WoK 3 Reason
What is reason? Webster s Dictionary defines reason as: The power of the mind to think, understand, and form judgments by a process of logic and logic as: reasoning conducted or assessed according to strict principles of validity More informally: Reason is a way of knowing that uses existing knowledge (from our senses, language emotion etc.) to generate new knowledge. The study of logic examines the rules, procedures and practices by that guide the creation of this new knowledge.
Reason is the opposite of subjectivism Subjectivism is the idea that all truth is determined at the level of the individual. If this is true, what ultimately determines shared knowledge? The power to impose one s subjective truth on the group. Reason provides the rules by which we negotiate rather than impose a shared truth. The practical application of this form of reason is the scientific method.
Astrophysicist Adam Frank on the relationship of reason, science and politics When the methods of science are pursued as intended, what is returned is public knowledge. This knowledge, composed of facts and an understanding of their limits, are critical for a functioning democracy. The founders of the American experiment in selfgovernment understood the urgency of public knowledge. It's why they held science in such high regard. It was, for them, the principle means of establishing the background needed for our public life, a background composed of a shared reality. If the point of science is to provide us with a method for establishing public knowledge, then its rejection is also the rejection that such public knowledge is possible. If we hold science in esteem because it represents a best practice for establishing shared facts that hold regardless of ethic, religious or political background, then denying science means denying the possibility of such facts. It implies there can be no means for establishing facts about the world and no reason to award authority to mechanisms that deliver those facts. Without doubt, politics will always be about more than facts. The advocacy for different policy choices can have as much resonance with personal values as it can with numbers established through science or other mechanisms. There can and should be vigorous debate about how our values shape public policy from immigration to economics....but that debate has to be couched within a landscape whose contours are shared as public knowledge. (Accessed on 1.6.16 at http://www.npr.org/sections/13.7/2016/04/12/473850478/politics-and-thefracturing-of-shared-reality? utm_campaign=storyshare&utm_source=twitter.com&utm_medium=social)
The language of reason Arguments Premises and conclusions An argument in logic is a formal construction by which one proposition is held to follow from a group of other propositions All arguments are composed of two essential elements: premises and conclusions Premises: the reasons offered for the acceptance of a conclusion Conclusion: the claim made by an argument In our discussion of logic we will often utilize logical forms by which two premises make the case for a conclusion: Examples: 1. All democrats believe in Santa Claus Mr. Haydock is a democrat Therefore Mr. Haydock believes in Santa Claus 2. 3. All A are B All B are C Therefore: All A are C 2+2 = 4
The language of reason Induction v. deduction Fallacies A deductive argument is one where, if the premises are true, and the argument is properly constructed, the conclusion must be true. All reptiles are cold blooded Snakes are reptiles Therefore snakes are cold blooded The conclusion here that snakes are cold blooded is inescapable if the premises above are true An inductive argument is one where, if the premises are true, the conclusion is likely to be true. The sun has come up every Saturday since I have been alive Tomorrow is Saturday Therefore: The sun will come up tomorrow The conclusion that the sun will come up tomorrow is based on experience. Experience is predictive but not certain. Fallacies are flaws in reasoning that result from the violation of either formal or informal rules of logic An example from math 2(9-2) = 16 This violates the rules for order of operation and thus the argument is invalid
The difference between induction and deduction An inductive argument is an argument that is intended by the arguer merely to establish or increase the probability of its conclusion. In an inductive argument, the premises are intended only to be so strong that, if they were true, then it would be unlikely that the conclusion is false. There is no standard term for a successful inductive argument. But its success or strength is a matter of degree, unlike with deductive arguments. A deductive argument is valid or else invalid. The difference between the two kinds of arguments does not lie solely in the words used; it comes from the relationship the author or expositor of the argument takes there to be between the premises and the conclusion. If the author of the argument believes that the truth of the premises definitely establishes the truth of the conclusion (due to definition, logical entailment, logical structure, or mathematical necessity), then the argument is deductive. If the author of the argument does not think that the truth of the premises definitely establishes the truth of the conclusion, but nonetheless believes that their truth provides good reason to believe the conclusion true, then the argument is inductive. (accessed on 1.24.16 at http://www.iep.utm.edu/ded-ind/) Inductive arguments are either strong or weak. Deductive arguments are valid or invalid
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.Most Democrats support gun control. Bernie Sanders is a Democrat. Bernie Sanders supports gun control. 4.The last time the dragons attacked, the town was destroyed. If they return we will have to rebuild again. 5.What goes up must come down. 6.If the first student to enter room D210 is Ms. Frankel, it is Wednesday. Ms. Frankel was the first student to enter room D210. It is Wednesday. 7.Mr. Malogan eats apples and he is healthy. If I eat apples I will be healthy as well. 8.All diploma candidates have straight As. John is a diploma candidate. John has straight As.
