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critical c5
| Question | Answer |
|---|---|
| disjunction | a disjunction is just a statement containing the word “or.” |
| A disjunction can be true if both disjuncts are true | true |
| A disjunction is inclusive if all of its disjuncts can be true at once. | true |
| what is denying a disjunct | This kind of reasoning starts by listing a series of possibilities in the form of a disjunction, and then denying one or more of the disjuncts, concluding that the remaining disjunct must be true. |
| example of denying a disjunct | Either P or Q or R is the case. But it is not the case the P. And it is not the case that R. So, it must be the case that Q. |
| In reasoning about alternatives by denying a disjunct, the premises are always dependent | true |
| Denying a disjunct is reasoning by ruling out a possibility and concluding that the remaining possibility must be the case. It is always valid | true |
| symbolic form of denying a disjunc | A or B (1) + (2) |
| Mistake of the False Disjunction | It is a mistake because an argument with a false premise is not sound. Moreover, in the case of reasoning by Denying a Disjunct, if the disjunction is false, then the conclusion will be false too. |
| if the disjunction is false, then the conclusion of our reasoning will be false too. | true |
| A disjunction is exhaustive when it includes all the possibilities that have not yet been ruled out. | true |
| So exhaustive disjunctions are preferable not just because they are guaranteed to be true | they are also preferable because they eliminate the need to rely on luck in our reasoning. |
| Mistake of Appeal to Ignorance | it is a mistake to believe that something just because you do not have evidence that it is false. |
| One form of this mistake is to believe that a disjunction is true just because you cannot think of any other possibilities | true |
| what is an exclusive disjunction | A disjunction is exclusive if its disjuncts cannot all be true at once. |
| Affirming a disjunct is valid only when the disjunction is exclusive. | true |
| affirming a disjunct | a formal logical fallacy that occurs when one incorrectly assumes that because one part of an "either/or" statement (a disjunction) is true, the other part must be false |
| it is possible for a disjunction to be partly exclusive: only some of the disjuncts are incompatible one with another | true |
| It is a mistake to conclude that one disjunct is true just because the other one is false. | true. This reasoning is valid only if the disjunction is an exclusive disjunction. But if one knows that the disjunction is exclusive, then one should add this piece of information as an additional premise in one's reasoning. |
| If we claim that someone is reasoning with a false disjunction, then we should be ready to say what alternative she has overlooked. | true |
| Red Herring Fallacy | one would be introducing an irrelevant possibility simply in order to criticize the author's position. |
| exhaustive disjunction | logical statement comprising a set of possibilities where at least one must be true, covering all potential outcomes |
| conditionals | |
| antecedent | The part of the conditional that follows the “if,” we call the antecedent |
| consequent | the part that follows the “then,” we call the consequent. |
| In asserting a conditional, neither the antecedent nor the consequent is asserted. Rather, what is asserted is that the truth of the antecedent is sufficient for the truth of the consequent. | true |
| If a conditional is true, then the antecedent is sufficient for the consequent. | true |
| A condition can be sufficient for something without being necessary for it. | true |
| example of sufficient condition | One way for Stephen Harper to be a politician is for him to be the PM of Canada. Being a PM is sufficient for, or guarantees, that one is a politician |
| If a conditional is true, then the consequent is necessary for the antecedent. | true |
| A condition can be necessary for something without being sufficient for it. | true |
| A biconditional asserts that the antecedent is both necessary and sufficient for the consequent. | true |
| a conditional is false if the antecedent is true but the consequent is false. | true |
| What does a conditional assert? | asserts a relationship or a promise between two ideas. It claims that if the first part (the condition) is true, then the second part (the result) must also be true. |
| Could a conditional be true if its consequent is false | yes |
| modus ponens | mode of reasoning from a hypothetical proposition according to which if the antecedent is affirmed, the consequent is affirmed. It means that if one thing is true, then another will be |
| modus tollens | denying the consequent |
| Pure Conditional Reasoning | all the premises and the conclusion are conditionals |
| Modus ponens, modus tollens, and pure conditional reasoning are always valid. | true |
| affirming the consequent | |
| Affirming a consequent confuses a necessary condition for a sufficient one. | true |
| Denying an antecedent confuses a sufficient condition for a necessary one. | true |
| Slippery Slope mistake | An argument that has a false conditional is thus not a good argument, because it is not sound, even if it is valid. So it is always a mistake to reason with a false conditional |
| Why modus ponens is valid. | it is impossible for its premises to be true while its conclusion is false. In logic, "validity" doesn't mean the statements are factually true in the real world; it means the conclusion must follow if you assume the premises are true. |
| Why modus tollens is valid. | its structure makes it impossible for the premises to be true while the conclusion is false |
| Why denying the antecedent is not valid | Denying the antecedent is invalid because it assumes there is only one way for an event to happen. It treats a "sufficient" cause as if it were the "only" cause |
| Why affirming the consequent is not valid. | Affirming the consequent is invalid because it confuses a result with its only possible cause. |
| counterexample | A counterexample is a case, either real or fictional, that shows that the conditional is false. A counterexample would be a case where the antecedent is true but the consequent is not (showing that the antecedent is not sufficient for the consequent). |
| Counterexample Strategy | The Counterexample Strategy can help us to decide whether a conditional is acceptable or true. A counterexample to a claim is an example that shows that claim to be false. |
| finding a counterexample to a claim proves that the claim is false; failing to find one does not prove that it is true. | true |
| equivocate | To equivocate is to use a word to mean different things without realizing it. |
| common factual ground | it is important in a disagreement to find what all sides agree on, in order to help them focus on their actual disagreements. |
| common linguistic ground | it is important that all sides agree on how to use their words to say what the facts are or might be. |
| Strawman mistake | A strawman mistake (or fallacy) occurs when someone misrepresents, exaggerates, or oversimplifies an opponent’s argument to make it easier to attack |
| A causal condition | causal condition is a condition that is necessary or sufficient to produce or bring about some event or phenomena. |
| A condition can be necessary for something to happen without being sufficient. | true |
| a condition can be sufficient for something to happen without being necessary. | true |
| counterfactual conditional, | In using a counterfactual conditional, one asserts (or at least, assumes) that the event specified in the antecedent did not occur, and one asserts that if it had occurred, the consequent would have been true too. |
| Post Hoc Fallacy. | it would be a mistake to conclude that just because one thing happened before another, the first thing caused the other. while causes do precede their effects, this is just a necessary condition for a causal link not a sufficient one |
| Method of Agreement | So, to find an event's necessary causal conditions, what we need to do is to look for the common factor. |
| To identify a sufficient causal condition for some effect, | look for a condition that is always followed by that effect. |
| The method of difference | The idea is that if something is sufficient for an effect, then it is enough to guarantee that effect |
| concomitant variation | When phenomena vary together—what we call concomitant variation—then this is some reason to think that there is a causal link involved. |
| jointly sufficient | Jointly sufficient means that a group of factors, when taken together, are enough to guarantee a specific result. |
| What is the difference between a necessary and a sufficient condition? | a necessary condition is a requirement you must have, while a sufficient condition is a guarantee that is enough on its own |
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