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23 Cards in this Set
- Front
- Back
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Logically consistent
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it is possible for all the members of the set to be true
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logically inconsistent
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it is not possible for all members of the set to be true
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standard form
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list of stated premises followed by the conclusion
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deductive validity
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an argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false
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deductive soundness
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an argument is sound if it is valid and the premises are all true
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logically true
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it is not possible for the sentence to be false
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logically indeterminate
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a sentence is logically indeterminate if and only if it is neither logically true nor logically false
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logically equivalent
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the members of a pair of sentences are logically equivalent if and only if it is not possible for one of the sentences to be true while the other is false
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entailment
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a set entails a sentence P of SL if and only if there is no tva under which each member of set is true but P is false
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TF truth
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true on every TVA
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TF false
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false on every TVA
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TF indeterminacy
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not TF true nor false
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TF equivalence
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sentences P and Q are TF equivalent iff there is no TVA on which P and Q have different truth values
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a set is TF consistent if...
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there is at least one TVA in which all members of the set are true
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using a truth tree, a set is tf consistent if
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there is at least one open branch
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using a truth tree, a set is tf inconsistent if
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it has a closed truth tree
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P is tf false using a tree iff
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set {P} has a closed truth tree
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P is tf true using a tree iff
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set {~P} has a closed true
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P is tf indeterminate using a tree iff
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neither {P} nor {~P} has a closed truth tree
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If the truth tree for {P} is open, how does one find out if it is tf true or indeterminate
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if there are 2^n recovered tvas, it is tf true. otherwise, it is tf indeterminate
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P and Q are t.f. equivalent iff
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{~(P≡Q)} has a closed tree
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a set of sentences tf entails P iff
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setU{~P} has a closed tree
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An argument is TF valid if (using a tree)
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the set consisting of the premises and the negation of the conclusion has a closed truth tree
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