Logic and Fallacies Flashcards
Definition: Post hoc, ergo proctor hoc
After this, therefore because of this
What is a declarative sentence?
A grammatical sentence that can be put in place of x in:
Is it true that x?
What is lexical ambiguity?
Where a word can be understood in more than one way.
What is structural ambiguity?
Where words in the string can be grouped together in different ways.
What is ambiguity of cross reference?
When a word or phrase refers back to something mentioned elsewhere, but isn’t clear which thing.
What does token-reflexive mean?
Words or phrases whose reference depends on the context in which they are uttered.
What does cross referencing mean?
Words or phrases that have a reference which depends entirely on the reference of some previously used phrase.
What is referential failure?
When a phrase that ought to have (a real) reference has none.
What is a scaling adjective?
Words that cover a scale, in which the same word applies for more or less, e.g. fat, happy, expensive, heavy.
What is a borderline case?
Where a specific example is somewhere on the border between descriptions, e.g. when someone isn’t obviously definitely fat or thin, bald or non-bald.
When can a set of declarative sentences be described as consistent?
If there is some possible situation in which all the sentences are true.
What does monotonocity entail?
You cannot remove an inconsistency by adding more sentences.
Though you could modify existing sentenced through reference?
In Logic, what does it mean to say a situation is possible?
That it could have been the actual situation (we put aside what we know about the world).
When is an argument valid?
If there is no possible situation in which its premises are all true and its conclusion is not true. When an argument is valid, its premises are said to entail its conclusion.
What are necessary truths?
Declarative sentences which are true in every possible situation.
What is a rational argument?
One which has premises that give us good reason to believe the conclusion, even if the reason is not absolutely decisive.
p => q
Implication
P = antecedent Q = consequent
Material implication?
Basic cause and effect. Only false when cause and effect is violated, otherwise true.
P therefore Q
Only false implication if P is true and Q is false.
Denying the antecedent
If P, then Q
Not P
Therefore not Q
P is only sufficient, not necessary, so it’s absence does not entail the absence of Q.
Biconditional
True if the truth values of the constituents agree.
What makes a sentence valid?
If and only if every interpretation satisfies it.
What makes a sentence contingent?
If and only if some interpretation satisfies it and some interpretation falsifies it.
What makes a sentence unsatisfiable?
If and only if no interpretation satisfies it.
De Morgan’s Laws
~(X&Y) is logically equivalent to ~Xv~Y
and
~(XvY) is logically equivalent to ~X&~Y
The Distributive Law
X&(YvZ) is the same as (X&Y)v(X&Z)
and
Xv(Y&Z) is the same as (XvY)&(XvZ)
Antecedent?
The IF / prior part of a conditional
Consequent?
The THEN part of a conditional
Modus Ponens
If P then Q
P
Therefore Q
(‘Arrow/implication elimination’)
Premise versus assumption
Premise asserted to be true. Categorical reasoning.
Assumptions assumed. Hypothetical reasoning.
Affirming the Antecedent
Modus Ponens
If P then Q
P
Therefore Q
(‘Arrow/implication elimination’)
Affirming the consequent
Invalid reasoning:
If P then Q
Q
Therefore P
Denying the antecedent
Invalid
If P then Q
~ P
Therefore ~Q
Denying the consequent
Valid
If P, then Q
~ Q
Therefore ~P
Modus Tollens
Denying the consequent
Disjunction
Or
Conditional
->
If… Then…
Conjunction
And
Biconditional
If and only if
Law of Identity
P -> P
Modus Tollens
P -> Q
~ Q
Therefore ~ P
Proposition
Statement believed to be true and presented as arguments or reasons for consideration. May be true or false.
Predicate
The foundation of the argument / underlying assumption
The thing being asserted
In “John went home” it is “went home”
Principle of Bivalence
Every sentence is either true or false but not both and not neither
Law of excluded middle
P v ~P
Abduction
Reasoning from effects to possible causes
Commutativity
If you swap the order around it has the same value (e.g. for + and * but not - and /)
