Beginning Logic Flashcards
If… statements can become part of other statements, how are the new statements referred to?
sorites
What are the two parts of if…then… statements?
What are these two parts?
Antecedent, Consequent.
sub-statements of a whole statement.
The words Like and Every allow for what?
categorization into sets and subsets
Which words reveal overlapping sets? What is an overlapping called?
some, there is, there exists: intersections
What words reveal the absence of an overlapping set?
no, there is no, none
What are the three steps to building logical arguments?
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
What are the two components of arguments?
premises at the beginning, conclusion at the end
What is a premise?
facts of the matter or what is believed to be true
What is a conclusion?
outcome of the argument
When is validity determined?
When a conclusion necessarily follows from the premises
what is an enthymeme?
hidden premises within an argument, rhetoric
What are the three laws of thought according to Bertrand Russell?
- The law of Identity: every individual thing is identical to itself
- The law of the excluded middle: every statement is true or false
- The law of non-contradiction: given a statement and its opposite one is true and one is false.
What is the foundation of math?
logic
What is a syllogism?
- argument structure that is designed to appear indisputably valid.
- accepting the premises means necessarily accepts the conclusion.
What is a categorical statement?
statements that talk about whole groups of people or things
How many types of categorical statements are there? What are they? What are their definitions?
two: 1. universal statements tell something about an entire category 2.particular statements tell of the existence of one example within a category
What is the function of a square of opposition?
- organizes the four basic categorical statements of syllogisms
- to show the sixteen possible statements of universals and particulars relations to one another
What are the symbols representing universal and particular statements within the square of opposition?
universal: A,E particular: I,O
Give an example of an universal A statement?
- all cats are sleeping
Give an universal E statement?
- no cats are sleeping
Say a particular I statement?
- some cats are sleeping
Say a particular O statement?
- not all cats are sleeping
Statements positioned diagonally within the square of opposition have a specific relationship, what is it? What are the diagonally positioned symbols?
they are contradictory, uA opposes pO, pI opposes uE
What is an axiom?
statements that are considered to be self evident
what is a theorem?
statements that Euclid thought needed proof
What is Indirect Proof?
assume the opposite of what you want to prove and show how that belief leads to false conclusions.
also known as Proof by Contradiction
What is symbolic logic?
computable symbols stand for words and statements
What is Boolean algebra?
first form of symbolic logic where 1=true and 0=false +=or x=and
What is a set? Describe the significance of set theory?
a collection of things that may or may not have something in common
set theory is the foundation of logic
what are the two interlocking systems of Frege’s formal logic?
sentential logic and quantifier logic
what is sentential logic?
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
What is Quantifier logic?
uses the rules of sentential logic but adds rules allowing for the symbolization of subject and predicate
What is Godels Proof?
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.
What is the definition of logic?
the study of argument validity
What characterizes a valid argument?
true premises and a necessarily true conclusion, the form in which this takes place
In logic what are arguments?
sets of premises followed by conclusions, connected by intermediate statements
That a statement is true or false is indicative of what?
the statements truth value
A sound argument has what properties?
the argument must be valid with true premises
What is deduction?
start with a set of possibilities and reduce until a smaller subset remains
What is induction?
start with a limited number of possibilities and increase that number of possibilities
