Transcript Slide 1

PHILOSOPHY 101
Maymester 2007
Day 2
Logic and Knowledge
PHILOSOPHY 101
Some Logic
• Arguments!
Premises
Conclusion
• Example:
[A1] All Cars have engines
My Honda is a car
Therefore, …
Logic (2)
Premise 1
All Cars have engines
Premise 2
My Honda is a car
Therefore, …
Conclusion INDICATOR
My Honda has an engine. THE CONCLUSION!
Note:
1) If I tell you what the premises are, you know what
the conclusion would be before I told you!!!
2) It is impossible for the conclusion to be false, give
these premises!
Standard Form of an Argument
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•
Socrates is mortal because all men are
mortal
Standard form isolates conclusion and
lists ALL premises.
1) All men are mortal (given premise)
2) Socrates is a man (implied premise)
3) Socrates is mortal. (Conclusion)
Logic (3)
• Deductive vs. Inductive Arguments
• Deductive: The truth of the premises is
supposed to require the truth of the
conclusion (Necessary)
• Inductive: The truth of the premises is
supposed to increase the probability of the
conclusion (Probability)
Logic (4)
• An Inductive Argument
[A2] Every person I have met from
Poland loves potato soup.
Karlov is from Poland.
Therefore,…
i) Karlov will love potato soup.
ii) Karlov will probably love potato soup.
Logic (5)
• Logical FORM
If Al likes Sally then
Al will ask Sally out
If -- P -- then - Q--
Al likes Sally
-- P –
Therefore Al will ask
Sally out
Therefore -- Q --
Why Logic?
• One way to support a theory is to offer an
argument in its favor.
• One way to criticize a theory is to offer an
argument against that theory.
• Which arguments should we take
seriously?
Good vs. Bad Arguments
• Deductive Validity – if the premises are
true the conclusion MUST be true
• Inductive Strength – if the premises are
true the conclusion will be probable
• Deductive Soundness – the deductive
argument is valid AND premises are all
true
• Inductive Cogency—The inductive
argument is strong and the premises are
all true
Argument Family Tree
Argument
Deductive
Valid
Invalid
Sound
Inductive
Strong
Weak
Cogent
Evaluating Deductive
Arguments
• To determine VALIDITY you first identify
the form of the argument.
• Try to develop counter-examples with the
same logical form
• Employ methods of formal logical analysis
• Determining SOUNDNESS depends upon
the truth of the premises (beyond logic)
Argument Family Tree (D)
Argument
Deductive
Valid
Invalid
Sound
Inductive
Strong
Weak
Cogent
Evaluating Inductive Arguments
• To determine STRENGTH you must
evaluate whether the truth of the premises
would in fact enhance the probability of the
conclusion. This requires knowledge of
how things work and how they are related.
• To determine COGENCY you must know
the truth of the premises (beyond logic)
Argument Family Tree (I)
Argument
Deductive
Valid
Invalid
Sound
Inductive
Strong
Weak
Cogent
Counter-Example Test for
Validity
1) Start with an argument
2) Determine its form
(Important to do correctly)
3) Formulate another argument:
a) With the same form
b) with true premises
c) with a false conclusion.
An example counter-example…
1. If Lincoln was shot,
then Lincoln is dead.
2. Lincoln is dead.
3. Therefore, Lincoln
was shot.
The FORM IS:
1. If Lincoln was shot,
then Lincoln is dead.
2. Lincoln is dead.
3. Therefore, Lincoln
was shot.
1. IF --P-- , THEN --Q--.
2. --Q-3. Therefore -- P--
NEXT: We go from FORM back
to ARGUMENT…
1. IF --P-- , THEN
--Q--.
2. --Q-3. Therefore -- P-
1. IF Ed passes Phil
101, then Ed has
perfect
attendance.
2. Ed has perfect
attendance.
3. Therefore, Ed
Passes Phil 101
NO WAY!
Ed’s Perfect Attendance does NOT make it
necessary that Ed pass PHIL 101.
SO: Even if it is true that
1. IF Ed passes Phil 101, then Ed has
perfect attendance.
2. ..AND that..Ed has perfect attendance.
IT DOES NOT FOLLOW THAT ED
MUST PASS PHIL 101!
It is possible to have perfect
attendance and not pass
•It is also possible to pass and have
imperfect attendance
This shows that the original LINCOLN
argument is INVALID.
This is ED…
Another Example?
1. All fruit have seeds
2. All plants have seeds
3. Therefore, all fruit are plants
1.All Balls are round.
