Unit 4. Reason as a way of knowing

Unit 4 Reason as a way of knowing

Zendo The Master will present two Koans - one that follows the rule and one that does not. Teams will take turns presenting their own koans to the master to see if they follow the rule. With each new Koan, the presenting team with either say master or mondo If the team says master - the master will mark the koan with a white (follows the rule) or a black (does not follow the rule) stone. Play proceeds to the next team. If a team says mondo all teams must guess whether the new koan follows the rule by secretly revealing either their white (follows the rule) or black (does not follow the rule stones. Teams that are correct will receive guessing stones. Teams may turn in guessing stones on their turns to guess at the rule. Guesses should be clearly stated using the command terms presented on the next slide If the guess is incorrect, the master will present an example that follows the rule but violates the guess, or a counter example that follows the guess but violates the rule The winning team is the first to make a correct claim regarding the rule.

Zendo descriptors Color - yellow, blue, pink, black, green, red Number Size - small, medium, large Spacial relation - touching, not touching, nested, level in a nested stack Existence - is, is not Placement - flat, standing Grounded or not grounded At least or precisely

Rule 1

Rule 2

Rule 3

Rule 4

Rule 5

Journal Describe, in as much detail as you can, the process by which the correct rule was determined. What ways of knowing, that we have discussed did this activity demonstrate (explain)? What new way of knowing did this activity highlight? How does this new way of knowing differ from the WoKs we have discussed so far? What real-world activities does this game model? Explain at least one and describe what makes them similar.

Suspects Weapons Locations Mr. Alexandre The Beast Mrs. Sorgent A Graphing Calculator The IB office Room A211 Mr. Kalis A Tamale The Principal s Office Mrs. Wallace A Referral Mrs. McKay The Common App Mrs. Herman A knowledge question The Parking Lot Los Potros The Gym The Football Field The Biotech room

Journal Describe, in as much detail as you can, the process by which the correct answer was determined. In what essential ways was the process used to determine truth in the clue activity different from the process used in the Zendo activity? Which process was more reliable?

I. Reason Reason is a way of knowing that uses existing knowledge to generate new knowledge. The study of reason examines the rule, procedures and practices by that guide the creation of this new knowledge.

II. Basic terminology Arguments Premises and conclusions Induction v. deduction Fallacies

8. All diploma candidates have straight As. John is a diploma candidate. John has straight As. Deductive or inductive? Discuss each argument with your group and explain your rationale 1. All of the Giants are team players. Buster Posey is a Giant. Buster posey is a team player. 2. All stars contain plutonium. The sun is a star. The sun contains plutonium. 3. Use slide four of the unit presentation for this argument. The rule was not that there was a small pyramid, nor that there is a blue pyramid so therefore the rule is that there must be a green pyramid. 4. The last time the dragons attacked, the town was destroyed. If they return we will have to rebuild again. 5. The game of clue we played (answer carefully and explain your answer) 6. If the first student to enter room a211 is Mr. Banaag, it is Wednesday. Mr. Banaag was the first student to enter room a211. It is Wednesday. 7. Mr. Tsang eats apples and he is healthy. If I eat apples I will be healthy as well.

Deductive or inductive? Discuss each argument with your group and explain your rationale 1. All of the Giants are team players. Buster Posey is a Giant. Buster Posey is a team player. Deductive 2. All stars contain plutonium. The sun is a star. The sun contains plutonium. 3. Use slide four of the unit presentation for this argument. The rule was not that there was a small pyramid, nor that there is a blue pyramid so therefore the rule is that there must be a green pyramid. 4. The last time the dragons attacked, the town was destroyed. If they return we will have to rebuild again. Inductive Inductive Deductive Deductive 5. The game of clue we played (answer carefully and explain your answer) 6. If the first student to enter room a211 is Mr. Banaag, it is Wednesday. Mr. Banaag was the first student to enter room a211. It is Wednesday. Deductive 7. Mr. Tsang eats apples and he is healthy. If I eat apples I will be healthy as well. Inductive 8. All diploma candidates have straight As. John is a diploma candidate. John has straight As. Deductive

