PHILOSOPHY 101 Maymester 2007 Day 2 Logic and Knowledge.

PHILOSOPHY 101 Maymester 2007

Day 2Logic and Knowledge

PHILOSOPHY 101Some Logic

• Arguments!

Premises

Conclusion

• Example:

[A1] All Cars have engines

My Honda is a car

Therefore, …

Logic (2)

All Cars have engines

My Honda is a car

Therefore, …

My Honda has an engine.

Premise 1

Premise 2

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!

Conclusion INDICATOR

Standard Form of an Argument• 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 If Al likes SallyAl likes Sally then then Al will ask Sally outAl will ask Sally out

Al likes SallyAl likes Sally

Therefore Therefore Al will ask Al will ask Sally outSally out

If -- P -- then -- If -- P -- then -- Q--Q--

-- P –-- P –

Therefore -- Q --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

ArgumentArgument

DeductiveDeductive InductiveInductive

ValidValid InvalidInvalid StrongStrong WeakWeak

SoundSound CogentCogent

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)

ArgumentArgument




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)

ArgumentArgument




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 Ed passes Phil 101, then Ed has perfect attendance.

2. Ed has perfect attendance.

3. Therefore, Ed Passes Phil 101

1. IF --P-- , THEN --Q--.

2. --Q--

3. Therefore -- P--

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

• Modus Ponens

• Modus Tollens

• Disjunctive Syllogism

• Hypothetical Syllogism

• Reductio Ad Absurdum


• Modus Ponens

If P then Q, P --- Therefore Q

• Modus Tollens

If P then Q, Q is false --- Therefore P is false


• 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?

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 X2) 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

Belief N-3

?

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…

There must be a special kind of knowledge that can be obtained from either prior knowledge, or something else (maybe experience?)

Aristotle’s ViewAristotle 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. KnowledgeEverything 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

• 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)

PHILOSOPHY 101 Maymester 2007 Day 2 Logic and Knowledge.

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