2.All Planets are round.
3.All Balls are Planets.
Common Logical Forms
•
•
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•
Modus Ponens
Modus Tollens
Disjunctive Syllogism
Hypothetical Syllogism
Reductio Ad Absurdum
Common Logical Forms
• Modus Ponens
If P then Q, P --- Therefore Q
• Modus Tollens
If P then Q, Q is false --- Therefore P is
false
Common Logical Forms
• Disjunctive Syllogism
P or Q, P is false --- Therefore Q
• Hypothetical Syllogism
If P then Q , If Q then R
--- Therefore If P then R
DO IT NOW!
Take a moment and try to formulate an
argument in each of the first four basic
common forms!
Common Forms
• Reductio Ad Absurdum
(Reduces to Absurdity)
a) Assume that P
b) On the basis of the assumption if you
can prove ANY contradiction, then you
may infer that P is false
Case of : Thales and Anaximander
Formal Evaluation?
The counter-example test for validity has
limits.
The rules and procedures of classical and
modern formal logic can also be
employed… (Take PHIL 103 for more
details)
Induction?
The evaluation of inductive
arguments is less clear. If you can
give determinate quantitative
values to probabilities, then the
rules of statistics apply.
Otherwise you need to try and reflect
on the probabilities to the best of
your ability.
Induction
Some factors to keep in mind about
inductive data:
• Typicality (How common?)
• Generality (How General?)
• Frequency (How Frequent?)
• Analogy / Dis-analogy?
PHILOSOPHY 101
Epistemology Slides
© Robert Barnard 2006
EPISTEMOLOGY
• Epistemology is the philosophical study of
the nature of human knowledge
• It traditionally includes the study of human
understanding and perception
• Our focus will be on the nature of
knowledge and sources of knowledge.
What is Knowledge?
Plato asked this question
2300 years ago in his work
Meno.
We are still looking for a
good answer.
Meno claimed that knowledge could be taught by
those with knowledge and learned by others.
[Necessary Conditions for Knowledge?]
But Plato wasn’t convinced…
The Meno Paradox
It is impossible to learn about X, because…
1) Either you know about X already or you
don’t know about X
2) If you already know about X, then
learning is impossible.
3) If you don’t already know about X, then
you cannot seek out knowledge of X
because you do not know what to seek.
So learning is impossible.
Plato thinks that….
Because of the Meno Paradox, Plato concludes
that if we have knowledge, it must be innate (we
have it already when born).
But this means learning is impossible, except as a
kind of remembering.
Plato says we are born with knowledge of general
concepts and ideas. This is called the
‘Recollection Theory’ of knowledge.
Plato’s Servant Boy example
How do you draw a square twice the size of
a given square?
Another view…
Aristotle claimed in his
Posterior Analytics that all
human knowledge comes
from previous cognition.
But where did the first
knowledge come from?
The Regress Problem
Belief N
Belief N-1
Belief N-2
For Any Belief N, it will depend
on a Belief or Beliefs N-1, N-1
will depend upon N-2, and so on.
Either there is no knowledge
because there is no first
knowledge
…or…
Belief N-3
?
There must be a special kind of
knowledge that can be obtained
from either prior knowledge, or
something else (maybe
experience?)
Aristotle’s View
Aristotle concluded that we must block the
regress!
• Aristotle began with experience
• Experience gets organized by the
understanding until patterns and general
“rules” emerge
• These patterns and rules come to be
known as “First Principles.”
• Since the first principles bottom-out the
chain of beliefs, this sort of view is called
“Foundationalism”
Beliefs vs. Knowledge
Everything that we know is also something
that we believe.
Believing that P is a necessary condition for
Knowing that P
But, Believing that P is NOT sufficient for
knowing that P.
(What would be sufficient for knowledge?)
True Belief vs. Knowledge
I cannot KNOW what is false.
(BUT…I might have a strong sense that I am
certain of P, even if P is false)
That P is true is a necessary condition for
knowing that P.
Is True belief the same as knowledge?
True Belief is not Knowledge
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The Jury Example
The Guide to Larissa
Camouflaged Tanks
Brain Lesions
Clairvoyance about President
Bush
Justification
• The Statues of Daedelus example
• What is missing is a LINK connecting the True
Belief that P to P through some process or
history that is ‘knwledge making’
• I know 5 > 4 because I was born with knowledge
of general truths (Plato)
• I know that Fido is a Dog because my
experience of Fido is governed by the first
principles of Dog-ness acquired by experience
(Aristotle)