Inductive Reasoning Definitions Ampliative Observed to unobserved Predictive Deductive reasoning is truth preserving but non ampliative. Inductive reason is not truth preserving but ampliative - which means that the conclusion provides information not contained within the premises. 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 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
Significance Inductive reasoning is the most common form of reasoning we use List three examples of how you have reasoned inductively today Basis for science Inductive reasoning pragmatic
Types of Induction - Generalization/ enumeration Form 1. Most of a sample of X is Y. 2. Therefore, probably, all Xs are Ys. Example 1. Almost all the sixth-graders we interviewed love Harry Potter. 2. Therefore, Harry Potter probably appeals to most sixth-graders. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 4908-4909). Bloomsbury Publishing. Kindle Edition. An inductive generalization is an inference from a sample of some population or a set of past events to every member of that population or future events. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 4900-4902). Bloomsbury Publishing. Kindle Edition.
Form Types of Induction - Analogy 1. Object A has features v, w, x, y, and z. 2. Object B has features v, w, x, and y. 3. 3. Therefore, object B probably also has feature z. Example Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 5229-5231). Bloomsbury Publishing. Kindle Edition.. 1. My old Ford had a 4.6 liter, V8 engine, four-wheel drive, a towing package, and ran well for many years. 2. This new Ford has a 4.6 liter, V8 engine, four-wheel drive, and a towing package. 3. Hence, it will probably also run well for many years. 4. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 5241-5244). Bloomsbury Publishing. Kindle Edition. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 4908-4909). Bloomsbury Publishing. Kindle Edition. In an argument from analogy, a comparison is made between two states of affairs (usually an object or event), one of which is better understood than the other. Then, on the basis of their similarities and differences, new information is inferred about the lesser known object. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 5209-5211). Bloomsbury Publishing. Kindle Edition.
Types of Induction - Causal Form 1. A repeatedly follows B 2. Therefore, B probably causes A.. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 5229-5231). Bloomsbury Publishing. Kindle Edition. Example 1. When offer my dog food, she will sit 2. My dog will not sit when I do not offer her food 3. Therefore: Offering my dog food causes her to sit 4. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 5241-5244). Bloomsbury Publishing. Kindle Edition. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 4908-4909). Bloomsbury Publishing. Kindle Edition. A causal argument is an inductive argument whose premises are intended to support a causal claim. A causal claim is a claim that expresses a causal relationship between two events. Arp, Robert; Watson, Jamie Carlin (2015-10-22). Critical Thinking: An Introduction to Reasoning Well (Kindle Locations 5335-5336). Bloomsbury Publishing. Kindle Edition.
For Friday... Read the articles provided. Based on each article, write a standard form inductive argument. Determine what type of inductive argument each article represents and explain why you categorized it as you did.
Assessing the strength of enumerative inductions 1. Is the sample random/ unbiased? Random samples drawn information from all parts of the population. Factors that play a role in whether a sample is random: Geography Sex Ethnicity Method of survey Religion Be careful of hidden biases!
Assessing the strength of enumerative inductions 2.Is the sample proportionate? 3.Is the instrument valid and reliable? In 2014 a poll that asked whether people supported Obamacare the result was 51 to 43 Opposed However the same poll found 75% support for children being able to stay on their parents insurance until 26 and 66% support for the ban on denying coverage to those with pre-existing conditions (Accessed on 1.13.17 at http://politicalticker.blogs.cnn.com/2014/03/31/five-things-polling-tells-us-about-obamacare/ Accessed on 1.13.17 at http://politicalticker.blogs.cnn.com/2013/09/27/poll-obamacare-vs-affordable-care-act/comment-page-1/ Is the sample proportionate This means is the sample large enough to support a conclusion about the larger population. Is the Instrument valid and reliable? A valid instrument is one that measures what it claims to measure Obamacare examples Abortion - Do you support killing Babies v. do you approve of a women s right to control her body Avoiding confirmation bias
Assessing the strength of arguments by analogy 1.Are their more dissimilarities than similarities? 2.Are the similarities relevant to the conclusion of the argument Earth has Nitrogen in its atmosphere Earth contains life Titan has in nitrogen in its atmosphere Therefore: Titan contains life The argument for life is stronger given the more qualities it shares with earth (oxygen, liquid water, in the habitable range from its star etc.) In Titan s case, the three characteristics listed above are all differences. Atmospheric Nitrogen is also not relevant to the existence of life, whereas the other characteristics are. This is how NASA finds planets that are good candidates to have life. http://planetquest.jpl.nasa.gov
Assessing the strength of arguments by analogy 3.Is the strength of the conclusion consistent with the strength of the premises? Earth is in the habitable zone, Earth has liquid water, Earth has oxygen in its atmosphere and Earth has life Gliese 581 g is in the habitable zone, Gliese 581 g has liquid water, Gliese 581 g has oxygen in its atmosphere Therefore: Gliese 581 g is home to an advanced civilization The conclusion makes a far more specific claim than is supported in the premises
Assessing the strength of causal arguments 1.Is the observed relationship causal or correlative? 2.Have other causes been considered/ controlled for? Examples: I get a headache the day before every major earthquake I have a headache today Therefore: Tomorrow there will be a major earthquake People who take vitamin supplements are healthier than those who don t take vitamin supplements Therefore: Taking vitamin supplements makes people healthier In causal relationships A causes B In correlative relationships A and B occur together but there is no causal relationship. Is the causal claim a good explanation for the observed correlation? (Is the correlation serial rather than causal) I get a headache the day before every major earthquake I have a headache today Therefore: Tomorrow there will be a major earthquake Is there any other reasonable explanation for the correlation? A classic example of this is provided by Michael Pollan in his book Food Rules People who take vitamin supplements are healthier than those who don t take vitamin supplements Therefore: Taking vitamin supplements makes people healthier This looks like a compelling argument. But what happens when we look at what types of people generally take vitamin supplements? We find they generally eat more
Small pox 1. Dairymaids are exposed to cowpox 2.Dairy maids are often protected from Smallpox 3.Therefore: Exposing people to cowpox will prevent smallpox
Education gap 1.Achievement gaps have been observed between students in American schools 2.Between 1960 and 2007 achievement gaps between poor students and rich students grew by 40% 3.Between 1960 and 2007, achievement gaps between White and Black students shrunk significantly 4.Therefore: Low income is a greater cause of poor achievement than race
Poverty 1.People who live in poverty experience a greater incidence of heart disease. 2.Therefore: poverty causes heart disease.
