Disjunction of Conditionals
- Disjunction with Tautology/Proof 1
- Double Negation/Intuitionist Perspective

### E

### I

### L

- Law of Excluded Middle
- Law of Excluded Middle for Two Variables
- Law of Excluded Middle implies Peirce's Law
- Law of Excluded Middle/Also known as
- Law of Excluded Middle/Explanation
- Law of Excluded Middle/Intuitionist Perspective
- Law of Excluded Middle/Proof Rule
- Law of Excluded Middle/Proof Rule/Tableau Form
- Law of Excluded Middle/Sequent Form
- Law of Excluded Middle/Sequent Form/Proof 1
- Law of Excluded Middle/Sequent Form/Proof 2
- Law of Excluded Middle/Sequent Form/Proof by Truth Table
- Template:LEM

### M

### N

- No Injection from Power Set to Set
- No Injection from Power Set to Set/Proof 1
- Non-Equivalence as Disjunction of Conjunctions/Formulation 1
- Non-Equivalence as Disjunction of Conjunctions/Formulation 1/Forward Implication
- Non-Equivalence as Disjunction of Conjunctions/Formulation 1/Forward Implication/Proof
- Non-Equivalence as Disjunction of Conjunctions/Formulation 1/Proof 1
- Non-Equivalence as Equivalence with Negation/Formulation 1
- Non-Equivalence as Equivalence with Negation/Formulation 1/Forward Implication
- Non-Equivalence as Equivalence with Negation/Formulation 1/Forward Implication/Proof
- Non-Equivalence as Equivalence with Negation/Formulation 1/Proof 1

### P

- Peirce's Law implies Law of Excluded Middle
- Peirce's Law is Equivalent to Law of Excluded Middle
- Peirce's Law/Formulation 1
- Peirce's Law/Formulation 1/Proof 1
- Peirce's Law/Formulation 1/Proof 2
- Peirce's Law/Formulation 2/Proof 1
- Peirce's Law/Strong Form
- Principium Tertii Exclusi
- Principium Tertium Non Datur
- Principle of Bivalence
- Principle of Dilemma
- Principle of Dilemma/Formulation 1/Forward Implication
- Principle of Dilemma/Formulation 1/Forward Implication/Proof 1
- Principle of Dilemma/Formulation 1/Forward Implication/Proof 2
- Principle of Dilemma/Formulation 1/Forward Implication/Proof 3
- Principle of Dilemma/Formulation 2/Forward Implication/Proof 2
- Principle of Excluded Third

### R

- Reductio ad Absurdum
- Reductio ad Absurdum/Sequent Form
- Reductio ad Absurdum/Variant 1
- Reductio ad Absurdum/Variant 1/Proof 1
- Reductio ad Absurdum/Variant 2
- Reductio ad Absurdum/Variant 2/Proof 1
- Relative Complement of Relative Complement
- Relative Complement of Relative Complement/Proof 1
- Relative Frequency is Probability Measure
- Rule of Material Implication/Formulation 1/Forward Implication
- Rule of Material Implication/Formulation 1/Forward Implication/Proof
- Rule of Material Implication/Formulation 2
- Rule of Material Implication/Formulation 2/Forward Implication
- Rule of Material Implication/Formulation 2/Proof 1
- Rule of Transposition/Formulation 1/Reverse Implication
- Rule of Transposition/Formulation 1/Reverse Implication/Proof
- Rule of Transposition/Formulation 2
- Rule of Transposition/Formulation 2/Proof 1
- Rule of Transposition/Formulation 2/Reverse Implication/Proof
- Rule of Transposition/Variant 2/Formulation 1
- Rule of Transposition/Variant 2/Formulation 1/Forward Implication
- Rule of Transposition/Variant 2/Formulation 1/Forward Implication/Proof
- Rule of Transposition/Variant 2/Formulation 1/Proof 1
- Rule of Transposition/Variant 2/Formulation 1/Reverse Implication
- Rule of Transposition/Variant 2/Formulation 1/Reverse Implication/Proof
- Rule of Transposition/Variant 2/Formulation 2
- Rule of Transposition/Variant 2/Formulation 2/Forward Implication
- Rule of Transposition/Variant 2/Formulation 2/Forward Implication/Proof
- Rule of Transposition/Variant 2/Formulation 2/Proof
- Rule of Transposition/Variant 2/Formulation 2/Reverse Implication
- Rule of Transposition/Variant 2/Formulation 2/Reverse Implication/Proof