Theory of Knowledge Unit #2: Arguments. Ways of Knowing : Reason & Language Areas of Knowledge : Informal logic and math Knowledge concepts: Validity & Justification. Unit Questions. What are the strengths and limits of reason (rationalism) as a way of knowing ?
Theory of KnowledgeUnit #2: Arguments WaysofKnowing: Reason & Language AreasofKnowledge: Informal logicand math Knowledge concepts: Validity & Justification
Unit Questions • What are the strengths and limits of reason (rationalism) as a way of knowing? • How do we ensure that arguments are logical, valid, and justified in their conclusions? • Why are mathematical systems of argument and modeling so powerful? • What roles do language, logic, and numbers play in complex real-world arguments? • How do we combine language and emotion to construct arguments that are persuasive even if they are not “reasonable”? http://www.youtube.com/watch?v=kQFKtI6gn9Y
Definition & types • “A collective series of statements to establish a definite proposition.” • “A intellectual process” • the use of Reason as the primary Way of Knowing with Language as the “conveyer” of that knowledge • Arguments can be expressed… • Formally (math, symbolic logic, deductive syllogism) • Informally (verbal language – written or spoken)
Formal: Symbolic logic After several hundred or so pages of symbolic logic… The Russell-Whitehead proof that 1+1=2 (Mathematica Principia, 1910) -- but even so, note what they haven’t done yet
Informal: Verbal “Students seeking the finest preparation available for an American college should consider the International Baccalaureate. The IB offers an integrated curriculum that provides students with the skill needed to be world-class scholars and an educational philosophy that prepares them to be first-class citizens. I do not know of a more comprehensive and appropriate learning model.” (Director of Admissions, Macalaster College)
Validity: key knowledge concept A function of the structural and logical relationship among the parts of an argument • When the requisite parts of the argument… • [ claim, evidence, reasons, warrant, backing, etc. ] • …are relevant, justified, and appropriately related to each other… • [ without logical errors, gaps, or informal fallacies ] • …then we say the argument is valid. • You may not find an argument’s main claim persuasive (or even “true”), but that’s not the same thing as validity.
Justification: key knowledge concept The general means used to support a claim • “Sufficientgrounds” (evidence/reasons) + “warrant” (the principle or explanation that connects the evidence to the claim) • Typically a function of the ways of knowing • A knowledge claim is true because… • I was told (language) • I saw it (sensory perception) • It fits the facts (reason) • It feels right (emotion) • The Areas of Knowledge build on these simple types of justification • Science: Sensory perception (empirical data) + reason (induction) • Math: Reason “rigorous proof” (logical deduction) • Ethics (as in the claim, “You should love your neighbor.) • Reason “utilitarianism” (what’s right is what maximizes happiness for the greatest number of people) • Intuition/Emotion/Language “divine command theory” (God orders it so) • Sensory perception (data collection) + Reason evolutionary psychology (as social creatures, we favor members of our own group) • History: Language (the written record) + reason (inferring causes/effects, motivations, etc.)
Structure: The Toulmin model [ See handout ]
IB Argument: Toulmin model CLAIM: Consider the IB program if what you want is the finest college preparation available to American students. GROUNDS/EVIDENCE: 1. IB provides … an integrated curriculum to prepare students to become world class scholars … an educational philosophy to prepare students to become first class citizens 2. “I [authority figure – director of competitive college admissions office] do not know of a more comprehensive or appropriate learning model.” So – what is the WARRANT here? – Remember: The warrant is the principle, provision, or chain of reasoning that connects the evidence to the claim – that is, that shows how/why the evidence really does support the claim itself. (NOTE: In very brief arguments, the warrant is often implied / unstated, as is the case here.)
Unit plan • Casestudy: “the persuasion industries” (advertising, politics, etc.) • Arguments “beyond all reason” • Language, emotion, and “the reptilian brain.” • Complex arguments about real life situations • High school: sports & academics • Media violence • Applied math • Statistical arguments • Fractals: modeling the real world • “Proofiness” • the manipulation of numbers in arguments