Formal Logic, And, Not, If Then Flashcards
What symbol do we use for ‘and’?
&
What type of logical operator is ‘and’?
A conjunction, binary
What is the truth table for ‘&’?
A¦ B¦ A&B ¦
T¦ T¦ T ¦
T¦ F¦ F ¦
F¦ T¦ F ¦
F¦ F¦ F ¦
What are some synonyms of ‘and’?
‘also’, ‘but’, ‘as well’, ‘however’, ‘and yet’, ‘too’, ‘moreover’, ‘additionally’
They have the same truth table, and also meaning. Sounds different because they have different rhetorical force
What symbol do we use for ‘not’?
~
What type of logical operator is ‘not’?
negation, singulary
What’s a less ambiguous way of saying ‘not’?
It is not the case that…
What are some other synonyms of ‘not’?
‘it is not the case that’, ‘neither..nor’, ‘un-‘ (e.g. unapologetic = not apologetic)
What is the truth table for ‘~’
A¦~A¦
T¦ F¦
F¦ T¦
What does the double negation elimination rule mean?
~~A = A
or in standard form:
P1 ~~A
_____________
C A
What does the bad style of argument, an appeal to ignorance look like?
‘We don’t know whether A is true, so A is false (or neither true nor false)’
Give an example of an appeal to ignorance (bad) argument?
P1: It has not been determinately show whether there is a planet orbiting Alpha Centauri A
__________________________________________
C1: There is no such planet
C2: P1 is neither true nor false
It is true or false but we simply don’t know
What symbol do we use for ‘If-then’?
->
What type of logical operator is ‘If-then’?
Conditional
What are some synonyms of ‘if then’?
‘if’, ‘only if’, ‘conditional on’, ‘when’, ‘only when’, ‘in case’
In ‘A->B’ which is the antecedent and which is the consequent of the conditional?
A is the antecedent and B is the consequent
What is the truth table for ‘->’?
A¦ B¦ A->B ¦
T¦ T¦ T ¦
T¦ F¦ F ¦
F¦ T¦ T ¦
F¦ F¦ T ¦
Give an example of a modus ponens argument using ‘if-then’
P1 A->B If Serena is muscular
then serena is strong
P2 A Serena is muscular
___________________ ________________________
C B Serena is strong
Give an example of a modus tollens argument using ‘if-then’
P1 A->B If Daphne is a cat, then
Daphne meows
P2 ~B Daphne doesn’t meow
___________________ ________________________
C ~A Daphne is not a cat
Give an example of a bad argument using ‘if-then’, denying the antecedent
P1 A->B If you smoke, you’re
likely to get heart
disease
P2 ~A I don’t smoke
___________________ ________________________
C ~B I’m not likely to get
heart disease
This conclusion could be false as the risk might be genetic.
Give an example of a bad argument using ‘if-then’, affirming the consequent
P1 A->B If vaccination is
widespread infections
are down
P2 B Infections are down
___________________ ________________________
C A Vaccination is
widespread
This conclusion could be false as it could be the lockdown.
What’s the correct truth table for ‘A if B’?
B->A
IM NOT SURE
What’s the correct truth table for ‘A only if B’?
A->B
The second row shows this
IM NOT SURE
What are some other ways of signalling the conclusion?
‘so’, ‘hence’, ‘thus’, ‘therefore’, ‘it follows that…’
