Midterm 2 Definitions Flashcards
When is a (particular) argument Deductively Valid?
If and only if it is an instance of a valid form.
When is an argument FORM Deductively Valid?
If and only if there are no instances of that form in which all the premises are true and the conclusion false, aka it has no counterexample.
When is a sentence a Compound Sentence?
If and only if it logically contains another complete sentence (simple sentence) as a component.
When is a sentence a Simple Sentence?
If and only if it is not a compound sentence.
What is a Sentential Operator?
An expression containing blanks such that, when the blanks are filled with complete sentences, the result is a complete sentence.
When is a sentential operator Truth-Functional?
If and only if the truth or falsity of a compound sentence containing that operator is completely determined by the truth or falsity of its component sentences.
What is a Counterexample to an argument form?
An instance of that form where all the premises are true and the conclusion false.
When is a statement form a Tautology?
If and only if every instance of that form is true; that is, it is true in every row in its truth table.
When is a statement form a Contradiction (or inconsistent)?
If and only if every instance of that form is false; that is, it is false in every row in its truth table.
When is a statement form a Contigency?
If and only if some instance of that form is true and some is false; that is, it is true in at least one row in its truth table and false in at least one row in its truth table.
Fill in the blank: Deductive Validity of an argument depends on its ____.
Form.
What is the study of argument forms called?
Formal Logic.
What is an Instance of a form?
When a form’s variables (ex: “p” and “q” in “p->q”) are replaced with sentences (ex: “cold” and “windy” in “if cold then windy”).
Is the following sentence compound or simple: Jason Bay hit 3 homers and struck out.
Compound. Can be deconstructed as “JB hit 3 homers and JB struck out.” – still logically means the same thing though.
Fill in the blanks: Compound sentences are built from _____ sentences by means of ______.
Component, sentential operators.
True or False: Component sentences are simple sentences.
True.
Name four common sentential operators.
“Either – or –.”
“– and –.”
“If –, then –.”
“— if and only if —“
True or False: There are an infinite number of sentential operators in the English language.
True.
Fill in the blank: If you want to know whether a (compound) sentence is true or not, determine the truth or falsity of the ___ sentences.
Component.
Name the five Truth-Functional Sentential Operators.
Conjunction, disjunction, negation, conditional, and biconditional.
What are a conjunction’s component sentences are called?
Conjuncts.
What is an ampersand and what is it used for?
“And” or “&”
Used for conjunctions.
What are a disjunction’s component sentences are called?
Disjuncts.
What is the TFSO in this sentence: (B&F).
“&” or “and”
This is a conjunction.
What is a wedge and what is it used for?
“Either, or” or “v”
This is a disjunction.
What is the TFSO in this sentence:
(LvF).
“v” or “either, or”
This is a disjunction.
What are a negation’s component sentences called?
Negated formulas.
What is a tilde and what is it used for?
“Not” or “it is not the case that” or “~”
It is used for negations.
What is the TFSO in this sentence: ~W.
”~” or “not” or “it is not the case that”
This is a negation.
What are a conditional’s component sentences called?
First component sentence is called the Antecedent. Second component sentence is called the Consequent.
What is the only TFSO where order matters?
Conditional.
What is an arrow and what is it used for?
“If, then” or “->”
Used for conditionals.
What is the TFSO in this sentence: (T->S).
”->” or “if, then”
This is a conditional.
Which goes first, “if” or “then”?
If, always.
True or False: Consequent arrow Antecedent.
False, it is Antecedent arrow Consequent.
What is a double arrow and what is it used for?
”<->” or “if and only if”
Used for biconditionals.
What is the TFSO in this sentence: (R<->A).
”<->” or “if and only if”
This is a biconditional.
Translate this sentence: The would be WET if i had STIRRED it.
(S -> W). “If” goes first always.
True or False: Only if = If.
False, “Only if” = “then.”
True or False: Only if = Then.
True!
True or False: Only if = If and only if.
False.
Translate this sentence: The dog will BITE only if PROVOKED.
(B -> P). Only if = then.
Fill in the blank: “Unless” can also be “___” plus a _____.
“if”, negation.
Translate this sentence using a negation: W unless C.
(~C -> W).
True or False: “I believe that” is a TFSO.
False.
True or False: “___ because ___” is a TFSO.
False
How do TFSOs differentiate from SOs?
With regular SOs, it is not enough to just know components to determine if the sentence is true or not. With TFSOs, it is.
True or False: All compound sentences have TFSOs.
False, all compound sentences have SOs but not all of them are TFSOs.
What is a WFF?
