SSH 105

Disjunction

-a statement containing the word "or." -also known as reasoning about alternatives eg. Jones can go to law school or to medical school -does not assert either disjunct, but instead claims that its one or the other -is only true at lest one of the disjuncts is true.

False Disjunctions

-a way in which alternative reasoning can go wrong -when a disjunction is false (neither disjunct is true), reasoning by denying the disjunct will inevitably yield a false conclusion -valid, but always false.

Mistake of the False Disjunction/False Alternative

-an argument that has a false disjunction as a premise -occurs when the disjunction is false (ie. niether disjunct is true) -reasoning by denying the disjunct will inevitably yield a false conclusion when the disjunction is false. eg: The car won't start. Either its batter is dead or it is out of has. I just check and there is plenty of gas. So, the battery must be dead. -if it is the case that neither the battery is not dead and it isn't out of gas, then the conclusion will inevitably be false. -for this reason, we must make sure that our disjunctions are true.

Exclusive Disjunctions

-at most one of its disjuncts is true -The soccer team won, tied, or lost -Either P or Q is the case But only one of them can be the case P is the case So Q is not the case -always valid

Overlooked conditions

-because there are so many different factors present in any series of cases, there can rarely be a guarantee that every single common factor has been identified

Mistake of the Lucky Disjunction

-getting lucky by getting the same results even though you overlooked stuff

Sufficient Conditions

-if a conditional is true, then the truth of the antecedent is sufficeint for the truth of the concequent. In other words, all that it would take for the consequent to be true is for the antecedent to be true eg. If Stephen is the prime minister of Canada, then Stephen is a politician

Necessary Conditions

-if a conditional is true, then the truth of the consequent is necessary for the truth of the antecedent. In other words, there is no way that the antecedent could be true if the consequent were false. -usually there are lots of necessary conditions for something

Exhaustive Disjunctions

-includes all the possibilities that have not been ruled out one way to make sure that our disjunctions are true even when we do not know the disjunct is true -a disjunction is exhaustive when it includes all the possibilities that have not yet been ruled out -help to aboid the mistake of the false disjunction eg: The baby will be born either a girl, a boy, or a hermaphrodite.

Pure Conditional

-involves claims about necessary and sufficient conditions as conclusions -reasoning from two or more conditionals to a conditional If P, then Q If Q, then R If P, then R eg: If Aristotle is human, then Aristotle is mortal If Aristotle is mortal, then Aristotle is not God So, if Aristotle is human, then Aristotle is not God

Mistake of Appealing to Ignorance

-it is a mistake to believe that something is the case simply because it has not been proven otherwise. eg: James must have spilled the milk. Either he did it or the cat did it. What other possibility could there be? And there is no way the cat did it, since she would be covered in milk if she had. So this is why I'm sure James spilt it. -the fact that the author could not think of other possibilities is not sufficient reason to believe that those are the only two possibilities

Affirming the Consequent

-mistake comes from taking a necessary condition to being a sufficient one eg Susan feels sick most mornings, which is exactly how she would feel if she was pregnant. So, I think she's going to have a baby If P, then Q Q So, P not valid The fact that Q is necessary fr P does not show that P is the case.

Denying the Antecedent

-not valid even if the premises were true, the conclusion may still be false -mistake comes from taking a sufficient condition to be a necessary one eg If Jones has diabetes, then he shouldn't be eating that cake and ice cream. But he doesn't have diabetes, so he can eat some of it If P, then Q Not P So not Q

Multiple Causes

-perhaps both potatoes and liver were infected, and some that were infected were the only ones who ate the potatoes and some were the only ones who ate the liver and it was just a coincedence that everyone ate the tomatoes

Method of Agreement

-to identify the causal conditions that are necessary for some event, we need to see what is present every time the event is present to find a necessary causal condition, look for an antecedent condition that occurred EVERY time the effect occurred. Common factor. eg: 5 Individuals began ill after eating tomatoes -there are 3 cases where this doesn't work Five people got sick. Each of them ate the purple mushrooms. So, maybe, the purple mushrooms caused their sickness.

Mixed Reasoning

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Look for Common Ground

1. Common factual ground 2. Common linguistic ground

Affirming a Disjunct

Affirming a disjunct is reasoning from the truth of one disjunct to the conclusion that the other disjunct is falst. 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.

