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Philosophy 1200: Critical Thinking- Term 2.docx

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Western University
Philosophy 1200
Eric Desjardins

Deductive Reasoning, Modern Symbolic Logic & Truth Tables 9/13/2013 5:44:00 PM Lecture 1: DEDUCTIVE ARGUMENTS  linguistic or logical object  logical implication  allows you to be lazy Soundness  two parts: premises must be true and it must be valid (logical strength) Validity  depends on form not content  context disappears from the argument  applies only to deductive arguments Valid Argument Forms Modus ponens  if p, then q  p  therefore q Modus tollens  if p then q  not q  therefore not p Simplification  p and q  therefore p Conjunction  p  q  therefore p and q Addition  p  therefore p or q Hypothetical syllogism  if p then q  if q then r  therefore if p then r Disjunctive syllogism  p or q  not p  therefore q Constructive Dilemma  p or q  if p then r  if q then s  therefore r or s Destructive Dilemma  if p then r  if q then s  not r or not s  therefore not p or not q Categorical (universal)  all p are q  all q are r  therefore all p are r Categorical (existential)  all p are q  some q are r  therefore some p are r DETERMINING VALID FORM  even if an argument has instances where both the conclusion and premises are true, it does not necessarily mean the argument is valid or sound Method of Counterexample Example: If coal is black (p), then snow is white (q) Snow is white (q) Therefore, coal is black (p) 1. Find the form of the argument  if p then q  q  therefore p 2. Find a counterexample to that form  If the prof is a monkey (p), then the prof is a mammal (q).  The prof is a mammal (q)  Therefore, the prof is a monkey (p) Example: Is this argument sound? P1: Ice is slippery. P2: Species evolve. P3: I wear grey socks P4: Pluto is not a planet C: Human is lonely in this universe.  no, it isn’t. Lecture 2: Either we take job actions or we go to work. If the government passes Bill 115, which is an unconstitutional and short-sighted legislation, then our fundamental right to manifest against social injustices will be violated. If our right to manifest is baffled, then we will not go to work. Last week, the provincial government decided to pass this unconstitutional bill. Simple Statements A: We take job actions. W: We go to work. B: Government passes Bill 115. V: The right to manifest is violated. Deductive Reasoning 1. A or W 2. If B then V 3. If V then ~W 4. B 5. V (modus ponens 2, 4) 6. ~W (modus ponens 3,5) C: A (disjunctive syllogism 1, 6) Either teachers will go to work on Friday, or they will protest against new contract conditions. Protesting on Friday would be equivalent of going on strike, which would be illegal. I know that teachers are law abiding. So they will go to work on Friday. Simple Statements S: Teachers will strike. W: Teachers will work. P: Teachers will protest. L: Teachers will perform legal acts. Deductive Reasoning 1. W or P 2. If P then S 3. If S then ~L 4. ~~L 5. ~S (modus tollens 3, 4) 6. ~P (modus tollens 2,5) C: W (disjunctive syllogism 1, 6) TRUTH TABLE METHOD  a way of testing for validity of argument form by setting all the possible instances of the form  ie. all the possible combination of truth values for the simple component sentences  form of algebraic propositional calculus Simple vs. Compound Sentences  declarative sentences are compound if it contains another complete declarative sentence as component  eg. John eats fudge and flowers.  negations are always compounds  eg. Governments don’t like strikes.  declarative sentences are simple if it is not a component  eg. Sam runs every weekend. Sentential Operators  operators are words connecting simple sentences into more complex sentences  sentential operation: an expression containing blank(s) such that when the blanks are filled with complete sentences, the result is a sentence Examples of Sequential Operators  either/or  If/then  and  unless  if and only if  it is not the case that  after/before  because  it is possible that  it is necessary that  I believe that Truth Functional Operators  truth value of the compound sentence depends only on the truth value of the simple sentences that are combined with the operator Examples:  conjunction: ___ and ___ ( ___ & ___)  disjunction _or_ (_v_)  conditional: if _ then _ ( rotated left U; =>)  equivalence: _ if and only if _ (triple line; <=>)  negation: not (~) Lecture 3: TRUTH VALUE  a bivalent (two-value) system of logic: we assume that each sentence must be either true or false  negation (~): invert truth value  ~ P F T T F  and (&): conjunction is truth if and only if both conjuncts are true  P & Q T T T F F T T F F F F F  or (v): disjunction is true if at least one disjunct is true  P v Q T T T F T T T T F F F F  biconditional (<=>): true when both sentences are equivalent (ie. same truth value)  P <=> Q T T T F F T T F F F T F  same as exclusive or  conditional (=>): if the antecedent (ie. P => Q) is true and its consequent (ie. P => Q) is false, then the conditional is always false  If it rains => I stay in bed T F F  if the antecedent is false, then the conditional is always true  If jeans could talk => they would lie F T T/F  truth functional  Recognizing Conditional Statements, Antecedents and Consequents  If France gets involved in Mali, then many people will die.  p => q  Innocent prisoners might be saved if France gets involved in Mali.  p => q  France gets involved in conflicts only if its people are suffering from injustice.  p => q  Mali will be attacked by France unless it releases all innocent prisoners.  A if not R o ~p => q o equivalent to p v q  French soldiers will depart for Mali provided that Holland gives them the order.  D if O o p => q Examples: Assume that A, B and C are true, whereas X and Y are false. 