A well-formed formula (or grammatically correct sentence)
Fill in the blank: S, L, and R are all examples of ___?
Sentence letters.
Fill in the blanks: WFFs are built from ______ in _____ using the 5 _____.
Sentence letters, stages, sentential operators.
What is a Major Operator?
The last operator added when a wff is built up in stages.
True or False: Any sentence that uses sentence letters that are WFFs are NOT also WFFs.
False, they ARE also WFFs.
How do you say a particular argument is valid/invalid?
“This particular argument is invalid/valid because its form is invalid/valid. Its form is invalid/valid because it has counterexamples/no counterexamples.”
How do you say a statement form is a contradiction/tautology/contingency?
“Since the statement form is — in every row, it is a contradiction/tautology/contingency.”
When are two statement forms are Logically Equivalent?
When the columns below their major operators are identical (i.e. all T or all F), aka they agree in every row.
How do you say a statement form is logically equivalent?
“The 2 statement forms are logically equivalent because their major operators agree in every row.”
Fill in the blank: If an argument p,q :. r is invalid, then (p&q) & ~r is a ____.
Contingency or tautology.
Fill in the blank: If an argument p,q :. r is valid, then (p&q) & ~r is a ____.
Contradiction.
Fill in the blank: If p is a contradiction, then p,q :. r is ____.
Valid.
Fill in the blank: If r is a tautology, then p,q :. r is ____.
Valid.
Fill in the blank: If an argument p,q :. r is valid, then (p&q) -> r is a _____.
Tautology.
Fill in the blank: If an argument p,q :. r is invalid, then (p&q) -> r is a _____.
Contingency or contradiction.
What part of a statement form determines if it is a contradiction/tautology/contingency?
The major operator.
Fill in the blank: When testing deductive validity using truth tables, you can start with the _____ to rule out “T” rows (as they cannot be counterexamples) as a shortcut.
Conlusion.
Fill in the blanks: (I v W) is a ____ and (p v q) is a ______.
Instance, form.
True or False: Each row in a truth table is a possible world.
True.
Recite the Conditional Truth Table.
T, T = T
T, F = F
F, T = T
F, F = T
Recite the Biconditional Truth Table.
T, T = T
T, F = F
F, T = F
F, F = T
Recite the Conjunction Truth Table.
T, T = T
T, F = F
F, T = F
F, F = F
True or False: (B & O) is an instance of (p & q).
True. Note that for a sentence to be an instance of a form it must have the same MO.
Recite the Negation Truth Table.
T = F
F = T
Recite the Disjunction Truth Table.
T, T = T
T, F = T
F, T = T
F, F = F
What is the hint for Conjunction Truth Tables?
True if both conjuncts are true, false otherwise.
What is the hint for Negation Truth Tables?
Flip-flop, opposites. If p=true, ~p=false and vice versa.
What is the hint for Disjunction Truth Tables?
If its both or one or the other, then its true. If its neither, its false.
What is the hint for Conditional Truth Tables?
No counterexamples, aka TF is only false.
What is the hint for Biconditionals Truth Tables?
Same truth value on both sides of <-> means its true.
Why do logicians only care about the part of the sentences that represent the conditions under which they are true/false?
Because they give meaning to the sentential operators.
Translate “q if p.”
p -> q.
Can “q if p” be translated as q -> p?
No, it must be p -> q because “if” always goes first.
True or False: “Unless” can be translated to “either, or.”
True.
Rewrite “p unless q.”
(Either) p or q.
Rewrite “unless p, q.”
(Either) p or q.
Which one is “only if”?
1) (p <-> q)
2) (p -> q)
2. #1 is “if and only if.”
True or False: “Only if” = “then.”
True.
Rewrite and translate “p only if q.”
“if p then q”
(p -> q)
Rewrite and translate “only if p, q.”
“p, if q” or “if q then p”
(q -> p)
True or false: “Neither, nor” = “not either, or.”
True.
What are the two ways to translate “neither p nor q” ?
~(p v q) and (~p & ~q)
True or False: “Neither p nor q” can be translated as (~p v ~q) or ~(p & q).
False, these are translations for “not both” which is different from “neither, nor.”
Fill in the blanks: When translating “not both,” use ____ or ____.
Negation, disjunction.
What are the two translations of “not both p and q” ?
~(p & q) and (~p v ~q)
True or False: “Not both” can be translated as ~(p v q) and (~p & ~q).
False, those are translations for “neither, nor” which is different.
Fill in the blank: Use the sentence’s _____ to point you towards the major operator.
Commas.
