stage 2 Logic & Knowledge

stage 2 Logic & Knowledge

What logic puts in order is the way we reason out. Logic makes explicit the rules of reasoning.

Logical Inference Determining if an argument is valid or not is important, but how can we know whether a conclusion should be accepted? or that argument is cogent? or a conclusion true? It turns out we can, and this process of going from the premises to the conclusion to assess validity is called logical inference. Premises Inferring Conclusion

Mind vs Verbal Expression Acts of the Mind Verbal Expression Simple Apprehension Terms Judgment Proposition Inference Syllogism

Deductive & Inductive Arguments

Deductive Argument An argument with premises that if accepted to be true, inevitably makes the conclusion true. There is no space for uncertainty. If the premises are true, then the conclusion MUST also be true. If premises are true inferring guarantees the conclusion is also true

Inductive Argument Argument with premises that support but do not guarantee the necessity of its conclusion. There will always exist some uncertainty since the data we observe can always come out differently upon new measurements Premises may or may not be true but inferring gives good reasons to believe that the conclusion is true

Valid or invalid? Medieval kings did not have absolute power over their subjects Louis XIV was a medieval king so, Louis XIV did not have absolute power over his subjects

Valid or invalid? Medieval kinks did not have absolute power over his subjects Louis XIV was a medieval king therefore, Louis XIV was a great horsemen.

1. that this kind of reasoning does have application to the world 2. when details are involved the statements can become difficult to manipulate quickly as you reason. To clarify the reasoning process, we often substitute letters for entire terms in syllogisms removing language to deal with the pattern of thinking in more abstract terms. Try this:

Fallacies

Fallacy Bad method of argument or error in reasoning (whether deductive or inductive) one or more of its premises are false, or the reasoning from them may be invalid, or the language expressing them may be ambiguous or vague. typical faults in arguments that sounds persuasive. sometimes fallacies are used intentionally to persuade, convince or influence others towards accepting our claims.

Fallacies There are over 100 accepted fallacies. We will only focus in the most relevant to our understanding of human reasoning and the ways in which it goes wrong. Knowing how to spot and identify fallacies is a priceless skill. It can save you time, money, and personal dignity. Usually, fallacies are best understood and identified by looking at their occurrence in daily life. Identifying and understanding fallacies can be a powerful tool in your development as a critical thinker.

Ad ignorantiam This first fallacy in reasoning is quite astonishing. Why would anyone believe a claim on the basis of no evidence at all? Yet chilling examples have been part of the pageant of history: claims have been believed and acted upon because there was apparently no evidence to the contrary. No one has ever been able to prove definitively that extra-terrestrials exist, so they must not be real. No one has ever been able to prove definitively that extra-terrestrials do not exist, so they must be real. Sunk Cost Fallacy Sometimes we invest ourselves so thoroughly in a project that we re reluctant to ever abandon it, even when it turns out to be fruitless and futile. It s natural, and usually not a fallacy to want to carry on with something we find important, not least because of all the resources we ve put into it. However, this kind of thinking becomes a fallacy when we start to think that we should continue with a task or project because of all that we ve put into it, without considering the future costs we re likely to incur by doing so. Example: I know this relationship isn t working anymore and that we re both miserable. No marriage. No kids. No steady job. But I ve been with him for seven years, so I better stay with him.

Post hoc (False Cause) Post hoc comes from the Latin phrase, post hoc, ergo propter hoc which, when translated, is after this, because of this. This fallacy assumes that because X precedes Y, therefore X caused Y. This is a common fallacy found in news articles, especially those pertaining to some scientific or medical study. Remember what we discussed about correlation does not imply causation Superstitious beliefs are often due to the Post hoc fallacy: An athlete wears their lucky socks and wins the game, etc. Video Example 1 Example 2 Ex: Cell phone usage has increased exponentially in the last 20 years. Researchers discovered that the incidences of brain cancer have also increased in that time. Therefore, cell phone usage must cause brain cancer. Ad hominem In logic and rhetoric, personal attacks are called ad hominems. Ad hominem is Latin for against the man. Instead of advancing good sound reasoning, ad hominems replace logical argumentation with attack-language unrelated to the truth of the matter. It attacks the person instead of attacking the argument.

