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Philosophy 1200 Critical Thinking Textbook Notes.docx

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Philosophy 1200
Eric Desjardins

Chapter 1: Deductive Arguments What Makes a Good Argument? Argumentation is a rational practice. arguing is a process of showing reasonableness of an assertion the presentation of a collection of premises that are rationally persuasive of a conclusion, ie. premises make it reasonable to accept the conclusion Arguments are linguistic or logical objects. looks at the truth of the premises and their logical relation to the conclusion soundness: validity: premises true = conclusion true all premises are true LOGIC once though to be univocal: only a single meaning or interpretation Laws of Thought: Law of Identity: P if and only if P Law of Non-Contradiction: not both P and not-P Law of Excluded middle: P or not-P intuitionisitic logic: does not include Law of Excluded Middle requires direct proof of P: not-P is not taken as proof of P dialetheic logic: does not include Law of Non-Contradiction when contradictory statements arise, must be arbitrary in concluding which statement is discarded modal logic: factor in notions such as belief, knowledge, obligation, etc. basically logic is not monolithic Valid Argument Forms Simplification form: P and Q Therefore P example: Rules say that prisoners (P) aren‘t allowed to vote. A repentant prisoner (P and Q) is a prisoner (P). So the rules applies to them too. Conjunction form: P Q Therefore P and Q example: Eric is a doctor. (P) Ellen is a doctor. (Q) Therefore, Eric and Ellen are both doctors. (P and Q) Addition form: P Therefore P or Q example: Foxes are mammals. Therefore, either foxes are mammals or cows are mammals. Foxes are mammals. Therefore, either foxes are mammals or lizards are mammals. Hypothetical Syllogism form: If P then Q If Q then R Therefore, if P then R example: If the dollar is devalued, exports will rise. (if P, then Q) If exports rise, then unemployment will fall. (if Q then R) Therefore, if the dollar is devalued, unemployment will fall. (P then R) Constructive Dilemma form: P or Q If P then R If Q then S R or S example: Either it will snow tomorrow or there will be a quiz in class. (P or Q) If it snows tomorrow, class will be cancelled. (if P then R) If there‘s a quiz in class tomorrow, I will fail. (if Q then S) Either classes will be cancelled or I will fail a quiz tomorrow. (R or S) Destructive Dilemma form: If P then R If Q then S Not R or not S Therefore not P or not Q example: If she called her mother, the answering machine took a message. (if P then R) If her brother called her mother, the line was busy. (If Q then S) But the machine didn‘t take a message, or the line wasn‘t busy. (not R or not S) So she didn‘t call her mother, or her brother didn‘t. (not P or not Q) TYPES OF ARGUMENTS linked argument: premises essentially tie together to support a single overall conclusion convergent argument: a range of independent grounds for a conclusion assembled together as premises sequential argument: premises establish intermediate conclusions, which serve as premises for a further conclusion TRUTH CONDITIONS truth values: either true or false reasonableness: are there grounds to believe the premises? necessary truths: true no matter how things might have turned out definitional truths: dependent on the meaning we attribute to the words necessary and sufficient conditions Factual and Non-Factual Statements some do not really have truth conditions statements about morality, humor, etiquette, aesthetics Scientific Reasoning Causation/Correlation two ways in which things may be related: temporally: order in time empirical; can be observed causally complete causal account specifies necessary and sufficient conditions involves counterfactual statements: what would happen if necessary and sufficient conditions are not met antecedent circumstance: correlated circumstance usually occurring prior to the event Rival Hypotheses Rival Restricted Hypotheses some observations explained by each hypothesis but neither explains all circumstances requires auxiliary hypothesis: second hypothesis logically required by hypothesis in question Rival Unrestricted Hypothesis two incompatible hypotheses explained by the same observations usually due to the interpretation of the observations incommensurable: when two theories differ so much it becomes impossible to test their hypotheses with the same observation statements no available standard, independent of both theories, to test which theory should prevail standard of explanatory accuracy is used here— the hypothesis with more precise observations to confirm it is more explanatorily powerful Critical Thinking about Numbers representative numbers encode important information but can misrepresent affairs percentages create a loss of information major percentage change in small populations = minor small percentage change in major populations = major Fallacies