III. Induction A. Definitions Inductive reasoning uses observed experience to make judgments about the unobserved Inductive reasoning uses the past to predict the future Inductive reasoning assumes that nature/reality follows predictable patterns

III. Induction B. Significance Inductive reasoning is the most common form of reasoning we use List three examples of how you have reasoned inductively today Inductive reasoning is the basis for science Inductive reasoning works - it is pragmatic

III. Induction C. Three types of inductive arguments Induction by generalization or enumeration Induction by analogy Causal induction With a partner discuss and record in your journal one inductive argument in each category. The arguments can be informally written (ie - not standard form)

III. Induction C. Three basic types of inductive arguments 3 examples: Small pox Education Public health Induction by generalization or enumeration Induction by analogy Causal induction Which type of inductive argument is each of the above examples?

C. Assessing Inductive arguments Three general principles Does the argument start with justified premises? Does the argument include all relevant information? Is the argument valid? (does acceptance of the premises justify acceptance of the conclusion?)

Example 1 1.Carbon dioxide does not trap heat in the atmosphere 2.Global average temperatures have been shown to fluctuate widely over time Therefore: The current increase in global temperatures results from natural rather than manmade factors

Example 2 Global average temperatures have been shown to increase the frequency of unusual weather events and this means the current drought in California is caused by global warming.

Example 3 All of the students currently here care about their grades, therefore all Tracy High students care about their grades.

C. Assessing Inductive arguments Assessing enumerative arguments (3 questions) On how many cases is the conclusion based? Are the cases examined representative? Could other conclusions be drawn?

C. Assessing Inductive arguments Assessing analogical arguments How many times does the analogy apply? In what number of respects are the things involved analogous? What is the strength of the conclusion relative to the strength of the premises? How many dissimilarities are there between the two things being compared? Is the analogy relevant?

C. Assessing Inductive arguments Assessing Causal arguments Is the causal claim a good explanation for the observed correlation? (Is the correlation serial rather than causal) Is there any other reasonable explanation for the correlation?

Convert the ad to an argument in standard form. What type of argument is it? How strong is the argument? Explain.

Informal fallacies Fallacies are problems of reasoning. Informal fallacies fall into three general categories: Fallacies of pathos Fallacies of ethos Fallacies of logos (Materials on slides 29-39 were adapted from the Texas State philosophy department homepage - Accessed on 1.16.14 at http://www.txstate.edu/philosophy/resources/fallacy-definitions.html)

Ad Hominem (Attacking the person): This fallacy occurs when, instead of addressing someone's argument or position, you irrelevantly attack the person or some aspect of the person who is making the argument. The fallacious attack can also be direct to membership in a group or institution.

Appeal to ignorance This fallacy occurs when you argue that your conclusion must be true, because there is no evidence against it. This fallacy wrongly shifts the burden of proof away from the one making the claim.

Begging the question The fallacy of begging the question occurs when an argument's premises assume the truth of the conclusion, instead of supporting it. In other words, you assume without proof the stand/position, or a significant part of the stand, that is in question. Begging the question is also called arguing in a circle.

Confusion of Necessary with a Sufficient Condition A causal fallacy you commit this fallacy when you assume that a necessary condition of an event is sufficient for the event to occur. A necessary condition is a condition that must be present for an event to occur. A sufficient condition is a condition or set of conditions that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event. Only the sufficient grounds can do this. In other words, all of the necessary elements must be there.

Equivocation The fallacy of equivocation occurs when a key term or phrase in an argument is used in an ambiguous way, with one meaning in one portion of the argument and then another meaning in another portion of the argument.

False dilemma When you reason from an either-or position and you haven't considered all relevant possibilities you commit the fallacy of false dilemma.

Irrelevant Authority The fallacy of irrelevant authority is committed when you accept without proper support for his or her alleged authority, a person's claim or proposition as true. Alleged authorities should only be used when the authority is reporting on his or her field of expertise, the authority is reporting on facts about which there is some agreement in his or her field, and you have reason to believe he or she can be trusted. Alleged authorities can be individuals or groups. The attempt to appeal to the majority or the masses is a form of irrelevant authority. The attempt to appeal to an elite or select group is a form of irrelevant authority.

