Sound Reasoning and Avoiding Fallacies Necessary and sufficient conditions Sufficient condition When something is enough on it own to bring about something else Necessary condition when something is needed to bring about something else If X is a necessary condition for Y whenever you have Y you will always have X P implies Q Complicating Either P or Q Example a Either P or Q or R b P c R d Q conclusions Single Premise Arguments 1 I am your father c You are my son Evaluating Soundness Conclusion and Sub conclusions Some conclusions are premises within a larger argument these are called sub Formal fallacies are problems with an argument s structure Informal fallacies are problems with an argument s content FALLACIES Affirming the Consequent Denying the Antecedent Ad Hominem Attacking the person instead of their argument which results in your argument being weak due to focusing on something irrelevant to the truth to their claim Begging the question The argument s conclusion is already smuggled into the premises Your premises fail to prove your conclusion to someone who didn t already accept it ahead of time because the premises depend upon your conclusion Straw person Presenting someone else s argument as weaker than it actually is and then Knocking down that misconstrued argument Because you haven t attacked their actual argument you haven t shown their argument to be flawed Rene Descartes Mathematician and philosopher Originator of Cartesian Coordinate system Father of modern philosophy Wrote the Meditations on First Philosophy in 1641 Methodological Skepticism Descartes methodological skepticism uses deductive reasoning Key premise P Q If and only if something cannot be doubted then that thing is known with certainty If and only if something is known with certainty that thing cannot be doubted First stage of Doubt Sensory Illusions Perspective and Muller Lyer Illusions Concern sometimes our senses mislead us Second Stage of Doubt Am I Dreaming Concern Can I be certain that I am in fact not dreaming right now What are we left with colors shapes parts concepts logic and mathematics Third Stage of Doubt The Evil Demon Concern Can I be certain that an all powerful being is not always deceiving me The evil demon stage of doubt seems to undermine certainty in everything Cogito Ergo Sum In order for something to be deceived that something must exist I think therefore I am Plato s Republic Socrates 470 399 BC Plato 428 to 423 348 BC Socrates was a philosopher in Athens who had numerous students that he shared his ideas with Plato was one of his students and is arguably the most famous The Socratic Problem What is the relationship between Socrates thought Socrates thought as represented by Plato and Plato s own thought What bearing does Socrates ultimate fate have upon this question The Socratic Method All I know is that I know nothing Socrates does not present arguments like other philosophers that are covered in the course Often takes a claim that someone makes and then engages in what we now call Socratic questioning a method that interrogates particular claims through a series of follow up questioning Socratic Questioning There are two types of argument that Socrates frequently employs in his method Argument from Analogy Analogical Reasoning 1 P and Q are similar in certain aspects 2 P has property X c Q has property X Reductio ad Absurdum Indirect proof The deductive argument we ve looked at so far in this class are examples of direct proof Reductio ad Absurdum by contrast works to arrive at conclusions indirectly Reductio ad Absurdum arrives at conclusions through demonstrating that accepting a claim leads to something false unacceptable or absurd Such arguments start with two premises Plato s most famous work The Republic Begins with Socrates and company being compelled into visiting the house of their acquaintance Polemarchus during a festival While at Polemarchus house everyone gathered round to listen to the house patriarch At one point during the discussion Socrates questions a definition of justice Cephalus Cephalus offers Cephalus Account of Justice Cephalus definition Justice is speaking truth and paying one debts Reductio Time p 224 One should not give weapons to someone who is not in their right mind Cephalus accepts this If justice is repaying one s debts and someone lends not gifts something to you you re indebted to return that thing to them when they ask for it If someone has lent you their weapons and that person asks for their weapons back when they are not in their right mind justice requires you return the weapons to them Cephalus rejects this because of the premise he accepts above But this followed from his own definition of justice Cephalus Response I m leaving Polemarchus Definition Justice is the practice of doing good to one s friends and evil harm to one s enemies A just man does not harm good people Polemarchus accepts this Reductio Time pp 228 229 People are often mistaken about who is their friend and who only seems like their friend and vice versa Correspondingly people are often mistaken about who is a good persona dn who is a bad person People who intend to benefit their friends will sometimes help bad people and people who intend to harm their enemies will sometimes harm good people So the just man will sometimes harm good people and sometimes bad people Polemarchus Revised Account of Justice Polemarchus Definition Justice is the practice of doing good to one s friends when they are in fact good and harm to one s enemies when they are in fact evil 1 When horses are harmed they deteriorate in whatever qualities make for good horses E g they aren t as fast 2 When dogs are harmed they deteriorate in whatever qualities make for good dogs Time for some analogies pp 229 230 E g they won t hunt as well C When people are harmed they will deteriorate in whatever qualities make for good people E g they are not as just which is the virtue of good people Accepted Premises When people are harmed they will deteriorate in whatever qualities make for good people Justice is what makes people good A just person cannot while practicing their craft make other people unjust or lacking in justice