Affirming the consequent

Affirming the consequent is a form of reasoning using conditionals where one premise asserts a conditional, another premise asserts the consequent of that conditional, and the conclusion asserts the conditional's antecedent. This is not valid. The conditional asserts that the truth of the consequent is necessary for the truth of the antecedent, but it does not assert that it is also sufficient. So even if the conditional is true and the consequent is true, the antecedent might still be false. Example 1: If my cat is purring, then she is sleeping. She is sleeping, therefore she must be purring. Example 2: If the waves are calm, then the boat will not tip. The boat did not tip, so the waves must have been calm. If A, then B B, so A

Denying the antecedent

Denying the antecedent is a form of reasoning using conditionals where one premise asserts a conditional, another premise asserts that the antecedent is false, and the conclusion asserts that the consequent is false too. But this is not valid. The conditional asserts that the truth of the antecedent is sufficient for that of the consequent, but it does not assert that it is necessary. So even if the conditional is true and the antecedent is false, it might still be that the consequent is true. So, denying the antecedent is not valid. Example 1: If James passed his class, then he will be really pleased. James is not really pleased, therefore, he didn't pass his class. Example 2: If Julie gets stuck in traffic, then she will not be home on time. She didn't get stuck in traffic, so she will be home on time If A, then B Not A So B

Causal Claims

Drowning causes death, watering your lawn will make it grow

Denying a Disjunct

Either P, or Q, or R is the case. But it is not the case that P. And it is not the case that R. So, it must be the case that Q. -Because the second and third premise involve ruling out a possibility, we can call this form of reasoning about alternatives "denying a disjunct" -starts by listing a series of possibilities in the form of a disjunction, then denying one or more of the disjuncts, -premises are always dependent Test Answer: Denying a disjunct is reasoning by ruling out a possibility and concluding that the remaining possibility must be the case. It is always valid. Eg: A or B It is not the case that A So it must be the case that B

Bi-Conditional

Joint of conditionals easier than a conjunction of conditionals Jones is a bachelor if and only if Jones is an unmarried man. -we use these to say that certain conditions are both necessary and sufficient for something.

modus ponens

Modus Ponens is a valid form of reasoning about necessary and sufficient conditions, where the antecedent of a conditional is affirmed. eg: 1. If P, then Q 2. P 3. So, Q 1 + 2 3

Modus Ponens

Modus ponens is a form of reasoning using conditionals where one premise asserts a conditional, another premise asserts the antecedent of that conditional, and the conclusion asserts the conditional's consequent. Since a conditional asserts that the truth of the antecedent is sufficient for the truth of the consequent, if the conditional is true and if the antecedent is true, then so must be its consequent. So, modus ponens is valid. Example 1: If Jeff is scared, then he is also nervous. Jeff is scared. Therefore, Jeff is also nervous Example 2: If it rains, then my feet will get wet. It's raining, so my feet will get wet If A then B A, so B

Why modus tollens is valid. Give two examples.

Modus tollens is a form of reasoning using conditionals where one premise asserts a conditional, another premise asserts that the consequent of the conditional is false, and the conclusion asserts that the conditional's antecedent is false. Since a conditional asserts that the truth of the consequent is necessary for the truth of the antecedent, if the conditional is true and its consequent is false, then its antecedent must be false too. So, modus tollens is valid. Example 1: If the team won their game, then they would be in the finals. The team is not in the finals. Therefore, they did not win their game. Example 2: If Sam goes to the store, then he will buy groceries. He did not buy groceries, so he did not go to the store. If A then B Not B So Not A

Necessary and Sufficient Conditions

a condition that is necessary for something and sufficient for it eg: Jones is an unmarried male -on their own, neither condition is sufficient, though they are both necessary. conditions can be both necessary and sufficient. For example, being the child of a human is both necessary and sufficient for being a human.

Reasoning about Causal Conditions

a condition that is necessary or sufficient for the occurrence of some event or phenomena -caused by a condition that is sufficient for that event's occurrence and that condition must include everything that is necessary for the occurrence of that event. eg If you take ibuprofen your headache will subside salmolnella causes illness

Valid

an argument is valid in case it is not possible for the evidence contained in the premises to be true and the conclusion to be false. eg. British shorthair cats are grey. That cat is grey. That is a British Shorthair.