in Reasoning with Rates linear projection: assumption that the observed rate will extend into times yet to be observed misquotation: incorrectly relaying information spoken by another Ratings and Rankings percentage vs. percentile: percentage is out of 100, while percentile is a term used to numerically rank values in comparison to other values th eg. 90 percentile means better than 90% of the population, whereas 90% means to have a raw score of 90% inherently comparative within a group bar graphs indicate changes that apply to different absolute amounts eg. rich income increase by 50% and poor income increase by 15% are of amounts of their own categories, not that the poor income increased by 15% of the rich income ordinal rankings can be misleading because we don‘t know the gap between the first place and last place finishers position on the list and use of seemingly hard numbers convey the sense of a major difference when there may be little to no difference think about a ranking of the ―best cars of 2013‖— depends on buyer‘s needs and wants Fallacies of Numerical Reasoning pseudo-precision: use of numerical expressions in order to heighten the perception that it is reliable eg. ―8422 jobs were created in Nova Scotia this month.‖ — creating a job is a process spread out over time graphical fallacies: misrepresentation of quantities/rates by misleading graphs or charts scaling of the axes cumulative graphs be wary of data portrayed by mean, median, mode Probability and Statistics Significance and Margins of Error statistical significance: measure of confidence in the probabilistic conclusion confidence interval: range of values within which we can be statistically confident that the true value falls eg. 50-60% of voters will support Trudeau. margin of error: numerical value half of the midpoint of the confidence interval the smaller margin of error, the more data we need to have high confidence in it smaller margins of error = less confidence in truth values larger margins of error = more confidence in truth values ―observed result is significant to the 5% level‖  over the long run, such a result will show up at most 1 time in 20 if the null hypothesis is true Basic Probabilistic Concepts probability = prediction and explanation statistics = analyzing observed data heuristics can cause us to reason incorrectly Basics of Probability P(e) = probability that some event occurs P(~e) = probability that some event does not occur Axioms: P(e) + P(~e) = 1.0 0 ≤ P(e) ≤ 1.0 P(S) = 1, where S is the set of all possible outcomes P(e) = 1 – P(~e) FALLACIES gambler’s fallacy: to think that if a series of independent events has the conjoint probability p, then the probability of any single event in the series is somehow dependent on the probability of the series as a whole eg. A dice is to be rolled 4 times. The first three rolls are 5‘s. The gambler‘s fallacy is to think that the next roll has less than a 1/6 chance of being a 5, because the probability of 4 5‘s in a row is (1/6 ), when really the events are independent (so the probability of rolling another 5 is just ½). Simpson’s Paradox: a trend that appears in different groups of data disappears when the groups are combined, and the reverse trend appears instead regression fallacy: confusing a pattern in random events by overlooking regression effects (a random sample within a normal distribution is close to the mean) eg. we start off in a tail of some distribution and then trend toward the mean as our experience grows: we think that there is a correlational or causational explanation for this rather than as a trend that is entirely consistent with randomness Biases Within Reason repetition effect: tendency to judge claims you hear often to be true often applied when watching TV— commercials BIASES Perceptual Biases low-level biases: the result of the basic structure of our perceptual and neurological mechanisms eg. McGurk effect (multi-modal), cutaneous rabbit top-down effects: the role of expectations in our perceptions eg. ―hearing‖ things when songs are played backwards inattentional blindness: concentration on one task causing you not to notice other events happening in front of you eg. basketball bounces/gorilla Cognitive Biases confirmation bias: beliefs or expectations about a hypothesis can lead to its seeming more highly confirmed than the evidence warrants eg. ―Most famous scientists were men.‖ situational, attentional, interpretive biases self-fulfilling prophecies Egocentric Biases attribution theory: how the perceiver uses information to arrive at causal explanations for events self-serving bias: emotions, desires, expectations combine to produce an explanation that makes ourselves look good eg. talented but lazy vs. modestly gifted but hard-working optimistic self-assessment: people assess themselves as better than they are eg. everyone rating themselves ―above-average‖: clearly not possible for everyone to be above-average
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