hunan rostomyan
- The Contribution of λ—Calculus to the Theory of Computation
- Knuth's Definition of Computational Methods
- λ—Calculus as a Type Theory
- Basic vs Complex vs Terminological Facts
- Type Theories vs Type Systems
- Symmetric Substitution
- Proving that S4 ≤ S5
- Temporal Logics and Forcing
- Proof of (p → r) ∧ (q → r) ≡ (p ∨ q) → r
- Proof of a ∨ (a ∧ b) = a
- The use of Parentheses in Logic & The Negation Evaluation Order
- Proof of P ⊕ (P → B) ≡ ¬(P ∧ B)
- Proof of ¬∀x(M(x) ∨ W(x)), ∃x¬M(x) ⊢ ∃x¬W(x)
- Presentation of Inductive Definitions
- The Axiom of Unrestricted Comprehension
- A Definition of Similarity for Sets
- Proofs of (A → (B → A)) and ((A → B) → A) → A
- An Interesting Logic Problem
- Encoding Lists and Projectors in λ—Calculus
- Defining Logical Operators in λ—Calculus
- Proof of I ≡ λx.x ⊣⊢ ((S K) K) in λ—Calculus with Combinators
- Contradictoriness & Self-Referentiality
- Proof of ((p → q) ∧ (q → r)) → (p → r)
- Defining the Nestedness of First-Order Formulas
- Inapplicability of the Law of Excluded Middle
- An Epistemic Logic Problem
- Proof of {(P ∨ ¬Q),(R → ¬P)} ⊢ (Q → ¬R).
- A First-Order Logic Semantics Problem
- Proof-Theoretic vs Model-Theoretic Proofs of Validity
- Proving the Soundness of Inference Rules
- Using De Morgan's Laws to Complement a Function
- Proof of (¬q → ¬p) → (p→q) without modus tollens
- Two Proofs of ¬(p ∧ q) → ¬p ∨ ¬q
- Syntactical Differences between PL, FOL, SOL, HOL, and Type Theory
- Codd's Theorem
- What Exactly is Metaphysical Possibility?
- Well-typedness & Carnap's 'Caesar is not a Prime Number' Problem
- Making sense of Falsifiability
- Possibility, Contingency, and a Modal Logic Problem
- A Cheap Linguistic Trick
- What Does it Mean for an Axiom to be Logical?
- On the Number of Empty Sets
- Logical Consequence vs Material Implication
- Statements vs Propositions
- Proving the Validity of Modus Tollens
- The Categorical Syllogistic as a Formal System
- Tensed vs Tenseless Propositions
- The Intuitionistic Notion of Falsity
- Prerequisites for Studying Modal Logic
- Proving that for all L ≤ S5, ◾◊φ ⊯ L Aφ.
- Dispelling a Semantical Confusion
- Semantic Brackets vs Corner Quotes
- Aristotle's Syllogistic and Proofs by Contradiction
- Reflexivity, Symmetry, and Transitivity
- Dispelling a Modal Confusion
- Contradiction vs Paradox
- Proof of (P ∨ (P ∧ Q)) ≡ P
- Is There a Hierarchy of Natural Laws?
- Concluding without Proving
- Functions vs Relations
- Aristotelian Said-of Predication
- Aristotle on Homonymy
- Syntactic vs Semantic Consequence & Soundness vs Completeness
- Proving that Apples aren't Oranges
- Chang & Keisler's Definition of Abstract Logics
- Free Variables
- Proofs of {G ∧ ¬H, ¬H → H} ⊢ (S ∧ I) and H ⊢ S → (B → H)
- Proofs of ¬(A ∨ B) ⊢ ¬(B ∨ A) and ¬(A ∨ ¬(A ∧ B)) ≡ ⊥
- The Syllogistic as a Special Case of Set Theory
- Defining n-ary Relations and Tuples
- Dispelling Another Modal Confusion
- An Appeal to Probability
- Object Language vs Metalanguage, & Metavariables
- Two Meanings of 'and'
- Positivism is Self-Defeating?
- Possible-Worlds Models
- Analyticity 1
- Analyticity 2
- Determining Truth-Functionality
- Dispelling a Confusion about Time
- Tautology, Logical Truth, Logical Consequence, & Logical Necessity
- Dispelling a Confusion about 'Nothing'
- Intensional Explication of Analyticity
- Valuation Functions
- Implication vs Entailment
- Conception vs Explication
- Philosophy as the Logic of Science
- The Logic of Nothingness
- The Rule of A-I Conversion
- The Definition of Logical Validity
- Proving that (φ → ◊φ) is Valid over Reflexive Frames
- Principles of Explosion
- Unrestricted vs Bounded Quantification
- The Monotonicity of Implication
- Fictional Quantifiers
- ¬—Eliem vs ⊥—Intro
- Dispelling a Confusion about Irrationality and Belief
- Dispelling a Confusion about Temporal Logic and Paraconsistency
- Can Every Proposition be Written in a Subject-Verb Form?
- Problems with Standard Deontic Logic
- The difference between Axioms and Theorems in Propositional Logic
- Mathematics and the Absolute Truth
- Important changes in Formal Logic in the last 100 years
- Mathematical Fallacies
- Proving the Axiom of Transitivity
- Background Logics
- Alternatives to Set Theory as a Foundation of Mathematics
- Resources on π—Calculus
- The Usefulness of Paraconsistent Logics
- The Relationship between Language, Mathematics, Logic, Reason and Truth
- Derivation vs Inference
- Drawing Conclusions vs Making Suppositions
- Logical (In)validity
- Logic is a part of Mathematics
- Three Meanings of '='
- Parallel Universes without Parallel Universes are (obviously) Impossible
- The Relationship between Logic and Truth
- A Priori vs Analytic Statements
- Logical vs Causal Necessitiy