Ad misericordium Emotional content and emotional appeals are not necessarily inappropriate in an argument. A critical thinker will not reject emotion outright. Indeed, it is often necessary to insist on the relevance to decision-making of compassion or people's happiness as basic premises for logical argument, or as justifications in themselves for conclusions. However, we need to be on guard against the use of emotion to persuade us to conclusions that are against our "better judgment", often by sweeping aside all consideration of justifications to carry us towards a conclusion based solely on emotion What makes this appeal a fallacy in some contexts is its use to "prove" innocence or to distract attention from other justifications more legitimate for reaching a sound conclusion. Video Example. Non sequitur Occurs when the conclusion does not follow logically from the premises or there is no logical connection between the two. Example: A black cat crossed my way. It brings bad luck, something terrible will happen to me today.

Hasty Generalization Making assumptions about an entire group of people, or a range of cases based on an inadequately small sample. Video Example. Example Creates a general rule based on a single case Stereotypes are a common example Ad populum Also referred to as the bandwagon fallacy, the arguer tries to convince the audience to do or believe something because everyone else (supposedly) does. Video Example. Example: An increasing number of people are turning to yoga as a way to get in touch with their inner-being Therefore, yoga helps one get in touch with their inner being.

Equivocation Equivocation means to slide between two or more different meanings of a word or phrase that is critical to the argument. For an argument to work, the words must have the same meaning throughout the premise and the conclusion. Example: I don t understand why you re saying I broke a promise. I said I d never speak again to my ex-girlfriend. And I didn t. I just sent her some pictures and text messages. Slippery Slope The slippery slope fallacy is that in which it is claimed that one event will inevitably cause a chain of unrelated or catastrophic events. Some causal chains are perfectly reasonable. The slippery slope fallacy slides right over that difficulty by assuming that chain of future events without really proving their likelihood. The slippery slope fallacy, however, suggests that unlikely or ridiculous outcomes are likely when there s just not enough evidence to think so. Click here to see an example

Ad verecumdiam Insisting that a claim is true simply because a valid authority or expert on the issue said it was true, without any other supporting evidence offered. Not to confuse with 'appeal to false authority.' Video Example Example: Richard Dawkins, an evolutionary biologist and perhaps the foremost expert in the field, says that evolution is true. Therefore, it's true. Appeal to False Authority Using an alleged authority as evidence in your argument when the authority is not really an authority on the facts relevant to the argument. As the audience, allowing an irrelevant authority to add credibility to the claim being made. Example: The Pope told me that priests could turn bread and wine into Jesus body and blood. The Pope is not a liar. Therefore, priests really can do this. Careful! Beware of your confirmation bias. You may want a person to be an authority on the topic, and this desire will result in your seeking out confirming information and ignoring conflicting information.

Fallacy Activity #7

Arguments Syllogisms

Syllogisms Syllogism refers to the format of arguments, particularly deductive arguments. Syllogisms have 3 propositions: 2 premises and 1 conclusion, as follows:

Let s look at the most famous syllogism in philosophy: All men are mortal (major premise) Socrates is a man (minor premise) Socrates is mortal (conclusion)

Alcohol is a habit forming drug All habit-forming drugs can cause addiction Therefore, alcohol can cause addiction. Is this argument valid? Yes! The logical validity of the syllogism is not a matter of opinion, because the conclusion really does follow from the premises. That is, if the premises are true, then the conclusion must be true as well. That makes it a logically valid syllogism regardless of whether or not you agree with the premises or the conclusion!

There are rules in which to create syllogisms, you cannot just create them based on assumptions or the format itself. The propositions you use have to be related. What does that mean? This means that your premises have to be related in some way. In syllogisms this is called the middle term. Important is to note that the middle term appears in the premises but never in the conclusion.

The Subject is the "main" in a proposition. It is the main argument of the whole proposition, the actor in the sentence. The Subject can be thought of as the What we are talking about? The Copula is the word (or set of words) that connects the subject and the predicate. How are they verbally connected? The Predicate tells us something about the Subject. The Predicate can be thought as the What we are talking about of the Subject? Socrates is mortal subject copula predicate

Examples of subjects include the following: «Griezmann» in «Griezmann is the best soccer player» «All people» in «All people know someone» «Real Madrid» in «Real Madrid is not be the best team in the world» «Parrots» in «Parrots cannot fly» Examples of copulas include the following: «is» in «Griezmann is the best soccer player» "know" in «All people know someone» «is not» in «Real Madrid is not the best team in the world» «cannot» in «Parrots cannot fly» Examples of predicates include: «the best soccer player» in «Griezmann is the best soccer player» «Someone» in «All people know someone" «the best team in the world» in «Real Madrid is not the best team in the world» «fly» in «Parrots cannot fly»

The Middle Term A term that appears in both premises to relate them, but it does not appear in the conclusion. It is one of the most powerful ways of determining the validity of a deductive argument, which many times may divert us from a correct reasoning. All scientists are biased. All engineers are scientists. Therefore all engineers are biased All m are X. All Y are m. all Y are X. Valid!

