Logic - Disclaimer
Logic - Disclaimer

CHAPTER 1. SENTENTIAL LOGIC 1. Introduction In sentential logic
CHAPTER 1. SENTENTIAL LOGIC 1. Introduction In sentential logic

Sample Chapter
Sample Chapter

A MODAL EXTENSION OF FIRST ORDER CLASSICAL LOGIC–Part
A MODAL EXTENSION OF FIRST ORDER CLASSICAL LOGIC–Part

Logic
Logic

Gödel Without (Too Many) Tears
Gödel Without (Too Many) Tears

... Gödel’s doctoral dissertation, written when he was 23, established the completeness theorem for the first-order predicate calculus (i.e. a standard proof system for first-order logic indeed captures all the semantically valid inferences). Later he would do immensely important work on set theory, as ...
Proof Search in Modal Logic
Proof Search in Modal Logic

you can this version here
you can this version here

Mathematical Logic Fall 2004 Professor R. Moosa Contents
Mathematical Logic Fall 2004 Professor R. Moosa Contents

In defence of an argument against truthmaker maximalism
In defence of an argument against truthmaker maximalism

this PDF file
this PDF file

Primitive Recursive Arithmetic and its Role in the Foundations of
Primitive Recursive Arithmetic and its Role in the Foundations of

CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction

A Recursively Axiomatizable Subsystem of Levesque`s Logic of Only
A Recursively Axiomatizable Subsystem of Levesque`s Logic of Only

A. Pythagoras` Theorem
A. Pythagoras` Theorem

Logic - United States Naval Academy
Logic - United States Naval Academy

... Two (compound) expressions are logically equivalent if and only if they have identical truth values for all possible combinations of truth values for the sub-expressions. If A and B are logically equivalent, we write A  B . (Another notation for logical equivalence is  ; that is, if A and B are lo ...
Russell`s logicism
Russell`s logicism

Chapter 1 Elementary Number Theory
Chapter 1 Elementary Number Theory

... The fundamental theorem of arithmetic states that any integer n > 1 can be expressed uniquely as a product of prime numbers apart from the order of primes. ...
Supplement: Conditional statements and basic methods of proof
Supplement: Conditional statements and basic methods of proof

Inference and Proofs - Dartmouth Math Home
Inference and Proofs - Dartmouth Math Home

... then there is a j with n = 2j. Thus if m is even and n is even, there are a k and j such that m + n = 2k + 2j = 2(k + j). Thus if m is even and n is even, there is an integer h = k + j such that m + n = 2h. Thus if m is even and n is even, m + n is even.” This kind of argument could always be used t ...
Completeness theorems and lambda
Completeness theorems and lambda

Answers
Answers

Plural Quantifiers
Plural Quantifiers

n - Stanford University
n - Stanford University

1.5 Methods of Proof
1.5 Methods of Proof

Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem.The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an ""effective procedure"" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.