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62 Cards in this Set
- Front
- Back
Therefore
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Conclusion indicator
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Thus
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Conclusion indicator
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So
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Conclusion indicator
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Hence
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Conclusion indicator
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For this reason
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Conclusion indicator
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Accordingly
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Conclusin indicator
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Consiquntly
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Conclusion indicator
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This being so
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Conclusion indicator
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It follows that
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Conclusion indicator
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The moral is
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Conclusion indicator
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Which proves that
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Conclusion indicator
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Which means that
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Conclusion indicator
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From whichwe can infer that
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Conclusion indicator
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As a result
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Conclusion indicator
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In conclusion
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Conclusion indicator
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For
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Premise indicators
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Since
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Premise indicators
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Because
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Premise indicators
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Assuming that
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Premise indicators
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Seeing that
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Premise indicators
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Granted that
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Premise Indicators
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This is true because
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Premise indicators
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The reason is that
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Premise indicators
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For the reason that
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Premise indicators
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In view of the fact that
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Premise indicators
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It is a fact that
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Premise indicators
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As shown by the fact that
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Premise indicators
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Given that
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Premise indicators
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Inasmuch as
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Premise indicators
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One cannot doubt that
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Premise indicators
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Formation Rule 1
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Any sentence letter is a wff.
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Formation Rule 2
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If phi is a wff,
then ~ phi is also a wff. |
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Formation Rule 3
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If phi and psi are wffs,
then so are (phi & psi), (phi V psi), (phi -> psi), and (phi <-> psi). |
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(~R)
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Not a wff. Brackets are introduced only with binary operations (rule 3).
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PQ
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Not a wff. Two or more sentence letter can produce a wff only in combination with a binary operator (rule 3).
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((P->(Q))
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Not a wff. No rule allows us to surround sentence letters with brackets.
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(P V Q V R)
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Not a wff. Rule 3 allows us to combine only two sentence letters at a time.
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If
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Consequent before the antecedent.
Sufficient condition. Implies that there are other ways to satisfy the condition, this is just one. |
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Only if
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antecedent before the consequent
Necessary condition. The consequent will only be true under the condition that the antecedent is true. This implies that this is the ONLY way to satisfy the condition. |
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If and only if
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antecedent/consequent order is irrelevant.
Sufficient and necessary condition. Combines both conditions, 'if' and 'only if'. |
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Argument
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is a sequence of declarative sentences including:
one conclusion AND one or more premises that are supposed to provide evidence for the conclusion |
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Deductively Valid
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an argument is DV if it is impossible for the premises to be true but the conclusion false.
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Inductively Probable
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an argument is IP if the conclusion is probably true if the premises are true; an argument is IP to varying degrees
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Connectives
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and (conjunction)
or (disjunction) if (conditional) if...then (conditional) if and only if (bi-conditional) not (negation) |
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Conditional
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Statements formed by if..then.
The statement following 'if' is called the antecedent; the other statement is the consequent. If (antecedent) then, (consequent) |
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Bi-Conditional
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Statements formed by 'if and only if'.
A conjunction of two conditionals. If and only if (consequent) then, (antecedent) |
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Truth table for conjunction
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a conjunction is true if both of its conjuncts are true, and false otherwise
phi psi phi&psi T T T T F F F T F F F F |
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Truth table for a disjunction
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a disjunction is true if at lease one of its disjuncts is true, and otherwise false.
phi psi phiVpsi T T T T F T F T T F F F |
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Truth table for conjunctions
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A conjunction (&) is true if both of its conjuncts (psi, phi, P,Q...) are true, and otherwise false
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Truth table for disjunctions
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A disjunction (V) is true if at least one of tis disjuncts is true, and false otherwise
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P -> Q
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has the same meaning as ~(P&~Q)
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Truth table for material conditionals
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A material conditional (->) is false if its antecedent is true and its consequent false; otherwise it is true.
NB: as for the biconditional, the form P<->Q means the same thing as (P->Q) & (Q->P). |
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Formula for truth tables
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2 to the n
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Truth table for bi-conditional
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if the two components have the same truth value then they are true; otherwise, false
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counterexample
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a possible situation in which the conclusion of an argument or argument form is false while the assumptions are true. a counterexample showe the argument or argument form to be invalid.
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tautology
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a wff of propositional logic whose truth table contains only T's under its main operator. derivatively, any statement whose formalization is such a wff.
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contradiction
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a truth-functionally inconsistent statement. any formula whose truth table contains only F's under its main operator.
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contingent
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formulas which are true at seom lines of their truth tales and false at others are said to be truth-functionally contingent. this type of statement could be either true or false, so far as the logical operators are concerned.
NB: be careful with the semantics of propositional logic. if a statement is logically impossible, then it is inconsistent but may have a truth table that reveals it to be contingent. |
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valid form
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an argument form every instances of which is valid. no situation where the premises are true and the conclusion is false.
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invalid form
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an argument form at least one instance of which is not valid. just takes one situation where the premises are true but the conclusion is false to make the argument invalid.
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To determine whether an argument from of propositional logic is valid
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put the entire form on a truth table, making as many lines as determined by the number of distinct sentence letters occurring in the relevant formulas.
If the table displays no counterexample, then the form is valid (and hence so is any instance of it). If the table displays one or more counterexamples, then the form is invalid |
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Evaluate an argument
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1. determine whether all the premises are true.
2. determine whether the conclusion is at least probable, given the truth of the premises. 3. determine whether the premises are relevant to the conclusion. 4. determine whether the conclusion is vulnerable to new evidence. |