A. The major term is the predicate (P) of the conclusion B. The minor term is the subject (S) of the conclusion C. The middle term is the term repeated in the premises, but not in the conclusion D. The major premise is the premise that contains the major term (P) E. The Minor Premise is the premise that contains the minor term (S) Major Premise (P) P1: All scientists are biased. Minor Premise (S) P2: All engineers are scientists. C: All engineers are biased

Conditional Statements Hypothetical propositions also known as «if then» statements.

The antecedent is the "IF" part of the statement The consequent is the "THEN" part IF (antecedent; first term), THEN (consequent; second term)

Checkpoint review

Key Terms (yes, again!) Logic the science of correct reasoning. Inference the process of deducing or extracting a statement (conclusion) from the previous statement/s. Argument is a kind of reasoning/inference in which statements are offered to support or justify another statement. Syllogism the format of arguments with three statements. Conclusion the statement being supported. Premises the statement/s that support/s the conclusion. Truth the correspondence or equivalence of the mind to reality/object. Judgment the act by which the mind affirms or denies an attribute of a subject. Propositions verbal expression of judgments.

It might help to phrase your sentences with familiar vocabulary for central concepts: for example, perspectives, ways of knowing (and specific ones), areas of knowledge (and particular ones), knowledge claims, justification, evidence, certainty/uncertainty, prediction, causation, fallacies, methodology, confirmation bias, cognitive biases, truth, assumptions, values.

Bias & Science

Reason Our capacity for reason is born in us, but both how we think and what we think are influenced by our place in the world. Significantly, we can use reason to recognize the biases of our own experiences: we can use reason to think about our thinking. As a result, we can be critical of our shortcomings and construct methodologies that help us to check ourselves: using reason, we can learn to reason better.

The Methods of Science Children as well as scientists though with different degrees of rigor question, put forth hypotheses and test them, seek evidence, analyze the results, and reach conclusions. We select, compile, include, exclude, compare, contrast, count, estimate, and calculate. We build from generalizations about falling rocks to laws of physics about gravity, or from generalizations on buying potatoes in the neighborhood store to economic correlations between supply and demand.

Errors in Reasoning Confirmation Bias Fallacies False or Hasty Generalization Correlation and Causation Misinterpretation of Probabilities

Paradigm The set of scientific theories, instruments and conclusions that scientists take «for granted» and accept as sufficient for conducting a scientific method». According to modern philosophers of science, scientific progress has only been possible thanks to the paradigm, since it allows scientists to focus exclusively on their hypothesis, without having to validate any assumed conclusion, belief or instrumenteffectiveness.

Paradigm in Scientific Progress For example: scientists accept that a microscope is an accurate and adequate instrument to observe cells. In this way, the scientist interested in testing osmosis, does not have to spend time finding an instrument for conducting his observations. He accepts that a microscope is the best (ot at least sufficiently effective) to conduct his research. Without the paradigm, scientific progress would not be possible, or at least not at the rates that we have seen in the past centuries.

Bias

Confirmation Bias The tendency to collect and take evidence seriously that supports our beliefs, and to disregard or ignore evidence that conflicts with our beliefs.

Confirmation Bias Example 1 Background: My roommate has always been very rude and has never contributed to the apartment's well being. I consider him selfish. Events My roommate does not chip in to my birthday party favors shopping. I expected such behavior, which is normal in him, he is a selfish guy False! The conclusion is totally biased! It may be the case he did not hone money that day, or that he wasn't asked, or that he had already done something to make up for the party. Yet, I affirm and defend the conclusion that he did not chip in because he is selfish, which fits my personal opinion. My conclusion is entirely biased, which makes my conclusion a flawed one. Events my roommate brings in candy for everyone of my friends. Nah, he is being false and wants to be liked by my friends. Again, this conclusion is totally biased on the opinion that I have from him. Hence, my conclusion is wrong. we are guilty of bias almost every day of our likes

Confirmation Bias Think of the following questions, as it may follow some discussion activities. You notice that your friend s mother has a very different attitude from your own mother about the oil pipeline that has had people in your town going to protests. How is it that they have such different perspectives? You and your friend are both political science scholars and both of you have studied Cuban history. You, a Latin American student, thinks Fidel Castro was one of the great leaders of the XX century by freeing and bringing peace to Cuba, while your fellow American student, asserts he was an oppressive dictator who did much harm to Cuba. Your history teacher is a male at a Catholic school where one of his female students accused him of being seducing and provocative, without having any strong evidence but her interpretation of his own gestures. The issue became well known between students, faculty and parents although he was never proved to be guilty of seducing or sexually harass his student. One day, the local news broadcasts a story about sexual harassment in which a teacher of your school (but whose name was not disclosed), had been arrested for sexual harassment. Everyone inferred that it was your history teacher. You are asked to find the best 100 goals in Spanish football. You happen to be a fan to death of Atlético Madrid, but also the best sport analyst. Your findings make up a video in which 34 of the 100 best goals are from Atlético de Madrid players.