1936 Election 1.Surveys indicate that Landon is more popular than FDR 2.Therefore: Landon will win the 1936 election.
Convert the ad to an argument in standard form. What type of argument is it? How strong is the argument? Explain.
Informal fallacies Materials on slides 26-36 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, article 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
What is the argument being made by this add? Put the argument into standard form, describe its type and assess its strength.
Definitions Deduction 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
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
4 types of categorical propositions Universal affirmative - A propositions All caudillos are tyrants Universal negative - E propositions No caudillos are democrats Particular affirmative - I propositions AffIrmo nego 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 4 No 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 Invalid 2 3 4 5 Some No 6 All crunchy things are apples Some bland things are crunchy things No Therefore: All apples are bland things 7 Crunchy
Assessing the validity of syllogisms using Venn diagrams goblins Green 1 No Invalid 2 No 5 Some 4 3 6 All Goblins are monsters Some monsters are green things Therefore: Some goblins are green things 7 monsters
All syllogisms can be expressed symbolically, since each of the terms simply represents a variable A C 1 Invalid 2 3 4 5 Some No 6 All B are A Some C are B Therefore: All A are C No 7 B
Bingles Nonsense words are fun, too Woot-Woots 1 Invalid 2 3 4 5 Some 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
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: All C are A Invalid! 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
Ooh! Ooh! It s invalid when we do then Venn too! Winged vehicles Transponder 1 2 3 Valid 3 Most airplanes have a transponder. I 4 5 Some No 6 All airplanes are winged vehicles. A No Therefore, some winged vehicles have a transponder. I 7 Airplanes
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 No 3 No All A are B No B are C Therefore: All C are A 4 No 5 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 Either Fido ran away or he was hit by a car Fido ran away Invalid Therefore: Fido did not get hit by a car Invalid 1. Invalid for either exclusive or inclusive
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 The first valid form: If Gandalf fails then Gondor Falls If Gondor 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 Boromir comes to the party then Frodo will not come If Frodo does not come, then Sam will not come Therefore: If Boromir comes to the party then Sam will not come Symbolically If p then not r If not r, then not q Therefore: If p then not q
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 Modus Ponens (AA) Symbolically If p then q not q Therefore: not p 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 The two invalid forms result from affirming the consequent (AC) and denying the antecedent (DA)
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 Invalid - DA
Logic Unit Quiz On Friday we will have a culminating quiz on the logic unit. The quiz will count for 3 annotations. The quiz will be open notes. You will be asked to do the following on the quiz: Examine three inductive arguments and identify the informal fallacy that they commit (I will be fairly obvious here). Examine five deductive arguments and: Describe the type of argument each represents (categorical syllogism, mixed or pure hypothetical syllogisms, disjunctive syllogism) Assess the validity of each syllogism Assess each categorical syllogism using the Venn diagram and figure and mood methods Identify the deductive fallacy committed by each invalid categorical syllogism
Logic quiz practice 1.All dogs have fur. Some dogs are black. All furry things are black 2.No cats are happy. Some happy things are mammals. All cats are mammals 3.Either dogs or cats. Cats. Therefore not dogs 4.If today is Wednesday then there will be no lunch. Today is Wednesday. There will be no lunch 5.If fish then chips. Chips. Fish. 1. AIA3 - Invalid, undistributed minor 2. EIA4 - Invalid, affirmative conclusion negative premise 3. Disjunctive. Invalid (inclusive or) 4. Mixed hypothetical. Modus Ponens (AA) 5. Mixed hypothetical. Invalid (AC)
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!
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.
1 2 3 Arguments 5 1. 4 6 2. 7 Therefore: 1 2 5 3 Arguments 1. 4 6 2. Therefore: 7