Logic definitions

Question 1

Syntax

Answer 1

The rules of combination of the elements of a language.

Question 2

Semantics

Answer 2

The study of meanings attached to linguistic signs

Question 3

Deduction

Answer 3

A type of inference in which the conclusion follows necessarily by virtue of the form of the argument.

Question 4

Induction

Answer 4

A type of inference which seeks to establish general principles on the basis of less general principles

Question 5

Fallacy

Answer 5

A form of argument which is invalid, ie which does not guarantee truth at its conclusion.

Question 6

Syllogism

Answer 6

A deductive argument consisting of two or more premises and one conclusion.

Question 7

Subject / predicate

Answer 7

A proposition or statement is made up of a subject, about which a claim is made, and a predicate which is the claim made about the subject.

Question 8

Premise / conclusion

Answer 8

Logical argument = number of premises (propositions which are presented as given) + conclusion (a proposition which follows logically from the premises)

Question 9

Major / minor premise

Answer 9

Aristotelian syllogism: premise which contains the term which is the predicate of the conclusion - major premise.
Premise containing subject of conclusion - minor premise

Question 10

Universal / particular

Answer 10

Universal proposition makes claims about all members of a class.
Particular proposition: claims about at least one but not all members of a class.

Question 11

Proposition

Answer 11

Information content of a statement or any well formed formula

Question 12

Compound proposition

Answer 12

Any proposition longer than a single statement letter.

Question 13

Logic of propositions

Answer 13

System of symbolic formal logic whose formulas are made up principally of statement letters and connectives

Question 14

Local connective

Answer 14

An operator which can be combined with one or two propositions to form a new proposition

Question 15

Statement letter

Answer 15

A letter than can represent any statement

Question 16

Well formed formula

Answer 16

(In strictly formal logical systems) a syntactically correct arrangement of symbols

Question 17

Axiom

Answer 17

(In strictly formal systems) a compound proposition which is taken as given

Question 18

Rule of inference

Answer 18

1. Rule by means of which the conclusion of an argument is derived from the premises
2. (Formal systems) a rule for deriving theorems from axioms or other theorems

Question 19

Theorem

Answer 19

(Formal systems) a compound proposition which can be derived from axioms by the correct use of rule of inference

Question 20

Tautology

Answer 20

A compound proposition which is necessarily true

Question 21

Contradiction

Answer 21

A compound proposition which is necessarily false.

Question 22

Truth table

Answer 22

An arrangement of the truth values that shows in every possible case how the truth values of a compound proposition is determined by the truth values of its simple components

Question 23

Predicate logic

Answer 23

A kind of formalised logic in which statement letters of propositional logic are replaced by symbols which represent predicates and terms and which makes use of qualifiers.

Question 24

Terms / predicates

Answer 24

In predicate logic, the simplest propositions are formed of predicates joined with one or more terms. Frege: Px where P is the predicate and x is the term.

Question 25

Universal quantifier

Answer 25

A logical operator (inverted A)x read ‘for all x’

Question 26

Existential quantifier

Answer 26

Logical operator written (backward E)x read ‘there exists x such that’.

Question 27

Logic

Answer 27

1. Study of methods and principles used to distinguish correct and incorrect reasoning
2. The science of reason. (Aquinas)
3. The systematic formulation and cataloging of valid methods of reasoning
4. A system or codification of the principles of proof and inference