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Lecture 2

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

by OC829611

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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.

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