Class Notes
(808,384)

Canada
(493,172)

Western University
(47,688)

Philosophy
(1,278)

Philosophy 1200
(17)

Eric Desjardins
(11)

Lecture

# Philosophy 1200: Critical Thinking- Term 2.docx

Unlock Document

Western University

Philosophy

Philosophy 1200

Eric Desjardins

Winter

Description

Deductive Reasoning, Modern Symbolic Logic & Truth
Tables 9/13/2013 5:44:00 PM
Lecture 1:
DEDUCTIVE ARGUMENTS
linguistic or logical object
logical implication
allows you to be lazy
Soundness
two parts: premises must be true and it must be valid (logical strength)
Validity
depends on form not content
context disappears from the argument
applies only to deductive arguments
Valid Argument Forms
Modus ponens
if p, then q
p
therefore q
Modus tollens
if p then q
not q
therefore not p
Simplification
p and q
therefore p
Conjunction
p
q
therefore p and q
Addition p
therefore p or q
Hypothetical syllogism
if p then q
if q then r
therefore if p then r
Disjunctive syllogism
p or q
not p
therefore q
Constructive Dilemma
p or q
if p then r
if q then s
therefore r or s
Destructive Dilemma
if p then r
if q then s
not r or not s
therefore not p or not q
Categorical (universal)
all p are q
all q are r
therefore all p are r
Categorical (existential)
all p are q
some q are r
therefore some p are r
DETERMINING VALID FORM even if an argument has instances where both the conclusion and
premises are true, it does not necessarily mean the argument is valid or
sound
Method of Counterexample
Example:
If coal is black (p), then snow is white (q)
Snow is white (q)
Therefore, coal is black (p)
1. Find the form of the argument
if p then q
q
therefore p
2. Find a counterexample to that form
If the prof is a monkey (p), then the prof is a mammal (q).
The prof is a mammal (q)
Therefore, the prof is a monkey (p)
Example: Is this argument sound?
P1: Ice is slippery.
P2: Species evolve.
P3: I wear grey socks
P4: Pluto is not a planet
C: Human is lonely in this universe.
no, it isn’t.
Lecture 2:
Either we take job actions or we go to work. If the government passes Bill
115, which is an unconstitutional and short-sighted legislation, then our
fundamental right to manifest against social injustices will be violated. If our
right to manifest is baffled, then we will not go to work. Last week, the
provincial government decided to pass this unconstitutional bill.
Simple Statements
A: We take job actions. W: We go to work.
B: Government passes Bill 115.
V: The right to manifest is violated.
Deductive Reasoning
1. A or W
2. If B then V
3. If V then ~W
4. B
5. V (modus ponens 2, 4)
6. ~W (modus ponens 3,5)
C: A (disjunctive syllogism 1, 6)
Either teachers will go to work on Friday, or they will protest against new
contract conditions. Protesting on Friday would be equivalent of going on
strike, which would be illegal. I know that teachers are law abiding. So they
will go to work on Friday.
Simple Statements
S: Teachers will strike.
W: Teachers will work.
P: Teachers will protest.
L: Teachers will perform legal acts.
Deductive Reasoning
1. W or P
2. If P then S
3. If S then ~L
4. ~~L
5. ~S (modus tollens 3, 4)
6. ~P (modus tollens 2,5)
C: W (disjunctive syllogism 1, 6)
TRUTH TABLE METHOD
a way of testing for validity of argument form by setting all the possible
instances of the form ie. all the possible combination of truth values for the simple component
sentences
form of algebraic propositional calculus
Simple vs. Compound Sentences
declarative sentences are compound if it contains another complete
declarative sentence as component
eg. John eats fudge and flowers.
negations are always compounds
eg. Governments don’t like strikes.
declarative sentences are simple if it is not a component
eg. Sam runs every weekend.
Sentential Operators
operators are words connecting simple sentences into more complex
sentences
sentential operation: an expression containing blank(s) such that when
the blanks are filled with complete sentences, the result is a sentence
Examples of Sequential Operators
either/or
If/then
and
unless
if and only if
it is not the case that
after/before
because
it is possible that
it is necessary that
I believe that
Truth Functional Operators
truth value of the compound sentence depends only on the truth value of