Red Herring This fallacy consists in diverting attention from the real issue by focusing instead on an issue having only a surface relevance to the first.

Slippery Slope In a slippery slope argument, a course of action is rejected because, with little or no evidence, one insists that it will lead to a chain reaction resulting in an undesirable end or ends. The slippery slope involves an acceptance of a succession of events without direct evidence that this course of events will happen.

Straw man This fallacy occurs when, in attempting to refute another person's argument, you address only a weak or distorted version of it. Straw person is the misrepresentation of an opponent's position or a competitor's product to tout one's own argument or product as superior. This fallacy occurs when the weakest version of an argument is attacked while stronger ones are ignored.

Two wrongs If you try to justify an act/belief by pointing out in others a similar act/belief, you are committing the fallacy of "two wrongs make a right." This fallacy can occur by suggesting "if others are doing it, I can too" (common practice). Another form of the fallacy occurs when you dismiss a criticism of your action/belief, because your critic is acting/ believing in a similar way (you do it, too).

Induction Project Induction is everywhere in the media. In this assignment you will identify, analyze and critique an argument found in an advertisement or a political cartoon. 1.Find an advertisement or a political cartoon containing an inductive argument. Reproduce that argument so that is is approximately 8.5x 11 (so that it can be mounted on a single sheet of binder paper). On a separate piece of paper which you will attach below the advertisement complete the following (please word process Times 12 point font): 2.Identify the argument contained in the piece and put that argument into standard form. Your argument should have at least two premises and a conclusion. 3.Identify whether the argument is enumerative, causal or analogical. 4.Assess the argument based on the tools for assessing analogical arguments discussed in class. This should be done in 50 to 100 words. 5.Identify and explain how the advertisement demonstrates at least one of the informal fallacies. You may use both those discussed in class and those on the IEP website. This section should also be 50-100 words

IV. Deduction A. Definitions Deduction - Truth preserving! Truth - What is the case Validity - Whether a conclusion follows from its premises Syllogism - A deductive argument with exactly two premises and a conclusion which uses categorical propositions to express relationships between three terms Critical Note: Truth and validity are independent! True premises may lead to an invalid conclusion and false premises may lead to a valid conclusion!

Anatomy of a syllogism The term which doesn t appear in the conclusion is the middle term All violists are clever All virtuosos are a violists Therefore: virtuosos are clever The subject of the conclusion is the minor term The predicate nominative of the conclusion is the major term

Categorical propositions are assertions about classes of objects which affirm or deny that one class is included in another either in whole or in part. Anatomy of a syllogism All violists are clever All virtuosos are a violists Therefore: virtuosos are clever It is because syllogisms always contain categorical propositions that they are often called categorical syllogisms

4 types of categorical propositions Universal affirmative - A propositions All caudillos are tyrants Universal negative - E propositions No caudillos are democrats AffIrmo nego Particular affirmative - I propositions Some caudillos are good for their country Particular negative - O propositions Some caudillos are not Mexican

Using the definitions just provided, write three valid arguments that meet the following conditions: Two true premises and a true conclusion Two true premises and a false conclusion One true and one false premise and a true conclusion

B. Assessing the validity of categorical syllogisms

Assessing syllogisms diagrams using Venn diagrams First Draw a triple Venn diagram, numbering the quadrants as shown. Second - Label the circles of a three circle Venn diagram with the syllogism s three terms. It is customary to label the top left circle as the minor term (s), the top right circle as the major term (p) and the bottom circle as the middle term (m). Third Diagram any universal premises by shading the areas excluded by those premises. Remember, the shaded areas are those excluded by the premise. Fourth Diagram any particular premises by placing an x either Completely within a circle if it is clear from the premises that the particular term is wholly included in the circle Or On a line if the premises do not determine on which side of the line it should go Finally Inspect the diagram to see if the diagram of the premises is consistent with the conclusion. 1 Uruks 4 All Orcs are evil All Uruks are Orcs Therefore: All Uruks are evil 2 5 7 Orcs Evil 3 6

