Definitions

Question 1

Define sentence

Answer 1

A sentence is a grammatically formed string of words in a language. Sentences may express commands or questions. And two different sentences may express the same proposition in that they make the same assertion.

Question 2

Define proposition

Answer 2

A proposition is an assertion, something expressed by a declarative sentence, rather than a question or a command. It states that things are a certain way. Propositions can therefore be true or false. One test for being a proposition is whether or not it can act as the reference of a ‘that’ clause.

Question 3

Define simple sentence

Answer 3

A simple (atomic) sentence is a type of declarative sentence which cannot be broken down into other simpler sentences. For example, “the dog ran”.

Question 4

Define compound sentence

Answer 4

A compound (molecular) sentence expresses logical relationships between the simpler sentences of which they are composed.

Question 5

Define simple proposition

Answer 5

A simple proposition is expressed by a simple sentence.

Question 6

Define compound proposition

Answer 6

A compound proposition is expressed by a compound sentence. It contains more than one proposition.

Question 7

Outline the five types of compound propositions

Answer 7

The five types of compound propositions are:
Negations: ¬p i.e. not p
Conjunctions: p ^ q i.e. p and q
Disjunctions: p v q i.e. p or q.  
Conditionals: p —> q i.e. if p then q
Biconditionals: p  q i.e. p iff q

Question 8

Define antecedent

Answer 8

The antecedent (if p) is the first half of a hypothetical proposition.

Question 9

Define consequent

Answer 9

The consequent (then q) is the second half of a hypothetical proposition.

Question 10

define propositional variables

Answer 10

If the interpretation of p and q in an argument is not fixed then they are called propositional variables.

Question 11

State the formalisations of exclusive ‘or’

Answer 11

(p v q) ^ ¬(p ^ q) / (p ^ ¬q) v (¬p ^ q) / ¬(p ↔ q) / p ↔ ¬q

Question 12

State the formalisations of p unless q

Answer 12

p unless q: ¬q —> p / p v q

Question 13

State the formalisations of unless p then q

Answer 13

unless p then q: ¬p —> q / p v q

Question 14

State the formalisations of p only if q

Answer 14

p only if q: p —> q

Question 15

State the formalisations of only if p can q

Answer 15

only if p can q: q —> p

Question 16

State the formalisations of all p’s are q’s

Answer 16

all p’s are q’s: p —> q

Question 17

Define argument, premises & conclusion

Answer 17

An argument is a group of statements which affirms one or more of its members on the basis of the others. A list of declarative sentences or propositions are asserted. These are the premises of the argument. And then a further sentence or proposition is claimed to follow from the premises. This is the conclusion of the argument.

Question 18

Define paraphrasing

Answer 18

Paraphrasing sets out the argument in logical order with premises leading to the conclusion.

Question 19

Define diagramming

Answer 19

Diagramming is used to make clear an argument’s structure. Propositions are represented by letters and inferences by arrows.

Question 20

Define explanation and state how they differ from argument

Answer 20

An explanation is a groups of statements that say why something is the case. They differ from arguments in that they give reasons why something is the case, as opposed to reasoning in support of a conclusion.

Question 21

Define deductive argument

Answer 21

A deductive argument is an argument that claims that a conclusion must hold given that the premises hold.

Question 22

Define inductive argument

Answer 22

An inductive argument is an argument that claims that a conclusion plausibly holds given that the premises hold.

Question 23

Define validity

Answer 23

Validity is a property of arguments. An argument is valid if the conclusion must hold whenever the premises hold. The truth of the premises guarantees the truth of the conclusion. An argument is valid if it is not possible for the premises to be true and the conclusion false. In other words, the premises together with the denial of the conclusion would be inconsistent, that is, a contradiction.

Question 24

Outline two distinct ways that invalidity can be shown in an argument

Answer 24

An argument can be shown to be invalid syntactically, by finding a fault in its structure, or semantically, by dreaming up a world in which the premises are true but the conclusion false.

Question 25

Define soundness

Answer 25

Soundness is a property of arguments. An argument is sound if it is valid and the premises are true —so the conclusion is also true.

Question 26

Define consistency, consistent & inconsistent

Answer 26

Consistency is a property of sets of propositions. A set of propositions is consistent if they all may be true simultaneously. A set of propositions is inconsistent when not all of the propositions can be simultaneously true. A contradiction can be deduced from the set.

Question 27

Assign the properties of validity, truth, and consistency to arguments, propositions, & sets of propositions

Answer 27

arguments are valid/invalid; propositions are true/false; sets of propositions are consistent/inconsistent.

Question 28

Define tautology

Answer 28

A tautology is a proposition that is necessarily true. A proposition is a tautology iff it takes the value T in all lines of its truth table.

Question 29

Define contradiction

Answer 29

A contradiction is a proposition that is necessarily false. A proposition is a contradiction iff it takes the value F in all lines of its truth table.

Question 30

Define contingent

Answer 30

A contingent proposition is one which can be T or F depending on circumstances.

Question 31

When are atomic propositions s and t logically equivalent?

Answer 31

Atomic propositions s and t are logically equivalent if the bicondtional s t is a tautology.

Question 32

How does validity relate to tautology?

Answer 32

argument valid IFF conditional who’s antecedent is conjunction of all premises and consequent is conclusion is tautology i.e. (P1 ^ P2 ^ …) —> C

Question 33

Outline the required rules of inference

Answer 33

MMSS CASCA

Question 34

What is ex falso quodlibet and what does it show?

Answer 34

Ex falso quodlibet (principle of explosion): p, -p, therefore q. It is valid!!! No rows in truth table where both premises T but C is F. This shows that as soon as there is a contradiction in your belief system, then you should believe everything.

Question 35

State De Morgan’s laws

Answer 35

¬(p ^ q) is logically equivalent to ¬p v ¬q i.e. the negation of a conjunction is the disjunction of the negations.

¬(r v s) is logically equivalent to ¬r ^ ¬s i.e. the negation of a disjunction is the conjunction of the negations.

Question 36

Outline 6 steps to critically engage with an argument

Answer 36

paraphrase the argument

diagram the argument

make an ‘implicit’ critique - point out implicit propositions

make a formal critique i.e. formal fallacies

make an informal critique i.e. informal fallacies

is it sound? demonstrate that you understand what it is for each premise to be false

Question 37

What is the biconditional of p & q equivalent to?

Answer 37

(p ^ q) v (-p ^ -q) or (p –> q) ^ (q–> p)

Question 38

What is a ^ -b equivalent to?

Answer 38

-(a—>b)

Question 39

How do we challenge hypotheticals?

Answer 39

we challenge it by imagining a situation where the antecedent holds, but the consequent fails.