the simple sentences that are combined with the operator Examples:
conjunction: ___ and ___ ( ___ & ___)
disjunction _or_ (_v_)
conditional: if _ then _ ( rotated left U; =>)
equivalence: _ if and only if _ (triple line; <=>)
negation: not (~)
Lecture 3:
TRUTH VALUE
a bivalent (two-value) system of logic: we assume that each sentence
must be either true or false
negation (~): invert truth value
~ P
F T
T F
and (&): conjunction is truth if and only if both conjuncts are true
P & Q
T T T
F F T
T F F
F F F
or (v): disjunction is true if at least one disjunct is true
P v Q
T T T
F T T
T T F
F F F
biconditional (<=>): true when both sentences are equivalent (ie. same
truth value)
P <=> Q
T T T
F F T
T F F
F T F
same as exclusive or conditional (=>): if the antecedent (ie. P => Q) is true and its
consequent (ie. P => Q) is false, then the conditional is always false
If it rains => I stay in bed
T F F
if the antecedent is false, then the conditional is always true
If jeans could talk => they would lie
F T T/F
truth functional
Recognizing Conditional Statements, Antecedents and Consequents
If France gets involved in Mali, then many people will die.
p => q
Innocent prisoners might be saved if France gets involved in Mali.
p => q
France gets involved in conflicts only if its people are suffering from
injustice.
p => q
Mali will be attacked by France unless it releases all innocent prisoners.
A if not R
o ~p => q
o equivalent to p v q
French soldiers will depart for Mali provided that Holland gives them the
order.
D if O
o p => q
Examples:
Assume that A, B and C are true, whereas X and Y are false.
1. ~A v ~B (disjunction)
F
2. (A & X) v (B & Y) (disjunction)
F
3. ~(A v B) => (X v Y) (conditional)
T
4. (~A => B) <=> (A v B) (biconditional)
T 5. ~ (((X => A) v (Y => B)) => ((X & Y) => (A v C))) (negative)
F
Lecture 4:
TRUTH TABLE METHOD
symbolize argument and replace capital letters for variables
1. line up argument premises and conclusion
2. construct base columns
on the left, create a column for each variable
calculate number of rows needed using following formula: 2^N,
where N stands for the number of variables (if N=3, then table
will contain 8 rows)
enter truth values under each variable, making sure you have all
possible combinations accounted for
st
i. 1 variable: half true, half false, ie. TTTTFFFF
ii. 2d variable: half the first true, half the first false—
alternating, ie. TTFFTTFF
iii. 3d variable: half the second true, half the second false—
alternating, ie. TFTFTFTF
3. compute the truth value of all premises and conclusion rules for truth-
functional operators
4. look for a row where premises are T but conclusion is F
if such instance exists, argument form is invalid
if such instance does not exist, argument form is valid
shortcut: only compute lines where the conclusion is false, or where
conjunctions are true
partial truth table
Lecture 5:
PARTIAL TRUTH TABLE
1. place premises and conclusion
2. construct base columns (variables and possible combinations on left)
3. compute truth values of conclusion, ignoring cases where it is obviously
true
4. compute truth value of premises only where conclusion is false and
premises could be true Short Method
systematic search for counterexamples without drawing base columns
1. layout premises and conclusion
2. assign values to variables and try to construct a counterexample
typically easier to start with conclusion
short method is hard to prove validity
must exhaust all instances where the conclusion is false Inductive Reasoning 9/13/2013 5:44:00 PM
Lecture 6:
Deductive vs. Inductive
Strength
D: validity
I: C is more or less probable
D: only form matters
I: content and context are crucial
Knowledge
D: nothing new is added in C
I: creates knowledge (more in C than what is contained in Ps)
P-C Relation
D: implication (sufficiency)
I: support (P not sufficient to infer C; counterexamples are always an
issue)
Four Types of Induction
1. Generalization: particular general
form:
z percent of observed fs are g
it is therefore probable that z percent of all fs are g
problems:
sample is not always representative of population, ie. when certain
groups are over or underrepresented in the sample
