Valid deductive argument: an argument in which assuming the premises are true, it is impossible for the the conclusion to be false, conclusion necessarily follows the premises. Invalid Deductive argument: argument in which the premises are true, it is possible for the argument to be false, conclusion doesn’t necessarily follow the premises. Sound Argument: When an argument is shown to be valid and all premises are true then it is sound. Unsound argument: when an argument is invalid or at least one of a valid arguments premises are false. Cogent Argument: An inductive argument is cogent when the argument is strong and the premises are true. Uncogent: an argument is un-cogent if either the argument is weak or it has at least one false premise. Strong Argument: given premises are true it is unlikely for conclusion to be false. Weak argument: argument is weak when assuming premises are true that it is likely the conclusion is false. Tautology: A statement that is necessarily true. “Ethan is tall or he is not tall”. Contingent Statement: statements that are either true or false, their truth tables have both true and false values. Non-contingent statement: statements thats truth values don’t depend on truth values of components. “Tautologies, self-contradictions”. Self-contradiction: a statement that is necessarily false. “2 is an even number and the number 2 is not an even number. Contradictory statements: statements that have opposing values on every line of their respective truth tables. Consistent Statements: statements that have at least one line on their truth tables where the main operators are true and match across. Inconsistent Statements: statements that don’t have even one matching true on their respective truth tables. Can have a matching false though. Square of opposition: Contradictories- differ in both quality and quantity that is A props are contradictory to O props as they are diagonal across the square “All A are B” and “Some A are not B” are contradictory just as E and I props are contradictory “All A are not B and some A are B” A,E,I,O props explained: A= All A are B, universal affirmative, E=No A are B, universal negative, I=Some A are B, Particular Affirmative, O=Some A are not B, Particular negative. Contraries: pairs of props that cannot both be true at the same time but can both be false “A and E props. Sub-contraries: cannot both be false at the same time but can both be true. I and O props. Subalternation: Essentially the relationship between a particular and universal A and I as well as E and O. the universal dominates the particular if it is true then the particular is true. If it is false however, the particular could be either true or false. On the other hand, if the Particular is True then the universal can be either true or false. If however the particular is false, the Universal must be false as well. Abduction: inferring explanations for certain facts. The car crashed so the driver must be bad. Inferences can be different however. The car crashed so the road was bad. Argument Identification: Arguments must have a conclusion and statements that support that specific conclusion there must also be some form of inferential claim. Given the premise the conclusion should follow. opinion does not support conclusion as it is not absolute meaning its truth value cannot be determined. It may be true for you but for someone else it is not. Conclusion Indicators: Precede the conclusion; therefore, thus, so, hence, consequently, in conclusion, it follows that, we can infer that, it proves that, suggests that, implies that, we can conclude that. Premise indicators: Because, since, Given that, assuming that, As shown by, for the reasons that, as indicated by, the fact that, it follows from. Translation into standard categorical form: when translating ordinary language into categorical propositions always make sure that the statement contains nouns that denote a class in both the subject and predicate. i.e. some political parties are disorganized groups is not a standard form cat. prop. when you switch it, there is no second group to denote a B. “some disorganized are political parties” instead give it a noun some disorganized groups are political parties, some political parties are disorganized groups. This functions as a some A are B (I prop). Also, sometimes when translating short or unclear sentences there is no linking verb (are, are not) that being said you must create specific groups as well as generate the verb that is implied (no pain, no gain) no exercises without physical pain are exercises that offer physical gain . More examples of translation: Leo was ill last night --- all persons identical to leo are persons who were ill last night. Whenever you are audited by the IRS you should get help----- all times you are audited by the IRS are times that you should get help. What goes around comes around---- all things that go around are things that come around. Standard form negations: when you hear statements such as all athletes are slow people, you can negate it by saying it is false that… or some other form of negation. basically, since it is the negation of an A, it gets translated as an O meaning some athletes are not people that are slow. Implied numbers in standard categorical props.: all, no, some. essentially you have to be able to determine the type, universal or particular, through what normal language implies: “we will not be able to finish all the costumes by 5---- some costumes made by us are not costumes that will be finished by five. Translating conditionals: Basically, conditionals are If, then statements. So normal if then statements get translated the same as any other statement would (If a salesperson calls then I just hang up---- all calls from sales people are calls where I hang up) If the word if appears later in the sentence: then we move the antecedent; the phrase that follows if, to the front where it belongs but keep the subject. (Pizza is a healthy meal if it has vegetable toppings------ all pizzas that have vegetable toppings are healthy meals) Transposition: during conditional translation: two step procedure that requires switching the antecedent and consequent and then negating both of them then translating. ex. (if your cup of coffee is not perfect then you are not drinking a cup of big bucks coffee----- if you are drinking a cup of big bucks coffee then your cup of coffee is perfect---- all cups of big bucks coffee are perfect cups of coffee) ex.2 (if murderers do not get punished then they do not change their behavior----transpo---if murderers change their behavior then they get punished-----all murderers who change their behavior are murderers who have been punished) Various Forms (modus ponens, modus tollens, etc.) Modus ponens- affirming the antecedent. A if B / A so B. Modus Tollens- Denying the consequent. A if B / not B so not A. Denying the Antecedent- A if B / Not A so not B (invalid). Affirming the Consequent- A if B / B so A. the main operator in these sequences must be the horseshoe. Hypothetical syllogism- A if B / B if C so A if C (When I type A if B what I really mean was If A then B.) Disjunctive syllogism- either A or B, Not A so B If a statement says a only if b, keep it in that order for evaluation. Types of fallacies for identification: Ad Hominem- against the person: essentially attacking the person to discredit their argument whether it be through stereotypes, character flaws, or circumstances. Tu Quoque: you too or look who’s talking. Attempts to invalidate the argument by painting the other person as a hypocrite. Appeal to the people/Ad Populum: meant to fuel emotions and substitute objective evidence for emotional response. Appeal to Pity: an emotional plea that relies on pity for support of the argument, supplies no objective evidence as to why a certain decision should be made. Appeal to force, ad baculum: an appeal to the stick, basically a threat either physical or non, in place for objective evidence supporting the conclusion. You better do this or this bad thing will happen rather than you better do this because if you don’t it will result in this statistic which will lead to this route which will be worse than the previous. Appeal to ignorance, ad ignorantiam: basically a claim that says must be false because never proven true, or must be true because never proven false. Usually a lack of something. Missing the point irrelevant proof: basically where the premises lead to an irrelevant conclusion (hey guess what I found out? The insurance will only be an additional 400 a year if we buy a second car. Lets go get one before the company changes the rate. Appeal to unqualified authority: essentially appealing to the expertise of someone unrelated to the field like a professional athlete. A-priori probability: fraction between 1 and 0, essentially the number of positive outcomes over the number of total outcomes possible.