Flashcards in Definitions Deck (39)
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.
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.
Define simple sentence
A simple (atomic) sentence is a type of declarative sentence which cannot be broken down into other simpler sentences. For example, “the dog ran”.
Define compound sentence
A compound (molecular) sentence expresses logical relationships between the simpler sentences of which they are composed.
Define simple proposition
A simple proposition is expressed by a simple sentence.
Define compound proposition
A compound proposition is expressed by a compound sentence. It contains more than one proposition.
Outline the five types of compound propositions
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
The antecedent (if p) is the first half of a hypothetical proposition.
The consequent (then q) is the second half of a hypothetical proposition.
define propositional variables
If the interpretation of p and q in an argument is not fixed then they are called propositional variables.
State the formalisations of exclusive ‘or’
(p v q) ^ ¬(p ^ q) / (p ^ ¬q) v (¬p ^ q) / ¬(p ↔ q) / p ↔ ¬q
State the formalisations of p unless q
p unless q: ¬q —> p / p v q
State the formalisations of unless p then q
unless p then q: ¬p —> q / p v q
State the formalisations of p only if q
p only if q: p —> q
State the formalisations of only if p can q
only if p can q: q —> p
State the formalisations of all p’s are q’s
all p’s are q’s: p —> q
Define argument, premises & conclusion
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.
Paraphrasing sets out the argument in logical order with premises leading to the conclusion.
Diagramming is used to make clear an argument’s structure. Propositions are represented by letters and inferences by arrows.
Define explanation and state how they differ from argument
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.
Define deductive argument
A deductive argument is an argument that claims that a conclusion must hold given that the premises hold.
Define inductive argument
An inductive argument is an argument that claims that a conclusion plausibly holds given that the premises hold.
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.
Outline two distinct ways that invalidity can be shown in an argument
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.
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.
Define consistency, consistent & inconsistent
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.
Assign the properties of validity, truth, and consistency to arguments, propositions, & sets of propositions
arguments are valid/invalid; propositions are true/false; sets of propositions are consistent/inconsistent.
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.
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.