# Logic and Mathematics

@inproceedings{Simpson1999LogicAM, title={Logic and Mathematics}, author={S. G. Simpson}, year={1999} }

1 Logic 2 1.1 Aristotelean logic . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Subjects and predicates . . . . . . . . . . . . . . . . . . . 3 1.1.2 Syllogisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 The predicate calculus . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Predicates and individuals . . . . . . . . . . . . . . . . . . 5 1.2.2 Formulas and logical operators . . . . . . . . . . . . . . . 6 1.2.3 Logical validity and logical consequence… Expand

#### 7 Citations

Alice Ambrose and the American Reception of Wittgenstein's Philosophy of Mathematics, 1935–75

- Philosophy
- 2020

abstract:Alice Ambrose (1906–2001) worked throughout her intellectual life to unpack her teacher Ludwig Wittgenstein's contributions to philosophy. Unlike her more renowned Cambridge-educated… Expand

Ethical Mission Definition and Execution for Maritime Robots Under Human Supervision

- Engineering
- IEEE Journal of Oceanic Engineering
- 2018

Experts and practitioners have worked long and hard toward achieving functionally capable robots. While numerous areas of progress have been achieved, ethical control of unmanned systems meeting… Expand

Predicate Logic

- Computer Science
- Encyclopedia of Machine Learning and Data Mining
- 2017

Predicate logic is sound, meaning that every sentence that can be derived using the rules in its proof theory holds in every possible structure, and Gödel in 1929 shows that predicate logic is complete in the sense that if a sentence is true in every structure then it can bederived from the empty set of premises. Expand

Ways of approaching truth: tracing the source of inflationary theories of truth's predicament

- Mathematics
- 2015

Inflationary theories of truth are prone to the scope problem. This is the problem of identifying a single explanation that could cover the various statements that most of us are willing to accept as… Expand

STUDIES IN LOGIC, GRAMMAR AND RHETORIC 4 (17) 2001

- 2011

Logic as a formal mathematical theory is interesting in itself. It poses problems, like any other body of knowledge. Some of them, especially questions concerning axiomatization, consistency,… Expand

Symbolic logic

- 2011

The roots of symbolic logic can be traced as far back as to the study of syllogisms by Aristotle. However, it was not until the second half of the nineteenth century that its modern form began… Expand

Proof Theory in Philosophy of Mathematics

- Mathematics
- 2010

A variety of projects in proof theory of relevance to the philosophy of mathematics are surveyed, including Godel's incompleteness theorems, conservation results, independence results, ordinal… Expand

#### References

SHOWING 1-10 OF 33 REFERENCES

From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931

- Mathematics
- 1967

The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded… Expand

The Thirteen Books of Euclid's Elements

- Nature
- 1909

OUR island is the last home of ignorant Euclidolatry; argal, a German scholar has been allowed to edit, and a German firm to publish, the best and only critical text of Euclid's works. Our ancient… Expand

The collected works

- Geography
- 1996

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has… Expand

Subsystems of second order arithmetic

- Mathematics, Computer Science
- Perspectives in mathematical logic
- 1999

The results show clear trends in the development of mathematics within Subsystems of Z2 and in particular in the areas of arithmetical comprehension and models of Sub system design. Expand

Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic

- Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic
- 1999

First-Order Logic and Automated Theorem Proving

- Mathematics, Computer Science
- Graduate Texts in Computer Science
- 1996

This monograph on classical logic presents fundamental concepts and results in a rigorous mathematical style and is intended for those interested in computer science and mathematics at the beginning graduate level. Expand

First-Order Logic and Automated Theorem Proving. Graduate Texts in Computer Science

- First-Order Logic and Automated Theorem Proving. Graduate Texts in Computer Science
- 1996

Introduction to Logic and to the Methodology of Deductive Sciences

- XXII +
- 1994

Metamathematics of First-Order Arithmetic

- Mathematics, Computer Science
- Perspectives in mathematical logic
- 1993

This chapter discusses Arithmetic as Number Theory, Set Theory and Logic, Fragments and Combinatorics, and Models of Fragments of Arithmetic. Expand