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23 Cards in this Set
- Front
- Back
Truth-functionally valid applies to ___.
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Arguments
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Truth-functional tautology applies to ___
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Single Statements
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Truth-Functionally Self-Contradictory applies to ___.
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Single Statements
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Truth-Functionally Equivalent or Non-Equivalent applies to ___.
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Pair of Statements
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Truth-Functional Consistency applies to ___.
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Sets/groups of statements
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What is an argument?
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An argument is a collection of statements, one of which is the conclusion and the rest of which are premises.
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What is the definition for deductively valid?
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An argument is deductively valid when it is impossible for all of the premises to be true and the conclusion to be false.
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What does it mean for an argument to be sound?
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An argument is sound when it is a deductively valid argument with all true premises.
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A necessary condition is ___
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something that must be the case in order for something else to be the case.
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A sufficient condition is ___
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if the statement's being true would be enough to make another statement true.
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Semantics are concerned with ___.
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Truth and Falsity
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Syntax is concerned with ___.
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Grammatical and Logical Form
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What is an interpretation?
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An interpretation is is an association of truth values to each statement letter that occurs within a set.
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What does it mean to say that a statement is tautologous?
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It means that the statement is true under every interpretation.
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What does it mean to say that a statement is truth-functionally self-contradictory?
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There is no interpretation under with the statement is true
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What does it mean to say that a statement is truth-funtionally contingent?
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There is at least one interpretation under which it is true and under which it is false.
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What does it mean to say that two statements are truth-functionally equivalent?
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The two statements (p&q) have the same truth value under every interpretation.
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What does it mean to sat that two statements are truth-functionally mutually contradictory?
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p and q have opposite truth values under every interpretation
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What does it mean to say that a set of statements is truth-functionally consistent?
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There is at least one interpretation under which all the elements of the set are true.
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Modus Ponens
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if p then q
p therefore q |
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Conjunction Elimination
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A&B
therefore A therefore B |
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Conjunction Introduction
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A
B Therefore A&B |
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Modus Tollens
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if p then q
not q therefore not p |