PHLA10F 2
PHLA10F – What is Philosophy?
PHLA10F
What is Philosophy ?
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Philosophical Questions
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Fundamental
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General
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Conceptual Analysis
Why no Philosophical Labs?
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Thought experiments
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The ‘Hand Off’
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No mystic gurus!
Plato
PHLA10F
Logic and Argument
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What is an argument?
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A structure of statements
designed to prove some point.
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Premises
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Conclusion
Premises must be relevant to
the conclusion.
Relevance = the premises
must give good reasons to
believe the conclusion
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Aristotle
PHLA10F
Logic and Argument
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Sample arguments (?)
All New Yorkers are happy.
Some people live in New York.
Some people are happy.
All dogs have four legs.
All animals have four legs.
All dogs are animals.
I read the second amendment literally.
It says "arms". It doesn't say "guns".
Nuclear weapons are arms. If you
don't accept a literal interpretation of
the second amendment, then you're
problem is with the Constitution, not
with me. God bless America.
By reducing the size of the droplets in clouds, thereby making
them more reflective, the sulphate particles lowered the
temperature of the sea’s surface in the northern hemisphere.
The result was to shift the Intertropical Convergence Zone
southwards.
PHLA10F
Logic and Argument
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Deductive Arguments – Validity
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Arguments which are supposed to be deductively
valid.
An argument is deductively valid when: IF the
premises are true then the conclusion MUST be
true.
Like this:
If someone lives in Edmonton then they live in Canada.
Fred lives in Edmonton.
So Fred lives in Canada.
PHLA10F
Logic and Argument
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Deductive Arguments – Validity
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Philosophical Interlude: What about this
argument?
Definition: a sentence is “positive” if it does not
contain any negations. A sentence that contains
a negation is “negative”.
Consider this argument:
All sentences are positive.
Therefore, no sentences are negative.
PHLA10F
Logic and Argument
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Deductive Arguments – Validity
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The word ‘valid’ in logic is ONLY about arguments – there
are no valid statements or ideas, ONLY arguments.
Form versus Content
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Validity arises from the ‘logical form’ of an argument (see
exs. above – you could change the words).
(Is this really true? What about this argument: This dress is
scarlet, therefore this dress is red? Is that valid? What is its
logical form?)
Logical form might not be obvious. Compare
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‘Stephen Harper is P.M.’ with ‘Spiderman lives in New York.’
PHLA10F
Logic and Argument
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Deductive Arguments – Validity
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Is this argument deductively valid:
All spiders are dangerous.
Therefore, all spiders are dangerous.
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So what is wrong with it?
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‘begging the question’
Validity and information
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a valid argument never adds any information that is
not already in the premises
PHLA10F
Logic and Argument
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Deductive Arguments – Invalidity
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You can deduce what an invalid deductive
argument is from the definition of validity.
An invalid deductive argument is one where it is
possible for the premises to all be true but the
conclusion is false.
Like this:
No philosophers are rich.
Some philosophers are happy.
No rich people are happy.
PHLA10F
Logic and Argument
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Deductive Arguments – Invalidity
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How can you tell if an argument is invalid?
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(you could study logic !?)
The method of counterexample.
No philosophers are rocks.
Some philosophers are employed.
No rocks are employed.

No women are men.
Some women are parents.
No men are parents.
PHLA10F
Logic and Argument
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Deductive Arguments – Invalidity
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Patching invalid arguments.
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By adding premises, an invalid argument can be made
into a valid argument.
Fish can swim.
Therefore, some women are wealthy.

Fish can swim.
If any fish can swim, some women are wealthy.
Therefore, some women are wealthy.
Why is the
patched and
valid argument
worthless?
PHLA10F
Logic and Argument
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Deductive Arguments – Validity and Soundness
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A valid deductive argument is a sound argument if its
premises are all true.
You can deduce something about the conclusion of a
sound deductive argument.
Debates about the quality of a deductive argument can
take two forms:
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Debate about whether the logical form is valid.
Debate about whether the premises are true.
Nuclear power is safe.
Nuclear power emits zero greenhouse gases.
Therefore, we should use nuclear power.
PHLA10F
Logic and Argument
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Deductive Arguments – Conditionals
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A basic argument structure:
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Valid versus Invalid Conditionals
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If X then Y, X; therefore Y.
(note we defined validity using a conditional)
Four forms:
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X > Y, X; therefore Y
X > Y, not-X; therefore not-Y
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X > Y, Y; therefore X
X > Y, not-Y; therefore not-X
Which are valid? Which are invalid?
Necessary and Sufficient Conditions.
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Given ‘If X then Y’, X is a sufficient condition for Y.
Given ‘if X then Y’, Y is a necessary condition for X.
PHLA10F
Logic and Argument
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What is truth?
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We used the concept of truth to define validty.
The nature of truth however is a deep philosophical
question.
Theories of truth
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correspondence
coherence
redundancy theory
Alfred Tarski
PHLA10F
Logic and Argument
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What is truth?
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Correspondence
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Coherence
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Problem: what is this mysterious relation of
correspondence?
In what way does ‘the cat is on the mat’ correspond to the
truth of things
Problem: more than one system of sentences can be
coherent – think of ‘possible worlds’
Redundancy
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‘neige est blanc’ is true just in case snow is white
“‘snow is white’ is true” says just ‘snow is white’
PHLA10F
Logic and Argument
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Truth and Objectivity
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Objectivity versus Subjectivity
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Could truth itself be subjective
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compare ‘1+2=3’ with ‘oranges are the best tasting fruit’
Maybe ‘true’ means ‘true for me’ or ‘true for us [society]’
Can this be proven?
Suppose truth is subjective
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Is this claim merely subjective or is this supposed to be the
objective nature of truth?
If it is merely subjective, then it is not proven (I could – and do –
deny it and the subjectivist can’t complain).
If it is objective, then truth is not subjective after all.
Logic and Argument
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Reductio ad absurdem argument form
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The argument about truth illustrates a powerful mode
of argument.
Assume the opposite of what you want to prove, and
show that this assumption leads to a clear ‘absurdity’
(something impossible or obviously false). Example:
Prove: the government has a right to limit our freedom.
Assume: the government has no right to limit our freedom.
Deduce: therefore, I am free to acquire nuclear arms.
The conclusion is absurd (isn’t it?).
So the assumption is wrong and we get our proof.
PHLA10F
Logic and Argument
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Reductio ad absurdem argument
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A most beautiful example:
Prove: √2 is irrational.
Assume: √2 is rational.
Deduce: √2 = a/b (where this fraction is in ‘lowest terms’)
Deduce: 2 = a2/b2
Deduce: 2*b2 = a2
Deduce: a2 is an even number, so a is an even number.
Deduce: if a is an even number there is a c where a = 2*c
Pythagoras
2
Deduce: 2*b = 2*c*2*c
Deduce: b2 = 2*c2
Deduce: so b2 is an even number, so b is an even number
Deduce: both a and b are even numbers, so they have a common factor
Deduce: this contradicts that a/b is in lowest terms !!!
So our first assumption is wrong and √2 is irrational.