Arguments Flashcards
Definition of an argument and an example
A set of premises and a conclusion where the former is intended to support the latter
P1 All whales are mammals
P2 All mammals are warm-blooded
__________
C All whales are warm-blooded
What is rhetoric?
Any device designed to convince us of something that is not reason
Antecedent v Consequent
Antecedent - if part
Consequent - then
2 Different types of Ambiguity definitions
When the same sentence can have more than one meaning:
- lexical ambiguity - Introduced by an ambiguous word
- Syntactic ambiguity - introduced by the structure of the language
What does the term propositions mean?
The meaning of a declarative sentence:
Ie a sentence that makes a statement, so not a question or a command.
Must be true or false
Define a Deductively Valid Argument
•A deductively valid argument, intuitively, is one where the conclusion is a logical consequence of the premises (it follows, logically, from them).
Definition of deductive validity:
•An argument is deductively valid if and only if its form is such that whenever all the premises are true, the conclusion is true.
Ie if the premises are true- the conclusion cannot be false
Is validity the same as truth?
What is the difference?
Eg
validity is not the same as truth:
–Propositions are true or false; arguments are valid or invalid.
–An argument may be perfectly valid without containing any true propositions:
- All mammals are dogs
- Pegasus is a mammal
__________________
•Pegasus is a dog
Definition of soundness
True premises and true conclusion
•An argument is deductively sound if and only if it is valid and its premises are true.
–So a (deductively) sound argument must have a true conclusion.
–Validity is a precondition for soundness.
arguments can be valid, sound; propositions can be true or false.
–There is no such thing as a true argument.
What is standard form argument?
With an example
- It has numbered premises, a line (‘inference bar’) between the premises and conclusion, and the conclusion marked with ‘C’.
- Arguments can have any number of premises. Multiple conclusions also sometimes occur, in which case you can mark them with ‘C1’, ‘C2’, etcetera.
P1 If voting was not important, there would be no voter suppression
P2 There is voter suppression
__________________________
C Voting is important.
Example of a valid but unsound argument
P1 If Boris is a vegetarian, then Boris is a redhead
P2 Boris is a vegetarian
__________________________
C Boris is a redhead
If you inserted true premises the conclusion would be true
Modus Ponens
Affirm the antecedent and affirm the consequent (Antecedent – ‘If’ part of the argument) (Consequent – ‘then’ part of the argument)
Eg If a president commits a high crime and misdemeanour, then the president has committed an impeachable offence. Trump tweeting “Fight” was a high crime and misdemeanour and therefore trump committed an impeachable offence.
P1 If there is barking to be heard, there are dogs nearby
P2 There is no barking to be heard
C Therefore, there are no dogs nearby
(Denying the antecedent (‘If’ part) means the argument is invalid. If the argument went there is barking to be heard, therefore there are dogs nearby – then this is a valid argument (even if not sound)
Modus Tollens
Modus Tollens – negation of the consequent and then negate the antecedent.
There are two ways to make a valid argument out of a conditional (If-then), either affirm the if part and the then part will be affirmed, or you can deny the then part and the if part will be denied. You cannot mix and match affirming and denying.
P1: If there is barking to be heard, there are dogs nearby
P2: There are no dogs nearby
C: Therefore, no barking to be heard.
