Beginning Logic

Question 0

If… statements can become part of other statements, how are the new statements referred to?

Answer 0

sorites

Question 1

What are the two parts of if…then… statements?

What are these two parts?

Answer 1

Antecedent, Consequent.

sub-statements of a whole statement.

Question 2

The words Like and Every allow for what?

Answer 2

categorization into sets and subsets

Question 3

Which words reveal overlapping sets? What is an overlapping called?

Answer 3

some, there is, there exists: intersections

Question 4

What words reveal the absence of an overlapping set?

Answer 4

no, there is no, none

Question 5

What are the three steps to building logical arguments?

Answer 5

1.figure out what we know to be true 2.spend time thinking about what we know is true 3.find the best course of action

Question 6

What are the two components of arguments?

Answer 6

premises at the beginning, conclusion at the end

Question 7

What is a premise?

Answer 7

facts of the matter or what is believed to be true

Question 8

What is a conclusion?

Answer 8

outcome of the argument

Question 9

When is validity determined?

Answer 9

When a conclusion necessarily follows from the premises

Question 10

what is an enthymeme?

Answer 10

hidden premises within an argument, rhetoric

Question 11

What are the three laws of thought according to Bertrand Russell?

Answer 11

1. The law of Identity: every individual thing is identical to itself
2. The law of the excluded middle: every statement is true or false
3. The law of non-contradiction: given a statement and its opposite one is true and one is false.

Question 12

What is the foundation of math?

Answer 12

logic

Question 13

What is a syllogism?

Answer 13

1. argument structure that is designed to appear indisputably valid.
2. accepting the premises means necessarily accepts the conclusion.

Question 14

What is a categorical statement?

Answer 14

statements that talk about whole groups of people or things

Question 15

How many types of categorical statements are there? What are they? What are their definitions?

Answer 15

two: 1. universal statements tell something about an entire category 2.particular statements tell of the existence of one example within a category

Question 16

What is the function of a square of opposition?

Answer 16

1. organizes the four basic categorical statements of syllogisms
2. to show the sixteen possible statements of universals and particulars relations to one another

Question 17

What are the symbols representing universal and particular statements within the square of opposition?

Answer 17

universal: A,E particular: I,O

Question 18

Give an example of an universal A statement?

Answer 18

1. all cats are sleeping

Question 19

Give an universal E statement?

Answer 19

1. no cats are sleeping

Question 20

Say a particular I statement?

Answer 20

1. some cats are sleeping

Question 21

Say a particular O statement?

Answer 21

1. not all cats are sleeping

Question 22

Statements positioned diagonally within the square of opposition have a specific relationship, what is it? What are the diagonally positioned symbols?

Answer 22

they are contradictory, uA opposes pO, pI opposes uE

Question 23

What is an axiom?

Answer 23

statements that are considered to be self evident

Question 24

what is a theorem?

Answer 24

statements that Euclid thought needed proof

Question 25

What is Indirect Proof?

Answer 25

assume the opposite of what you want to prove and show how that belief leads to false conclusions. also known as Proof by Contradiction

Question 26

What is symbolic logic?

Answer 26

computable symbols stand for words and statements

Question 27

What is Boolean algebra?

Answer 27

first form of symbolic logic where 1=true and 0=false +=or x=and

Question 28

What is a set? Describe the significance of set theory?

Answer 28

a collection of things that may or may not have something in common set theory is the foundation of logic

Question 29

what are the two interlocking systems of Frege's formal logic?

Answer 29

sentential logic and quantifier logic

Question 30

what is sentential logic?

Answer 30

sentential(predicate) logic allows letters to stand for simple statements which are linked together with symbols. the symbols stand for key concepts: not, and, or, if, if and only if

Question 31

What is Quantifier logic?

Answer 31

uses the rules of sentential logic but adds rules allowing for the symbolization of subject and predicate

Question 32

What is Godels Proof?

Answer 32

The Incompleteness Theorem states any attempt to reduce math to a complete set of axioms leads to an infinite number of undecidable statements, truths, that cannot be proven within the set of axioms.

Question 33

What is the definition of logic?

Answer 33

the study of argument validity

Question 34

What characterizes a valid argument?

Answer 34

true premises and a necessarily true conclusion, the form in which this takes place

Question 35

In logic what are arguments?

Answer 35

sets of premises followed by conclusions, connected by intermediate statements

Question 36

That a statement is true or false is indicative of what?

Answer 36

the statements truth value

Question 37

A sound argument has what properties?

Answer 37

the argument must be valid with true premises

Question 38

What is deduction?

Answer 38

start with a set of possibilities and reduce until a smaller subset remains

Question 39

What is induction?

Answer 39

start with a limited number of possibilities and increase that number of possibilities