Assessing the validity of syllogisms using Venn diagrams Uruks Evil 1 2 3 No No 4 No 5 Valid 6 All Orcs are evil All Uruks are Orcs Therefore: All Uruks are evil No 7 Orcs

Assessing the validity of syllogisms using Venn diagrams Apples Bland 1 2 Invalid 5 Some 3 4 No 6 All crunchy things are apples Some bland things are crunchy things Therefore: All apples are bland things No 7 Crunchy

All syllogisms can be expressed symbolically, since each of the terms simply represents a variable A C 1 2 Invalid 5 Some 3 4 No 6 All B are A Some C are B Therefore: All A are C No 7 B

Nonsense words are fun, too Bingles Woot-Woots 1 2 Invalid 5 Some 3 4 No 6 All Bangles are Bingles Some Woot-Woots are Bangles Therefore: All Bingles are Woot-Woots No 7 Bangles

An on-line venn diagram tool can be found at: http://www.poweroflogic.com/cgi/venn/ venn.cgi?exercise=6.3a http://www.poweroflogic.com/cgi/venn/ venn.cgi

Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition (AffIrmo, nego) Thus All A are B No B are C Therefore: All C are A Would be in the Mood AEA

Mood and figure The figure of a categorical syllogism has to do with the position of the middle term We can draw lines through the middle terms in each of these four diagrams to create a collar-like shape, like this: Accessed on 2.6.14 at http://rintintin.colorado.edu/~vancecd/phil1440/syllogisms.pdf)

Aristotle, you re the man, but don t fool with Boole!

Aristotle, you re the man, but don t fool with Boole! All A are B No B are C Therefore: Invalid! All C are A Mood = AEA Figure = 4

Ooh! Ooh! It s invalid when we do then Venn too! C A 1 2 3 4 No No 5 Invalid No 6 No All A are B No B are C Therefore: All C are A 7 B

Other means of assessing categorical syllogisms Formal fallacies - No syllogism that commits one of the following formal fallacies is valid Fallacy of the undistributed middles - Any syllogism in which the middle term is undistributed (to be distributed means all members of a term s class are affected by the proposition*) is invalid. Fallacy of Illicit Major/Illicit Minor - If a term is distributed in the conclusion, it must be distributed in one of the premises or the argument is invalid. Fallacy of Exclusive premises - Any categorical syllogism with two negative premises is invalid Fallacy of Affirmative Conclusion/Negative Premise and Negative Conclusion/ Affirmative Premise - If an argument has a negative conclusion, one of the premises must be negative; if one of the premises is negative, the conclusion must be negative. Existential fallacy - If both of the premises are universal, the conclusion cannot be particular (Boole only) *A term is said to be distributed if it is either the subject of a universal or the predicate of a negative.

An now we can name the reason why this argument is invalid C A 1 2 3 No No All A are B No B are C Therefore: All C are A 4 5 No No Fallacy of Affirmative Conclusion/NegativePremise 7 6 B

No Mr. Haydock, not another way to test validity! But wait, this one s so much fun... Remember that the conclusion of a valid syllogism must be true if the premises are true. So... If we take any syllogism and substitute premises which we know to be true (taking care to make sure the form is the same), if the the conclusion is true, the syllogism is valid. This is called assessing by substitution/counter example.

Let s try it! All A are B No B are C Therefore: All C are A All ferns are plants No plants are dogs Therefore: All dogs are ferns All Giggles are Googles All Sniglets are Giggles Therefore: All Sniglets are Googles All sharks are fish All Great Whites are sharks Therefore: All Great Whites are fish

Two other types of syllogism Disjunctive syllogisms Hypothetical syllogisms

Disjunctive syllogisms A disjunction is a statement that claims that at least one of two possibilities is true. For example: Either A or B Not A Therefore B

Inclusive or exclusive In common usage or is used exclusively: Entrees come with fries or coleslaw means you can get fries of coleslaw, but not both. But in logic (and computer science) or is generally inclusive, meaning that at least one of a series must be true (but both could be).

