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Lecture 2

# PHI 1101 Lecture Notes - Lecture 2: Quantum Superposition, Law Of Excluded Middle, Classical Logic

Department
Philosophy
Course Code
PHI 1101
Professor
Laura Byrne
Lecture
2

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2016-03-15
CLASS 2: TUESDAY, SEPTEMBER 15
UNIT ONE: Reasoning and Critical thinking (part one)
Readings: CT, chp 1 & additional concepts
The basic concepts of critical thinking
The philosopher’s toolbox
Statements:
true Vs false
Sets:
consistent Vs inconsistent
Arguments:
logically strong (inductively strong; deductively valid) Vs
logically weak (induc weak; deduc invalid)
Statement:
A sentence used to make a claim, statements are capable of being
either true or false
Bc they can be true or false, statements are not sentences which
are not being capable of being either true or false: commands,
questions, and expressions of volition (wishes), poetry, rhetoric
The most basic concept of critical thinking is that of the statement
Logic also calls them assertions or propositions
*plato’s republic: central character is Socrates (plato’s teacher)—
Xanthippe (wife) had to wash other’s cloth since Socrates did not
earn money (shameful for free citizens to work for others)
examples:
proposition: Socrates is a man
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command: be a man, Socrates
Question: is Socrates a man?
Expression of volition: Oh, that Socrates were a man.
Two laws of logic for statements: what separates the rational from
the irrational (Aristotle)
1. Law of non-contradiction
2. Law of the excluded middle or the law of bivalence
ex: using 2 simple propositions
Socrates is a manproposition
Socrates is not a mannegation of that proposition
*for the sake of clarity: logicians and philosophers sometimes like
to represent statements w/ symbols : represent statements w/
letters such as a, b, c or p, q,r
Socrates is a man p
Socrates is not a man not-p ( or ~p or –p)
~ (tilde)
the law of non-contradiction: it is impossible for both a
proposition and its negation to be true at the same time (p and not-
p cannot be simultaneously true at the same time in the same
respect)
fundamental to classical logic (what is studied in this class)
can be contradicted in the realm of quantum physics: Schrodinger’s
Cat—can be both alive and dead (quantum superposition)
Defines the boundary of rationality and meaningful speech
ex: Simultaneously passing and failing a test
student: prof, did I pass the test?
Prof: yes you did pass the test
Student: I passed the test?
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Prof: No, you did not pass the test
Student: ???
Prof: you did pass the test, and you did not pass the test
Law of the excluded Middle or the Law of Bivalence: every
proposition must be either true or false; iow, any middle position
btwn truth and falsity is excluded in classical logic
It follows from this law that for any given proposition and its
negation, one must be true and the other one false
If a proposition is false, its negation must be true
“If Socrates is man” is true, then its negation, must be false
If p is true, not-p must be false
If “lassie is a dog’ is true, then ‘lassie is not a dog’ must be false
Analogy of the two laws
Law of non contradiction: You can’t have both milk and chocolate
Law of the excluded middle: You have to choose either one or the
other (coin: head or tails)
Consistency and inconsistency
Consistency: a set of propositions is consistent if and only if it is
possible for all of the propositions in that set to be true at the same
time. IOW, a set of propositions is consistent if these propositions
do not contradict one another
Is consistent if it avoid contradiction (does not have to be true)
Ex: the following sets of propositions are consistent because it is
possible for their members to be true at the same time.
Socrates is mortal.
Socrates is a philosopher.
Lassie is a dog.
Lassie barks.
Ex: The following sets of propositions are inconsistent because they
contain a contradiction. In other words, it is not possible for their
members to be true at the same time.
find more resources at oneclass.com
find more resources at oneclass.com
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