o avoid this by using Simple Random Sample: each member of
population has equal chance of being selected
o pollsters often use stratified sample: divide population into
groups, then sample randomly within these groups
sampling biases: non-response bias, self-selection bias
must have large enough sample
2. Statistical Syllogism: general particular
form:
z percent of fs are g
x is an f
therefore, it is probable to degree 0.z that x is g
problems: ensure no relevant information has been overlooked about x
3. Induction by Confirmation
form:
if h, then o
o
therefore h is probable
commonly used in sciences, diagnostics, criminal trials
can alter hypothesis if negative results occur
problems:
must gather a large number of incidences to prove hypothesis true
must look at disconfirming incidences
4. Analogical Reasoning: generalize from model target
analogical model
x has A, B, C
y has A, B
It is probable that y has C.
relational analogical model:
x is to y as a is to b
x is R to y
It is probable that a is R to b
causal analogical model:
common properties {a, b, c, d, e} must be causal properties
property f to be projected from model to system modeled should
stand in a causal relationship to the properties {a, b, c, d, e} in the
model
there should be no relevant causal disanalogies between the model
and the target 9/13/2013 5:44:00 PM
Assignment #5
read chapters 16 & 17 of Hughes and Lavery
750-1000 words
topic: Atheism and evolution vs. creationism and intelligent design
discussed in Dennett’s paper, ―Atheism and Evolution.‖
make reference to Dennett’s paper and paper you read in producing the
annotated bibliography in Applied Assignment #4
both papers listed in bibliography
may include others but not necessary
must begin with standard form representation of argument followed by
diagram of argument, with a max of 15 premises (not part of word count)
include at least one deductive inference and one inductive inference
indicate in diagram
DUE MARCH 6
tips on page 294-295
know your audience
aim for clarity, simplicity, coherence
brief and specific
examples and quotations
avoid padding
respect style of argumentative essay
Macro-structure of Argumentative Essays
Introduction
1. announce subject
2. establish context and specify issues
3. announce views of others
4. state your position/contribution, ie. thesis you will defend
Body
1. reasons & arguments
2. rebut plausible objection(s)
Conclusion
1. brief summary of main arguments and rebuttals
emphasize how they support thesis 2. restate thesis Scientific Reasoning 9/13/2013 5:44:00 PM
Lecture 8:
inductive
CAUSATION
causes are necessary and sufficient conditions
event C causes event E iff C is a necessary and sufficient condition for the
occurrence of E
o supports counterfactual statements
Mills’ Methods
1. Agreement
2. Difference
3. Agreement and Difference
4. Concomitant Variants
5. Residue
Agreement
when several instances of the same phenomenon are observed, all of
them are expected to be the result of the same cause
o if the same antecedent circumstances in all these instances are also
observed, then we reason to believe that this may be the cause we
are seeking
Inference form:
P occurs in 1 when x, y, z
P occurs in 2 when x, z
P occurs in n when x, …, …
It is likely that x is the cause of P
Difference
when all antecedent circumstances in two instances are the same except
one and a specific phenomenon is observed in one instance but not the
other single difference in the circumstances is significant
form:
P is observed in 1 in circumstances a, b, c, d
P is not observed in 2 in circumstances b, c, d
It is likely that a is the cause of P A variation: controlled experiments
instances can be groups
control group: part of population where experimental is absent or
present
subject group: part of population where experimental is present or
absent
if P is observed in SG but not CG, then experimental variable is the cause
of P
Concomitant Variations
when variations in two phenomena coincide with each other, there is
reason to believe they are causally related
form:
o P1 occurs with P2 in 1
o P1+ occurs with P2+ in 2
o P1- occurs with P2- in 3
o It is likely that P2 causes

More
Less
Related notes for Philosophy 1200