Unit 4. Reason as a way of knowing. Tuesday, March 4, 14


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1 Unit 4 Reason as a way of knowing
2 I. Reasoning At its core, reasoning is using what is known as building blocks to create new knowledge I use the words logic and reasoning interchangeably. Technically, logic is reasoning conducted according to formal rules.
3 II. Basic terminology Arguments Premises and conclusions Inductive v. deductive Fallacies
4 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
5 IV. Deduction A. Definitions
6 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
7 III. Induction C. Three basic types 3 examples: Small pox Politics Education Public health of inductive arguments Induction by generalization or enumeration Induction by analogy Causal induction Which type of inductive argument is each of the above examples?
8 Assignment Read and annotate the two short articles Rewrite each article as a standard form argument with 24 premises and 1 conclusion Review the paper assignment. How might these articles be relevant to the paper assignment?
9 III. Induction C. Three basic types 3 examples: Small pox Politics Education Public health of inductive arguments Induction by generalization or enumeration Induction by analogy Causal induction Which type of inductive argument is each of the above examples?
10 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?)
11 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 is the results from natural rather than manmade factors
12 Example 2 1. Global warming causes unusual weather events 2. This week s deep freeze in the central and eastern parts of the country was an unusual weather event Therefore: This week s deep freeze was caused by global warming
13 Example 3 1. Global warming leads to temperature increases 2. This week s deep freeze in the central and eastern parts of the country saw temperatures plummet Therefore: Global warming is not true
14 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?
15 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?
16 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?
17 Informal fallacies This section of the presentation is drawn from materials on the website of the Texas State University Department of Philosophy website. (Accessed on at
18 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.
19 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.
20 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.
21 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.
22 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.
23 False dilemma When you reason from an eitheror position and you haven't considered all relevant possibilities you commit the fallacy of false dilemma.
24 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.
25 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.
26 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.
27 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.
28 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).
29 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!
30 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
31 Anatomy of a syllogism 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. 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
32 4 types of categorical propositions Universal affirmative  A propositions All violinists are talented Universal negative  E propositions No violinists are mean AffIrmo nego Particular affirmative  I propositions Some violinists are lefthanded Particular negative  O propositions Some violinists are not Democrats
33 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
34 B. Assessing the validity of categorical syllogisms
35 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, the top right circle as the major term and the bottom circle as the middle term. 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 All violists are clever All virtuosos are violists Therefore: All virtuosos are clever Virtuosos Violists Clever 3 6
36 Assessing the validity of syllogisms using Venn diagrams Virtuosos Clever No No 4 No 5 Valid 6 All violists are clever All virtuosos are violists Therefore: All virtuosos are clever No 7 Violists
37 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
38 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
39 Nonsense words are fun, too Bingles WootWoots 1 2 Invalid 5 Some 3 4 No 6 All Bangles are Bingles Some WootWoots are Bangles Therefore: All Bingles are WootWoots No 7 Bangles
40 An online venn diagram tool can be found at: venn.cgi?exercise=6.3a venn.cgi
41 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
42 Other means of assessing categorical syllogisms 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 collarlike shape, like this: Accessed on at
43 Aristotle, you re the man, but don t fool with Boole!
44 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
45 Ooh! Ooh! It s invalid when we do then Venn too! C A No No 5 Invalid No 6 No All A are B No B are C Therefore: All C are A 7 B
46 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.
47 An now we can name the reason why this argument is invalid C A 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
48 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.
49 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
50 Two other types of syllogism Disjunctive syllogisms Hypothetical syllogisms
51 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
52 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).
53 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
54 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
55 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
56 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 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:
57 Valid mixed hypothetical syllogisms 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 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
58 Are the following valid or invalid? Why? 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 Invalid  DA
59 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
60 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 ===
61 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!
62 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!
63 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.
64 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 fallacies 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.
65 1 2 3 Arguments Therefore: Arguments Therefore:
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