You are a very fond believer in democracy and think that Andrés Manuel López Obrador is not a democrat but a socialist. Your teacher, while also a believer in democracy, thinks that AMLO may be a good fit for Mexico. Both students engage in a argument in which each try to convince the other why or why not will Andrés Manuel be a good president. The first day of class you were assigned some homework that you did not do. You know that the teacher does not know anyone of his students yet, so he cannot know if a student is making up the solutions or copying them from another student. You claim to be a smartass «The teacher is unbiased, I can copy the homework without the risk of being caught!». The next day, early in the morning, you ask two peers (which you happened to know from previous years in school) if they could share their homework with you. One of them happened to be the top student in Mathematics, while the other was known to you as a responsible, hardworking student with OK grades in maths. You copy the answers from the top student. You receive a failing grade the next day. What went wrong?

You are the principal of some school and you are in desperate need of a Robotics teacher. It happens that your best friend, which you happen to know to be a professional and who has always been there for you, is an electrical engineer with sufficient knowledge in Robotics. You tell him about the situation, and he offers to take the job to teach that one class. Throughout the semester, you receive several complaints about the Robotics teacher and his inability to teach the class. Some assert that «he doesn t know anything about Robotics, he was hired because he is the principal s best friend» You assert «He is a professional and every instance has been followed through. It is not an easy class and students must make a greater effort»

Symbolic Logic

Quantity universal or particular Universal the predicate is affirmed or denied of the whole subject. All men are beings with heart. Not all men are beings with heart. Particular the predicate is affirmed or denied of only part of the subject. Some men are haughty. Some men not are haughty.

Quality affirmative negative Affirmative - predicate is affirmed of the subject. The audience is kind. Negative - predicate is denied of the subject. The audience is not kind.

Logic symbol Reads as not equal Set Theory Overview R in not in such that Set of real numbers Q Set of rational numbers N Set of natural numbers

Symbol Name Reads Examples ~ negation not p conjunction and disjunction or Universal Quantification for all; for every; for each ( A) A p q R A B C xy = 0 x y = 0 n R : 2n + 1 is odd Existence Quantification there exists! Uniqueness Quantification there exists exactly one x y (x=y) n N : n = 3!n N : n + 5 = 2n Indicator therefore Equivalence iff if and only if it means the same as B A A B = 0 x + 5 = 6 x = 1 x + 5 = 6 x + 2 = 3 AB = 1 (B A) 1 Implication If then implies A B B A A B A C

both p and q are in the set of rational numbers p q R

read, then assess if true ( A) p ( p) A

xy = 0 x y = 0 xy = 0 implies that either x = 0 or y = 0

It is important to recognize that when the premises are true and the reasoning is valid, then the conclusion is also true. What a powerful tool deductive reasoning can be to be able to take true statements and from them create more!

We will see that also in symbolic logic, that deal with deductive arguments, it is still possible to make errors in reason and commit fallacies. If p then q therefore if q then p or to simplify p q q p Here, it may not be that easy to spot a fallacy, but let s take a closer look at how studying logic can indeed help us improve our way of reasoning.

«If Maria voted last year then she is over 18. therefore, if Maria is over 18, then she voted last year» Let s replace the arguments with some symbols «If Maria voted last year she is over 18. if Maria is over 18 she voted last year» Now let s try to replace events, or situations with letters. If A if B B A A = Maria voted B = Maria is 18 years or older

Do you see the fallacy? p q q p

Translate using symbols of logic For any integer k in R, there exists an integer number n such that k = 2n+1 must be odd.

B A A B = 0 B is identical to A, therefore their difference is zero. B is equivalent to A, therefore the difference between A and be is zero.

x y For all x, there is one y

p ~p T F If p is true, then ~ p is false. F T If p is false, then ~ p is true. ~p reads «not p»

Bibliography The IB Companion Book: Theory of Knowledge (Oxford) Los Caminos del Conocimiento (UANL) Hume, D. (2004). An Enquiry Concerning Human Understanding. Courier Corporation. https://thebestschools.org/magazine/15-logical-fallacies-know/