1. ~A v ~B (disjunction)  F 2. (A & X) v (B & Y) (disjunction)  F 3. ~(A v B) => (X v Y) (conditional)  T 4. (~A => B) <=> (A v B) (biconditional)  T 5. ~ (((X => A) v (Y => B)) => ((X & Y) => (A v C))) (negative)  F Lecture 4: TRUTH TABLE METHOD  symbolize argument and replace capital letters for variables 1. line up argument premises and conclusion 2. construct base columns  on the left, create a column for each variable  calculate number of rows needed using following formula: 2^N, where N stands for the number of variables (if N=3, then table will contain 8 rows)  enter truth values under each variable, making sure you have all possible combinations accounted for st i. 1 variable: half true, half false, ie. TTTTFFFF ii. 2d variable: half the first true, half the first false— alternating, ie. TTFFTTFF iii. 3d variable: half the second true, half the second false— alternating, ie. TFTFTFTF 3. compute the truth value of all premises and conclusion rules for truth- functional operators 4. look for a row where premises are T but conclusion is F  if such instance exists, argument form is invalid  if such instance does not exist, argument form is valid  shortcut: only compute lines where the conclusion is false, or where conjunctions are true  partial truth table Lecture 5: PARTIAL TRUTH TABLE 1. place premises and conclusion 2. construct base columns (variables and possible combinations on left) 3. compute truth values of conclusion, ignoring cases where it is obviously true 4. compute truth value of premises only where conclusion is false and premises could be true Short Method  systematic search for counterexamples without drawing base columns 1. layout premises and conclusion 2. assign values to variables and try to construct a counterexample  typically easier to start with conclusion  short method is hard to prove validity  must exhaust all instances where the conclusion is false Inductive Reasoning 9/13/2013 5:44:00 PM Lecture 6: Deductive vs. Inductive Strength  D: validity  I: C is more or less probable  D: only form matters  I: content and context are crucial Knowledge  D: nothing new is added in C  I: creates knowledge (more in C than what is contained in Ps) P-C Relation  D: implication (sufficiency)  I: support (P not sufficient to infer C; counterexamples are always an issue) Four Types of Induction 1. Generalization: particular  general  form:  z percent of observed fs are g  it is therefore probable that z percent of all fs are g  problems:  sample is not always representative of population, ie. when certain groups are over or underrepresented in the sample o avoid this by using Simple Random Sample: each member of population has equal chance of being selected o pollsters often use stratified sample: divide population into groups, then sample randomly within these groups  sampling biases: non-response bias, self-selection bias  must have large enough sample 2. Statistical Syllogism: general  particular  form:  z percent of fs are g  x is an f  therefore, it is probable to degree 0.z that x is g  problems:  ensure no relevant information has been overlooked about x 3. Induction by Confirmation  form:  if h, then o  o  therefore h is probable  commonly used in sciences, diagnostics, criminal trials  can alter hypothesis if negative results occur  problems:  must gather a large number of incidences to prove hypothesis true  must look at disconfirming incidences 4. Analogical Reasoning: generalize from model  target  analogical model  x has A, B, C  y has A, B  It is probable that y has C.  relational analogical model:  x is to y as a is to b  x is R to y  It is probable that a is R to b  causal analogical model:  common properties {a, b, c, d, e} must be causal properties  property f to be projected from model to system modeled should stand in a causal relationship to the properties {a, b, c, d, e} in the model  there should be no relevant causal disanalogies between the model and the target 9/13/2013 5:44:00 PM Assignment #5  read chapters 16 & 17 of Hughes and Lavery  750-1000 words  topic: Atheism and evolution vs. creationism and intelligent design  discussed in Dennett’s paper, ―Atheism and Evolution.‖  make reference to Dennett’s paper and paper you read in producing the annotated bibliography in Applied Assignment #4  both papers listed in bibliography  may include others but not necessary  must begin with standard form representation of argument followed by diagram of argument, with a max of 15 premises (not part of word count)  include at least one deductive inference and one inductive inference  indicate in diagram  DUE MARCH 6  tips on page 294-295  know your audience  aim for clarity, simplicity, coherence  brief and specific  examples and quotations  avoid padding  respect style of argumentative essay Macro-structure of Argumentative Essays Introduction 1. announce subject 2. establish context and specify issues 3. announce views of others 4. state your position/contribution, ie. thesis you will defend Body 1. reasons & arguments 2. rebut plausible objection(s) Conclusion 1. brief summary of main arguments and rebuttals  emphasize how they support thesis 2. restate thesis Scientific Reasoning 9/13/2013 5:44:00 PM Lecture 8:  inductive CAUSATION  causes are necessary and sufficient conditions  event C causes event E iff C is a necessary and sufficient condition for the occurrence of E o supports counterfactual statements Mills’ Methods 1. Agreement 2. Difference 3. Agreement and Difference 4. Concomitant Variants 5. Residue Agreement  when several instances of the same phenomenon are observed, all of them are expected to be the result of the same cause o if the same antecedent circumstances in all these instances are also observed, then we reason to believe that this may be the cause we are seeking  Inference form:  P occurs in 1 when x, y, z  P occurs in 2 when x, z  P occurs in n when x, …, …  It is likely that x is the cause of P Difference  when all antecedent circumstances in two instances are the same except one and a specific phenomenon is observed in one instance but not the other  single difference in the circumstances is significant  form:  P is observed in 1 in circumstances a, b, c, d  P is not observed in 2 in circumstances b, c, d  It is likely that a is the cause of P A variation: controlled experiments  instances can be groups  control group: part of population where experimental is absent or present  subject group: part of population where experimental is present or absent  if P is observed in SG but not CG, then experimental variable is the cause of P Concomitant Variations  when variations in two phenomena coincide with each other, there is reason to believe they are causally related  form: o P1 occurs with P2 in 1 o P1+ occurs with P2+ in 2 o P1- occurs with P2- in 3 o It is likely that P2 causes
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