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Philosophy 1200
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Philosophy

Philosophy 1200

Eric Desjardins

Winter

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Chapter 1: Deductive Arguments
What Makes a Good Argument?
Argumentation is a rational practice.
arguing is a process of showing reasonableness of an assertion
the presentation of a collection of premises that are rationally persuasive of
a conclusion, ie. premises make it reasonable to accept the conclusion
Arguments are linguistic or logical objects.
looks at the truth of the premises and their logical relation to the conclusion
soundness:
validity: premises true = conclusion true
all premises are true
LOGIC
once though to be univocal: only a single meaning or interpretation
Laws of Thought:
Law of Identity: P if and only if P
Law of Non-Contradiction: not both P and not-P
Law of Excluded middle: P or not-P
intuitionisitic logic: does not include Law of Excluded Middle
requires direct proof of P: not-P is not taken as proof of P
dialetheic logic: does not include Law of Non-Contradiction
when contradictory statements arise, must be arbitrary in concluding which
statement is discarded
modal logic: factor in notions such as belief, knowledge, obligation, etc.
basically logic is not monolithic
Valid Argument Forms
Simplification
form:
P and Q
Therefore P
example:
Rules say that prisoners (P) aren‘t allowed to vote.
A repentant prisoner (P and Q) is a prisoner (P). So the rules applies to them
too.
Conjunction form:
P
Q
Therefore P and Q
example:
Eric is a doctor. (P)
Ellen is a doctor. (Q)
Therefore, Eric and Ellen are both doctors. (P and Q)
Addition
form:
P
Therefore P or Q
example:
Foxes are mammals. Therefore, either foxes are mammals or cows are
mammals.
Foxes are mammals. Therefore, either foxes are mammals or lizards are
mammals.
Hypothetical Syllogism
form:
If P then Q
If Q then R
Therefore, if P then R
example:
If the dollar is devalued, exports will rise. (if P, then Q)
If exports rise, then unemployment will fall. (if Q then R)
Therefore, if the dollar is devalued, unemployment will fall. (P then R)
Constructive Dilemma
form:
P or Q
If P then R
If Q then S
R or S
example: Either it will snow tomorrow or there will be a quiz in class. (P or Q)
If it snows tomorrow, class will be cancelled. (if P then R)
If there‘s a quiz in class tomorrow, I will fail. (if Q then S)
Either classes will be cancelled or I will fail a quiz tomorrow. (R or S)
Destructive Dilemma
form:
If P then R
If Q then S
Not R or not S
Therefore not P or not Q
example:
If she called her mother, the answering machine took a message. (if P then
R)
If her brother called her mother, the line was busy. (If Q then S)
But the machine didn‘t take a message, or the line wasn‘t busy. (not R or
not S)
So she didn‘t call her mother, or her brother didn‘t. (not P or not Q)
TYPES OF ARGUMENTS
linked argument: premises essentially tie together to support a single
overall conclusion
convergent argument: a range of independent grounds for a conclusion
assembled together as premises
sequential argument: premises establish intermediate conclusions, which
serve as premises for a further conclusion
TRUTH CONDITIONS
truth values: either true or false
reasonableness: are there grounds to believe the premises?
necessary truths: true no matter how things might have turned out
definitional truths: dependent on the meaning we attribute to the words
necessary and sufficient conditions
Factual and Non-Factual Statements
some do not really have truth conditions statements about morality, humor, etiquette, aesthetics Scientific Reasoning
Causation/Correlation
two ways in which things may be related:
temporally: order in time
empirical; can be observed
causally
complete causal account specifies necessary and sufficient conditions
involves counterfactual statements: what would happen if necessary and
sufficient conditions are not met
antecedent circumstance: correlated circumstance usually occurring
prior to the event
Rival Hypotheses
Rival Restricted Hypotheses
some observations explained by each hypothesis but neither explains all
circumstances
requires auxiliary hypothesis: second hypothesis logically required by
hypothesis in question
Rival Unrestricted Hypothesis
two incompatible hypotheses explained by the same observations
usually due to the interpretation of the observations
incommensurable: when two theories differ so much it becomes
impossible to test their hypotheses with the same observation statements
no available standard, independent of both theories, to test which theory
should prevail
standard of explanatory accuracy is used here— the hypothesis with more
precise observations to confirm it is more explanatorily powerful Critical Thinking about Numbers
representative numbers encode important information but can
misrepresent affairs
percentages create a loss of information
major percentage change in small populations = minor
small percentage change in major populations = major