Disjunctive syllogisms Assuming the inclusive or, determine whether the following are valid or invalid. Be prepared to explain why you believe each statement is valid or invalid. Remember, validity means the conclusion must follow Either A or B A Invalid Therefore B Either not A or B A Valid Therefore B Either A or not both B and C A Therefore both B and C Invalid Either Fido ran away or he was hit by a car Fido ran away Therefore: Fido did not get hit by a car Invalid

Hypothetical syllogisms Hypothetical syllogisms are two premise deductive arguments in which (at least) one premise is a conditional (if) statement. There are two types of hypothetical syllogisms: Pure hypotheticals Mixed hypotheticals

Pure hypothetical syllogisms In a pure hypothetical syllogism, both premises are hypothetical statements If Gandalf fails then Godor Falls If Godor falls then the Shadow will triumph Therefore: If Gandalf fails then the Shadow will triumph Symbolically If p then q if q then r Therefore: If p then r The other valid form: If Mary comes to the party then Dale will not come If Dale does not come, then Ernie will not come Symbolically If p then not r If not r, then not q Therefore: If p then not q Therefore: If Mary comes to the party then Ernie will not come

Mixed hypothetical syllogisms In a mixed hypothetical syllogism, there is a conditional premise followed by a premise which registers agreement or disagreement with either the antecedent or the consequent of the conditional. The antecedent is the if part of the statement, while the consequent is the then part of the statement. There are two valid and two invalid forms of mixed hypothetical syllogism:

Valid mixed hypothetical syllogisms Modus Tolens (DC) If we are the only life in the universe, then the universe sucks The universe does not suck Therefore: We are not the only life in the universe Symbolically If p then q not q Therefore: not p Modus Ponens (AA) If Legolas is an elf, then he is immortal Legolas is an elf Therefore: Legolas is immortal Symbolically If p then q p Therefore: q

Are the following valid or invalid? Why? Identify what type of argument is being made (PH/MH) and why the argument is valid. 1. If Andy is here then I am not late Andy is here Therefore: I am not late Valid - AA 3. If I am lying then Kant is right Kant is right Therefore: I am not not Lying Invalid - AC 5. If A then B If B the C Therefore: If A then C Valid HS 2. If Andy is here then I am not late If I am not late then I will pass Therefore: If Andy is not here then I will not pass Invalid HS 4. If A then B Not B Therefore: Not A Valid - DC 6. If there are monkeys then there will be trees There are no monkeys Therefore: There are no trees nvalid - DA

Logic and computer science Logic is an essential component of how computers work We will be doing a small project to demonstrate the connection between computers and logic from codeacademy.org

JavaScript basics for our project Declare a variable: var dogs Assign a value to a variable var dogs = 1.5 var dogs = rock var dogs = prompt( What is your favorite animal? ) Key concept - variables can change their value! in JS = is used to assign variables, mathematical equivalency is indicated by ===

JavaScript basics for our project If statement syntax if(some condition) {some action;} else {some action;} if/else if/else syntax if(some condition) {some action;} else if (some condition) {some action;} else {some action;} Key concept - syntax matters!

JavaScript basics for our project console.log - prints something to the console console.log( some string ); return - returns a value and stops a function return you are right!

Functions Functions are special variables that, when called, carry out a specific task. Function syntax var functionname=function(argument1, argument2) {instructions to be carried out be the function} The function we will write will contain some if/else statements which will return various strings. Calling a function - Functions do nothing until called. When a function is called, it will carry out its assigned task. Syntax for calling a function: functionname(argument1, argument2) The arguments in our case will be variables that we have previously defined and assigned values to.

Logic Unit Quiz On Monday we will have a culminating quiz on the logic unit. The quiz will count for 100 points in the minor assignments category. The quiz will be open notes You will be asked to do the following on the quiz: 1.Explain the difference between inductive and deductive reason. 2.Examine three inductive arguments and identify the informal fallacy that they commit (I will be fairly obvious here). 3.Assess whether or not two arguments are valid categorical syllogisms using the venn diagram method and one other method (not substitution). 4.Identify whether three arguments are hypothetical or disjunctive syllogisms and assess the validity of each. 5.Briefly explain (one paragraph) why logic and coding are similar.

1 2 3 Arguments 5 1. 4 6 2. 7 Therefore: 1 2 3 Arguments 5 1. 4 6 2. 7 Therefore: