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?
• 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
• “Sufficient grounds” (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
• 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
• Case study: “the persuasion
industries” (advertising, politics, etc.)
• Arguments “beyond all reason”
• Language, emotion, and “the
reptilian brain.”