Fallacies in Reasoning with Rates
linear projection: assumption that the observed rate will extend into
times yet to be observed
misquotation: incorrectly relaying information spoken by another
Ratings and Rankings
percentage vs. percentile: percentage is out of 100, while percentile is a
term used to numerically rank values in comparison to other values
th
eg. 90 percentile means better than 90% of the population, whereas 90%
means to have a raw score of 90%
inherently comparative within a group
bar graphs indicate changes that apply to different absolute amounts
eg. rich income increase by 50% and poor income increase by 15% are of
amounts of their own categories, not that the poor income increased by 15%
of the rich income
ordinal rankings can be misleading because we don‘t know the gap
between the first place and last place finishers
position on the list and use of seemingly hard numbers convey the sense of
a major difference when there may be little to no difference
think about a ranking of the ―best cars of 2013‖— depends on buyer‘s needs
and wants
Fallacies of Numerical Reasoning
pseudo-precision: use of numerical expressions in order to heighten the
perception that it is reliable
eg. ―8422 jobs were created in Nova Scotia this month.‖ — creating a job is
a process spread out over time
graphical fallacies: misrepresentation of quantities/rates by misleading
graphs or charts
scaling of the axes cumulative graphs
be wary of data portrayed by mean, median, mode Probability and Statistics
Significance and Margins of Error
statistical significance: measure of confidence in the probabilistic
conclusion
confidence interval: range of values within which we can be statistically
confident that the true value falls
eg. 50-60% of voters will support Trudeau.
margin of error: numerical value half of the midpoint of the confidence
interval
the smaller margin of error, the more data we need to have high confidence
in it
smaller margins of error = less confidence in truth values
larger margins of error = more confidence in truth values
―observed result is significant to the 5% level‖ over the long run, such
a result will show up at most 1 time in 20 if the null hypothesis is true
Basic Probabilistic Concepts
probability = prediction and explanation
statistics = analyzing observed data
heuristics can cause us to reason incorrectly
Basics of Probability
P(e) = probability that some event occurs
P(~e) = probability that some event does not occur
Axioms:
P(e) + P(~e) = 1.0
0 ≤ P(e) ≤ 1.0
P(S) = 1, where S is the set of all possible outcomes
P(e) = 1 – P(~e)
FALLACIES
gambler’s fallacy: to think that if a series of independent events has the
conjoint probability p, then the probability of any single event in the series is
somehow dependent on the probability of the series as a whole
eg. A dice is to be rolled 4 times. The first three rolls are 5‘s. The gambler‘s
fallacy is to think that the next roll has less than a 1/6 chance of being a 5, because the probability of 4 5‘s in a row is (1/6 ), when really the events are
independent (so the probability of rolling another 5 is just ½).
Simpson’s Paradox: a trend that appears in different groups of data
disappears when the groups are combined, and the reverse trend appears
instead
regression fallacy: confusing a pattern in random events by overlooking
regression effects (a random sample within a normal distribution is close to
the mean)
eg. we start off in a tail of some distribution and then trend toward the mean
as our experience grows: we think that there is a correlational or causational
explanation for this rather than as a trend that is entirely consistent with
randomness Biases Within Reason
repetition effect: tendency to judge claims you hear often to be true
often applied when watching TV— commercials
BIASES
Perceptual Biases
low-level biases: the result of the basic structure of our perceptual and
neurological mechanisms
eg. McGurk effect (multi-modal), cutaneous rabbit
top-down effects: the role of expectations in our perceptions
eg. ―hearing‖ things when songs are played backwards
inattentional blindness: concentration on one task causing you not to
notice other events happening in front of you
eg. basketball bounces/gorilla
Cognitive Biases
confirmation bias: beliefs or expectations about a hypothesis can lead
to its seeming more highly confirmed than the evidence warrants
eg. ―Most famous scientists were men.‖
situational, attentional, interpretive biases
self-fulfilling prophecies
Egocentric Biases
attribution theory: how the perceiver uses information to arrive at
causal explanations for events
self-serving bias: emotions, desires, expectations combine to produce an
explanation that makes ourselves look good
eg. talented but lazy vs. modestly gifted but hard-working
optimistic self-assessment: people assess themselves as better than
they are
eg. everyone rating themselves ―above-average‖: clearly not possible for
everyone to be above-average

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