Conditionals

asserting that there is a relation of a certain kind between the antecedent and the consequent - claiming that if the antecedent is true, then the consequent is true too -or, in asserting a conditional, one is asserting that the truth of the antecedent is sufficient for the truth of the consequent, and that the truth of the consequent is necessary for the truth of the antecedent. Test Answer: A conditional is an 'if, then' sentence and it asserts that there is a specific relationship between the antecedent (the sentence that follows the "if") and the consequent (the sentence that follows the "then"). More specifically, a conditional asserts (i) that the truth of the antecedent is sufficient for the truth of the consequent, and (ii) that the truth of the consequent is necessary for the truth of the antecedent. It is important to note that a conditional is not asserting the truth of the antecedent or the consequent, but rather, just that the two have this relationship. For example, in the conditional "If it rains, then my feet will get wet" the truth of the antecedent "it rains," is being claimed to be sufficient for the truth of the consequent "my feet will get wet," and the truth of the consequent is being claimed to be necessary for the truth of the antecedent.

Counterfactual Conditional

asserts that the event specified in the antecedent did not occur, and that if it had occurred, the consequent would have been true too eg If Hitler had not invaded Poland, WW2 would not have happened

Simulation

create fake cases to make more data

Stating a sufficient condition

eg If Stephen Harper is prime minister of Canada, then Stephen is a politician If P, then Q

Stating a necessary condition

eg Stephen Harper is a prime minister of Canada only if Stephen is a politician P only if Q

Affirming a Disjunct

eg. Either the maid did it or the butler did it. The butler just confessed. So the maid is innocent. -valid only when the disjunction is exclusive because only if one and only one of the disjuncts is true does it follow from the fact that one is true that the other is false. (e.g. The baby is a boy or a girl. The baby is a boy, so it is not a girl) -if one knows that the disjunction is exclusive, then one should add this piece of information as an additional premise: Either the student is a male or the student is a female, and the student cannot be both male and female. The student is male. So, the student is not female.

Reasoning with Definitions and Standards

eg: A geomentrical figure is a triangle if and only if the sum of its internal angles is 180 degrees A restuarant deservs 4 starts only if the service is exceptional

Counter-Example Strategy

helps us decide whther a conditional is acceptable or true -an example that shows that the conditional is false by having an example that shows that the antecedent could be true even if the consequent were false. If Jones is a bachelor, then Jones is happy - Jones could still be a bachelor and be miserable.

Concomitant Variation

if two phenomena vary together, then this is some reason to think they are causally related. The frog population grows as the temperature rises and shrinks as the temperature falls. So, the changes in temperature might be causally related to the changes in frog population.

Slippery Slope Fallacy

it is a mistake to argue using a causal conditional that is false or unjustified -reasoning with a false or unacceptable causal conditional eg We should not let the country close the mental hosptial because if they do, all of its patients will be let out on the streets works for overly negative and over positive (emissions reduction)

Overlooked Effects

maybe someone who got sick didn't report it not all the cases where the effect was present get identified

Conjunction of Conditionals

state the fact that certain conditions are individually necessary and jointly sufficient eg: If Jones is a bachelor, then he is an unmarried man and if he is an unmarried man, then he is a bachlor

Testing for Logical Strength

suppose that the premises were true. Then ask how likely it is that the conclusion would be true too? The higher the likelihood, the more logical support the premises provide

Antecedent

the part of the conditional that follows the "if"

Consequent

the part of the conditional that follows the then

Method of Difference

to find a sufficient causal condition, compare cases when the effect is present and when it is absent and look for a difference. eg: Jane had trouble sleeping several nights last week. She had coffee after dinner on the nights she had trouble sleeping but not on the nights that she slept well. Probably, the coffee caused her trouble sleeping.

Equivocation

use a word to mean different things eg: Only man is a rational animal Susan is not a man So Susan is not a rational animal Man in the first premise means different than the second premise

Modus Tollens/denying the consequent

use this when we know that a condition that is necessary for something is absent -a form of reasoning about necessary and sufficient conditions -always vaild, because if a conditional is true, then the truth of the consequent is necessary for that of the antecedent (in other words, if a conditional is true, then the consequent must be true of the antecedent is) If P, then Q Not P So, not Q

Modus Ponens/Affirming the antecedent

use this when we know that a condition that is suffiecient for something is true -a form of reasoning about necessary and sufficient conditions -always valid, because if a conditional is true, then the antecedent is sufficient for the consequent If P, then Q P So, Q

Experimentation

where we create new real cases to make more data and hold one variable fixed